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Journal of Computers<br />
ISSN 1796-203X<br />
Volume 8, Number 6, June 2013<br />
Contents<br />
REGULAR PAPERS<br />
Functional Networks Analysis from Multi Neuronal Spike Tra<strong>in</strong>s on Prefrontal Cortex of Rat dur<strong>in</strong>g<br />
Work<strong>in</strong>g Memory Task and Neuronal Network Simulation<br />
Dexuan Qi and X<strong>in</strong> Tian<br />
A Novel Heuristic Usage of Helpful Actions for Conformant-FF System<br />
Wei Wei, Dantong Ouyang, T<strong>in</strong>gt<strong>in</strong>g Zou, and Shuai Lu<br />
Assess<strong>in</strong>g Land Ecological Security Based on BP Neural Network: a Case Study of Hangzhou, Ch<strong>in</strong>a<br />
Heyuan You<br />
Magellan: Technical Description of a New System for Robot-Assisted Nerve Blocks<br />
Joshua Morse, Mohamad Wehbe, Riccardo Taddei, Shantale Cyr, and Thomas M. Hemmerl<strong>in</strong>g<br />
State Assignment for F<strong>in</strong>ite State Mach<strong>in</strong>e Synthesis<br />
Meng Yang<br />
A Rotation-based Data Buffer<strong>in</strong>g Architecture for Convolution Filter<strong>in</strong>g <strong>in</strong> a Field Programmable<br />
Gate Array<br />
Zhijian Lu, Yanxia Wu, Zhenhua Guo, and Guochang Gu<br />
AT-M<strong>in</strong>e: An Efficient Algorithm of Frequent Itemset M<strong>in</strong><strong>in</strong>g on Uncerta<strong>in</strong> Dataset<br />
Le Wang, L<strong>in</strong> Feng, and M<strong>in</strong>gfei Wu<br />
A Solution for Privacy-Preserv<strong>in</strong>g Data Manipulation and Query on NoSQL Database<br />
Yub<strong>in</strong> Guo , Liankuan Zhang, Fengren L<strong>in</strong>, and Xim<strong>in</strong>g Li<br />
Predicate Formal System based on 1-level Universal AND Operator and its Soundness<br />
Y<strong>in</strong>gcang Ma and Huacan He<br />
Analysis of Boolean Networks us<strong>in</strong>g An Optimized Algorithm of Structure Matrix based on Semi-<br />
Tensor Product<br />
J<strong>in</strong>yu Zhan, Shan Lu, and Guowu Yang<br />
Adaptive Chaotic Prediction Algorithm of RBF Neural Network Filter<strong>in</strong>g Model based on Phase<br />
Space Reconstruction<br />
Lisheng Y<strong>in</strong>, Yigang He, Xuep<strong>in</strong>g Dong, and Zhaoquan Lu<br />
Intrusion Detection Based on Improved SOM with Optimized GA<br />
Jian-Hua Zhao and Wei-Hua Li<br />
Fault Diagnosis System for NPC Inverter based on Multi-Layer Pr<strong>in</strong>cipal Component Neural Network<br />
Danjiang Chen, Y<strong>in</strong>zhong Ye, and Rong Hua<br />
Pulse Wave K Value Averag<strong>in</strong>g Computation and Pathological Diagnosis<br />
Li Yang, J<strong>in</strong>xue Sui, and Yunan Hu<br />
1377<br />
1385<br />
1394<br />
1401<br />
1406<br />
1411<br />
1417<br />
1427<br />
1433<br />
1441<br />
1449<br />
1456<br />
1464<br />
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Multi-Step Prediction Algorithm of Traffic Flow Chaotic Time Series based on Volterra Neural<br />
Network<br />
Lisheng Y<strong>in</strong>, Yigang He, Xuep<strong>in</strong>g Dong, and Zhaoquan Lu<br />
Adaptive Track<strong>in</strong>g Control for Nonaff<strong>in</strong>e Nonl<strong>in</strong>ear Systems with Zero Dynamics<br />
Hui Hu and Peng Guo<br />
Improved Feasible SQP Algorithm for Nonl<strong>in</strong>ear Programs with Equality Constra<strong>in</strong>ed Sub-Problems<br />
Zhijun Luo, Guohua Chen, Simei Luo, and Zhib<strong>in</strong> Zhu<br />
F<strong>in</strong>ite Element Analysis Based Design of Mobile Robot for Remov<strong>in</strong>g Plug Oil Well<br />
Xiaojie Tian, Yonghong Liu, Rongju L<strong>in</strong>, Baop<strong>in</strong>g Cai, Zengkai Liu, and Rui Zhang<br />
Contour Error Coupled-Control Strategy based on L<strong>in</strong>e Interpolation and Curve Interpolation<br />
Guoyong Zhao, Hongj<strong>in</strong>g An, and Q<strong>in</strong>gzhi Zhao<br />
Research of Leaf Quality Based on Snowflake Theory<br />
Lihui Zhou, Jiajia Sun, Juanjuan An, and Jun Long<br />
Oscillation Criteria for Second Order Nonl<strong>in</strong>ear Neutral Perturbed Dynamic Equations on Time<br />
Scales<br />
Xiup<strong>in</strong>g Yu, Hua Du, and Hongyu Yang<br />
Improved Quantum Ant Colony Algorithm based on Bloch Coord<strong>in</strong>ates<br />
Xiaofeng Chen, X<strong>in</strong>gyou Xia, and Ruiyun Yu<br />
Image Fusion Method Based on Directional Contrast-Inspired Unit-L<strong>in</strong>k<strong>in</strong>g Pulse Coupled Neural<br />
Networks <strong>in</strong> Contourlet Doma<strong>in</strong><br />
Xi Cai, Guang Han, and J<strong>in</strong>kuan Wang<br />
The Critical Legal Contention under the Challenge of Information Age and the Predom<strong>in</strong>ant Social<br />
Interests Concern for Develop<strong>in</strong>g Intelligent Vehicle Telematics <strong>in</strong> the United States<br />
Fa-Chang Cheng and Wen-Hs<strong>in</strong>g Lai<br />
MPC Controller Performance Evaluation and Tun<strong>in</strong>g of S<strong>in</strong>gle Inverted Pendulum Device<br />
Chao Cheng, Zhong Zhao, and Haixia Li<br />
A Metadata-driven Cloud Comput<strong>in</strong>g Application Virtualization Model<br />
Yunpeng Xiao, Guangxia Xu, Yanb<strong>in</strong>g Liu, and Bai Wang<br />
Robust Portfolio Optimization with Options under VE Constra<strong>in</strong>t us<strong>in</strong>g Monte Carlo<br />
X<strong>in</strong>g Yu<br />
A Novel Water Quality Assessment Method Based on Comb<strong>in</strong>ation BP Neural Network Model and<br />
Fuzzy System<br />
M<strong>in</strong>g Xue<br />
An Isolated Dual-Input Converter for Grid/PV Hybrid Power Systems<br />
Yu-L<strong>in</strong> Juan, Hs<strong>in</strong>-Y<strong>in</strong>g Yang, and Peng-Lai Chen<br />
Deformed Kernel Based Extreme Learn<strong>in</strong>g Mach<strong>in</strong>e<br />
Chen Zhang, Shixiong Xia, and B<strong>in</strong>g Liu<br />
Optimal Sleep Schedul<strong>in</strong>g Scheme for Wireless Sensor networks Based on Balanced Energy<br />
Consumption<br />
Shan-shan Ma, Jian-sheng Qian, and Yan-j<strong>in</strong>g Sun<br />
Identity Based Proxy Re-encryption From BB1 IBE<br />
J<strong>in</strong>dan Zhang, Xu An Wang, and Xiaoyuan Yang<br />
1480<br />
1488<br />
1496<br />
1504<br />
1512<br />
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1571<br />
1580<br />
1587<br />
1594<br />
1602<br />
1610<br />
1618
Corn Moisture Measurement us<strong>in</strong>g a Capacitive Sensor<br />
Hongxia Zhang, Wei Liu, Boxue Tan, and Wenl<strong>in</strong>g Lu<br />
1627
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1377<br />
Functional Networks Analysis from Multi<br />
Neuronal Spike Tra<strong>in</strong>s on Prefrontal Cortex of<br />
Rat dur<strong>in</strong>g Work<strong>in</strong>g Memory Task and<br />
Neuronal Network Simulation<br />
Dexuan Qi<br />
Tianj<strong>in</strong> Research Centre of Basic Medical Science, Tianj<strong>in</strong> Medical University, Tianj<strong>in</strong> 300070, Ch<strong>in</strong>a<br />
Email: dxqi@tju.edu.cn<br />
X<strong>in</strong> Tian*<br />
Tianj<strong>in</strong> Research Centre of Basic Medical Science, Tianj<strong>in</strong> Medical University, Tianj<strong>in</strong> 300070, Ch<strong>in</strong>a<br />
Email: tianx@tijmu.edu.cn<br />
Abstract—Functional connectivity networks on prefrontal<br />
cortex of rat dur<strong>in</strong>g work<strong>in</strong>g memory task <strong>in</strong> vivo are<br />
analyzed. Neural ensemble entropy cod<strong>in</strong>g is applied to f<strong>in</strong>d<br />
the time <strong>in</strong>terval of work<strong>in</strong>g memory event occurrence. The<br />
analysis of functional connectivity networks is carried out<br />
though the method of cross-covariance. And functional<br />
networks of the occurrence work<strong>in</strong>g memory event and<br />
rest<strong>in</strong>g state are obta<strong>in</strong>ed. The complex network topology<br />
parameters are calculated, the two networks satisfy the<br />
small-world network property as the cluster<strong>in</strong>g coefficients<br />
of them are larger than their correspond<strong>in</strong>g random<br />
networks and their characteristic path lengths are<br />
approximately equal to their correspond<strong>in</strong>g random<br />
networks. F<strong>in</strong>ally, the simulations of spik<strong>in</strong>g neuronal<br />
networks of work<strong>in</strong>g memory event occurrence and rest<strong>in</strong>g<br />
state are presented. H<strong>in</strong>dmarsh-Rose neuron model is<br />
chosen as s<strong>in</strong>gle neuron of prefrontal cortex that connected<br />
by functional network of work<strong>in</strong>g memory event occurrence<br />
and rest<strong>in</strong>g state, receptivity. The simulation results are<br />
agreed with experiment data <strong>in</strong> rat prefrontal cortex dur<strong>in</strong>g<br />
a work<strong>in</strong>g memory task.<br />
Index Terms—functional connectivity, neuronal entropy<br />
cod<strong>in</strong>g, spike tra<strong>in</strong>s, work<strong>in</strong>g memory, small-world network,<br />
neuronal network simulation<br />
I. INTRODUCTION<br />
Work<strong>in</strong>g memory is short-term memory, which is one<br />
of the most important research doma<strong>in</strong> of cognitive<br />
science, refers to a complex cognitive tasks <strong>in</strong> the bra<strong>in</strong><br />
which can provide temporary storage and process<strong>in</strong>g of<br />
the necessary <strong>in</strong>formation, such as learn<strong>in</strong>g and<br />
reason<strong>in</strong>g[1]-[2]. Physiological studies have found the<br />
neural activity of the prefrontal cortex changes <strong>in</strong> the<br />
Manuscript received March 7, 2012; revised September 27, 2012;<br />
The work was supported by grants (No. 91132722 and No.<br />
61074131) from the National Natural Science Foundation of Ch<strong>in</strong>a.<br />
*correspond<strong>in</strong>g author. Tel.:+86 022 23542744<br />
process of new learn<strong>in</strong>g task, suggest<strong>in</strong>g that work<strong>in</strong>g<br />
memory is mediated by cont<strong>in</strong>uous activities of prefrontal<br />
cortex neurons[3]-[8]. Therefore, understand<strong>in</strong>g the<br />
<strong>in</strong>formation of neural activity is important to grasp the<br />
basic pr<strong>in</strong>ciple of bra<strong>in</strong> function computations.<br />
In addition, many theories such as rate cod<strong>in</strong>g, time<br />
cod<strong>in</strong>g, and nonl<strong>in</strong>ear cod<strong>in</strong>g have laid the foundation for<br />
further studies of neural activities[9]-[10]. Entropy is a<br />
measurement of uncerta<strong>in</strong>ty or the amount of <strong>in</strong>formation,<br />
which can quantify the <strong>in</strong>formation and can describe the<br />
characteristics of neural activity[9]-[11]. Moreover, the<br />
nonl<strong>in</strong>ear entropy can make up for the deficiency of<br />
traditional l<strong>in</strong>ear cod<strong>in</strong>g methods and show the<br />
differences between two spike tra<strong>in</strong>s which have the same<br />
fir<strong>in</strong>g rates but different temporal structures. In the<br />
present paper, entropy cod<strong>in</strong>g is applied to study local<br />
spatiotemporal pattern of neuronal activity <strong>in</strong> the process<br />
of work<strong>in</strong>g memory task and to f<strong>in</strong>d the period of<br />
work<strong>in</strong>g memory event occurrence.<br />
The concept of bra<strong>in</strong> functional connectivity first<br />
appeared <strong>in</strong> the electroencephalogram (EEG) study,<br />
which measures the statistical dependencies of the<br />
correlation and functional activities on the spatial<br />
separation of time between different bra<strong>in</strong> regions.<br />
Functional network is the network obta<strong>in</strong>ed from<br />
deviation of statistical <strong>in</strong>dependence, <strong>in</strong>clud<strong>in</strong>g<br />
measur<strong>in</strong>g their correlation, covariance, coherent<br />
spectrum and phase synchronization between different<br />
bra<strong>in</strong> regions or neurons[12]. In the early 1990s, Friston<br />
KJ et al first proposed functional connectivity analysis on<br />
functional magnetic resonance imag<strong>in</strong>g (fMRI) data[13],<br />
s<strong>in</strong>ce then the complexity of bra<strong>in</strong> networks based on<br />
functional connectivity imag<strong>in</strong>g of EEG,<br />
Magnetoencephalography (MEG) or fMRI data has<br />
become an important research direction. For example,<br />
Eguiluz VM et al (2005)[14] applied the correlation<br />
coefficient method to measure functional connectivity of<br />
fMRI data, found that the human bra<strong>in</strong>s are small-world<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1377-1384
1378 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
networks; Achard S and Bullmore E (2007)[15] applied<br />
correlation, partial correlation and partial coherence<br />
measurement method to study the functional connectivity<br />
networks between different bra<strong>in</strong> regions, the results<br />
consistently <strong>in</strong>dicate that the human bra<strong>in</strong>s are efficient<br />
small-world networks.<br />
Traditional EEG, MEG, fMRI, and other macro<br />
technology, can directly measure the <strong>in</strong>tegrated electrical<br />
activity of neuronal population, but the measurement<br />
results cannot be acquired with high time resolution<br />
(millisecond) and spatial resolution (millimeter) at the<br />
same time. At the micro level, <strong>in</strong>dividual neuron is the<br />
basic functional unit of the activity <strong>in</strong> the bra<strong>in</strong>, its neural<br />
<strong>in</strong>formation transmission and storage is very complex and<br />
highly dynamic.<br />
Multi-channel neural discharge record<strong>in</strong>g technology,<br />
developed <strong>in</strong> recent years, is the use of electrophysiology<br />
- the extracellular record<strong>in</strong>g method to record the activity<br />
of neurons <strong>in</strong> the discharge. This new technology can also<br />
record the fir<strong>in</strong>g activity of neuronal populations of the<br />
different parts of a bra<strong>in</strong> region or multiple bra<strong>in</strong> regions.<br />
Therefore, the functional connectivity analysis from<br />
neuronal fir<strong>in</strong>g data of the multi-channel record<strong>in</strong>g<br />
technology is an effective method of access to the<br />
functional activity of neurons, and to achieve high<br />
temporal resolution and spatial resolution. Yu S et al<br />
(2008)[17] studied the functional networks of visual<br />
cortex neurons; Correlation analysis method was used to<br />
calculate the functional connectivity matrix; The visual<br />
responses data were simultaneously recorded from 24<br />
nerve cells <strong>in</strong> visual cortex of anesthetized cats; The<br />
functional networks had small-world properties. In<br />
addition, many statistical method has been used for<br />
establish<strong>in</strong>g statistical associations or causality between<br />
neurons, f<strong>in</strong>d<strong>in</strong>g spatiotemporal correlations, or study<strong>in</strong>g<br />
the functional connectivity <strong>in</strong> neuronal networks[18]-[24].<br />
The standard method of analysis functional connectivity<br />
from multi spike tra<strong>in</strong>s is cross-correlation method[16].<br />
A variety of neural network models have been<br />
proposed to simulate the spike potentials of neural<br />
population. For <strong>in</strong>stance, Xiao ZG and Tian X(2010) [25]<br />
built small-world neural network model of hippocampal<br />
CA3 based on the characteristics of the hippocampal CA3<br />
neurons, simulated the response spike tra<strong>in</strong>s of neuronal<br />
population under three types of stimulus, and studied the<br />
respective neural ensemble encod<strong>in</strong>g of three types of<br />
stimulus. Meeter M(2003)[26] built a neural nucleus<br />
model of hippocampus, which composed by CA1, CA3,<br />
dentate gyrus, and entorh<strong>in</strong>al cortex nucleus; The model<br />
was based on the neural <strong>in</strong>formation connection relation<br />
of hippocampus. Atallah HE and et al (2004)[27] used a<br />
computational neural network model to <strong>in</strong>vestigate how<br />
the hippocampus with together neocortex and basal<br />
ganglia operate, which can susta<strong>in</strong> cognitive and<br />
behavioral function <strong>in</strong> the bra<strong>in</strong>.<br />
In the present paper, we aim to provide functional<br />
connectivity networks analysis on prefrontal cortex of rat<br />
<strong>in</strong> the process of work<strong>in</strong>g memory task <strong>in</strong> vivo, dur<strong>in</strong>g the<br />
period of work<strong>in</strong>g memory event occurrence and the<br />
period of rest<strong>in</strong>g state. Neural ensemble entropy cod<strong>in</strong>g<br />
can be applied to f<strong>in</strong>d the period of work<strong>in</strong>g memory<br />
event occurrence and the period of rest<strong>in</strong>g state. The<br />
analysis of functional connectivity networks carried out<br />
though the method of cross-covariance. The complex<br />
network topology parameters are calculated. F<strong>in</strong>ally, the<br />
simulations of spik<strong>in</strong>g neuronal networks of work<strong>in</strong>g<br />
memory event occurrence and rest<strong>in</strong>g state are presented.<br />
H<strong>in</strong>dmarsh-Rose (HR) neuron model is chosen as s<strong>in</strong>gle<br />
neuron that is connected by functional network of<br />
work<strong>in</strong>g memory event occurrence and rest<strong>in</strong>g state,<br />
receptivity.<br />
II. METHODS<br />
A. Experimental Data Acquired on Prefrontal Cortex of<br />
Rats dur<strong>in</strong>g Work<strong>in</strong>g Memory Task <strong>in</strong> Vivo<br />
Experimental data were conducted with the approval<br />
from Animal Care and Use Committee of Tianj<strong>in</strong><br />
Medical University and were <strong>in</strong> conformity to the Guide<br />
for the Care and Use of Laboratory Animals. 16-channel<br />
micro-wire electrodes were planted <strong>in</strong> rat prefrontal<br />
cortex and neural activities were recorded while the rats<br />
performed a work<strong>in</strong>g memory task <strong>in</strong> Y-maze. Effective<br />
period of 7 seconds were selected, which is deemed to be<br />
enough to represent the entire work<strong>in</strong>g memory process.<br />
B. Neural Ensemble Entropy Cod<strong>in</strong>g for Work<strong>in</strong>g<br />
Memory <strong>in</strong> Rats Prefrontal Cortex<br />
Entropy, especially Shannon entropy <strong>in</strong> this paper, is<br />
computed from <strong>in</strong>ter-spike <strong>in</strong>tervals (ISIs), which are<br />
generally regarded as an important carrier of encoded<br />
<strong>in</strong>formation. Assume there is an N-element <strong>in</strong>formation<br />
source sequence{ z 1<br />
, z<br />
2<br />
, ..., z n<br />
}; Shannon entropy is<br />
def<strong>in</strong>ed as the follow<strong>in</strong>g (1) (Shannon CE, 1948)[28]:<br />
n<br />
E =− p log p , (1)<br />
i=<br />
1<br />
i<br />
where p<br />
i<br />
, ( i =1, 2, ..., n ), is the occurrence probability<br />
of each element of <strong>in</strong>formation source sequence. The<br />
algorithms of Shannon entropy for spike tra<strong>in</strong> from s<strong>in</strong>gle<br />
neuron estimation are described as the follow<strong>in</strong>gs: The<br />
Inter Spike Interval (ISI) sequence of the neural fir<strong>in</strong>g<br />
was measured and the ISI histogram was estimated; The<br />
ISI histogram was separated with appropriate b<strong>in</strong> base on<br />
the def<strong>in</strong>ed b<strong>in</strong> length and the characteristics of the spike<br />
tra<strong>in</strong>s; The spikes number Si<br />
<strong>in</strong> each b<strong>in</strong> i ( i =1, 2, ...,<br />
n ) was counted; The fir<strong>in</strong>g probability p i<br />
of b<strong>in</strong> i was<br />
calculated based on the equation of<br />
2<br />
i<br />
p = S / S ;<br />
n<br />
i i i<br />
i=<br />
1<br />
From (1) the entropy E of the fir<strong>in</strong>g sequence was<br />
calculated.<br />
Above entropy estimation method can be used to<br />
present nonl<strong>in</strong>earity of neural population activity. The<br />
steps of Neural ensemble entropy cod<strong>in</strong>g are summarized<br />
as: An appropriate w<strong>in</strong>dow length L was selected and<br />
Shannon entropy was calculated for the <strong>in</strong>dividual<br />
neuron k , ( k =1, 2, ... , L ) <strong>in</strong> the w<strong>in</strong>dow; The w<strong>in</strong>dow<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1379<br />
along the time till the end of spike tra<strong>in</strong>s was slid with a<br />
mov<strong>in</strong>g step; The entropy values <strong>in</strong> each w<strong>in</strong>dow were<br />
estimated; All the entropy values were normalized and<br />
the dynamical map can be represented the neural<br />
ensemble activity as a response to the event.<br />
C. Functional Network from Neuronal Spike Tra<strong>in</strong> Data<br />
The method to determ<strong>in</strong>e directed network is to<br />
calculate the covariance between neurons, which is used<br />
to analyze the <strong>in</strong>fluences between pairs of spike tra<strong>in</strong>s.<br />
Spike tra<strong>in</strong>s are b<strong>in</strong>ned <strong>in</strong> w<strong>in</strong>dow of 1 millisecond, and<br />
then 10 milliseconds time-step is applied to count the<br />
number of spikes of each spike tra<strong>in</strong>, the correspond<strong>in</strong>g<br />
vectors are obta<strong>in</strong>ed. To measure whether there is an<br />
<strong>in</strong>fluence from a reference neuron (vector y ) to a target<br />
neuron (vector x ), (2) is applied to calculate covariance<br />
between neurons,<br />
C<br />
N−| d|<br />
N N<br />
1 1 <br />
( n+<br />
d)<br />
i n i<br />
n 1 N<br />
<br />
i 1 N<br />
<br />
= = i=<br />
1 <br />
xy<br />
( d)<br />
= N−| d|<br />
N N<br />
<br />
<br />
<br />
x − x y − y d ≥0<br />
, (2)<br />
1 1 <br />
y − y x − x d < 0<br />
<br />
<br />
( n−d)<br />
i n i<br />
n= 1 N i= 1 N i=<br />
1<br />
where C ( d ) is covariance between reference neuron<br />
xy<br />
(vector y ) and target neuron (vector x ), d is time lag<br />
between reference neuron (vector y ) and target neuron<br />
(vector x ), x and y are length N vectors obta<strong>in</strong>ed from<br />
correspond<strong>in</strong>g spike tra<strong>in</strong>s of neuron. The Cxy<br />
( d ) will<br />
show a peak if there is some consistent pattern between<br />
vector y and vector x with a time lag d . When a peak<br />
occurs at a time lag d ≥ 0 <strong>in</strong> lag w<strong>in</strong>dow of 50<br />
milliseconds, there is an effect from reference neuron<br />
(vector y ) to target neuron (vector x ) with target neuron<br />
delay d , the <strong>in</strong>fluence strength is the value of peak. If the<br />
peak exceeded a threshold, we can obta<strong>in</strong> a connection<br />
from reference neuron to target neuron with connectivity<br />
weigh of peak value. Each neuron is considered with no<br />
connectivity to itself, <strong>in</strong> other words, the ma<strong>in</strong> diagonal<br />
elements of functional connectivity matrix are zero.<br />
D. Complex Network Topology Parameters<br />
Small-world networks theory is presented by Watts DJ<br />
and Strogatz SH(1998)[29]. Usually two parameters are<br />
used to characterize the complex network characteristics.<br />
One is cluster<strong>in</strong>g coefficient ( CC ), and another is<br />
characteristic path length ( CPL ). Suppose there are k<br />
edges connected to one node; there are at most<br />
kk− ( 1)/2 probable exist edges among k neighbor<br />
nodes which are connected to k edges. The CC of one<br />
node is the number of actual exist edges divide by the<br />
number of at most probable exist edges. The CC of the<br />
network is def<strong>in</strong>ed as the average value of all nodes, as<br />
the follow<strong>in</strong>gs (3).<br />
N<br />
2ei<br />
CC = , (3)<br />
k ( k −1)<br />
i=<br />
1 i i<br />
where N is the nodes number of the network, e i<br />
is the<br />
number of actual exist edges among k<br />
i<br />
nodes. Arbitrarily<br />
select two nodes <strong>in</strong> a complex network, connect<strong>in</strong>g these<br />
two nodes with the m<strong>in</strong>imum number of edges, which is<br />
def<strong>in</strong>ed as the shortest path length of these two nodes.<br />
The CPL of the network is def<strong>in</strong>ed as the average value<br />
of all shortest path length between node pairs, as the<br />
follow<strong>in</strong>gs (4),<br />
N<br />
2<br />
CPL = dij<br />
. (4)<br />
nn ( + 1) i=<br />
1<br />
where d<br />
ij<br />
is the shortest path length between the two<br />
nodes i and j <strong>in</strong> the complex network, N is the nodes<br />
number of the network.<br />
Characteristics of small-world network are high CC<br />
and shorter CPL . Meanwhile the two parameters are<br />
high <strong>in</strong> regular networks and low <strong>in</strong> correspond<strong>in</strong>g<br />
random networks[30].<br />
E. Spik<strong>in</strong>g Neuronal Network Simulation of<br />
Prefrontal Cortex<br />
S<strong>in</strong>gle spik<strong>in</strong>g neuron model is the basis computational<br />
model of the neural physiological activity study. The<br />
H<strong>in</strong>dmarsh-Rose (HR) model was proposed by<br />
H<strong>in</strong>dmarsh J and Rose RM (1984)[32]. Used HR neuron<br />
model, the action potential can be simulated. HR model<br />
can be used to study s<strong>in</strong>gle neuron spik<strong>in</strong>g characteristics<br />
as well as the basic unit of the large-scale network. HR<br />
neuron model is used as network nodes <strong>in</strong> our neural<br />
population model. The equations of HR neuron model are<br />
shown <strong>in</strong> (5), (6) and (7),<br />
dX 3 2<br />
= Y − aX + bX − Z + I<br />
stim<br />
, (5)<br />
dt<br />
dY<br />
2<br />
c dX Y<br />
dt = − − , (6)<br />
dZ<br />
1<br />
r( X ( Z- g))<br />
dt = − 4<br />
, (7)<br />
where X is the membrane potential of neuron, Y<br />
represents the fast recovery currents, Z represents slow<br />
adaptive currents, I stim<br />
is an external stimulus <strong>in</strong>put<br />
currents, a , b , c , d , r and g are constant parameters.<br />
The values of these parameters are set accord<strong>in</strong>g to [33].<br />
In HR neuron model, the parameter r is related to the<br />
concentration of calcium ions. By adjust<strong>in</strong>g the value of<br />
the parameter r , the neuron can be shown a different<br />
discharge mode.<br />
The prefrontal cortex neurons are ma<strong>in</strong>ly divided <strong>in</strong>to<br />
two categories: excitatory neurons and <strong>in</strong>hibitory neurons;<br />
The anatomical sampl<strong>in</strong>g of the neurons <strong>in</strong> the prefrontal<br />
cortex has shown that about 80% of the neurons are<br />
excitatory neurons and the rest 20% are <strong>in</strong>hibitory<br />
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neurons[31]. Excitatory neurons are pyramidal cells <strong>in</strong><br />
morphology. The fir<strong>in</strong>g characteristics of excitatory<br />
neurons are regular spik<strong>in</strong>g (RS) neurons, which present<br />
rapid and evident fir<strong>in</strong>g frequency adaptation respond<strong>in</strong>g<br />
to a cont<strong>in</strong>uous depolariz<strong>in</strong>g current <strong>in</strong>jection. Inhibitory<br />
neurons are <strong>in</strong>terneuron cells. The fir<strong>in</strong>g characteristics of<br />
excitatory neurons are fast spik<strong>in</strong>g (FS) neurons, which<br />
respond to long depolariz<strong>in</strong>g current stimulus with higher<br />
fir<strong>in</strong>g rate and less prom<strong>in</strong>ent spike frequency adaptation<br />
than RS neurons.<br />
In our Spik<strong>in</strong>g neuronal network simulation of<br />
prefrontal cortex, all HR neurons are coupled by<br />
functional connectivity. The equations of network model<br />
are shown as (8), (9), and (10):<br />
dX<br />
d<br />
N<br />
i<br />
3 2<br />
Yi aXi bXi Zi Istim<br />
w AijX<br />
j<br />
t j=<br />
1<br />
= − + − + + , (8)<br />
dYi<br />
dt<br />
= c−dX − Y , (9)<br />
2<br />
i<br />
dZi<br />
1<br />
= r( Xi<br />
− ( Zi<br />
- g))<br />
, (10)<br />
dt<br />
4<br />
where the subscript i represents the neuron number, N<br />
is the number of neurons. In our simulation we use<br />
N equals to the neuron number <strong>in</strong> work<strong>in</strong>g memory<br />
experiment <strong>in</strong> rat prefrontal cortex.<br />
i<br />
w<br />
N<br />
<br />
j=<br />
1<br />
A X<br />
ij<br />
j<br />
is the<br />
coupl<strong>in</strong>g term of the neural network model, where w is<br />
the coupl<strong>in</strong>g strength of connectivity from neuron j to<br />
neuron i . Aij<br />
is an N × N martix, which represents the<br />
coupl<strong>in</strong>g matrix of the neurons when a connection exists<br />
between neurons i and j .<br />
III. RESULTS<br />
A. Neural Ensemble Cod<strong>in</strong>g from Experimental Data<br />
After us<strong>in</strong>g software of spike sort<strong>in</strong>g (off-l<strong>in</strong>e sorter,<br />
Plexon, TX, USA) to separate s<strong>in</strong>gle neuron data from<br />
16-channel data, we obta<strong>in</strong> 34 neurons and correspond<strong>in</strong>g<br />
spike tra<strong>in</strong>s. Neuronal population spatiotemporal<br />
activities <strong>in</strong> rat prefrontal cortex dur<strong>in</strong>g the performance<br />
of work<strong>in</strong>g memory task <strong>in</strong> vivo are shown <strong>in</strong> Fig. 1.<br />
In Fig. 1, effective period of 7 seconds is selected to<br />
represent the whole work<strong>in</strong>g memory process. The<br />
dynamic entropy cod<strong>in</strong>g method was applied to<br />
characterize activity of neural population response to the<br />
work<strong>in</strong>g memory event. We calculated the entropy values<br />
of population fir<strong>in</strong>g dur<strong>in</strong>g work<strong>in</strong>g memory task. The<br />
neural fir<strong>in</strong>g entropy matrix is obta<strong>in</strong>ed <strong>in</strong> slid<strong>in</strong>g w<strong>in</strong>dow<br />
of 200 milliseconds with 50 milliseconds overlapp<strong>in</strong>g,<br />
represent<strong>in</strong>g the local entropy for each neuron. And<br />
neural ensemble entropy cod<strong>in</strong>g is shown <strong>in</strong> Fig. 2.<br />
Spike raster<br />
(neuron# 1-34)<br />
Figure 1. Neuronal population spatiotemporal activities <strong>in</strong> rat prefrontal<br />
cortex dur<strong>in</strong>g a work<strong>in</strong>g memory task <strong>in</strong> vivo. The triangle " "<br />
<strong>in</strong>dicates the time stamp.<br />
Entropy<br />
(neuron# 1-34)<br />
Normalized entropy<br />
Figure 2. Neural ensemble entropy cod<strong>in</strong>g <strong>in</strong> rat prefrontal cortex<br />
dur<strong>in</strong>g a work<strong>in</strong>g memory task <strong>in</strong> vivo. The triangle " " <strong>in</strong>dicates the<br />
time stamp.<br />
In Fig. 2, Normalization is achieved by divid<strong>in</strong>g spike<br />
tra<strong>in</strong>s by the maximum entropy values over the time<br />
period. Simultaneous <strong>in</strong>crease of fir<strong>in</strong>g rate and entropy<br />
demonstrate the occurrence of work<strong>in</strong>g memory event.<br />
Neuron 12, 13, 14, 15, 16, 17, 18 and 19 form a neural<br />
ensemble dur<strong>in</strong>g the occurrence of work<strong>in</strong>g memory<br />
event. The triangle " " <strong>in</strong>dicates the time stamp.<br />
B. Functional Connectivity Network<br />
The analyses of functional connectivity networks were<br />
carried out dur<strong>in</strong>g the occurrence of work<strong>in</strong>g memory<br />
event (time <strong>in</strong>terval [2.818s, 4.818s], before time stamp)<br />
and the period of rest<strong>in</strong>g state (time <strong>in</strong>terval [5.000s,<br />
7.000s], i.e. the period of 2s after time stamp). The<br />
method of cross-covariance between pairs of neurons has<br />
been used to determ<strong>in</strong>e directed connectivity edges. For<br />
34 neurons, N( N − 1)/2, or 561 pairs of neuron have<br />
been calculated. And at most there are 1122 crosscovariance<br />
peaks greater than zero. To determ<strong>in</strong>e the<br />
threshold of the connectivity, the peaks sorted by their<br />
values are shown <strong>in</strong> Fig. 3. If the threshold is too low, the<br />
result network is a fully connected graph. However, if the<br />
threshold is too high, the graph has several edges. Here,<br />
threshold was determ<strong>in</strong>ed with the value when the mean<br />
degree K ≈ ln( N)<br />
[34].<br />
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14<br />
12<br />
Work<strong>in</strong>g memory event occurrence<br />
Rest<strong>in</strong>g state<br />
Cross-covariance peaks<br />
10<br />
8<br />
6<br />
4<br />
Target neuron #<br />
2<br />
Threshold<br />
0<br />
0 200 400 600 800 1000 1200<br />
Pair <strong>in</strong>dex<br />
Figure 3. Cross-covariance peaks between neuronal pairs<br />
In Fig. 3, the threshold=2.0 at the po<strong>in</strong>t where the<br />
<strong>in</strong>crement of the curve changes notably. If the peak<br />
exceeds the threshold, a directed edge of functional<br />
connectivity network could be obta<strong>in</strong>ed from the<br />
reference neuron to the target neuron with the<br />
connectivity weight of peak value. Via the analysis of<br />
two time <strong>in</strong>tervals (the occurrence of work<strong>in</strong>g memory<br />
event <strong>in</strong> the time <strong>in</strong>terval before time stamp; period of<br />
rest<strong>in</strong>g state <strong>in</strong> the time <strong>in</strong>terval after time stamp), two<br />
correspond<strong>in</strong>g functional connectivity networks were<br />
obta<strong>in</strong>ed and their connectivity matrix are shown <strong>in</strong> Fig. 4<br />
and Fig. 5, respectively.<br />
In Fig. 4 and Fig. 5, each column of the matrix<br />
<strong>in</strong>dicates whether there is a direct connection from the<br />
reference neuron to the target neurons, where the neuron<br />
number corresponds to the column number is a reference<br />
neuron. The nonzero elements of the matrix <strong>in</strong>dicate that<br />
there is a functional connection from the reference to the<br />
target neuron and the color shows the strength of the<br />
connection. Compar<strong>in</strong>g the Functional connectivity<br />
matrix of work<strong>in</strong>g memory event occurrence network<br />
(Fig. 4) with rest<strong>in</strong>g state network (Fig. 5), the number of<br />
edges of work<strong>in</strong>g memory event occurrence network is<br />
more than the number of the latter network. And the<br />
mean connectivity strength shows the same, as shown <strong>in</strong><br />
Table 1.<br />
TABLE 1<br />
CONNECTION NUMBER AND MEAN CONNECTIVITY<br />
STRENGTH OF TWO NETWORKS<br />
Connection<br />
number<br />
Mean connectivity<br />
strength<br />
Work<strong>in</strong>g memory event<br />
occurrence network<br />
402 3.93 ± 1.93<br />
Rest<strong>in</strong>g state network 67 2.55 ± 0.51<br />
Figure 4. Functional connectivity matrix of neurons dur<strong>in</strong>g the<br />
occurrence of work<strong>in</strong>g memory event <strong>in</strong> vivo (time <strong>in</strong>terval [2.818s,<br />
4.818s], before time stamp)<br />
Target neuron #<br />
Figure 5. Functional connectivity matrix of neurons dur<strong>in</strong>g the period<br />
of rest<strong>in</strong>g state <strong>in</strong> vivo (time <strong>in</strong>terval [5.000s, 7.000s], i.e. the period of<br />
2s after time stamp).<br />
In work<strong>in</strong>g memory event occurrence network, the<br />
high strength and dense connection concentrates on<br />
several neurons (especially on neuron 12, 13, 14, 15, 16,<br />
17, 18 and 19). And this phenomenon was not found <strong>in</strong><br />
the latter network. It agrees with neural ensemble cod<strong>in</strong>g<br />
form experimental data that neuron 12, 13, 14, 15, 16, 17,<br />
18 and 19 form a neural ensemble dur<strong>in</strong>g the period of<br />
work<strong>in</strong>g memory event occurrence.<br />
Fig. 6 and Fig. 7 show the topological graphs of<br />
work<strong>in</strong>g memory event occurrence network and rest<strong>in</strong>g<br />
state network, respectively. The color of the edges<br />
reflects the connection strength from the reference<br />
neurons to the target neurons, with magenta be<strong>in</strong>g largest<br />
and blue be<strong>in</strong>g smallest.<br />
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1382 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 6. Connectivity graph of work<strong>in</strong>g memory event occurrence<br />
network <strong>in</strong> vivo (dur<strong>in</strong>g time <strong>in</strong>terval [2.818s, 4.818s], before time<br />
stamp)<br />
C. Results of Simulation<br />
The neuronal spik<strong>in</strong>g networks of work<strong>in</strong>g memory<br />
event occurrence and rest<strong>in</strong>g state were simulated. Our<br />
simulation model is composed of 34 neurons, of which<br />
the simulation time is 2000 milliseconds, respectively. In<br />
our Spik<strong>in</strong>g neuronal network simulation of prefrontal<br />
cortex, all HR neurons are coupled by two functional<br />
connectivity networks as show<strong>in</strong>g <strong>in</strong> Fig. 4 and Fig. 5.<br />
The Spike raster of neuronal network model simulation of<br />
work<strong>in</strong>g memory event occurrence and rest<strong>in</strong>g state are<br />
shown <strong>in</strong> Fig. 8 (a)(b), respectively. And we calculate<br />
neural ensemble entropy cod<strong>in</strong>g of the two simulation<br />
results as shown <strong>in</strong> Fig. 9 (a) (b), respectively. In Fig. 9<br />
(a)(b), normalization is achieved by divid<strong>in</strong>g by the<br />
maximum entropy values from spike tra<strong>in</strong>s over the time<br />
period.<br />
In Fig. 8(a) and Fig. 9(a), Several neurons <strong>in</strong>creases<br />
simultaneously <strong>in</strong> fir<strong>in</strong>g rate and <strong>in</strong>creases <strong>in</strong> Entropy,<br />
and Neuron 10, 12, 13, 14, 15, 16 and 17 form a neural<br />
ensemble dur<strong>in</strong>g the simulation of work<strong>in</strong>g memory event<br />
occurrence. In Fig. 8(b) and Fig. 9(b), there is no neural<br />
ensemble formed. The simulation results are agreed with<br />
experiment data <strong>in</strong> rat prefrontal cortex dur<strong>in</strong>g a work<strong>in</strong>g<br />
memory task <strong>in</strong> vivo.<br />
(a)<br />
(b)<br />
Figure 7. Connectivity graph of rest<strong>in</strong>g state network <strong>in</strong> vivo (dur<strong>in</strong>g<br />
time <strong>in</strong>terval [5.000s, 7.000s], i.e. the period of 2s after time stamp)<br />
To compare characteristics of different networks, the<br />
CC and CPL were calculated. The CPL of the<br />
work<strong>in</strong>g memory event occurrence network is 1.678, and<br />
its equivalent random network is 1.657; the CC of the<br />
work<strong>in</strong>g memory event occurrence network is 0.604, and<br />
its equivalent random network is 0.356. The CPL of the<br />
rest<strong>in</strong>g state network is 3.045, and its equivalent random<br />
network is 3.683; the CC of the work<strong>in</strong>g memory event<br />
occurrence network is 0.098, and its equivalent random<br />
network is 0.066. The two networks satisfy the smallworld<br />
network property as the cluster<strong>in</strong>g coefficients of<br />
them are larger than their correspond<strong>in</strong>g random<br />
networks and their characteristic path lengths are<br />
approximately equal to their correspond<strong>in</strong>g random<br />
networks.<br />
1 second 1 second<br />
Figure 8. Spike raster of neuronal network model simulation. (a)<br />
Neuronal network model of neurons spik<strong>in</strong>g of work<strong>in</strong>g memory event<br />
occurrence. (b) Neuronal network model of neurons spik<strong>in</strong>g of rest<strong>in</strong>g<br />
state.<br />
(a)<br />
Entropy<br />
(neuron# 1-34)<br />
(b)<br />
Entropy<br />
(neuron# 1-34)<br />
Normalized entropy<br />
Figure 9. Neural ensemble entropy cod<strong>in</strong>g of neuronal network model<br />
simulation. (a) Neural ensemble entropy cod<strong>in</strong>g of neurons spik<strong>in</strong>g of<br />
work<strong>in</strong>g memory event occurrence simulation. (b) Neural ensemble<br />
entropy cod<strong>in</strong>g of rest<strong>in</strong>g state simulation.<br />
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IV. CONCLUSIONS<br />
In the present paper, functional connectivity networks<br />
on prefrontal cortex of rat dur<strong>in</strong>g work<strong>in</strong>g memory task <strong>in</strong><br />
vivo are analyzed. Neural ensemble entropy cod<strong>in</strong>g is<br />
applied to f<strong>in</strong>d the time <strong>in</strong>terval of work<strong>in</strong>g memory<br />
event occurrence. The neural fir<strong>in</strong>g entropy matrix is<br />
obta<strong>in</strong>ed <strong>in</strong> slid<strong>in</strong>g w<strong>in</strong>dow of 200 milliseconds with 50<br />
milliseconds overlapp<strong>in</strong>g, represent<strong>in</strong>g the local entropy<br />
for each neuron. Simultaneous <strong>in</strong>crease of fir<strong>in</strong>g rate and<br />
entropy demonstrate the occurrence of work<strong>in</strong>g memory<br />
event (time <strong>in</strong>terval [2.818s, 4.818s]). Neuron 12, 13, 14,<br />
15, 16, 17, 18 and 19 form a neural ensemble dur<strong>in</strong>g the<br />
occurrence of work<strong>in</strong>g memory event. The analysis of<br />
functional connectivity networks carried out though the<br />
method of cross-covariance The analyses of functional<br />
connectivity networks were carried out dur<strong>in</strong>g the<br />
occurrence of work<strong>in</strong>g memory event (time <strong>in</strong>terval<br />
[2.818s, 4.818s], before time stamp) and the period of<br />
rest<strong>in</strong>g state (time <strong>in</strong>terval [5.000s, 7.000s], i.e. the period<br />
of 2s after time stamp). The complex network topology<br />
parameters are calculated. The number of edges of<br />
work<strong>in</strong>g memory event occurrence network is more than<br />
the number of the latter network. And the mean<br />
connectivity strength shows the same. In work<strong>in</strong>g<br />
memory event occurrence network, the high strength and<br />
dense connection concentrates on several neurons<br />
(especially on neuron 12, 13, 14, 15, 16, 17, 18 and 19).<br />
And this phenomenon was not found <strong>in</strong> the latter network.<br />
It agrees with neural ensemble cod<strong>in</strong>g form experimental<br />
data that neuron 12, 13, 14, 15, 16, 17, 18 and 19 form a<br />
neural ensemble dur<strong>in</strong>g the period of work<strong>in</strong>g memory<br />
event occurrence. The two networks satisfy the smallworld<br />
network property as the cluster<strong>in</strong>g coefficients of<br />
them are larger than their correspond<strong>in</strong>g random<br />
networks and their characteristic path lengths are<br />
approximately equal to their correspond<strong>in</strong>g random<br />
networks. F<strong>in</strong>ally, the simulations of spik<strong>in</strong>g neuronal<br />
network of work<strong>in</strong>g memory event occurrence and rest<strong>in</strong>g<br />
state are presented. H<strong>in</strong>dmarsh-Rose (HR) neuron model<br />
is chosen as s<strong>in</strong>gle neuron that connected by functional<br />
network of work<strong>in</strong>g memory event occurrence and rest<strong>in</strong>g<br />
state, receptivity. The two simulation models are<br />
composed of 34 neurons, of which the simulation time is<br />
2000 milliseconds, respectively. Several neurons<br />
<strong>in</strong>creases simultaneously <strong>in</strong> fir<strong>in</strong>g rate and <strong>in</strong>creases <strong>in</strong><br />
Entropy, and Neuron 10, 12, 13, 14, 15, 16 and 17 form a<br />
neural ensemble dur<strong>in</strong>g the simulation of work<strong>in</strong>g<br />
memory event occurrence. There is no neural ensemble<br />
formed dur<strong>in</strong>g the simulation of rest<strong>in</strong>g state. The<br />
simulation results are agreed with experiment data <strong>in</strong> rat<br />
prefrontal cortex dur<strong>in</strong>g a work<strong>in</strong>g memory task.<br />
ACKNOWLEDGEMENTS<br />
This work was supported by grants (No. 91132722 and<br />
No. 61074131) from the National Natural Science<br />
Foundation of Ch<strong>in</strong>a.<br />
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Dexuan Qi was born <strong>in</strong> Tianj<strong>in</strong>, Ch<strong>in</strong>a, <strong>in</strong> 1983. She<br />
received the Bachelor's degree <strong>in</strong> Mechanics Eng<strong>in</strong>eer<strong>in</strong>g <strong>in</strong><br />
2006, from Tianj<strong>in</strong> University, Tianj<strong>in</strong>, Ch<strong>in</strong>a. She received the<br />
Master's degree and Doctor's degree <strong>in</strong> 2010, from Tianj<strong>in</strong><br />
University, Tianj<strong>in</strong>, Ch<strong>in</strong>a.<br />
She is work<strong>in</strong>g as post-doctor <strong>in</strong> Tianj<strong>in</strong> Research Centre of<br />
Basic Medical Science, Tianj<strong>in</strong> Medical University. Her<br />
research <strong>in</strong>terests <strong>in</strong>clude neuronal network model, simulation<br />
of cortex spik<strong>in</strong>g model, and functional connectivity network.<br />
X<strong>in</strong> Tian was born <strong>in</strong> Shanghai, Ch<strong>in</strong>a, <strong>in</strong> 1946. She<br />
obta<strong>in</strong>ed the Bachelor's degree <strong>in</strong> 1968, from Ts<strong>in</strong>ghua<br />
University, Beij<strong>in</strong>g, Ch<strong>in</strong>a. She received the Master's degree <strong>in</strong><br />
1982, from Tianj<strong>in</strong> University, Tianj<strong>in</strong>, Ch<strong>in</strong>a. She received the<br />
Doctor's degree <strong>in</strong> 1991, from University of New South Wales,<br />
Australia.<br />
She is currently a professor of school of Biomedical<br />
Eng<strong>in</strong>eer<strong>in</strong>g, Tianj<strong>in</strong> Medical University. Her research <strong>in</strong>terests<br />
<strong>in</strong>clude neural <strong>in</strong>formation process<strong>in</strong>g, encod<strong>in</strong>g, nonl<strong>in</strong>ear<br />
systems and neural computation.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1385<br />
A Novel Heuristic Usage of Helpful Actions for<br />
Conformant-FF System<br />
Wei Wei, Dantong Ouyang, T<strong>in</strong>gt<strong>in</strong>g Zou and Shuai Lu<br />
College of Computer Science and Technology, Jil<strong>in</strong> University, Changchun, Ch<strong>in</strong>a<br />
Key Laboratory of Symbolic Computation and Knowledge Eng<strong>in</strong>eer<strong>in</strong>g of M<strong>in</strong>istry of Education, Jil<strong>in</strong> University,<br />
Changchun, Ch<strong>in</strong>a<br />
Email: wei_wei10@mails.jlu.edu.cn, ouyd@jlu.edu.cn, zout<strong>in</strong>gt@163.com, lus@jlu.edu.cn<br />
Abstract—Conformant plann<strong>in</strong>g is usually transformed <strong>in</strong>to<br />
a search problem <strong>in</strong> the space of belief states, where the<br />
comb<strong>in</strong>atorial explosion of search space has been one of the<br />
most <strong>in</strong>tractable problems. In this paper, we present a novel<br />
usage of the helpful action prun<strong>in</strong>g technique <strong>in</strong> the<br />
Conformant-FF planner. The key idea is to change the way<br />
it deals with helpful actions and first consider actions from<br />
the so-called implication path which was used by<br />
Conformant-FF for conclud<strong>in</strong>g which subgoal would be<br />
considered known to be true <strong>in</strong> the relaxed plann<strong>in</strong>g graph.<br />
We first po<strong>in</strong>t out the semantics of solv<strong>in</strong>g by cases,<br />
<strong>in</strong>dicated by the implication paths of the relaxed plann<strong>in</strong>g<br />
process. In l<strong>in</strong>e with the semantics, we then propose our<br />
heuristic idea of us<strong>in</strong>g these implication paths further by<br />
attempt<strong>in</strong>g to collect certa<strong>in</strong> groups of helpful actions such<br />
that execut<strong>in</strong>g all actions with<strong>in</strong> a group can achieve some<br />
subgoal while execut<strong>in</strong>g an <strong>in</strong>dividual action <strong>in</strong> the group<br />
cannot due to <strong>in</strong>complete <strong>in</strong>formation. This technique<br />
usually leads to the goal faster and cuts down the search<br />
space dramatically. We evaluate the idea experimentally. In<br />
a number of conformant benchmarks, our heuristic<br />
prun<strong>in</strong>g technique outperforms helpful actions prun<strong>in</strong>g <strong>in</strong><br />
both plann<strong>in</strong>g efficiency and the size of search space.<br />
Index Terms—Helpful actions, Conformant-FF, Heuristic<br />
Prun<strong>in</strong>g, Belief state<br />
I. INTRODUCTION<br />
Plann<strong>in</strong>g is an area of Artificial Intelligence that<br />
studies choos<strong>in</strong>g and organiz<strong>in</strong>g actions to achieve some<br />
objectives. Over the last few years we have seen a<br />
significant <strong>in</strong>crease of the efficiency of plann<strong>in</strong>g systems<br />
[1, 2]. There are several promis<strong>in</strong>g approaches <strong>in</strong> plan<br />
generation <strong>in</strong>clud<strong>in</strong>g plann<strong>in</strong>g graph analysis [3, 4],<br />
plann<strong>in</strong>g as satisfiability [5] and heuristic search<br />
plann<strong>in</strong>g [6, 7, 8]. Classical plann<strong>in</strong>g refers to plann<strong>in</strong>g<br />
under a restricted model which is determ<strong>in</strong>istic, static,<br />
f<strong>in</strong>ite and fully observable with restricted goals and<br />
implicit time. However, these assumptions are often<br />
unrealistic when model<strong>in</strong>g real-world tasks. For <strong>in</strong>stance,<br />
the <strong>in</strong>itial state may be <strong>in</strong>completely specified, actions<br />
may have non-determ<strong>in</strong>istic effects or the environment<br />
Manuscript received July 1, 2012; revised October 6, 2012; accepted<br />
October 11, 2012.<br />
Correspond<strong>in</strong>g author: Dantong Ouyang<br />
may be only partially observable. Several <strong>in</strong>terest<strong>in</strong>g<br />
models are obta<strong>in</strong>ed by relax<strong>in</strong>g some of the restrictive<br />
assumptions. Conformant plann<strong>in</strong>g is the problem of<br />
f<strong>in</strong>d<strong>in</strong>g a plan that guarantees goal achievement given<br />
nondeterm<strong>in</strong>istic <strong>in</strong>itial state or action effects, and no<br />
<strong>in</strong>formation can be observed at run time. A conformant<br />
plan is a sequence of actions that should be successful to<br />
achieve the goal regardless of uncerta<strong>in</strong>ty about the<br />
<strong>in</strong>itial state and action effects. Therefore, conformant<br />
plann<strong>in</strong>g turns out to be considerably harder than<br />
classical plann<strong>in</strong>g [9]. Effective approaches for<br />
conformant plann<strong>in</strong>g <strong>in</strong>clude heuristic guidance [10, 11],<br />
translation <strong>in</strong> to classical ones [12], approximation-based<br />
plann<strong>in</strong>g and so on [13].<br />
Heuristic search is one of the strongest trends <strong>in</strong> the<br />
plann<strong>in</strong>g community. We focus on the formulation that<br />
transfers a conformant plann<strong>in</strong>g task <strong>in</strong>to a search<br />
problem <strong>in</strong> the belief state space. In this way, uncerta<strong>in</strong>ty<br />
about the true current world state is modeled via a belief<br />
state, i.e., the set of world states that we consider<br />
possible at this time. Then a heuristic function is derived<br />
from the specification of the plann<strong>in</strong>g <strong>in</strong>stance and used<br />
for guid<strong>in</strong>g the search through the search space. FF’s<br />
heuristic function based on a relaxation of the plann<strong>in</strong>g<br />
task turns out to be the most successful idea <strong>in</strong> classical<br />
plann<strong>in</strong>g. Hoffmann and Brafman extended this<br />
technique to conformant plann<strong>in</strong>g and implemented the<br />
well known planner Conformant-FF [14]. In a number of<br />
benchmarks, Conformant-FF can provide very<br />
<strong>in</strong>formative heuristic values and shows f<strong>in</strong>e scalability.<br />
Conformant-FF uses the same overall search<br />
arrangement as FF, with reasonable modifications for<br />
conformant sett<strong>in</strong>g. In Conformant-FF, belief states are<br />
represented by an implicit approach where the truth<br />
values of all the propositions <strong>in</strong> a belief state are<br />
determ<strong>in</strong>ed us<strong>in</strong>g a CNF reason<strong>in</strong>g. FF’s relaxed<br />
plann<strong>in</strong>g process is also extended to handle conformant<br />
problems. For each action effect the relaxation is to<br />
ignore the effect’s delete list as well as all but one<br />
proposition of the effect’s condition. After build<strong>in</strong>g the<br />
relaxed plann<strong>in</strong>g graph successfully, a relaxed plan is<br />
extracted and the length of the relaxed plan is used to<br />
provide the heuristic value of the belief state. When<br />
solv<strong>in</strong>g the relaxed plann<strong>in</strong>g task for a belief state,<br />
implication relation is ma<strong>in</strong>ta<strong>in</strong>ed simultaneously to<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1385-1393
1386 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
capture constra<strong>in</strong>ts between propositions at adjacent time<br />
steps. Implication paths <strong>in</strong> this mach<strong>in</strong>ery can be used to<br />
check the truth value of uncerta<strong>in</strong> propositions when<br />
build<strong>in</strong>g the relaxed plann<strong>in</strong>g graph and to determ<strong>in</strong>e<br />
actions that must be <strong>in</strong>serted to the solution dur<strong>in</strong>g<br />
relaxed plan extraction. Besides the estimate of goal<br />
distance, Conformant-FF uses a prun<strong>in</strong>g technique of<br />
helpful actions select<strong>in</strong>g a set of promis<strong>in</strong>g successors to<br />
each search node.<br />
In conformant sett<strong>in</strong>g, we observe that some branches<br />
of the search tree are usually non-<strong>in</strong>dependent with each<br />
other when expand<strong>in</strong>g a belief state. All the actions on<br />
these branches will be <strong>in</strong>volved <strong>in</strong>to the f<strong>in</strong>al plan <strong>in</strong><br />
different search iterations. In this paper, we recognize<br />
such branches and consider them as a group. With that<br />
we propose a powerful prun<strong>in</strong>g technique suggested by<br />
implication paths when solv<strong>in</strong>g the relaxed plann<strong>in</strong>g task.<br />
Briefly, those actions which are <strong>in</strong>serted <strong>in</strong>to the relaxed<br />
plan by implication paths at the first time step concern<br />
the unknown propositions of the current belief state and<br />
thus permit to remove the uncerta<strong>in</strong>ty. We execute these<br />
actions <strong>in</strong> sequence with higher priority than other<br />
regular helpful action provided by Conformant-FF.<br />
Our novel usage of helpful actions is useful <strong>in</strong><br />
reduc<strong>in</strong>g the degree of uncerta<strong>in</strong>ty about the current<br />
belief state and get closer to the goal quickly. We run<br />
experiments to evaluate our idea. In a number of<br />
conformant benchmarks, the experimental results show<br />
that our prun<strong>in</strong>g technique can get a much smaller search<br />
space than before and improves the orig<strong>in</strong>al<br />
Conformant-FF system <strong>in</strong> both plann<strong>in</strong>g efficiency and<br />
the size of search space.<br />
The paper is organized as follows. In Section 2 we<br />
briefly describe the conformant plann<strong>in</strong>g framework we<br />
consider and give an overview of Conformant-FF’s<br />
architecture. In Section 3 we characterize the semantics<br />
of the implication paths <strong>in</strong> Conformant-FF firstly. Then<br />
we propose our idea of prun<strong>in</strong>g based on the usage of<br />
helpful actions, and illustrate the enforced hill-climb<strong>in</strong>g<br />
procedure adopt<strong>in</strong>g this prun<strong>in</strong>g technique. Section 4<br />
gives the experimental results and our analysis. We<br />
conclude the paper <strong>in</strong> Section 5.<br />
II. BACKGROUND<br />
A. Conformant plann<strong>in</strong>g problem<br />
The conformant plann<strong>in</strong>g problem considered <strong>in</strong> this<br />
paper extends a subset of the ADL language with<br />
uncerta<strong>in</strong>ty about the <strong>in</strong>itial state. The extensions to<br />
handle uncerta<strong>in</strong>ty about effects are conceptually<br />
straightforward by tak<strong>in</strong>g account of the<br />
non-determ<strong>in</strong>istic effects when comput<strong>in</strong>g state<br />
transitions.<br />
Def<strong>in</strong>ition 1 (Conformant plann<strong>in</strong>g problem)<br />
A conformant plann<strong>in</strong>g problem P is a triple (A, I, G)<br />
where A corresponds the action set, I is a propositional<br />
CNF formula denot<strong>in</strong>g the possible <strong>in</strong>itial world states<br />
and G is an non-empty set of propositions def<strong>in</strong><strong>in</strong>g the<br />
goal conditions.<br />
The <strong>in</strong>itial situation is a belief state represented by a<br />
propositional CNF formula I. Any world state that<br />
satisfies this formula is a possible <strong>in</strong>itial state. We use S I<br />
to denote the <strong>in</strong>itial belief state. An action a is a pair of<br />
(pre(a), E(a)) where pre(a) is a set of propositions<br />
represent<strong>in</strong>g the preconditions and E(a) is a set of<br />
conditional effects. A conditional effect e is a triple<br />
(con(e), add(e), del(e)) that correspond to e’s condition,<br />
add list and delete list respectively. An action a is<br />
applicable <strong>in</strong> a world state w if pre(a) w, i.e., all of a’s<br />
preconditions are satisfied <strong>in</strong> w. If action a is applicable<br />
<strong>in</strong> w, then all conditional effects eE(a) that satisfies<br />
con(e) w get executed. Execut<strong>in</strong>g a conditional effect e<br />
results <strong>in</strong> the world state w- del(e)∪add(e).<br />
Def<strong>in</strong>ition 2 (Conformant plan)<br />
An action sequence actA* is a conformant plan for<br />
problem P if, no matter what <strong>in</strong>itial world state one starts<br />
from, all actions <strong>in</strong> act are applicable at their po<strong>in</strong>t of<br />
execution and the associate run results <strong>in</strong> a goal state.<br />
B. Conformant-FF system<br />
Conformant-FF system transforms a conformant<br />
plann<strong>in</strong>g problem <strong>in</strong>to a search problem <strong>in</strong> belief state<br />
space. A belief state S is represented by the <strong>in</strong>itial belief<br />
state formula together with the action sequence that leads<br />
to S. For each belief state encountered dur<strong>in</strong>g search, the<br />
sets of known, negatively known and unknown<br />
proposition are computed. Given a conformant plann<strong>in</strong>g<br />
problem, a belief state S reached by an action sequence<br />
act and a proposition p, p is known <strong>in</strong> S if p is conta<strong>in</strong>ed<br />
<strong>in</strong> the <strong>in</strong>tersection of the worlds <strong>in</strong> S, i.e., p is always true<br />
after execut<strong>in</strong>g act and equally p is negatively known <strong>in</strong><br />
S if p is always false after execut<strong>in</strong>g act. A proposition p<br />
is unknown <strong>in</strong> S if it is neither known nor negatively<br />
known. The truth value of a proposition <strong>in</strong> a belief state<br />
can be computed by a SAT solver check<strong>in</strong>g the CNF<br />
formula that captures the semantics of the respective<br />
action sequence.<br />
Conformant-FF’s overall architecture is identical to<br />
FF system, illustrated <strong>in</strong> Fig. 1. The basic search<br />
algorithm is enforced hill-climb<strong>in</strong>g which comb<strong>in</strong>es local<br />
and systematic search. Start<strong>in</strong>g from current search state<br />
S, enforced hill-climb<strong>in</strong>g algorithm performs a<br />
breadth-first search for a better state S such that h(S) <<br />
Belief state S<br />
Conformant<br />
Plann<strong>in</strong>g problem<br />
Enforced hill-climb<strong>in</strong>g<br />
Relaxed plann<strong>in</strong>g task<br />
Plan/“Fail”<br />
Heuristic value h(S)<br />
Helpful actions H(S)<br />
Figure 1. Conformant-FF’s architecture<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1387<br />
h(S). Here, h(S) denotes the heuristic value, and H(S)<br />
denotes the helpful actions, which are the considered<br />
actions when expand<strong>in</strong>g S. If a state with lower heuristic<br />
value was reached, then S= S, else the hill-climb<strong>in</strong>g fails,<br />
a complete best-first search is <strong>in</strong>voked to solve the<br />
problem from scratch.<br />
III. THE HEURISTIC TECHNIQUE OF HELPFUL ACTIONS<br />
Dur<strong>in</strong>g search, the considered successors of a search<br />
state are generated by the helpful actions <strong>in</strong> H(S). In<br />
classical plann<strong>in</strong>g, H(S) is the set of actions at the first<br />
level of the relaxed plann<strong>in</strong>g graph that add a subgoal of<br />
this level. In the conformant sett<strong>in</strong>g, H(S) is the set of<br />
such actions at the first level of the relaxed plann<strong>in</strong>g<br />
graph, plus those actions that are selected for an<br />
implication path dur<strong>in</strong>g relaxed plan extraction.<br />
In this section, we propose our heuristic idea of<br />
helpful actions prun<strong>in</strong>g, which can be used to reduce the<br />
search space further <strong>in</strong> the enforced hill-climb<strong>in</strong>g<br />
procedure of Conformant-FF. The idea is derived<br />
accord<strong>in</strong>g to the semantics of the relaxed plann<strong>in</strong>g graph<br />
and the implication paths. For the purpose of exposition,<br />
we first po<strong>in</strong>t out the relation between the implication<br />
paths of the relaxed plan and the uncerta<strong>in</strong> aspect of the<br />
estimated belief state.<br />
A. Semantics of implication paths<br />
Consider a simplified example from the Blockworld<br />
doma<strong>in</strong>.<br />
Example 1 There are four blocks, b1, b2, b3 and b4.<br />
Initially b2, b3 and b4 are on the table and b1 is on b2 or<br />
b3. The <strong>in</strong>itial situation of b1 is not known, modeled as<br />
oneof((on b1 b2), (on b1 b3)). The goal is (on b1 table)<br />
and (on b4 b1). We have a simple (move b from to)<br />
action that can change the location of the blocks. The<br />
graphical sketch of this example is given <strong>in</strong> Fig. 2.<br />
To get the heuristic value, the relaxed task start<strong>in</strong>g<br />
from the <strong>in</strong>itial belief state is solved. In Fig. 3 we give<br />
the conformant relaxed plann<strong>in</strong>g graph built for Example<br />
1. Proposition layers P(t) and action layers A(t) are built<br />
alternatively. Propositions on the dashed area are<br />
unknown at their respective layers. Dashed l<strong>in</strong>es denote<br />
implication edges between two adjacent proposition<br />
layers and empty actions are represented by dots.<br />
We f<strong>in</strong>d that A(0) only <strong>in</strong>cludes actions given by<br />
implication edges plus some empty actions NOOP. The<br />
implication edges yielded by A(0) are:<br />
(move b1 b2 table): (on b1 b2)(0)→(on b1 table)(1)<br />
(move b1 b3 table): (on b1 b3)(0)→(on b1 table)(1)<br />
(move b1 b2 b4): (on b1 b2)(0)→(on b1 b4)(1)<br />
(move b1 b3 b4): (on b1 b3)(0)→(on b1 b4)(1)<br />
NOOP: (on b1 b2)(0)→(on b1 b2)(1)<br />
NOOP: (on b1 b3)(0)→(on b1 b3)(1).<br />
Here, timed implication edges represent that the truth<br />
values of some propositions at layer t are uncerta<strong>in</strong> and<br />
usually depend on their truth values at layer t-1.<br />
b1 b1<br />
b2 b3 b4<br />
table<br />
b4<br />
b1<br />
Initial situation<br />
b2<br />
Goal<br />
b3<br />
table<br />
Figure 2. An example of Blockworld<br />
Relaxed plan extraction starts with G 2 (S I )={(on b1<br />
table), (on b4 b1)}. The subgoal (on b1 table) is <strong>in</strong>serted<br />
at layer 1 of its first appearance. (on b1 b4) is not a<br />
subgoal s<strong>in</strong>ce it does not contribute to achieve the goal.<br />
However, there is no action <strong>in</strong> A(0) that can guarantee<br />
achievement of (on b1 table). Accord<strong>in</strong>g to implication<br />
edges, to make (on b1 table) true at layer 1, we have to<br />
check the truth value of (on b1 b2) or (on b1 b3) at layer<br />
0. In Conformant-FF, the implication edges of subgoal<br />
g(t) form an Imp tree <strong>in</strong> the relaxed plann<strong>in</strong>g graph<br />
between the lowest layer and layer t. For the subgoal g(t)<br />
that is not proved to be true at t, it is checked if the<br />
current state formula implies the disjunction of the leafs<br />
<strong>in</strong> the Imp tree, where the leafs are all the propositions <strong>in</strong><br />
the current belief state whose truth values determ<strong>in</strong>e the<br />
truth value of g at layer t. Impleafs(g(t)) is the set of such<br />
proposition leafs that are reachable from g(t) and then<br />
m<strong>in</strong>_Impleafs(g(t)) is computed to be the m<strong>in</strong>imal subset<br />
of Impleafs(g(t)). For this example, we get m<strong>in</strong>_Impleafs<br />
((on b1 table)(1))={(on b1 b2)(0), (on b1 b3)(0)} whose<br />
disjunction is obviously implied by the <strong>in</strong>itial state<br />
formula. Then we know that (on b1 table) can be<br />
achieved by (move b1 b2 table) or (move b1 b3 table).<br />
These two actions form the implication paths from<br />
m<strong>in</strong>_Impleafs ((on b1 table)(1)) to (on b1 table)(1). To<br />
guarantee (on b1 table) become true at layer 1, both of<br />
the two actions are selected <strong>in</strong>to the relaxed plan. Also<br />
these are collected as helpful actions. S<strong>in</strong>ce (on b1 b4) is<br />
not a necessary subgoal at layer 1, other actions of A(0)<br />
are not considered as helpful.<br />
For a subgoal g at layer t, sometimes there does not<br />
exists any support<strong>in</strong>g action that guarantees to always<br />
achieve g, i.e., any action with an effect that adds g and<br />
whose condition is known to hold at layer t-1. This<br />
complicated situation should trace back to the uncerta<strong>in</strong><br />
<strong>in</strong>itial state. Intuitively, g has been shown that at least<br />
one possible world state could make it true. To achieve g,<br />
implication paths for g are determ<strong>in</strong>ed from layer t go<strong>in</strong>g<br />
downwards to layer 0. All the actions that are responsible<br />
for the implication paths are selected at the respective<br />
times. m<strong>in</strong>_Impleafs(g(t)) is computed by a back<br />
cha<strong>in</strong><strong>in</strong>g loop over the implication edges end<strong>in</strong>g <strong>in</strong> g(t)<br />
and it must be a subset of unknown propositions at layer<br />
0, which corresponds to the uncerta<strong>in</strong> aspect of the<br />
estimated belief state. Check<strong>in</strong>g out the disjunction of the<br />
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1388 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
P(0)<br />
A(0)<br />
P(1)<br />
A(1)<br />
P(2)<br />
…<br />
…<br />
(on b2 table)<br />
(on b3 table)<br />
(on b4 table)<br />
(on b1 b2)<br />
(on b1 b3)<br />
(move b1 b2 table)<br />
(move b1 b3 table)<br />
(move b1 b2 b4)<br />
(move b1 b3 b4)<br />
(on b1 table)<br />
(on b2 table)<br />
(on b3 table)<br />
(on b4 table)<br />
(on b1 b2)<br />
(on b1 b3)<br />
(on b1 b4)<br />
(move b4 table b1)<br />
(on b4 b1)<br />
(on b1 table)<br />
(on b2 table)<br />
(on b3 table)<br />
(on b4 table)<br />
(on b1 b2)<br />
(on b1 b3)<br />
(on b1 b4)<br />
Figure 3. The relaxed plann<strong>in</strong>g graph for the <strong>in</strong>itial belief state<br />
m<strong>in</strong>_Impleafs(g(t)) aga<strong>in</strong>st the current state formula, g<br />
can be proved to be always true at layer t <strong>in</strong> the relaxed<br />
plann<strong>in</strong>g procedure. Each implication path from g(t) to<br />
one of its leaf corresponds to an action sequence that is<br />
executable <strong>in</strong> a particular current world state. Try<strong>in</strong>g out<br />
all these actions <strong>in</strong> the current belief state is the only way<br />
to make g to be true <strong>in</strong> despite of the uncerta<strong>in</strong>ty arisen<br />
from <strong>in</strong>itial state. This way, we remark that implication<br />
paths capture a form of solv<strong>in</strong>g by cases.<br />
In Example 1, as the situation of b1 is unknown,<br />
implication paths <strong>in</strong> the relaxed plan <strong>in</strong>dicate that action<br />
(move b1 b2 table) achieves (on b1 table) if (on b1 b2) is<br />
true <strong>in</strong> the <strong>in</strong>itial world state, otherwise action (move b1<br />
b3 table) achieves (on b1 table). S<strong>in</strong>ce b1 is only at one<br />
of the two locations, execut<strong>in</strong>g these two actions one by<br />
one could guarantee to make (on b1 table) true. Namely,<br />
given uncerta<strong>in</strong>ty about the <strong>in</strong>itial state, to solve the task,<br />
a plan must be able to solve each possible <strong>in</strong>itial world<br />
state.<br />
B. Prun<strong>in</strong>g of helpful implication paths<br />
In l<strong>in</strong>e with our analysis of implication paths, we give<br />
our chang<strong>in</strong>g on the usage of helpful actions dur<strong>in</strong>g<br />
search. To illustrate the algorithm, let us reconsider<br />
Example 1. After solv<strong>in</strong>g the relaxed plann<strong>in</strong>g task, we<br />
get the heuristic value supplied by the relaxed plan and<br />
collect the helpful actions. This <strong>in</strong>formation helps to lead<br />
the search procedure. The helpful actions here are (move<br />
b1 b2 table) and (move b1 b3 table), given by<br />
implication paths at the lowest level of the relaxed plan.<br />
These are the restricted choices to expand the estimated<br />
belief state. We get two successors by expand<strong>in</strong>g the<br />
belief state with these actions. Enforced hill-climb<strong>in</strong>g<br />
will perform an exhaustive search to select a better<br />
successor. In this example we f<strong>in</strong>d out that both<br />
successors generated by these two actions can give better<br />
heuristic evaluations. Thus to reach the subgoal (on b1<br />
table) for sure, search is iterated start<strong>in</strong>g from the<br />
<strong>in</strong>termediate state and the other action is also <strong>in</strong>volved<br />
<strong>in</strong>to the f<strong>in</strong>al plan.<br />
Based on the solv<strong>in</strong>g by cases semantics of<br />
implication paths, we pursue the idea of consider<strong>in</strong>g<br />
implication paths for some subgoal as a group of actions.<br />
The observation that forms our basic idea is obta<strong>in</strong>ed<br />
from the back cha<strong>in</strong><strong>in</strong>g process to determ<strong>in</strong>e implication<br />
paths dur<strong>in</strong>g the extraction of relaxed plan. Actually the<br />
implication paths <strong>in</strong> the relaxed plan are back cha<strong>in</strong>ed<br />
exactly to the uncerta<strong>in</strong> part of the estimated belief state<br />
and branches of the implication edges are used to deal<br />
with different possible world states <strong>in</strong> current belief state.<br />
To construct a conformant plan, all the actions that refer<br />
to uncerta<strong>in</strong>ty about the current belief state are necessary.<br />
Like helpful actions, we restrict to actions that are part<br />
of the implication paths and are at the lowest layer, i.e.,<br />
those that could be select to start the relaxed plan.<br />
Def<strong>in</strong>ition 3 Given the current belief state S, suppose<br />
rplan is the extracted relaxed plan, H(S) is the set of<br />
helpful actions and m<strong>in</strong>_Impleafs(g(t)) is the determ<strong>in</strong>ed<br />
m<strong>in</strong>imal subset of leafs for subgoal g of step t, the set of<br />
implication helpful actions achiev<strong>in</strong>g subgoal g(t) is<br />
def<strong>in</strong>ed as follows:<br />
imp_H(g(t), S)={a | aH(S) and one conditional effect<br />
of a is responsible for an edge <strong>in</strong> rplan from<br />
m<strong>in</strong>_Impleafs(g(t)) to g(t)}.<br />
We call actions from imp_H(g(t), S) to be<br />
responsible to achieve the subgoal g(t). Selection of<br />
imp_H(g(t), S) is done as a set union operation to avoid<br />
any superfluous action. We <strong>in</strong>tegrate these actions <strong>in</strong>to<br />
an action sequence <strong>in</strong> an arbitrary order and use this<br />
sequence to expand the current search state. However,<br />
before mak<strong>in</strong>g the action sequence, we have to address<br />
the problem of the <strong>in</strong>terference between actions. In<br />
relaxed plann<strong>in</strong>g graph, delete effects of actions are<br />
ignored and the <strong>in</strong>terference situation is not visible. Here<br />
we focus on the situation that the effect on an edge of the<br />
implication path may delete preconditions of action that<br />
has an effect on another edge. Entailment of an action<br />
precondition is checked aga<strong>in</strong>st the known propositions,<br />
so delet<strong>in</strong>g of one precondition would cause that the<br />
action does not work at its po<strong>in</strong>t of the sequence. We<br />
observe that conditional effects on the implication edges<br />
of the first layer refer to different world state. These<br />
effects do not <strong>in</strong>terfere with each other generally s<strong>in</strong>ce<br />
the possible current states are usually mutually exclusive.<br />
We call imp_H(g(t), S) to be executable if it can be made<br />
<strong>in</strong>to a sequence and each action is executable at the<br />
respective time. As imp_H(g(t), S) is selected from<br />
implication paths for subgoal g, to dist<strong>in</strong>guish from the<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1389<br />
regular helpful actions, we call them helpful implication<br />
paths for g(t).<br />
Def<strong>in</strong>ition 4 Given the belief state S, the set of helpful<br />
implication paths to S is def<strong>in</strong>ed as follows:<br />
HIP(S)={ imp_H(g(t), S) | g is a subgoal at time step<br />
t of the extracted relaxed plan and imp_H(g(t), S) is<br />
executable}.<br />
What we do <strong>in</strong> pr<strong>in</strong>ciple is to recognize and pick a<br />
group of actions that contribute to achieve a subgoal out<br />
of helpful actions. The notion of helpful implication<br />
paths shares some similarities with helpful actions. In a<br />
nutshell, action sequences <strong>in</strong> the set of helpful<br />
implication paths are usually made up of several helpful<br />
actions, which are deemed to have more potential for<br />
reach<strong>in</strong>g a state with a much lower heuristic value. Thus<br />
helpful implication paths take precedence over other<br />
helpful actions dur<strong>in</strong>g expand<strong>in</strong>g. The enforced<br />
hill-climb<strong>in</strong>g procedure that adopts the prun<strong>in</strong>g<br />
technique is specified <strong>in</strong> Fig. 4. The <strong>in</strong>put of the<br />
procedure is the plann<strong>in</strong>g problem . The<br />
procedure outputs the plan if the goal is achieved<br />
successfully, otherwise it returns “Fail” if the enforced<br />
hill-climb<strong>in</strong>g can not get any better state before the goal<br />
state.<br />
The search procedure starts out <strong>in</strong> the <strong>in</strong>itial belief<br />
state. Fac<strong>in</strong>g an <strong>in</strong>termediate search state S, the<br />
Search_for_better_state() procedure is <strong>in</strong>voked. Dur<strong>in</strong>g<br />
search, states are kept <strong>in</strong> a queue. In each iteration<br />
process, the first state is removed from the queue and<br />
evaluated. If the evaluation is lower than the current<br />
heuristic value, the iteration gets a better state. Otherwise,<br />
the removed state is expanded. Our implementation puts<br />
the successors generated by HIP(S) <strong>in</strong> the queue with<br />
higher priority beside the usual successors obta<strong>in</strong>ed by<br />
other regular helpful actions.<br />
Procedure EhcSearch-HIP(, plan)<br />
1 Initialize S to be the <strong>in</strong>itial belief state;<br />
2 Initialize the search queue U to be empty<br />
3 plan= ;<br />
4 while h(S) != 0 do<br />
5 Put S <strong>in</strong> the queue U;<br />
6 if (Search_for_better_state(S, h(S), S, h(S ))) then<br />
7 add the path from S to S at the end of plan;<br />
8 S = S ;<br />
9 reset U to be empty;<br />
10 else<br />
11 output “Fail”, stop;<br />
12 endif<br />
13 endwhile<br />
Procedure Search_for_better_state(S, h(S), S, h(S ))<br />
14 while (true) do<br />
15 Remove the first node S <strong>in</strong> the queue;<br />
16 if h(S ) < h(S) then<br />
17 return true;<br />
18 endif<br />
19 Collect HIP(S)<br />
20 for each action sequence p <strong>in</strong> HIP(S)<br />
21 put the state generated through p to the end of U;<br />
22 for each of other regular helpful action a<br />
23 put the successor generated by a to the end of U;<br />
24 endwhile<br />
Figure 4. Enforced hill-climb<strong>in</strong>g with helpful implication paths<br />
prun<strong>in</strong>g<br />
Our implementation cuts down the branch<strong>in</strong>g factor<br />
further. Usually an action sequence from helpful<br />
implication paths could reach a search state a few steps<br />
away with a strictly better heuristic evaluation, which<br />
would be reached <strong>in</strong> several iterations when us<strong>in</strong>g<br />
helpful actions only. Thus, helpful implication paths<br />
offer some short cuts to better states. This way, the<br />
number of evaluated states is also reduced because only<br />
the two states that are at the beg<strong>in</strong>n<strong>in</strong>g and end po<strong>in</strong>t of<br />
the action sequence need to get evaluated and all the<br />
<strong>in</strong>termediate states on this path are ignored. To take<br />
everyth<strong>in</strong>g considered, we just leave other helpful<br />
actions beh<strong>in</strong>d and <strong>in</strong> this way our idea appears to be a<br />
tie break<strong>in</strong>g preference for the search procedure.<br />
In the above example, the two actions (move b1 b2<br />
table) and (move b1 b3 table) come from helpful<br />
implication paths for the subgoal (on b1 table)(1) of the<br />
relaxed plan. Fig. 5 illustrates our implementation of<br />
expand<strong>in</strong>g process. Grayed parts are computations that<br />
are saved by our prun<strong>in</strong>g. The two helpful actions are<br />
<strong>in</strong>tegrated <strong>in</strong>to an action sequence to expand the <strong>in</strong>itial<br />
belief state S I . A better belief state S 3 is generated<br />
immediately by this sequence. Our prun<strong>in</strong>g cuts down<br />
the branch<strong>in</strong>g factor from two to one and reaches the<br />
subgoal (on b1 table) with<strong>in</strong> one search iteration, which<br />
will be accomplished by the normal helpful actions <strong>in</strong><br />
two iterations. Moreover, the state evaluation of S 1 is<br />
avoided.<br />
As our specific implementation collects helpful<br />
implication paths amongst the helpful actions, we can get<br />
the helpful implication paths totally for free, as another<br />
important side effect of the basic heuristic method, more<br />
strictly, as a side effect of the helpful actions for<br />
conformant sett<strong>in</strong>g. Moreover, just like helpful actions,<br />
helpful implication paths prun<strong>in</strong>g do not preserve<br />
completeness as well, so the prun<strong>in</strong>g technique is only<br />
(move b1 b2 table)<br />
(move b1 b3 table)<br />
F: (on b2 table)<br />
(on b3 table)<br />
(on b4 table)<br />
U: (on b1 b3)<br />
(on b1 table)<br />
F: (on b1 table)<br />
(on b2 table)<br />
(on b3 table)<br />
(on b4 table)<br />
F: (on b2 table)<br />
(on b3 table)<br />
(on b4 table)<br />
U: (on b1 b2)<br />
(on b1 b3)<br />
S 1<br />
h(S 1 )=2<br />
S 3<br />
h(S 3 )=1<br />
S I<br />
h(S I )=3<br />
(move b1 b3 table)<br />
F: (on b2 table)<br />
(on b3 table)<br />
(on b4 table)<br />
U: (on b1 b2)<br />
(on b1 table)<br />
Figure 5. The expand<strong>in</strong>g procedure for the <strong>in</strong>itial belief state<br />
S 2<br />
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1390 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
adopted <strong>in</strong> the enforced hill-climb<strong>in</strong>g search, which is<br />
not complete anyway, and the complete best-first search<br />
procedure is unchanged. In all of our test doma<strong>in</strong>s, the<br />
tasks can be solved successfully <strong>in</strong> the enforced<br />
hill-climb<strong>in</strong>g procedure with our new prun<strong>in</strong>g technique.<br />
IV. EXPERIMENTAL RESULTS<br />
We implemented the heuristic prun<strong>in</strong>g technique<br />
presented <strong>in</strong> the previous sections and evaluated it on a<br />
number of conformant plann<strong>in</strong>g benchmarks. The<br />
experiments were run on a PC runn<strong>in</strong>g Ubuntu 8.0 at<br />
1.90 GHz with 1 GB ma<strong>in</strong> memory. There are three<br />
heuristic setups <strong>in</strong> Conformant-FF and most of the time<br />
they yield similar performance. We select to use the<br />
state-formula heuristic function which gives the most<br />
precise comput<strong>in</strong>g. It is enough to evaluate the power of<br />
the prun<strong>in</strong>g technique under one heuristic function setup.<br />
The <strong>in</strong>dividual doma<strong>in</strong>s are described below respectively.<br />
For each problem we provide the runtime <strong>in</strong> seconds, the<br />
number of evaluated states dur<strong>in</strong>g search and the length<br />
of the found plan of the plann<strong>in</strong>g system that adopts our<br />
helpful implication paths prun<strong>in</strong>g and the orig<strong>in</strong>al helpful<br />
actions prun<strong>in</strong>g, respectively.<br />
A. The Uts doma<strong>in</strong><br />
The Uts doma<strong>in</strong> describes a series of tasks of universal<br />
transversal sequences. In this doma<strong>in</strong>, one is <strong>in</strong>itially<br />
located at any node on a graph with n nodes. Some nodes<br />
on the graph are connected by edges. One can execute<br />
the action “start” to switch to a “started” phase and make<br />
the current node visited. After started, one can “travel”<br />
through edges to change the locations and visit other<br />
nodes. The goal is to visit all the nodes with the <strong>in</strong>itial<br />
location uncerta<strong>in</strong>. There are three different test suites,<br />
k-n, l-n, r-n, correspond<strong>in</strong>g to tasks with different extents<br />
to which the graph is connected, where the number of<br />
nodes <strong>in</strong> 2n. Tab. 1 provides our experimental results <strong>in</strong><br />
the Uts doma<strong>in</strong>. “US” <strong>in</strong>dicates that the problem is<br />
unsolvable.<br />
From a quick glance, our idea improves the helpful<br />
actions prun<strong>in</strong>g significantly. To make every node<br />
visited eventually, a subgoal that gets to a “started”<br />
phase is required at first. S<strong>in</strong>ce the <strong>in</strong>itial location is<br />
unknown, one should apply a start action to each<br />
possible <strong>in</strong>itial location. Intuitively, the number of the<br />
required start actions is equal to the number of nodes <strong>in</strong> a<br />
task. Conformant-FF recognizes these helpful actions<br />
and to assure the “started” subgoal, these actions are<br />
applied one after another until all of them are <strong>in</strong>cluded<br />
<strong>in</strong>to the plan. For a task with 2n nodes, the subgoal<br />
becomes true after 2n search iterations. In our<br />
implementation, all these actions form helpful<br />
implication paths for the “started” subgoal. Us<strong>in</strong>g helpful<br />
implication path prun<strong>in</strong>g technique to expand the <strong>in</strong>itial<br />
belief state, the subgoal becomes true <strong>in</strong> the second<br />
search iteration <strong>in</strong> despite of the number of nodes <strong>in</strong> the<br />
task.<br />
Our prun<strong>in</strong>g technique of helpful implication paths<br />
leads to a decrease of evaluated states which refers to the<br />
TABLE I.<br />
RESULTS IN THE UTS DOMAIN<br />
Helpful implication paths Helpful actions<br />
T (s) S L T (s) S L<br />
k-01 0.00 2 4 0.01 4 4<br />
k-02 0.00 4 10 0.01 10 10<br />
k-03 0.01 6 16 0.04 16 16<br />
k-04 0.01 8 22 0.22 22 22<br />
k-05 0.02 10 28 0.83 28 28<br />
k-06 0.02 12 34 1.81 34 34<br />
k-07 0.04 14 40 4.45 40 40<br />
k-08 0.07 16 46 10.25 46 46<br />
k-09 0.12 18 52 23.58 52 52<br />
k-10 0.20 20 58 45.95 58 58<br />
l-01 0.00 2 4 0.00 4 4<br />
l-02 0.01 7 12 0.02 14 11<br />
l-03 0.01 17 24 0.03 28 22<br />
l-04 0.03 26 35 0.11 41 34<br />
l-05 0.08 40 51 0.39 56 48<br />
l-06 0.20 57 66 1.23 73 64<br />
l-07 0.42 76 86 3.03 92 82<br />
l-08 1.25 104 105 6.29 113 102<br />
l-09 2.48 129 129 16.95 136 124<br />
l-10 4.04 171 152 41.28 161 148<br />
r-01 0.00 1 US 0.00 1 US<br />
r-02 0.00 1 US 0.00 1 US<br />
r-03 0.00 8 8 0.02 17 16<br />
r-04 0.01 20 32 0.14 34 25<br />
r-05 0.04 29 37 3.23 1021 37<br />
r-06 0.08 28 47 18.18 4071 41<br />
r-07 0.26 52 53 2.63 74 45<br />
r-08 0.27 36 55 7.24 83 50<br />
r-09 0.17 40 56 13.59 112 58<br />
r-10 0.78 64 72 40.18 156 69<br />
size of search space. Most strik<strong>in</strong>gly, the number of<br />
evaluated states is even a lot smaller than the plan length<br />
<strong>in</strong> some problems. This means that helpful implication<br />
paths contribute to f<strong>in</strong>d a fragment of the plan with<strong>in</strong> one<br />
search iteration and don’t have to compute the heuristic<br />
values for all the states that are along the search path<br />
correspond<strong>in</strong>g to the plan. With the number of evaluated<br />
states decreased, the efficiency is improved dramatically.<br />
Regard<strong>in</strong>g runtime, our implementation is much superior<br />
and scales up more easily. We f<strong>in</strong>d that sometimes the<br />
plan length of our idea is a little longer due to the order<br />
of actions <strong>in</strong> the plan sequence. This, however, does not<br />
affect the plan quality seriously, s<strong>in</strong>ce Conformant-FF<br />
does not guarantee to f<strong>in</strong>d an optimal plan anyway.<br />
B. The Safe doma<strong>in</strong><br />
In the Safe doma<strong>in</strong>, there are several possible<br />
comb<strong>in</strong>ations for a safe. The right comb<strong>in</strong>ation is one out<br />
of these comb<strong>in</strong>ations which is <strong>in</strong>itially unknown. The<br />
goal is to get the safe door open. To assure the goal, one<br />
must “try” all comb<strong>in</strong>ations exhaustively. Tab. 2 and Tab.<br />
3 provides the experimental results for <strong>in</strong>stances with n<br />
possible comb<strong>in</strong>ations. “-” <strong>in</strong>dicates time-out, with a<br />
runtime cutoff 1200s.<br />
The plan for any problem <strong>in</strong> this doma<strong>in</strong> is to try all<br />
comb<strong>in</strong>ations <strong>in</strong> some order. In Conformant-FF’s<br />
implementation, the number of evaluated states is equal<br />
to the plan length, i.e., the number of possible<br />
comb<strong>in</strong>ations <strong>in</strong> the task. For each visited state, the goal<br />
proposition safe-open appears at the first layer of the<br />
relaxed plann<strong>in</strong>g graph, provid<strong>in</strong>g all the try actions at<br />
first layer that have not been applied as helpful actions.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1391<br />
TABLE II.<br />
RESULTS IN THE SAFE DOMAIN-1<br />
Helpful implication paths<br />
Helpful actions<br />
T (s) S L T (s) S L<br />
s5 0.00 1 5 0.00 5 5<br />
s10 0.01 1 10 0.03 10 10<br />
s30 0.14 1 30 3.87 30 30<br />
s50 1.34 1 50 72.87 50 50<br />
s70 6.06 1 70 368.74 70 70<br />
s100 28.22 1 100 - - -<br />
TABLE III.<br />
RESULTS IN THE SAFE DOMAIN-2<br />
Helpful implication paths Helpful actions -D<br />
T (s) S L T (s) S L<br />
s5 0.00 1 5 0.00 5 5<br />
s10 0.01 1 10 0.01 10 10<br />
s30 0.14 1 30 0.22 30 30<br />
s50 1.34 1 50 2.18 50 50<br />
s70 6.06 1 70 8.92 70 70<br />
s100 28.22 1 100 35.01 100 100<br />
Execut<strong>in</strong>g one of these helpful actions will get to a<br />
state closer to the goal. Such iterations are repeated until<br />
the goal is reached. Us<strong>in</strong>g our prun<strong>in</strong>g technique, all the<br />
try actions are selected as helpful implication paths <strong>in</strong> the<br />
first search iteration. After execut<strong>in</strong>g the helpful<br />
implication paths <strong>in</strong> the <strong>in</strong>itial belief state, the goal<br />
becomes known <strong>in</strong> the second iteration and the task is<br />
solved successfully. For tasks <strong>in</strong> different sizes, our idea<br />
can f<strong>in</strong>d plans by evaluat<strong>in</strong>g only one state.<br />
Regard<strong>in</strong>g runtime, our implementation behaves much<br />
faster. The poor runtime performance of Conformant-FF<br />
is also due to the special structure of the Safe doma<strong>in</strong><br />
that no proposition becomes known until the task is<br />
solved. As the number of possible comb<strong>in</strong>ations<br />
<strong>in</strong>creases, Conformant-FF gets <strong>in</strong> trouble with repeated<br />
states check<strong>in</strong>g. Helpful actions -D refers to the option<br />
that turns the repeated states check<strong>in</strong>g off, at this time the<br />
orig<strong>in</strong>al planner can solve the tasks quickly. Generally,<br />
our prun<strong>in</strong>g technique is still competitive <strong>in</strong> this doma<strong>in</strong><br />
with the helpful actions of Conformant-FF without<br />
repeated states check<strong>in</strong>g.<br />
C. The Dispose doma<strong>in</strong><br />
The Dispose doma<strong>in</strong> is a variation of Grid family,<br />
which is about pick<strong>in</strong>g objects and dropp<strong>in</strong>g them <strong>in</strong>to a<br />
trash. Initially the locations of all the objects are<br />
uncerta<strong>in</strong> and the location of the trash is given. One starts<br />
from a given location and can “move” between two<br />
adjacent locations. One can “pickup” an object with a<br />
condition that the object is at the current location. One<br />
can also “drop” an object <strong>in</strong>to a trash if the trash is at the<br />
current location. The goal is to get all the objects<br />
disposed of <strong>in</strong> the trash. Tab. 4 shows our results <strong>in</strong> the<br />
Dispose doma<strong>in</strong>.<br />
Once aga<strong>in</strong>, the old helpful action prun<strong>in</strong>g technique<br />
evaluates much more states and performs a lot worse. To<br />
drop an object <strong>in</strong>to a trash, one has to guarantee that the<br />
object is held <strong>in</strong> hand. Given that the <strong>in</strong>itial locations of<br />
the objects are unknown, a conformant plan should<br />
execute a pickup action for each object at all the possible<br />
TABLE IV.<br />
RESULTS IN THE DISPOSE DOMAIN<br />
Helpful implication paths Helpful actions<br />
T (s) S L T (s) S L<br />
2-1 0.00 9 9 0.00 11 9<br />
2-2 0.00 10 14 0.01 16 14<br />
2-3 0.01 11 19 0.02 21 19<br />
2-4 0.01 12 24 0.03 26 24<br />
2-5 0.02 13 29 0.04 31 29<br />
2-6 0.02 14 34 0.08 36 34<br />
2-7 0.04 15 39 0.13 41 39<br />
2-8 0.07 16 44 0.23 46 44<br />
2-9 0.10 17 49 0.32 51 49<br />
2-10 0.13 18 54 0.49 56 54<br />
3-1 0.00 25 20 0.01 36 24<br />
3-2 0.04 26 30 0.07 46 34<br />
3-3 0.15 27 40 0.30 56 44<br />
3-4 0.41 28 50 0.80 66 54<br />
3-5 0.66 29 60 1.84 76 64<br />
3-6 1.15 30 70 2.55 86 74<br />
3-7 2.11 31 80 5.53 96 84<br />
3-8 3.26 32 90 10.98 106 94<br />
3-9 5.17 33 100 18.11 116 104<br />
3-10 8.77 34 110 32.24 126 114<br />
4-1 0.06 61 43 0.07 61 39<br />
4-2 0.78 62 60 0.79 78 56<br />
4-3 1.94 63 77 2.37 95 73<br />
4-4 5.59 64 94 7.94 112 90<br />
4-5 18.09 65 111 27.82 129 107<br />
4-6 25.84 66 128 46.22 146 124<br />
4-7 47.63 67 145 93.87 163 140<br />
4-8 73.42 68 162 156.43 180 158<br />
4-9 189.02 69 179 462.63 197 175<br />
4-10 207.30 72 183 508.43 202 180<br />
locations. We observed that our prun<strong>in</strong>g technique<br />
explores a much smaller search space. As the size of the<br />
problem <strong>in</strong>creases, heuristic evaluation becomes more<br />
costly and the runtime spent mostly goes <strong>in</strong>to the<br />
computation of heuristic estimations, thus the reduction<br />
of search space is quite significant. Regard<strong>in</strong>g plan<br />
length, our implementation is somewhat longer <strong>in</strong> a few<br />
cases. But still the quality of the found plan is satisfy<strong>in</strong>g.<br />
D. The Logistics doma<strong>in</strong><br />
Logistics we consider <strong>in</strong> this section is a classical<br />
plann<strong>in</strong>g doma<strong>in</strong> enriched with uncerta<strong>in</strong>ty. A package<br />
can be loaded onto a truck if the package is at the same<br />
location as the truck. Packages are transported by trucks<br />
between different positions of a city. Airplanes fly<br />
between different cities. Instances <strong>in</strong> Tab. 5 are<br />
generated by choos<strong>in</strong>g the <strong>in</strong>itial positions of the trucks<br />
and airplanes, the <strong>in</strong>itial positions and goal positions of<br />
packages randomly. The uncerta<strong>in</strong>ty lies <strong>in</strong> the <strong>in</strong>itial<br />
position of each package with<strong>in</strong> its orig<strong>in</strong> city.<br />
Results from Tab. 4 show that the prun<strong>in</strong>g of helpful<br />
implication paths is generally competitive or faster,<br />
compared to helpful actions. Our prun<strong>in</strong>g technique<br />
avoids the computation of heuristic values for some<br />
search states which helps to save the runtime<br />
considerably. In the relatively small cases, the behavior<br />
of helpful implication path prun<strong>in</strong>g is not obvious that<br />
much. Large cases with 10 packages, cities, trucks and<br />
airplanes reveal the power of the prun<strong>in</strong>g strategy and<br />
show that our implementation scales better to large<br />
<strong>in</strong>stances. With respect to the plan quality, our technique<br />
© 2013 ACADEMY PUBLISHER
1392 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
TABLE V.<br />
RESULTS IN THE LOGISTICS DOMAIN<br />
Helpful implication paths<br />
Helpful actions<br />
T (s) S L T (s) S L<br />
2-2-2 0.00 16 16 0.00 23 16<br />
2-2-4 0.00 23 26 0.00 34 26<br />
2-3-2 0.01 19 17 0.00 37 17<br />
2-3-3 0.01 36 24 0.01 46 24<br />
2-10-10 0.89 211 83 3.59 324 83<br />
3-2-2 0.01 23 20 0.01 29 20<br />
3-2-4 0.01 29 33 0.02 36 33<br />
3-3-2 0.01 36 28 0.02 55 28<br />
3-3-3 0.01 32 32 0.07 72 34<br />
3-10-10 3.09 427 112 10.95 435 108<br />
4-2-2 0.00 15 19 0.01 19 19<br />
4-2-4 0.01 36 40 0.08 59 40<br />
4-3-2 0.00 24 23 0.01 31 23<br />
4-3-3 0.02 48 37 0.07 70 37<br />
4-10-10 2.51 281 127 11.45 356 121<br />
is a little longer only <strong>in</strong> two problems. In most of the<br />
time, our prun<strong>in</strong>g of helpful implication paths f<strong>in</strong>ds<br />
exactly the same conformant plan as the situation of<br />
helpful actions prun<strong>in</strong>g.<br />
All <strong>in</strong> all, from the experimental results above, we<br />
conclude that our prun<strong>in</strong>g technique has the potential to<br />
reduce the size of search space and consequently<br />
improve the runtime efficiency. In this aspect we<br />
consider that our idea is clearly superior to helpful<br />
actions technique.<br />
V. CONCLUSION<br />
In this paper, we addressed the Conformant-FF<br />
planner which solves conformant plann<strong>in</strong>g problem by<br />
belief state space search. The size of search space has<br />
been a bottleneck to this method which could be<br />
ameliorated by us<strong>in</strong>g heuristic function and prun<strong>in</strong>g.<br />
Based on our analysis of the implication paths <strong>in</strong> the<br />
relaxed plann<strong>in</strong>g heuristic function, we proposed the<br />
prun<strong>in</strong>g technique of helpful implications paths to reduce<br />
the search space further. We run a number of conformant<br />
benchmarks to evaluate our idea and the experimental<br />
results <strong>in</strong>dicate that our heuristic technique has two<br />
advantages:<br />
1) An action sequence that <strong>in</strong>tegrates several helpful<br />
action branches together usually cuts down the branch<strong>in</strong>g<br />
factor of a search state. At the same time, consider<strong>in</strong>g<br />
helpful implication paths over other branches often f<strong>in</strong>ds<br />
a better state faster.<br />
2) Execut<strong>in</strong>g a helpful implication path can get to a<br />
better state a few steps away with<strong>in</strong> one search iteration,<br />
which relates with recent tread on obta<strong>in</strong><strong>in</strong>g long<br />
sequence of actions <strong>in</strong>stead of apply<strong>in</strong>g one by one. Thus<br />
the evaluations of <strong>in</strong>termediate states on the helpful<br />
implication path are avoided, which leads to a<br />
considerable improvement of runtime efficiency.<br />
The planner Conformant-FF still has <strong>in</strong>herent<br />
limitations due to its implicit representation of belief<br />
states and <strong>in</strong>complete <strong>in</strong>formation add<strong>in</strong>g to the<br />
relaxation. These make the planner provide <strong>in</strong>accurate<br />
heuristic sometimes and get trouble <strong>in</strong> situations where<br />
an action may conta<strong>in</strong> many conditional effects or takes<br />
more complicated forms. It will be significant to propose<br />
promis<strong>in</strong>g ideas to overcome those disadvantages.<br />
In future, we will treat nondeterm<strong>in</strong>istic action effects<br />
and explore to use a similar prun<strong>in</strong>g idea to solve the<br />
more general sett<strong>in</strong>g of cont<strong>in</strong>gent plann<strong>in</strong>g, i.e. to<br />
handle partially observable plann<strong>in</strong>g problems. We also<br />
plan to <strong>in</strong>vestigate the search spaces of other<br />
non-classical plann<strong>in</strong>g sett<strong>in</strong>gs that can be formalized as<br />
search problems, <strong>in</strong> particular probabilistic plann<strong>in</strong>g and<br />
temporal plann<strong>in</strong>g.<br />
ACKNOWLEDGMENT<br />
The authors wish to thank Professor Dantong Ouyang<br />
for her comments, which was helpful to improve the<br />
paper. This work was Supported by the National Natural<br />
Science Foundation of Ch<strong>in</strong>a under Grant No.<br />
61272208,61133011,60973089,61003101,61170092;<br />
Jil<strong>in</strong> Prov<strong>in</strong>ce Science and Technology Development<br />
Plan under Grant No. 20101501,20100185,201101039;<br />
Doctoral Fund of M<strong>in</strong>istry of Education of Ch<strong>in</strong>a under<br />
Grant No.20100061110031;<br />
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[11] A. Albore, M. Ramirez, H. Geffner, “Effective Heuristics<br />
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Wei Wei was born Dec. 28, 1984, <strong>in</strong> Jil<strong>in</strong>,<br />
Ch<strong>in</strong>a. She received the Master degree at<br />
College of Computer Science and<br />
Technology of Jil<strong>in</strong> University, Ch<strong>in</strong>a, <strong>in</strong><br />
2007.<br />
She is a Ph.D candidate at College of<br />
Computer Science and Technology of Jil<strong>in</strong><br />
University. Her ma<strong>in</strong> research <strong>in</strong>terests <strong>in</strong>clude automated<br />
plann<strong>in</strong>g and reason<strong>in</strong>g.<br />
Dantong Ouyang was born <strong>in</strong> 1968, Jil<strong>in</strong>, Ch<strong>in</strong>a. She received<br />
the Ph. D degree at College of Computer Science and<br />
Technology of Jil<strong>in</strong> University, Ch<strong>in</strong>a, <strong>in</strong> 1998.<br />
She is Professor, Ph.D. supervisor, Deputy Dean of College<br />
of Computer Science and Technology of Jil<strong>in</strong> University. Her<br />
ma<strong>in</strong> field of expertise is model-based diagnosis and automated<br />
reason<strong>in</strong>g.<br />
T<strong>in</strong>gt<strong>in</strong>g Zou was born Nov. 24, 1984, <strong>in</strong> Jil<strong>in</strong>, Ch<strong>in</strong>a. She<br />
received the Master degree at School of Computer Science and<br />
Information Technology of North East Normal University,<br />
Ch<strong>in</strong>a, <strong>in</strong> 2007.<br />
She is a Ph.D candidate at College of Computer Science and<br />
Technology of Jil<strong>in</strong> University. Her ma<strong>in</strong> research <strong>in</strong>terest is<br />
description logic.<br />
Shuai LU was born Jul. 11, 1981, <strong>in</strong> Jil<strong>in</strong>, Ch<strong>in</strong>a. He received<br />
the Ph.D degree at College of Computer Science and<br />
Technology of Jil<strong>in</strong> University, Ch<strong>in</strong>a, <strong>in</strong> 2010.<br />
He is a lecturer at College of Computer Science and<br />
Technology of Jil<strong>in</strong> University. Her ma<strong>in</strong> research <strong>in</strong>terests<br />
<strong>in</strong>clude automated plann<strong>in</strong>g and reason<strong>in</strong>g.<br />
© 2013 ACADEMY PUBLISHER
1394 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Assess<strong>in</strong>g Land Ecological Security Based on BP<br />
Neural Network: a Case Study of Hangzhou,<br />
Ch<strong>in</strong>a<br />
Heyuan You<br />
College of Bus<strong>in</strong>ess Adm<strong>in</strong>istration, Zhejiang University of F<strong>in</strong>ance and Economics, Hangzhou, Ch<strong>in</strong>a<br />
Email: youheyuan@gmail.com<br />
Abstract— Due to the <strong>in</strong>creas<strong>in</strong>g stress on the land ecology,<br />
the land eco-security suffers damage. In this paper, the BP<br />
neural network and PSR framework were adopted to<br />
establish the model for assessment of land eco-security, and<br />
an empirical study of assess<strong>in</strong>g land eco-security <strong>in</strong><br />
Hangzhou was done. The results show that the city center<br />
district is at serious land eco-security risk; Xiaoshan district<br />
and Yuhang district are at high land eco-security risk; and<br />
others counties (cities) are at low risk or <strong>in</strong>termediate risk.<br />
In Hangzhou, although some measures are adopted to<br />
control the risk of land eco-security, the economic growth<br />
still has negative impact on the land ecology. The rapid<br />
<strong>in</strong>dustrialization and urbanization <strong>in</strong>crease the risk of land<br />
eco-security. Therefore the policy constitutors should do<br />
someth<strong>in</strong>g to strengthen the land ecology protection.<br />
Index Terms—land ecological security, pressure-state-response<br />
framework, BP neural network, Hangzhou<br />
I. INTRODUCTION<br />
As an essential resource for susta<strong>in</strong>able development,<br />
the land keeps human supplied with basic material and<br />
liv<strong>in</strong>g space. In Ch<strong>in</strong>a, land use is regulated strictly by<br />
government s<strong>in</strong>ce the socialist public ownership of land.<br />
However, <strong>in</strong> order to accelerate the economic growth, the<br />
local governments <strong>in</strong> Ch<strong>in</strong>a excessively exploit and<br />
utilize land resource [1], and the susta<strong>in</strong>able use of land<br />
resources is always neglected <strong>in</strong> many regions. Some<br />
serious problems such as soil loss, over-conversion of<br />
farmland to construction land, land contam<strong>in</strong>ation and<br />
deforestation threat the susta<strong>in</strong>able land use [2, 3, 4, 5].<br />
The scarcity of enough protection for land leads to<br />
<strong>in</strong>creased risk of land ecological security (eco-security)<br />
[6]. Consequently, the assessment of land eco-security<br />
necessarily is done to ascerta<strong>in</strong> ecological state of land<br />
use system. And the characteristic analysis of land<br />
eco-security can reveal important <strong>in</strong>formation for<br />
adopt<strong>in</strong>g measures to improve the land ecology.<br />
The current literature that related to land eco-security<br />
mostly focused on the susta<strong>in</strong>able use of land resources.<br />
The ecological susta<strong>in</strong>ability is considered as a vital<br />
Manuscript received July 5, 2012; revised October 21, 2012;<br />
accepted October 27, 2012.<br />
Project number: 70973047.<br />
Correspond<strong>in</strong>g author: Heyuan You.<br />
feature of susta<strong>in</strong>able land use [7]. The <strong>in</strong>dicator systems<br />
which were applied to assess the susta<strong>in</strong>able use of land<br />
resources <strong>in</strong>cluded some <strong>in</strong>dicators reflected land<br />
eco-security such as soil loss/formation ratio [8], forest<br />
cover [9], population density [10], and species loss [11].<br />
Ow<strong>in</strong>g to the defects <strong>in</strong> the accurate analysis of land<br />
ecology, the assessment of land ecological security<br />
aroused researchers’ attention [6, 12].<br />
Back-Propagation (BP) neural network, a method of<br />
tra<strong>in</strong><strong>in</strong>g a multi-layer feed-forward artificial neural<br />
network with the BP algorithm can approximate any<br />
nonl<strong>in</strong>ear function [13]. Due to its robust and<br />
fault-tolerance, the BP neural network is widely applied<br />
<strong>in</strong> predictor, optimization and classification [14, 15, 16].<br />
Given the subjectivity <strong>in</strong> the assessment of land<br />
eco-security, especially determ<strong>in</strong><strong>in</strong>g the weights of<br />
<strong>in</strong>dicators, and the fuzzy relationship among <strong>in</strong>dicators,<br />
the BP neural network whose advantage is suitable can be<br />
applied to establish model for assess<strong>in</strong>g land ecosecurity.<br />
The rest of this paper proceeds as follows: Section 2<br />
describes a survey of study area; Section 3 establishes the<br />
model for assessment of land eco-security based on BP<br />
neural network; Section 4 obta<strong>in</strong>s the orig<strong>in</strong>al data and<br />
pretreats the orig<strong>in</strong>al date; Section 5 shows the results of<br />
the assessment of land eco-security of 8 districts<br />
(county-level cities, counties) <strong>in</strong> Hangzhou; Section 6<br />
summarizes the discussion and conclusion.<br />
II. STUDY AREA<br />
Hangzhou which is adm<strong>in</strong>istered as a sub-prov<strong>in</strong>cial<br />
city, with a registered population of 6.8912 million as of<br />
2010, is the capital and largest city of Zhejiang prov<strong>in</strong>ce.<br />
Located <strong>in</strong> Eastern Ch<strong>in</strong>a, Hangzhou sits on the south<br />
edge of the Yangtze River Delta economic zone (Figure<br />
1). Hangzhou is the economic, political and cultural<br />
center of Zhejiang prov<strong>in</strong>ce. It is an <strong>in</strong>dustrial city, and is<br />
considered as an important manufactur<strong>in</strong>g base <strong>in</strong> coastal<br />
area of Ch<strong>in</strong>a. The Qiantang River passes through the<br />
northeast to the southwest of Hangzhou, and Hangzhou<br />
Bay ends at Hangzhou which lies south of Shanghai.<br />
Hangzhou extends to the border of the hilly-country<br />
Anhui Prov<strong>in</strong>ce on its west and the flat-land Hangzhou<br />
Bay on its east. The vast majority of land <strong>in</strong> Hangzhou is<br />
© 2013 ACADEMY PUBLISHER<br />
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JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1395<br />
hill and mounta<strong>in</strong>.<br />
Hangzhou city is composed of 8 districts, 3<br />
county-level cities and 2 counties. The city center of<br />
Hangzhou is composed of Shangcheng district, Xiacheng<br />
district, Jianggan district, Gongshu district, Xihu district<br />
and B<strong>in</strong>jiang district. And Xiaoshan district, Yuhang<br />
district, Tonglu county, Chun'an county, Jiande city,<br />
Fuyang city and L<strong>in</strong>'an city compose the suburban and<br />
rural area of Hangzhou. In empirical study, I assumed that<br />
the six central urban districts were one <strong>in</strong>tegrated region<br />
s<strong>in</strong>ce the six central urban districts were small districts<br />
and pr<strong>in</strong>cipal affairs of districts were adm<strong>in</strong>istered<br />
<strong>in</strong>dependently of suburban and rural area of Hangzhou<br />
by Hangzhou city people’s government.<br />
S<strong>in</strong>ce the rapid economic growth and large population,<br />
risk to land ecology <strong>in</strong> Hangzhou cont<strong>in</strong>ual <strong>in</strong>creases.<br />
Consideration of land eco-security <strong>in</strong> Hangzhou is<br />
required to preserve the land and to draw up measures<br />
whose purpose is susta<strong>in</strong>able utilization of land.<br />
Figure 1.<br />
Location of study area<br />
III. METHODS<br />
A. Indicator System for Assessment<br />
The pressure-state-response (PSR) framework has been<br />
widely used to describe and quantify the environment [17,<br />
18]. It was accepted to determ<strong>in</strong>e <strong>in</strong>dicator to understand<br />
complex realities about ecology [6, 19]. In this paper, I<br />
focus on the pressures on the land eco-security, the<br />
condition of land eco-security which results from these<br />
pressures and the actions taken to prevent negative land<br />
eco-security impacts. It is apparent that PSR framework<br />
can be chosen as a basis for select<strong>in</strong>g the <strong>in</strong>dicators that<br />
compose the <strong>in</strong>dicator system for assess<strong>in</strong>g land<br />
ecological security. Complied with the pr<strong>in</strong>ciples <strong>in</strong><br />
select<strong>in</strong>g <strong>in</strong>dicators that <strong>in</strong>clude substantive, simplicity,<br />
universality, consistency and availability, and learnt<br />
experience from previous literature, the <strong>in</strong>itial set of 12<br />
<strong>in</strong>dicators was selected. Then <strong>in</strong>dicators were adjusted<br />
based on experts’ op<strong>in</strong>ions who <strong>in</strong>vited to evaluate the<br />
suitability of <strong>in</strong>itial set. Some <strong>in</strong>dicators <strong>in</strong> <strong>in</strong>itial set<br />
were not selected by experts. The reasons for the experts’<br />
decision were as follows. (1) Soil erosion modulus was<br />
not the representative factor which affected the land<br />
eco-security <strong>in</strong> Hangzhou s<strong>in</strong>ce the geographical<br />
condition of Hangzhou. (2) Natural population growth<br />
rate was important <strong>in</strong>dicator of the land eco-security,<br />
however the cultivated land area per capita and water<br />
resources per capita implied the impact of natural<br />
population growth rate on the land eco-security. (3) The<br />
orig<strong>in</strong>al data of energy consumption per unit of GDP<br />
could not be obta<strong>in</strong>ed. The <strong>in</strong>dicator system applied <strong>in</strong><br />
study area <strong>in</strong> this paper is presented <strong>in</strong> Table 1.<br />
B. Grade Criterion<br />
It is important to grade the land eco-security and<br />
determ<strong>in</strong>e the grade criterion which used to assess the<br />
state of land eco-security <strong>in</strong> Hangzhou. However, there<br />
was no widely accepted grade criterion of land<br />
eco-security [6]. The land eco-security should be<br />
classified to correspond to local conditions. In this paper,<br />
the grade criterion of land eco-security was classified <strong>in</strong>to<br />
five grades. The range of land eco-security value was<br />
assumed [0, 1], and it can be divided <strong>in</strong>to five grades as<br />
no land eco-security risk (0.8, 1], low land eco-security<br />
risk (0.6, 0.8], <strong>in</strong>termediate land eco-security risk (0.4,<br />
0.6], high land eco-security risk (0.2, 0.4] and serious<br />
land eco-security risk (0, 0.2].<br />
The land eco-security was relative. The assessment<br />
standards of eco-security <strong>in</strong> the literature were<br />
classified <strong>in</strong>to four grades [12]. The numbers rang<strong>in</strong>g<br />
from 1 to 4 were assigned to “<strong>in</strong>secure”, “relatively<br />
<strong>in</strong>secure”, “relatively secure” and “secure”. Two grade<br />
criterions of land eco-security were similar <strong>in</strong> the method<br />
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TABLE I.<br />
INDICATOR SYSTEM FOR ASSESSING LAND ECO-SECURITY AND GRADE CRITERION OF LAND ECO-SECURITY<br />
Element Indicators Grade criterion of land eco-security<br />
(0.8, 1] a (0.6, 0.8] (0.4, 0.6] (0.2, 0.4] [0, 0.2]<br />
Pressure<br />
b<br />
Cultivated land area per capita(mu/person)x 1<br />
>1.4 0.8-1.4 0.7-0.8 0.6-0.7 0.6-0.5&2500 2000-2500 1500-2000 1000-1500 500-1000&12 10-12 8-10 6-8 5-6&30 25-30 20-25 15-20 10-15&25°proportion (%)x 7 4.0<br />
Population density(person/km 2 ) x 8 650<br />
Area of stable yields despite drought or excessive ra<strong>in</strong><br />
Response proportion (%)x 9<br />
>65 50-65 40-50 30-40 20-30&70 60-70 50-60 40-50 30-40&30 25-30 20-25 15-20 10-15&5 4-5 3-4 2-3 1-2&
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Where w ij (k+1) is the new vector of weight and bias,<br />
w ij (k) is the current vector of weight and bias, D(k) is the<br />
negative gradient of wij(k) at time k, D(k–1) is the<br />
negative gradient of wij(k) at time k–1, η is the learn<strong>in</strong>g<br />
rate, β is the momentum constant which is a number<br />
between 0 and 1.The learn<strong>in</strong>g rate usually is trialed with<br />
a range of 0.1 to 0.3, if the learn<strong>in</strong>g rate is too high, the<br />
algorithm may oscillate and becomes unstable. And the<br />
momentum constant usually is trialed with a range of 0.9<br />
to 1 s<strong>in</strong>ce the low momentum may prevent the network<br />
from learn<strong>in</strong>g. In empirical study, the values of η and β<br />
were selected as 0.3 and 0.94, respectively.<br />
The performance measure adopted <strong>in</strong> empirical study<br />
was mean-squared error (MSE) function. The MSE<br />
function is as follows:<br />
1<br />
MSE = q t −s t<br />
n<br />
2<br />
∑ ( ( ) ( ))<br />
(5)<br />
k<br />
k<br />
n t = 1<br />
Where MSE is net error. q k (t) is kth network node<br />
desired output of tth tra<strong>in</strong><strong>in</strong>g pattern and s k (t) is kth<br />
network node actual output of tth tra<strong>in</strong><strong>in</strong>g pattern.<br />
orig<strong>in</strong>al grade criterion of land eco-security presented<br />
Table Ⅰ were normalized between 0 and 1. The land<br />
eco-security grade is determ<strong>in</strong>ed by the particular<br />
comb<strong>in</strong>ation of <strong>in</strong>dicator values. Therefore the BP neural<br />
network should be tra<strong>in</strong>ed to learn the nonl<strong>in</strong>ear<br />
relationship from the learn samples. The endpo<strong>in</strong>ts of the<br />
<strong>in</strong>terval of land eco-security and <strong>in</strong>dicator values whose<br />
correspondence relationship was showed <strong>in</strong> Table Ⅲ<br />
were selected. Although the range of land eco-security<br />
values is assumed [0, 1], the values of land eco-security<br />
<strong>in</strong> Hangzhou that will be assessed by BP neural network<br />
may greater than 1 or less than 0. So as to prevent the<br />
assessment values of land eco-security to break the<br />
limitation of an <strong>in</strong>terval and enhance the<br />
dist<strong>in</strong>guishability of assessment values of land<br />
eco-security, some proper endpo<strong>in</strong>ts were selected to<br />
reflect the correspondence relationship between the<br />
<strong>in</strong>dicator values and land eco-security whose value was 0.<br />
There are a variety of methods for normalization. In<br />
this empirical study, the equation for normalization is as<br />
follows:<br />
S ′ = ( S −m<strong>in</strong> )/(max − m<strong>in</strong> ) (6)<br />
n n n. value n. value n.<br />
value<br />
Where max n.value is maximal value <strong>in</strong> <strong>in</strong>put vector n,<br />
and m<strong>in</strong> n.value is m<strong>in</strong>imal value <strong>in</strong> <strong>in</strong>put vector n. S n is the<br />
orig<strong>in</strong>al <strong>in</strong>put <strong>in</strong> <strong>in</strong>put vector n. S n′ is the normalized<br />
value of the orig<strong>in</strong>al <strong>in</strong> <strong>in</strong>put vector n.<br />
TABLE II.<br />
DESCRIPTIVE STATISTICS OF ORIGINAL DATA IN HANGZHOU<br />
M<strong>in</strong>. Max. Mean Std.Deviation<br />
x 1 0.05 0.82 0.61 0.25<br />
x 2 527.04 14001.76 4426.24 4454.91<br />
x 3 10.37 45.29 25.59 11.29<br />
Figure 2.<br />
Topological structure of BP neural network for<br />
assessment<br />
IV. ORIGINAL DATA AND PRETREATMENT<br />
The orig<strong>in</strong>al <strong>in</strong>dicator values of 8 districts<br />
(county-level cities, counties) applied to assess the land<br />
eco-security of Hangzhou were obta<strong>in</strong>ed from the<br />
statistical yearbooks and local municipal bureau of land<br />
and resources. The descriptive statistics of orig<strong>in</strong>al<br />
<strong>in</strong>dicator values is showed <strong>in</strong> Table Ⅱ.<br />
In order to improve the convergence rates and enhance<br />
the estimation accuracies s<strong>in</strong>ce the feature of logsig<br />
transfer function. The orig<strong>in</strong>al <strong>in</strong>dicator values and<br />
x 4 117.55 554.03 338.03 149.02<br />
x 5 3.89 38.31 16.01 11.54<br />
x 6 14.69 76.86 51.39 26.79<br />
x 7 0.04 5.47 2.18 2.01<br />
x 8 103.00 3209.00 730.25 1037.25<br />
x 9 6.79 87.43 49.02 26.13<br />
x 10 30.58 63.27 38.04 10.73<br />
x 11 1.69 190.31 34.87 64.00<br />
x 12 1.29 8.56 3.76 2.20<br />
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TABLE III.<br />
ENDPOINTS OF THE INTERVAL OF LAND ECO-SECURITY AND CORRESPONDING INDICATOR VALUES<br />
x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 values of land eco-security<br />
1.4 2500 5.00 220 12 30 1.0 450 65 70 30 5 0.8<br />
0.8 2000 15.00 300 10 25 1.5 500 50 60 25 4 0.6<br />
0.7 1500 20.00 400 8 20 2.0 550 40 50 20 3 0.4<br />
0.6 1000 25.00 500 6 15 2.5 600 30 40 15 2 0.2<br />
0.5 500 30.00 600 5 10 4.0 650 20 30 10 1 0.0<br />
V. RESULTS<br />
The BP neural network that was established to assess<br />
the land eco-security was performed under MATLAB<br />
version 7.0 by us<strong>in</strong>g Neural Network Toolbox [20, 21]. In<br />
the empirical study, performance goal of the BP neural<br />
network was set to 0.001 or if number of epoch reaches<br />
2000. The learn samples which were normalized were<br />
<strong>in</strong>put, and the Figure 3 showed that the tra<strong>in</strong><strong>in</strong>g error falls<br />
down to 0.001 with<strong>in</strong> 62 epochs. Therefore the BP neural<br />
network was accepted, and applied to assess of land<br />
eco-security <strong>in</strong> Hangzhou.<br />
The normalized <strong>in</strong>dicator values of city center district,<br />
Xiaoshan district, Yuhang district, Tonglu county,<br />
Chun'an county, Jiande city, Fuyang city and L<strong>in</strong>'an city<br />
were put <strong>in</strong>to the BP neural network which had been<br />
tra<strong>in</strong>ed, then the values of land eco-security of 8 districts<br />
(county-level cities, counties) were calculated by the BP<br />
neural network. The result of assessment was showed <strong>in</strong><br />
Table Ⅵ, and the spatial distribution of land eco-security<br />
of Hangzhou was presented <strong>in</strong> Figure 4.<br />
Figure 4.<br />
Spatial distribution of land eco-security of Hangzhou<br />
Figure 3.<br />
Tra<strong>in</strong><strong>in</strong>g error trend of BP neural network<br />
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City center<br />
district<br />
TABLE IV.<br />
NORMALIZED INDICATOR VALUES AND THE LAND ECO-SECURITY OF DISTRICTS IN HANGZHOU<br />
x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12<br />
values of land<br />
eco-security<br />
0.000 0.002 0.133 0.216 0.202 0.070 0.000 1.000 0.000 0.832 1.000 0.072 0.070<br />
Xiaoshan 0.456 0.014 1.000 0.905 1.000 0.094 0.000 0.245 0.943 0.112 0.170 0.283 0.274<br />
Yuhang 0.423 0.042 0.507 0.525 0.731 0.265 0.122 0.193 1.000 0.249 0.147 0.411 0.382<br />
Tonglu 0.555 0.313 0.544 0.305 0.228 0.914 0.503 0.038 0.436 0.015 0.025 0.839 0.599<br />
Chun'an 0.383 1.000 0.139 0.000 0.000 0.892 1.000 0.000 0.373 0.224 0.000 0.566 0.708<br />
Jiande 0.535 0.404 0.509 0.677 0.217 0.873 0.497 0.038 0.447 0.064 0.009 0.778 0.612<br />
Fuyang 0.390 0.167 0.610 0.271 0.286 0.844 0.236 0.082 0.595 0.061 0.047 0.689 0.574<br />
L<strong>in</strong>'an 0.570 0.384 0.645 0.757 0.155 1.000 0.791 0.021 0.396 0.053 0.009 1.890 0.601<br />
serious land<br />
eco-security risk<br />
high land<br />
eco-security risk<br />
high land<br />
eco-security risk<br />
<strong>in</strong>termediate land<br />
eco-security risk<br />
low land<br />
eco-security risk<br />
low land<br />
eco-security risk<br />
<strong>in</strong>termediate land<br />
eco-security risk<br />
low land<br />
eco-security risk<br />
VI. DISCUSSION AND CONCLUSIONS<br />
Districts whose land eco-security values are above 0.4<br />
and below 0.8 account for 60% of the entire region. It<br />
<strong>in</strong>dicates that the land ecology of districts <strong>in</strong> Hangzhou<br />
suffers damage, whereas the risk of land eco-security <strong>in</strong><br />
Hangzhou is <strong>in</strong> control. Actually the local government<br />
adopts some measures to adm<strong>in</strong>ister the land use and land<br />
ecology s<strong>in</strong>ce the ecological consciousness. These<br />
measures pr<strong>in</strong>cipally refer to farmland protection,<br />
<strong>in</strong>tensive and economical utilization of construction land,<br />
forests land preservation, contam<strong>in</strong>ation emission control,<br />
family plann<strong>in</strong>g, ect. Therefore the condition of land<br />
eco-security <strong>in</strong> Tonglu county, Chun'an county, Jiande<br />
city, Fuyang city and L<strong>in</strong>'an city is at low risk or<br />
<strong>in</strong>termediate risk.<br />
The economic growth has negative impact on the land<br />
ecology of the land ecology <strong>in</strong> Hangzhou. The city center<br />
district has a population of 226.74 million which<br />
accounts for 33% of the total population of Hangzhou,<br />
and the city center district produces largest GDP of<br />
Hangzhou which accounts for over 85% of Hangzhou<br />
GDP. A great deal of service <strong>in</strong>dustry and manufactur<strong>in</strong>g<br />
centralize the city center district. For example, biological<br />
medic<strong>in</strong>e <strong>in</strong>dustry, mechanical manufactur<strong>in</strong>g <strong>in</strong>dustry<br />
and food and beverage <strong>in</strong>dustry is geographically<br />
concentrated Hangzhou Economic & Technological<br />
Development Zone whose purpose is to attract the global<br />
<strong>in</strong>vestment. The local governments currently consider<br />
GDP as a most important <strong>in</strong>dicator of economic progress,<br />
however the improvement of land ecology dose not<br />
directly tied to the growth of GDP. Much farmland is<br />
converted to construction land for <strong>in</strong>dustrial and<br />
residential uses, and high population density <strong>in</strong>creases the<br />
ecological frangibility.<br />
Xiaoshan district and Yuhang district locate <strong>in</strong> the<br />
surround<strong>in</strong>g area fr<strong>in</strong>ged city center district of Hangzhou.<br />
The development plan of Hanghzhou proposes that<br />
concentrated distribution area of heavy <strong>in</strong>dustry locate <strong>in</strong><br />
Xiaoshan district and Yuhang district. Rapid<br />
<strong>in</strong>dustrialization and urbanization <strong>in</strong>crease the stress on<br />
the land ecology, <strong>in</strong> spite of the fact that orig<strong>in</strong>al<br />
ecological condition of land <strong>in</strong> Xiaoshan district and<br />
Yuhang district is appropriate to ma<strong>in</strong>ta<strong>in</strong> the relatively<br />
security of land ecology s<strong>in</strong>ce the large cultivated land<br />
area per capital, large proportion of cultivated land,<br />
low population density, ect.<br />
One goal of this paper is to provide a method to assess<br />
the land eco-security. The BP neural network and PSR<br />
framework were adopted to establish the model for<br />
assessment of land eco-security. Then the orig<strong>in</strong>al date<br />
was pretreated, and the tra<strong>in</strong><strong>in</strong>g error of BP neural<br />
network was acceptable. The values of land eco-security<br />
of 8 districts (county-level cities, counties) <strong>in</strong> Hangzhou<br />
were evaluated by the BP neural network which was<br />
tra<strong>in</strong>ed. The results showed that the city center district<br />
was at serious land eco-security risk; Xiaoshan district<br />
and Yuhang district were at high land eco-security risk;<br />
Tonglu county and Fuyang city were at <strong>in</strong>termediate land<br />
eco-security risk; Chun'an county, Jiande city and L<strong>in</strong>'an<br />
city were at low land eco-security risk. This phenomenon<br />
reveals that although some measures are adopted to<br />
control the risk of land eco-security, the economic<br />
growth still has negative impact on the land ecology <strong>in</strong><br />
Hangzhou, and the rapid <strong>in</strong>dustrialization and<br />
urbanization <strong>in</strong>crease the risk of land eco-security.<br />
Therefore the policy constitutor should do someth<strong>in</strong>g<br />
to strengthen the land ecology protection.<br />
The method for assess<strong>in</strong>g land eco-security <strong>in</strong> this<br />
paper is flexible enough to be modified to applied <strong>in</strong><br />
other areas accord<strong>in</strong>g to the local factors. The purpose of<br />
assessment of land eco-security is not only obta<strong>in</strong><strong>in</strong>g the<br />
state of the land eco-security but also understand<strong>in</strong>g of<br />
the factors affect the land eco-security. Consequently<br />
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1400 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
the similar research about land ecology <strong>in</strong> the areas<br />
where the land ecology may suffer damage should be<br />
done.<br />
ACKNOWLEDGMENT<br />
The author wishes to thank Hangzhou municipal<br />
bureau of land and resources for provid<strong>in</strong>g the orig<strong>in</strong> data.<br />
This work was supported <strong>in</strong> part by a grant from National<br />
Natural Science Foundation of Ch<strong>in</strong>a (No.70973047).<br />
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susta<strong>in</strong>able systems of land use,” Agroforestry Systems, vol.<br />
45, pp.1-21, January 1999.<br />
[8] C. Walter and H. Stützel, “A new method for assess<strong>in</strong>g the<br />
susta<strong>in</strong>ability of land-use systems (II): Evaluat<strong>in</strong>g impact<br />
<strong>in</strong>dicators,” Ecological Indicators, Ecological Economics,<br />
vol. 68, pp. 1288–1300, March 2009.<br />
[9] Y. Y. YIN; and J. T. PIERCE, “Integrated resource<br />
assessment and susta<strong>in</strong>able land-use,” Environmental<br />
Management, vol. 17, pp. 319–327, May-Jun 1993.<br />
[10] V. H. D. Zuazo, C. R. R. Pleguezuelo, D. Flanagan, I. G.<br />
Tejero, and J. L. M. Fernández, “Susta<strong>in</strong>able land use and<br />
agricultural soil,” Alternative Farm<strong>in</strong>g Systems,<br />
Biotechnology, Drought Stress and Ecological Fertilisation<br />
Susta<strong>in</strong>able Agriculture Reviews, vol. 6, pp.107-192, 2011.<br />
[11] A. Cooper, T. Sh<strong>in</strong>e, T. McCann, and D.A. Tidane, “An<br />
ecological basis for susta<strong>in</strong>able land use of Eastern<br />
Mauritanian wetlands,” Journal of Arid Environments, vol.<br />
67, pp. 116–141 October 2006.<br />
[12] S. Su, D. Li, X. Yu, Z. Zhang, Q. Zhang, R. Xiao, J.<br />
Zhi, and J. Wu, “Assess<strong>in</strong>g land ecological security <strong>in</strong><br />
Shanghai (Ch<strong>in</strong>a) based on catastrophe theory,” Stochastic<br />
Environment Research and Risk Assessment, vol. 25, pp.<br />
737–746, June 2011.<br />
[13] D. Svozil, V. Kvasnicka, and J. Pospichal, “Introduction to<br />
multi-layer feed-forward neural networks,” Chemometrics<br />
and Intelligent Laboratory Systems, vol. 39, pp.43–62,<br />
November 1997.<br />
[14] J. He; Z.He, ; D.Zou, and Y. Xia, “A BP neural network<br />
method for RNA secondary structure prediction based on<br />
ENSSEL labels,” Journal of Computers, vol. 6, pp.<br />
569-576, April 2009.<br />
[15] F. Zhang, P. Li, Z. Hou, Z. Lu, Y. Chen, Q. Li, and M. Tan<br />
a “sEMG-based cont<strong>in</strong>uous estimation of jo<strong>in</strong>t angles of<br />
human legs by us<strong>in</strong>g BP neural network,” Neurocomput<strong>in</strong>g,<br />
vol. 78, pp.139–148, February 2012.<br />
[16] W. Xiang, Y. Gu, and D. Ge, “Test<strong>in</strong>g of rounded corner<br />
for micro-drill on hybrid of BP neural network and<br />
adaptive particle swarm optimization,” Journal of<br />
Computers, vol. 7, pp. 1116-1121, May 2012.<br />
[17] OECD, Environmental <strong>in</strong>dicators. OECD core set,<br />
Organization for Economic Co-operation and Development,<br />
Paris, 1994.<br />
[18] B. Wolfslehner and H. Vacik, “Evaluat<strong>in</strong>g susta<strong>in</strong>able<br />
forest management strategies with the Analytic Network<br />
Process <strong>in</strong> a Pressure-State-Response framework,” Journal<br />
of Environmental Management, vol. 88, pp.1–10, July<br />
2008.<br />
[19] A. J. J. Lynch, “The usefulness of a threat and disturbance<br />
categorization developed for Queensland Wetlands to<br />
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Environmental Management, Vol. 47, pp.40-55, January<br />
2011.<br />
[20] D. Howard and M. Beale, Neural Network Toolbox for Use<br />
with MATLAB, User’s Guide, version 4. The Math Works,<br />
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Use with Matlab. Mathworks, Inc., Natick, MA ,2003.<br />
Heyuan You, he was born <strong>in</strong> Wenzhou<br />
City, Zhejiang Prov<strong>in</strong>ce of Ch<strong>in</strong>a <strong>in</strong> 1983.<br />
He received the PhD degree <strong>in</strong> land<br />
resource management from Institute of<br />
Land Science and Property Management,<br />
Zhejiang University <strong>in</strong> 2012.<br />
He is currently work<strong>in</strong>g as a lecturer <strong>in</strong> the<br />
College of Bus<strong>in</strong>ess Adm<strong>in</strong>istration,<br />
Zhejiang University of F<strong>in</strong>ance and<br />
Economics, Zhejiang, Ch<strong>in</strong>a. His research area centers on land<br />
use simulation and land ecology management.<br />
© 2013 ACADEMY PUBLISHER
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Magellan: Technical Description of a New<br />
System for Robot-Assisted Nerve Blocks<br />
Joshua Morse ∗ , Mohamad Wehbe ‡ , Riccardo Taddei † , Shantale Cyr § , and Thomas M. Hemmerl<strong>in</strong>g §<br />
∗ Department of Electrical and Computer Eng<strong>in</strong>eer<strong>in</strong>g, McGill University, Montreal, QC, Canada<br />
email: joshua.morse@mail.mcgill.ca<br />
‡ Department of Experimental Surgery, McGill University, Montreal, QC, Canada<br />
† Department of Anesthesiology, University of Pisa, Pisa, Italy<br />
§ Department of Anesthesia, McGill University, Montreal, QC, Canada<br />
Institute of Biomedical Eng<strong>in</strong>eer<strong>in</strong>g, University of Montreal, Montreal, QC, Canada<br />
email: thomas.hemmerl<strong>in</strong>g@mcgill.ca<br />
1<br />
Abstract—Nerve blocks are common procedures used to<br />
remove sensation from a specific region of the body via<br />
<strong>in</strong>jection of local anesthetic. Ultrasound-guided nerve blocks<br />
are common-place <strong>in</strong> anesthesia, but require specialized<br />
tra<strong>in</strong><strong>in</strong>g and advanced bi-manual dexterity. This paper describes<br />
a system designed to robotically assist <strong>in</strong> ultrasoundguided<br />
nerve blocks. Robot-assisted nerve blocks could allow<br />
for more precise needle placement, and therefore a higher<br />
efficacy of blocks. This system is the first step <strong>in</strong> develop<strong>in</strong>g a<br />
completely automated nerve block system, which would also<br />
require the <strong>in</strong>corporation of ultrasound image recognition<br />
of nerves and other physiological markers.<br />
Index Terms—Regional anesthesia, nerve blocks, robotic<br />
anesthesia.<br />
I. INTRODUCTION<br />
NERVE blocks are a procedure of regional anesthesia<br />
used to remove the sensitivity from an area of the<br />
body via the <strong>in</strong>jection of an anesthetic drug <strong>in</strong>to the nerve<br />
<strong>in</strong>nervat<strong>in</strong>g the target area. Nerve blocks were first used<br />
<strong>in</strong> surgery <strong>in</strong> 1885 [1] and are now a common procedure<br />
performed rout<strong>in</strong>ely around the world.<br />
Perform<strong>in</strong>g regional nerve blocks requires special tra<strong>in</strong><strong>in</strong>g.<br />
Anesthesiologists perform<strong>in</strong>g regional nerve blocks<br />
only on an occasional basis have a significant failure rate,<br />
as high as 45% [2]. Most regional blocks are performed<br />
us<strong>in</strong>g ultrasound guidance; this necessitates careful bimanual<br />
operation of the ultrasound probe and the nerve<br />
block needle. Precise movement of the needle is important<br />
for successful blocks. One centimeter movement <strong>in</strong> any<br />
direction can make the difference between a failed and a<br />
successful block.<br />
Mechanical robots have been used <strong>in</strong> surgery for more<br />
than 10 years, the da V<strong>in</strong>ci Surgical System (Intuitive<br />
Surgical, Inc., Sunnyvale, CA) be<strong>in</strong>g the latest. These<br />
mechanical robots are shown to <strong>in</strong>crease precision of<br />
movements and improve outcome [3]. Recently, Tighe et<br />
al. have used the da V<strong>in</strong>ci Surgical System to perform<br />
successful nerve blocks <strong>in</strong> an ultrasound phantom [4]. We<br />
present the first robotic system, called Magellan, designed<br />
specifically to perform rout<strong>in</strong>e nerve blocks.<br />
II. MATERIALS AND METHODS<br />
The Magellan system is designed to perform robotassisted,<br />
ultrasound-guided nerve blocks. The system has<br />
4 primary components: a standard nerve block needle<br />
and syr<strong>in</strong>ge mounted via a custom clamp to a robotic<br />
arm (JACO robotic arm, K<strong>in</strong>ova, Montreal, QC, Canada),<br />
an ultrasound mach<strong>in</strong>e, a joystick (ThrustMaster T.Flight<br />
Hotas X, Guillemot Inc., New York, NY, USA), and a<br />
software control system. The system is designed to work<br />
with any ultrasound mach<strong>in</strong>e with a video output. The ultrasound<br />
video signal is captured via a USB video capture<br />
device (Dazzle DVC100, P<strong>in</strong>nacle Systems, Mounta<strong>in</strong><br />
View, CA, USA).<br />
The software system is designed on a client/server model<br />
so that nerve blocks can be performed remotely. Both<br />
the client and server programs were written <strong>in</strong> C# and<br />
communicate us<strong>in</strong>g UDP/IP. The client software <strong>in</strong>terfaces<br />
with the ultrasound mach<strong>in</strong>e, robotic arm, and a<br />
webcam (Lifecam HD, Microsoft Corporation, Redmond,<br />
WA, USA). The ultrasound and webcam video feeds are<br />
streamed from the client to the server, where they are<br />
displayed <strong>in</strong> a graphical user <strong>in</strong>terface (GUI) created<br />
<strong>in</strong> LabView (National Instruments, Aust<strong>in</strong>, TX, USA).<br />
The webcam is positioned <strong>in</strong> order to provide a direct<br />
view of the target nerve <strong>in</strong>sertion area and the ultrasound<br />
probe. The server software <strong>in</strong>terfaces with the joystick and<br />
transmits the joystick commands to the client over the IP<br />
network. The client and server, as well as their software<br />
subsystems, are detailed <strong>in</strong> Fig. 1. Further explanation<br />
of the <strong>in</strong>dividual subsystems of both applications are<br />
presented below.<br />
A. Software Control System<br />
1) Server Application: The Controller Subsystem implements<br />
an <strong>in</strong>terface that decouples the precise controller’s<br />
driver from the system, allow<strong>in</strong>g for the controller<br />
to be easily changed. This subsystem reads the state of<br />
the controller and provides it to the Server Network<strong>in</strong>g<br />
Subsystem.<br />
The Server Network<strong>in</strong>g Subsystem is responsible for<br />
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2<br />
Client<br />
Robotic Arm API<br />
Safety Input Filter<br />
Client<br />
Network<strong>in</strong>g<br />
Subsystem<br />
Data Logg<strong>in</strong>g<br />
Subsystem<br />
Video Stream<strong>in</strong>g<br />
Software<br />
Server<br />
Joystick Controller<br />
Subsystem<br />
Server Network<strong>in</strong>g<br />
Subsystem<br />
GUI<br />
Fig. 1.<br />
Logical View of the Magellan system detail<strong>in</strong>g the <strong>in</strong>dividual software subsystems of both the client and server applications.<br />
Fig. 2. GUI of the Magellan system. Left: Ultrasound video feed. Right: Webcam video show<strong>in</strong>g ultrasound probe and <strong>in</strong>sertion area. The arm<br />
speed and network latency are displayed beneath the ultrasound video.<br />
transmitt<strong>in</strong>g the controller data to the client over the<br />
network. Furthermore, this subsystem encrypts all packets<br />
to be sent to the client and decrypts those received from<br />
the client. This subsystem also works with the client to<br />
monitor the latency of the network. The latency <strong>in</strong>formation<br />
is displayed prom<strong>in</strong>ently on the GUI <strong>in</strong> order to<br />
allow the user to estimate the lag between the commands<br />
they send us<strong>in</strong>g the joystick and the result<strong>in</strong>g movement<br />
on the video displays. The latency display is color-coded<br />
to provide a clear, visual <strong>in</strong>dication of the latency status:<br />
grey for latencies less than 200 ms, yellow for latencies<br />
between 201 and 400 ms, and red for latencies greater<br />
than 400 ms.<br />
The GUI is detailed <strong>in</strong> Fig. 2. The GUI prom<strong>in</strong>ently displays<br />
the ultrasound video feed and the view of the target<br />
area, as well as the network latency and current arm speed.<br />
The arm speed can be toggled between three different<br />
modes: high, used to place the needle <strong>in</strong>itially <strong>in</strong> position<br />
above the target area; medium, used to descend the needle<br />
towards the <strong>in</strong>sertion po<strong>in</strong>t; and low, used to drive the<br />
needle through the sk<strong>in</strong> and to the nerve sheath. The arm<br />
speed display is also color-coded, with green, yellow, and<br />
red denot<strong>in</strong>g low, medium, and high speeds, respectively.<br />
The arm moves .15 m/s, 0.075 m/s, and 0.0425 m/s for<br />
high, medium, and low speeds, respectively.<br />
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3<br />
2) Client Application: The Robotic Arm API subsystem<br />
is responsible for transmitt<strong>in</strong>g commands to the<br />
robotic arm. This subsystem also provides details on the<br />
location and status of the arm to the Client Network<strong>in</strong>g<br />
Subsystem.<br />
The purpose of the Safety Input Filter subsystem is to<br />
prevent unsafe commands from be<strong>in</strong>g sent to the robotic<br />
arm: by press<strong>in</strong>g a specific button on the joystick, the<br />
operator puts the system <strong>in</strong>to a needle <strong>in</strong>sertion mode that<br />
limits the depth that the needle can move; these limitations<br />
are dependent on the target nerve. For example, for the<br />
popliteal nerve, maximum depth is set to 4 cm. This<br />
feature prevents the needle from descend<strong>in</strong>g below the<br />
maximum depth of the target nerve. This subsystem also<br />
scales the magnitude of movement speeds to allow for<br />
small and precise changes <strong>in</strong> the orientation of the needle<br />
<strong>in</strong> order to provide the anesthesiologist with f<strong>in</strong>e control.<br />
Additionally, this subsystem implements the control<br />
scheme for the system as it is responsible for translat<strong>in</strong>g<br />
controller commands received over the network <strong>in</strong>to <strong>in</strong>dividual<br />
commands to be sent to the robotic arm.<br />
The Client Network<strong>in</strong>g Subsystem is responsible for<br />
handl<strong>in</strong>g all communications with the server application.<br />
This communication <strong>in</strong>cludes the reception of controller<br />
packets from the server, the monitor<strong>in</strong>g of latency <strong>in</strong> the<br />
network, and updates about the status of the robotic arm.<br />
Additionally, this subsystem handles the encryption of all<br />
data be<strong>in</strong>g transmitted to the server and the decryption of<br />
all data received from the server.<br />
The Data Logg<strong>in</strong>g Subsystem records all data that is<br />
received by the client from the server. Additionally, it<br />
records the output of the Safety Input Filter so that all<br />
commands that are transmitted to the robotic arm are<br />
logged.<br />
The Video Stream<strong>in</strong>g Software subsystem streams the<br />
local ultrasound and webcam video feeds to the server.<br />
B. Safety Features<br />
There are two safety classifications of medical robots:<br />
fail-safe and fault-tolerant [5]. A fail-safe robot is one<br />
which enters a safe state when an error occurs; a faulttolerant<br />
robot is one which cont<strong>in</strong>ues to operate <strong>in</strong> the<br />
presence of errors [5]. This system is fail-safe as it will<br />
enter a state that poses no risks to the patient if any errors<br />
occur.<br />
In the event of a disconnection of any critical device (i.e.,<br />
the joystick is disconnected from the server PC or the<br />
JACO arm is disconnected from the client PC), the robotic<br />
arm will immediately stop mov<strong>in</strong>g and rema<strong>in</strong> stationary<br />
until a connection can be re-established. The motors of the<br />
robotic arm cannot be manually moved while powered on.<br />
This same protocol is followed if a network connection<br />
is lost between the client and server PCs. Similarly, the<br />
robotic arm will also stop all movement if any critical<br />
exceptions occur <strong>in</strong> the client or server applications.<br />
A second important safety consideration of a medical<br />
robot is the magnitude <strong>in</strong> error between the actual, measured<br />
position of the motors of the robot and the position<br />
that motors were commanded to go [5]. The JACO robotic<br />
arm has a relative position tolerance of 1.6 mm, mean<strong>in</strong>g<br />
that the maximum error between the commanded and<br />
actual positions of the needle will be, with<strong>in</strong> 1.6 mm of<br />
the target. Additionally, the anesthesiologist can activate a<br />
safety limitation which will prevent the needle from go<strong>in</strong>g<br />
below the maximum depth of the current target nerve.<br />
The arm features several important safety features which<br />
make it suitable for use <strong>in</strong> this application: it has redundant<br />
error checks for each jo<strong>in</strong>t and the control system, it<br />
recalculates the position of each motor every 0.01 second,<br />
recovers automatically <strong>in</strong> case of a system fault, has zero<br />
backlash on each of its six axes, and is back drivable when<br />
shutdown. The arm also has a maximum translational<br />
speed of 15 cm/s and a maximum jo<strong>in</strong>t rotation speed<br />
of 8 rpm.<br />
The arm is powered by a 24V DC power adapter and<br />
is plugged <strong>in</strong>to an un<strong>in</strong>terruptable power supply (Back<br />
UPS XS 1300, APC, W. K<strong>in</strong>gston, RI, USA) that provides<br />
power to both it and the client computer <strong>in</strong> the case of<br />
a power failure. The arm draws between 1.7 and 10 A<br />
while <strong>in</strong> use and the UPS conta<strong>in</strong>s a battery with sufficient<br />
capacity to allow for a safe reversal of the procedure<br />
should power be lost.<br />
The JACO arm is connected to the client PC us<strong>in</strong>g a<br />
standard USB cable. In the case of a computer failure, the<br />
robotic arm also has a backup joystick that can be used<br />
to directly control it, <strong>in</strong>dependent of the client PC. This<br />
joystick allows full control of the arm and will operate as<br />
long as the arm has power.<br />
C. Robotic Arm<br />
The JACO robotic arm was developed to provide<br />
mechanical assistance to wheelchair-bound people and<br />
is certified by Health Canada as a medical device. The<br />
robotic arm has 6 degrees of freedom and can support<br />
a payload of 1.5 kg or 1 kg at full extension. The<br />
arm is built of carbon fiber, mak<strong>in</strong>g it lightweight at<br />
5 kg. It has a reach of 90 cm at full extension and<br />
conta<strong>in</strong>s 6 <strong>in</strong>dependently-controlled motors. The arm can<br />
also operate <strong>in</strong> both a left-handed and right-handed mode.<br />
These features make the JACO robotic arm versatile and<br />
allow great flexibility <strong>in</strong> the placement of the robotic arm.<br />
D. Control Scheme<br />
In order to provide an <strong>in</strong>tuitive control scheme to the<br />
user, each of the six primary movements available via the<br />
robotic arm were mapped to specific buttons and/or axes<br />
of the joystick.<br />
The left/right and forward/backward movements of the<br />
primary joystick handle are mapped to the same movements<br />
of the robotic arm. Twist<strong>in</strong>g the joystick handle to<br />
the left or right will cause the robotic arm to rotate the<br />
needle <strong>in</strong> a similar fashion. The throttle control of the<br />
joystick is used to rotate the tip of the needle forward<br />
or backwards, while rotat<strong>in</strong>g a slider bar on the rear of<br />
the throttle will rotate the syr<strong>in</strong>ge about the po<strong>in</strong>t of the<br />
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4<br />
needle. The hat switch is used to ascend or descend the<br />
needle. The trigger button <strong>in</strong>forms the system that the<br />
nerve block procedure is beg<strong>in</strong>n<strong>in</strong>g, and thus engages the<br />
safety limitations described <strong>in</strong> section II-B. Two buttons<br />
on the top of the joystick are used to either <strong>in</strong>crease or<br />
decrease the speed of the robotic arm.<br />
E. Operational Setup<br />
The JACO robotic arm is mounted to the rear of the<br />
operat<strong>in</strong>g table and placed <strong>in</strong> the handedness mode that<br />
would provide the easiest approach to the leg that will<br />
receive a block: left-handedness for perform<strong>in</strong>g a nerve<br />
block on the right leg, or right-handedness for perform<strong>in</strong>g<br />
a nerve block on the left leg.<br />
The ultrasound mach<strong>in</strong>e is placed so that the probe<br />
can be manipulated manually to locate and identify the<br />
target nerve. The ultrasound mach<strong>in</strong>e’s video output is<br />
connected to the client PC us<strong>in</strong>g a composite video cable<br />
and a USB video capture device. For all local tests<br />
performed with the system, the same PC was used as<br />
both the client and server. The PC and joystick were<br />
<strong>in</strong>stalled on a mobile cart which was placed close to the<br />
mannequ<strong>in</strong>. The webcam was then placed with a clear<br />
view of the <strong>in</strong>tended position and connected to the PC.<br />
III. TESTING & RESULTS<br />
The Magellan system was tested on an ultrasound<br />
nerve phantom (Blue Phantom Select Series Peripheral<br />
Nerve Block Ultrasound Tra<strong>in</strong><strong>in</strong>g Model, Blue Phantom,<br />
Redmond, WA, USA). This nerve phantom is designed to<br />
realistically mimic human tissue, both physically and <strong>in</strong><br />
an ultrasound image. These tests were made to ensure that<br />
the control scheme was easy to use and that the needle<br />
could be placed <strong>in</strong> the correct location by the robotic arm.<br />
An experiment was conducted to record and analyze the<br />
first 20 nerve blocks performed on the nerve phantom.<br />
These trials were performed by an anesthesiologist who<br />
had never previously used the Magellan nor been formally<br />
tra<strong>in</strong>ed <strong>in</strong> its control scheme. In this experiment, the<br />
anesthesiologist verbally guided an assistant to maneuver<br />
the ultrasound probe until the nerve was located and<br />
identified on the ultrasound screen and then directed the<br />
needle, us<strong>in</strong>g the joystick, from a rest<strong>in</strong>g position, to the<br />
proper <strong>in</strong>sertion position, and then directly <strong>in</strong>to the nerve.<br />
Success was def<strong>in</strong>ed as the <strong>in</strong>troduction of the tip of the 22<br />
gauge needle <strong>in</strong>to the nerve. The trial times are shown <strong>in</strong><br />
Fig. 3. The success rate for the first 20 trials on the nerve<br />
phantom was 90% with an average time of 95.2 s with a<br />
standard deviation of 49.9 s. The data was analyzed us<strong>in</strong>g<br />
l<strong>in</strong>ear regression and a trend l<strong>in</strong>e with a slope of -5.5 s<br />
was found, denot<strong>in</strong>g that the anesthesiologist was able to<br />
perform a block 5.5 seconds faster with each successive<br />
attempt that was made. The failures <strong>in</strong> these trials were<br />
identified to be due to improperly align<strong>in</strong>g the tip of the<br />
needle with the center of the ultrasound probe. Further<br />
tests performed by another anesthesiologist resulted <strong>in</strong> a<br />
100% success rate.<br />
Fig. 3. Blue: block times for first 20 phantom trials of the Magellan<br />
system. Black: trend l<strong>in</strong>e and equation.<br />
IV. CONCLUSION<br />
We present the first mechanical robotic system<br />
specifically designed to perform nerve blocks us<strong>in</strong>g a<br />
joystick and computer control center. Us<strong>in</strong>g the Magellan,<br />
a 90-100% success rate was achievable us<strong>in</strong>g a standard<br />
nerve block phantom. In addition, a rather steep learn<strong>in</strong>g<br />
curve was determ<strong>in</strong>ed <strong>in</strong>dicat<strong>in</strong>g great ease of learn<strong>in</strong>g to<br />
operate the nerve block needle us<strong>in</strong>g a joystick with rapid<br />
improvement of the operation times of the Magellan.<br />
A study of anesthesia residents study<strong>in</strong>g regional<br />
anesthesia techniques showed a success rate of 89%<br />
for ultrasound-guided nerve blocks after perform<strong>in</strong>g<br />
40 blocks on patients [6], show<strong>in</strong>g a similar success<br />
rate between the nerve phantom tests performed with<br />
Magellan and success rates by anesthesia students.<br />
Cl<strong>in</strong>ical tests will show whether the success rates<br />
achieved <strong>in</strong> dummy test<strong>in</strong>g can be confirmed <strong>in</strong> human<br />
test<strong>in</strong>g; further research needs to focus on automated<br />
nerve recognition, as well as automated nerve block<br />
performance – without human <strong>in</strong>tervention. Comb<strong>in</strong><strong>in</strong>g<br />
these two approaches, a completely automated nerve<br />
block system will be possible.<br />
ACKNOWLEDGMENT<br />
The authors would like to acknowledge the Department<br />
of Anesthesia <strong>in</strong> the Montreal General Hospital for their<br />
f<strong>in</strong>ancial support of this project.<br />
REFERENCES<br />
[1] W. S. Halsted, “Practical comments on the use and abuse of<br />
coca<strong>in</strong>e,” New York Medical Journal, vol. 42, pp. 294–299, 1885.<br />
[2] P. Marhofer and V. Chan, “Ultrasound-guided regional anesthesia:<br />
current concepts and future trends,” Anesthesia & Analgesia, vol.<br />
104, no. 5, pp. 1265–1269, 2007.<br />
[3] D. Willis, M. Gonzalgo, M. Brotzman, Z. Feng, B. Trock, and L. Su,<br />
“Comparison of outcomes between pure laparoscopic vs robotassisted<br />
laparoscopic radical prostatectomy: a study of comparative<br />
effectiveness based upon validated quality of life outcomes,” BJU<br />
<strong>in</strong>ternational, 2011.<br />
[4] P. Tighe, S. Badiyan, I. Luria, A. Boezaart, and S. Parekattil,<br />
“Robot-assisted regional anesthesia: A simulated demonstration,”<br />
Anesthesia & Analgesia, vol. 111, no. 3, pp. 813–816, 2010.<br />
[5] P. Kazanzides, “Safety design for medical robots,” <strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g<br />
<strong>in</strong> Medic<strong>in</strong>e and Biology Society, 2009. EMBC 2009. Annual<br />
International Conference of the IEEE, Sept. 2009, pp. 7208 –7211.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1405<br />
5<br />
[6] C. Luyet, G. Schupfer, M. Wipfli, R. Greif, M. Lug<strong>in</strong>b&, U. Eichenberger<br />
et al., “Different learn<strong>in</strong>g curves for axillary brachial plexus<br />
block: Ultrasound guidance versus nerve stimulation,” Anesthesiology<br />
research and practice, vol. 2010, p. 309462, 2010.<br />
Thomas M. Hemmerl<strong>in</strong>g received the MD<br />
degree from the Faculty of Medic<strong>in</strong>e, University<br />
of Saarland, Germany, <strong>in</strong> 1990. He leads<br />
the ITAG laboratory, Department of Anesthesia,<br />
McGill University. He is currently an<br />
Associate Professor <strong>in</strong> the department of Anesthesia<br />
at McGill University and the Institute<br />
of Biomedical Eng<strong>in</strong>eer<strong>in</strong>g at the University<br />
of Montreal, Montreal, Canada. His research<br />
<strong>in</strong>terests are automated and robotic anesthesia.<br />
Joshua Morse is currently an undergraduate<br />
student <strong>in</strong> the Department of Computer Eng<strong>in</strong>eer<strong>in</strong>g<br />
at McGill University, Montréal, QC,<br />
Canada.<br />
In 2010, he jo<strong>in</strong>ed the Intelligent Technology<br />
<strong>in</strong> Anesthesia Group (ITAG) as a research<br />
assistant. His research <strong>in</strong>terests <strong>in</strong>clude robotic<br />
anesthesia, telemedic<strong>in</strong>e and bio<strong>in</strong>formatics.<br />
Mohamad Wehbe received the B.Sc. degree<br />
<strong>in</strong> biomedical eng<strong>in</strong>eer<strong>in</strong>g from the American<br />
University of Science and Technology, Beirut,<br />
Lebanon, and the M.Sc. degree <strong>in</strong> biomedical<br />
eng<strong>in</strong>eer<strong>in</strong>g from the École Polytechnique de<br />
Montréal, Montréal, QC, Canada, <strong>in</strong> 2006 and<br />
2009, respectively.<br />
In 2010, he jo<strong>in</strong>ed the department of<br />
Experimental Surgery at McGill University,<br />
Montréal, QC, where he started work<strong>in</strong>g toward<br />
the Ph.D. degree <strong>in</strong> the Intelligent Technology<br />
<strong>in</strong> Anesthesia Group (ITAG). His research <strong>in</strong>terests are focused<br />
on <strong>in</strong>telligent biomedical devices and robotic anesthesia.<br />
Riccardo Taddei received the MD degree<br />
from the Faculty of Medic<strong>in</strong>e and Surgery,<br />
University of Pisa, Pisa, Italy <strong>in</strong> 2008.<br />
Dur<strong>in</strong>g 2011, he worked as a research fellow<br />
<strong>in</strong> the Department of Anesthesia <strong>in</strong> the<br />
Montreal General Hospital, McGill University,<br />
Montreal, Canada. He is currently a third year<br />
resident <strong>in</strong> the department of Anethesiology<br />
and Intensive Care <strong>in</strong> Cisanello Hospital, University<br />
of Pisa. His research <strong>in</strong>terests <strong>in</strong>clude<br />
automation <strong>in</strong> anesthesia.<br />
Shantale Cyr holds a PhD degree from the<br />
University of Montreal, Montreal, Canada.<br />
S<strong>in</strong>ce 2007, she has worked as a research<br />
associate <strong>in</strong> the ITAG laboratory, Department<br />
of Anesthesia <strong>in</strong> the Montreal General Hospital,<br />
McGill University, Montreal, Canada. Her<br />
research <strong>in</strong>terests <strong>in</strong>clude closed-loop anesthesia,<br />
device design and user <strong>in</strong>teraction and<br />
telemedic<strong>in</strong>e.<br />
© 2013 ACADEMY PUBLISHER
1406 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
State Assignment for F<strong>in</strong>ite State Mach<strong>in</strong>e<br />
Synthesis<br />
Meng Yang<br />
State Key Lab of ASIC and Systems, Fudan University, Shanghai, Ch<strong>in</strong>a<br />
Email: mengyang@fudan.edu.cn<br />
Abstract—This paper proposes simulated anneal<strong>in</strong>g based<br />
algorithm for the synthesis of a f<strong>in</strong>ite state mach<strong>in</strong>e to<br />
determ<strong>in</strong>e the optimal state assignment with less area and<br />
power dissipation. The algorithm has two anneal<strong>in</strong>g stages.<br />
In the first rough anneal<strong>in</strong>g stage it tries to search <strong>in</strong> global<br />
scope by the proposed rough search method. In the second<br />
focus<strong>in</strong>g anneal<strong>in</strong>g stage it tries to search <strong>in</strong> local scope by<br />
us<strong>in</strong>g proposed focus<strong>in</strong>g search methods <strong>in</strong>tend<strong>in</strong>g chang<strong>in</strong>g<br />
solution slightly. In both stages, the experience of past<br />
solution is utilised by comb<strong>in</strong>g the best solution <strong>in</strong> the past<br />
and the current solution. The experiments performed on a<br />
large suite of benchmarks have established the fact that the<br />
proposed method outperforms the published GA-based<br />
algorithms. The results have shown the effectiveness of the<br />
proposed method <strong>in</strong> achiev<strong>in</strong>g optimal state assignment for<br />
f<strong>in</strong>ite state mach<strong>in</strong>e.<br />
Index Terms—state assignment, f<strong>in</strong>ite state mach<strong>in</strong>e,<br />
optimisation algorithm, simulated anneal<strong>in</strong>g algorithm<br />
I. INTRODUCTION<br />
As the mobile applications are emerg<strong>in</strong>g, the power<br />
consumption of the circuits has become a major concern.<br />
Numerous researches have been <strong>in</strong>vestigated concern<strong>in</strong>g<br />
the power issues [1-3]. F<strong>in</strong>ite state mach<strong>in</strong>e (FSM) is<br />
mathematical model of the sequential circuits with<br />
discrete <strong>in</strong>puts, <strong>in</strong>ternal states and discrete outputs. The<br />
problem of f<strong>in</strong>d<strong>in</strong>g an optimal state assignment is NPhard<br />
[4]. As a result, the synthesis of an FSM plays an<br />
important role.<br />
The genetic algorithm (GA) technique [5] has been<br />
successfully applied to a variety of computationally<br />
complex problems s<strong>in</strong>ce it has a large search space. Many<br />
<strong>in</strong>vestigations have shown that GA can f<strong>in</strong>d good state<br />
assignments. Alma<strong>in</strong>i, et al [6] have demonstrated that<br />
the GA method produced significantly simpler solutions.<br />
In [7] multi objective GA (MOGA) has been used to<br />
optimise area and power simultaneously. Xia and<br />
Alma<strong>in</strong>i [8] have used GAs to optimise both area and<br />
power with good tradeoffs. Pradhan, et al [3] report on<br />
the application of power gat<strong>in</strong>g <strong>in</strong> the higher level of<br />
system design <strong>in</strong> the form of f<strong>in</strong>ite state mach<strong>in</strong>e (FSM)<br />
synthesis. In [9] Chattopadhyay has used GAs to obta<strong>in</strong><br />
power optimised two- and multilevel FSM realisations.<br />
Chattopadhyay [10] considers D flip-flops to store the<br />
state bits and <strong>in</strong>vestigates the avenue of GAs to achieve<br />
area reduction under flip-flop and output polarity<br />
selection.<br />
Other than GA based methods, a number of heuristic<br />
algorithms have been proposed, which are based on<br />
different cost functions estimat<strong>in</strong>g the effect of state<br />
assignment on logic m<strong>in</strong>imisation. It has shown a new<br />
comprehensive method <strong>in</strong> [11] consist<strong>in</strong>g of an efficient<br />
state m<strong>in</strong>imisation and state assignment technique. Goren,<br />
et al [12] present a heuristic for state reduction of<br />
<strong>in</strong>completely specified f<strong>in</strong>ite state mach<strong>in</strong>es. The<br />
proposed heuristic is based on a branch-and-bound search<br />
technique and identification of sets of compatible states<br />
of a given <strong>in</strong>completely specified f<strong>in</strong>ite state mach<strong>in</strong>e<br />
specification. In [13], the usage of a stochastic search<br />
technique <strong>in</strong>spired by simulated anneal<strong>in</strong>g is explored to<br />
solve the state assignment problem.<br />
Generally speak<strong>in</strong>g, it is relatively easy to f<strong>in</strong>d state<br />
assignments to m<strong>in</strong>imise the area only or the power<br />
dissipation only. However, it is known that m<strong>in</strong>imisation<br />
of either the power or logic complexity could be at the<br />
expense of the other and <strong>in</strong> most cases it is hard to f<strong>in</strong>d a<br />
solution that is optimum <strong>in</strong> both doma<strong>in</strong>s. For large<br />
circuits, there are millions or possibly billions of<br />
assignments [14] and hence to f<strong>in</strong>d the state assignment<br />
for the m<strong>in</strong>imisation of power consumption and area at<br />
the same time is computationally difficult. Besides, GA<br />
selects the next generation via a rank<strong>in</strong>g system, which is<br />
not always necessary but takes significant runtime. In this<br />
paper, <strong>in</strong> order to reduce the computational time but at the<br />
same time reta<strong>in</strong> the quality if the solution, simulated<br />
anneal<strong>in</strong>g based algorithm is proposed to solve FSM<br />
problem with low-power and small-area requirements.<br />
The rema<strong>in</strong>der of the paper is organised as follows.<br />
Section II gives term<strong>in</strong>ology of state assignment of the<br />
FSM. The two anneal<strong>in</strong>g stage simulated anneal<strong>in</strong>g<br />
approach is given <strong>in</strong> Section III. Section IV discusses the<br />
comparison results <strong>in</strong> details with respect to other<br />
approaches. Conclusions are then given <strong>in</strong> Section V.<br />
II. TERMINOLOGY<br />
An FSM can be characterised by a 5-tuple (I, O, M, X,<br />
Y) where I and O are the sets of primary <strong>in</strong>puts and<br />
primary outputs, M is the <strong>in</strong>ternal states, X and Y are the<br />
output and the next state functions, respectively. An FSM<br />
with M states requires a m<strong>in</strong>imum of S state variables for<br />
the assignment, where S = ⎡log<br />
2 M ⎤ and ⎡g ⎤ is the<br />
smallest <strong>in</strong>teger equal to or greater than g. The number of<br />
logically unique assignments for an FSM N is given as<br />
follows.<br />
© 2013 ACADEMY PUBLISHER<br />
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JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1407<br />
S<br />
(2 −1)!<br />
N = (1)<br />
S<br />
(2 − M )! S!<br />
The FSM is commonly represented by a state transition<br />
table (STT). Given the <strong>in</strong>put transition probability of an<br />
FSM, its state transition probability can be computed.<br />
The state transition probability tp ij between state s i and<br />
state s j occurs <strong>in</strong> an arbitrarily long sequence and is given<br />
as follows.<br />
tp = P p<br />
(2)<br />
ij<br />
The steady state probabilities P i can be obta<strong>in</strong>ed via<br />
Gaussian elim<strong>in</strong>ation methods to solve the set of l<strong>in</strong>ear<br />
equations as <strong>in</strong> (3) and (4).<br />
i<br />
i = M 1<br />
∑ −<br />
i<br />
i=<br />
0<br />
ij<br />
P = 1<br />
(3)<br />
j = M<br />
∑ − 1<br />
Pj<br />
j=<br />
0<br />
P = p<br />
(4)<br />
i<br />
The power consumption [15] of a sequential circuit is<br />
proportional to its switch<strong>in</strong>g activity which can be<br />
represented as <strong>in</strong> (5), where C is the capacitance of the<br />
output for the node, V dd is the supply voltage, f clk is the<br />
clock frequency and E is the expected switch<strong>in</strong>g activity.<br />
ji<br />
1 2<br />
P = CVdd<br />
fclk<br />
E<br />
(5)<br />
2<br />
S<strong>in</strong>ce the register capacitance is fixed and cannot be<br />
affected, therefore the E is considered as part of the cost<br />
function <strong>in</strong> terms of power consumption.<br />
i = M<br />
∑∑<br />
− 1 j=<br />
M −1<br />
i=<br />
0 j=<br />
0<br />
E = tp ij dist i j<br />
(6)<br />
where dist i,j represents the hamm<strong>in</strong>g distance between the<br />
cod<strong>in</strong>g of state s i and state s j and tp ij is the total state<br />
transition probability from state s i and state s j as def<strong>in</strong>ed<br />
<strong>in</strong> (2).<br />
III. SIMULATED ANNEALING BASED ALGORITHM<br />
The problem of f<strong>in</strong>d<strong>in</strong>g the state assignment for the<br />
m<strong>in</strong>imisation of power consumption and area is<br />
computationally difficult. GA has been successfully<br />
applied to a variety of computationally difficult problems.<br />
It has been shown that it can produce good results <strong>in</strong> a<br />
reasonable computation time. The basic idea of GA is<br />
<strong>in</strong>itially to generate a breed<strong>in</strong>g pool of potential solutions<br />
to a problem. These solutions are encoded as<br />
chromosomes, and each chromosome is subjected to an<br />
evaluation function which assigns fitness depend<strong>in</strong>g on<br />
the quality of the solution it encodes. Exist<strong>in</strong>g solutions<br />
are recomb<strong>in</strong>ed by crossover operator. Mutation operator<br />
makes random changes <strong>in</strong> a few randomly selected<br />
chromosomes <strong>in</strong> order to prevent premature convergence<br />
by ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g the diversity of the population. The GA<br />
uses a tournament selection method via population<br />
rank<strong>in</strong>g system to reproduce new generation. As a result,<br />
,<br />
the rank<strong>in</strong>g system itself takes significant computational<br />
time. However, <strong>in</strong> most cases only the best solution at last<br />
is required, therefore the entire rank<strong>in</strong>g is not always<br />
necessary. Furthermore, if some parents are not excellent<br />
enough, these solutions have little chance to jo<strong>in</strong> the<br />
competition <strong>in</strong> GA.<br />
Simulated anneal<strong>in</strong>g (SA) algorithm on the other hand<br />
is another method to solve problems such as 3D pack<strong>in</strong>g<br />
problem [16] and s<strong>in</strong>gle conta<strong>in</strong>er load<strong>in</strong>g problem [17].<br />
It starts with high temperature. The <strong>in</strong>spiration of the<br />
algorithm demand an <strong>in</strong>terest<strong>in</strong>g feature related to the<br />
temperature variation to be embedded <strong>in</strong> the operational<br />
characteristics of the algorithm. This necessitates a<br />
gradual reduction of the temperature as the simulation<br />
proceeds. The algorithm starts <strong>in</strong>itially with a high value<br />
temperature, and then it is decreased at each step<br />
follow<strong>in</strong>g some anneal<strong>in</strong>g schedule. However there are<br />
several significant disadvantages of traditional SA, such<br />
as its slow search speed. Hence, <strong>in</strong> order to overcome the<br />
mentioned shortcom<strong>in</strong>gs, follow<strong>in</strong>g simulated anneal<strong>in</strong>g<br />
based algorithm is proposed.<br />
A. Solution Representation<br />
Let the state-code array for an M-state FSM be<br />
S 0 , S1,<br />
, S M −1<br />
, where M is the number of FSM states.<br />
The solution representation is an array of size equal to the<br />
number of states <strong>in</strong> the FSM. Each entry <strong>in</strong> the array is an<br />
<strong>in</strong>teger between 0 and M-1. Take a ten-state mach<strong>in</strong>e<br />
S 0 , S1,<br />
S 2 , S3,<br />
S 4 , S5<br />
, S 6 , S 7 , S8<br />
, S9<br />
for example. One<br />
possible representation is 9, 6, 8, 2, 3, 0, 4, 1, 5, 7, which<br />
is shown <strong>in</strong> Figure 1.<br />
Figure 1. State assignment for ten-state mach<strong>in</strong>e.<br />
B. Rough Anneal<strong>in</strong>g Stage<br />
The proposed simulated anneal<strong>in</strong>g is designed<br />
purposely <strong>in</strong>to two stages as the temperature schedules. In<br />
the rough anneal<strong>in</strong>g stage, it tends to alter the solution<br />
with bigger changes at high temperature, consequently<br />
escape local optima. The rotation swap method randomly<br />
selects the cutt<strong>in</strong>g l<strong>in</strong>e from the representation. The<br />
cutt<strong>in</strong>g l<strong>in</strong>e is treated as a mirror. Copy the state<br />
assignments <strong>in</strong> the left part of the mirror to the right part<br />
of the mirror. Similarly, the right part is copied to the left<br />
part. Figure 2 shows an example of exchange method.<br />
C. Focus<strong>in</strong>g Anneal<strong>in</strong>g Stage<br />
The focus<strong>in</strong>g anneal<strong>in</strong>g stage differs to the previous<br />
anneal<strong>in</strong>g stage, which tends to alter the solution with<br />
smaller changes at low temperature, consequently to<br />
achieve an effective convergence. In this stage, it<br />
randomly selects a state assignment and its neighbour<strong>in</strong>g<br />
state assignment from the representation and swaps these<br />
two state assignments. These two states can be close to<br />
each other, as shown <strong>in</strong> Figure 3, or apart from each other,<br />
as shown <strong>in</strong> Figure 4.<br />
© 2013 ACADEMY PUBLISHER
1408 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
new solution. State entry 9, 2, 3, and 7 from the best<br />
solution form part of new solution. State entry 8, 3, 9, 2, 4<br />
and 6 from current solution form the other part of new<br />
solution. Modification of the new solution is carried out<br />
to make sure that duplicated state entry 2, 3, and 9 do not<br />
appear <strong>in</strong> the solution. By do<strong>in</strong>g so, unassigned state<br />
entry 0, 1 and 5 are filled <strong>in</strong>.<br />
Figure 2. Exchange method.<br />
Figure 3. Swap method for two states close to each other.<br />
Figure 4. Swap method for two states apart from each other.<br />
D. Crossover<br />
Crossover operator is designed to escape the local<br />
optimum <strong>in</strong> the GA. In this paper crossover operator is<br />
adapted <strong>in</strong> the simulated anneal<strong>in</strong>g to generate a new<br />
solution by comb<strong>in</strong><strong>in</strong>g the best solution with the current<br />
solution. Consequently, some potential parts of the<br />
solution can be <strong>in</strong>herited from the previous solution.<br />
It operates as a position-based crossover [18]. An array<br />
of b<strong>in</strong>ary bits is <strong>in</strong>itialised randomly, <strong>in</strong> which the length<br />
of the array equals to the length of the representation.<br />
When 1s appear <strong>in</strong> the array, copy the states from the best<br />
solution to new solution. When 0s appear <strong>in</strong> the array,<br />
copy the states from the current solution to new solution.<br />
S<strong>in</strong>ce each entry of state assignment solution is unique,<br />
cont<strong>in</strong>uous check is required avoid<strong>in</strong>g the repetition of<br />
the same states which is not allowed. If state entry is<br />
duplicated, the first unassigned state entry is assigned.<br />
Figure 5 shows an example of relay operator to generate<br />
Figure 5. Crossover operator.<br />
E. Cost Function<br />
By m<strong>in</strong>imis<strong>in</strong>g (6), low power dissipation could be<br />
achieved. Unfortunately, this may lead to area overhead,<br />
result<strong>in</strong>g <strong>in</strong> power overhead <strong>in</strong> the comb<strong>in</strong>ational part of<br />
the circuit. Therefore, objectives of area and power<br />
should be optimised simultaneously. The total cost<br />
function is C total = γC area + (1-γ) E, where C area is area<br />
function, E is power function and γ is a parameter<br />
specify<strong>in</strong>g the tradeoff of E with respect to C area .<br />
F. Proposed Algorithm<br />
To beg<strong>in</strong> with, an <strong>in</strong>itiation solution is randomly<br />
produced. The anneal<strong>in</strong>g approach is divided <strong>in</strong>to rough<br />
anneal<strong>in</strong>g and focus<strong>in</strong>g anneal<strong>in</strong>g, which is identified by<br />
Temperature threshold T threshold . In the rough anneal<strong>in</strong>g<br />
stage the temperature is high and uses exchange method.<br />
In the focus<strong>in</strong>g anneal<strong>in</strong>g stage the temperature is low<br />
and uses swap methods. The solution is evaluated by the<br />
cost function. The solution is accepted accord<strong>in</strong>g to a<br />
probability P = exp (-∆C/T), where ∆C is the difference<br />
cost between new solution and current solution, T is the<br />
temperature. P is between 0 and 1. If the solution is<br />
improved and kept accord<strong>in</strong>g to P, the new solution will<br />
be compared with the best recorded solution to decide<br />
whether updat<strong>in</strong>g the best record is necessary. If new<br />
solution is rejected <strong>in</strong>stead, this solution is then ignored<br />
and reverses the current solution. Outer loop updates the<br />
temperature. The temperature schedules at each outer<br />
iteration. In the <strong>in</strong>ner loop it generates possible solutions<br />
at each temperature. The algorithm term<strong>in</strong>ates when<br />
reach<strong>in</strong>g the lowest temperature and the output will be the<br />
best record. The pseudo code is shown <strong>in</strong> Algorithm 1.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1409<br />
Algorithm 1: Two stage Simulated Anneal<strong>in</strong>g<br />
Inputs: Temperature coefficient α<br />
Number of state variables N<br />
Exit temperature T 0<br />
Temperature threshold T threshold<br />
Outputs: The best solution S best<br />
beg<strong>in</strong><br />
<strong>in</strong>itialise a solution S current and temperature T<br />
while (T < T 0 ) { // outer loop<br />
k = 0<br />
while (k < N 3 ) { // <strong>in</strong>ner loop<br />
if (T > T threshold ) S new = generate solution via<br />
exchange method<br />
else<br />
S new = generate solution via swap methods<br />
k= k + 1<br />
r = random (0, 1)<br />
∆C = cost (S new ) – cost (S current )<br />
if (r < exp (–∆C/T)) {<br />
S current = S new<br />
if (cost (S best ) > cost (S current ))<br />
S best = S current<br />
}<br />
} // end of <strong>in</strong>ner loop<br />
T =αT<br />
} // end of outer loop<br />
Output the best solution S best<br />
IV. EXPERIMENTAL RESULTS<br />
The algorithm has been implemented <strong>in</strong> C++ and the<br />
results have been obta<strong>in</strong>ed on a personal computer with<br />
an INTEL CPU 2.4 GHz and 4 GB RAM. A Gaussian<br />
elim<strong>in</strong>ation method is used to f<strong>in</strong>d the total transition<br />
probabilities accord<strong>in</strong>g to the STT of an FSM.<br />
ESSPRESSO is used to m<strong>in</strong>imise the circuit for each state<br />
assignment. The product terms from this m<strong>in</strong>imisation<br />
determ<strong>in</strong>e the number of cubes for that assignment.<br />
Switch<strong>in</strong>g activity is calculated by (6). T, T threshold and T 0<br />
are set to 10000, 100 and 0.1, respectively. In order to<br />
balance the required solution quality and computational<br />
time, temperature schedule coefficient α is selected to<br />
0.95 and 0.8 <strong>in</strong> the rough anneal<strong>in</strong>g stage and focus<strong>in</strong>g<br />
anneal<strong>in</strong>g stage, respectively. Based on the numerous<br />
experimental results, when γ is 0.3, it performs the best<br />
trade-off between area and power consumption.<br />
The results are given <strong>in</strong> Table I, <strong>in</strong> which the first<br />
column shows the name of the circuit, the second column<br />
shows the number of states for the given circuit <strong>in</strong> the<br />
first column. Next three columns show comparison<br />
results among GA [8], MOGA [7] and the proposed<br />
method <strong>in</strong> terms of CPU time. The proposed method can<br />
convergence quicker than results compared to GA<br />
method <strong>in</strong> [8]. MOGA m<strong>in</strong>imises the logical expressions<br />
via communication with ESSPRESSO, result<strong>in</strong>g that it<br />
takes significant more time than the proposed method.<br />
It can be seen <strong>in</strong> Table II that on average the proposed<br />
method produces results requir<strong>in</strong>g 13.2% fewer product<br />
terms and 44.1% less switch<strong>in</strong>g activity compared to<br />
results obta<strong>in</strong>ed from NOVA [19]. Methods used <strong>in</strong> [20]<br />
and [21] achieve good power reduction but pay<strong>in</strong>g<br />
penalty of area consumption. MOGA [7] and GA [8]<br />
perform well <strong>in</strong> both area and power. The proposed<br />
algorithm outperforms other methods <strong>in</strong> both area sav<strong>in</strong>g<br />
and less power consumption <strong>in</strong> the tested suite.<br />
TABLE I.<br />
RECENTLY PUBLISHED RESULTS IN TERMS OF CPU TIME<br />
Circuits States GA[8] (s) MOGA[7] Ours (s)<br />
bbara 10 0.17 0h and 8 m<strong>in</strong>s 0.12<br />
cse 16 0.59 3hs and 9 m<strong>in</strong>s 1.1<br />
donfile 24 0.77 6hs and 4 m<strong>in</strong>s 1.58<br />
keyb 19 1.61 3hs and 32 m<strong>in</strong>s 0.87<br />
modulo12 12 0.13 5hs and 56 m<strong>in</strong>s 0.15<br />
planet 48 2.75 25hs and 23 m<strong>in</strong>s 2.77<br />
s1 20 4.37 6hs and 0 m<strong>in</strong> 3.94<br />
styr 30 4.44 6hs and 5 m<strong>in</strong>s 2.57<br />
ex1 20 3.26 6hs and 7 m<strong>in</strong>s 2.68<br />
ex4 14 0.27 6hs and 1 m<strong>in</strong>s 0.38<br />
opus 10 0.21 0h and 40 m<strong>in</strong>s 0.22<br />
Total 606 18.57 69h and 5 m<strong>in</strong>s 16.38<br />
V. CONCLUSIONS<br />
In the paper, two-stage simulated anneal<strong>in</strong>g based<br />
algorithm approach to the state assignment problem is<br />
proposed with the aim of m<strong>in</strong>imis<strong>in</strong>g area and power<br />
dissipation for sequential circuits. By us<strong>in</strong>g designed twostage<br />
anneal<strong>in</strong>g approach, the algorithm is able to f<strong>in</strong>d the<br />
best assignment with fast convergence, which has<br />
reduced switch<strong>in</strong>g activity to m<strong>in</strong>imise the power<br />
dissipation and the area simultaneously. By comb<strong>in</strong>g the<br />
best and current solutions, it utilises the experience of<br />
past solutions, overcom<strong>in</strong>g the problem that rank<strong>in</strong>g<br />
system <strong>in</strong> GA selection takes significant runtime. As a<br />
result, the algorithm outperforms the exist<strong>in</strong>g GA-based<br />
FSM state-encod<strong>in</strong>g strategies achiev<strong>in</strong>g 13.2% fewer<br />
product terms and 44.1% less switch compared to NOVA<br />
and is therefore more suitable for area/power-optimised<br />
realisation of FSMs.<br />
ACKNOWLEDGMENT<br />
This work was supported by a grant (No. 11MS011)<br />
from State Key Lab of ASIC and System, Ch<strong>in</strong>a.<br />
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[8] Y. Xia, and A. E. A. Alma<strong>in</strong>i, “Genetic algorithm based<br />
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[9] S. Chattopadhyay and P. Reddy, “F<strong>in</strong>ite state mach<strong>in</strong>e state<br />
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[10] S. Chattopadhyay, “Area conscious state assignment with<br />
flip flop and output polarity selection for f<strong>in</strong>ite state<br />
mach<strong>in</strong>e synthesis genetic algorithm approach,” Comput. J.,<br />
vol. 48, pp. 443-450, 2005.<br />
[11] W. T. Shiue, “Novel state m<strong>in</strong>imization and state<br />
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[12] S. Goren and F. J. Ferguson, “On state reduction of<br />
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[13] W. M. Aly, “Solv<strong>in</strong>g the state assignment problem us<strong>in</strong>g<br />
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[14] T. A. Dolotta, and E.J. McCluskey, “The cod<strong>in</strong>g of <strong>in</strong>ternal<br />
states of sequential circuits,” IEEE Trans. Electron.<br />
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[15] S. Chattopadhyay, and P. N. Reddy, “F<strong>in</strong>ite state mach<strong>in</strong>e<br />
state assignment target<strong>in</strong>g low power consumption,” IET<br />
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[16] Y. Q. Sheng, A. Takahashi, S. Ueno, “2-Stage Simulated<br />
Anneal<strong>in</strong>g with Crossover Operator for 3D-Pack<strong>in</strong>g<br />
Volume M<strong>in</strong>imization,” Proceed<strong>in</strong>gs of the 17th Workshop<br />
on Synthesis And System Integration of Mixed Information<br />
Technologies, pp. 227-232, 2012.<br />
[17] H. T. Wang; Z. J. Wang; J. Luo, “A simulated anneal<strong>in</strong>g<br />
algorithm for s<strong>in</strong>gle conta<strong>in</strong>er load<strong>in</strong>g problem,”<br />
Proceed<strong>in</strong>gs of the 9th Intl. Conf. on Service Systems and<br />
Service Management, pp. 551-556, 2012.<br />
[18] A. E. A. Alma<strong>in</strong>i, N. Zhuang, and F. Bourset,<br />
“M<strong>in</strong>imisation of multioutput Reed–Muller b<strong>in</strong>ary decision<br />
diagrams us<strong>in</strong>g hybrid genetic algorithm,” IEE Electron.<br />
Lett., vol. 31, pp. 1722-1723, 1995.<br />
[19] T. Villa, and A. Sangiovanni-V<strong>in</strong>centelli, “NOVA: state<br />
assignment of f<strong>in</strong>ite state mach<strong>in</strong>e for optimal two-level<br />
logic implementation,” IEEE Trans. Comput. Aided Des.<br />
Integr. Circuits Syst., vol. 9, pp. 905-924, 1990.<br />
[20] S. K. Hong, I. C. Park, S. H. Hwang, and C. M. Kyung,<br />
“State assignment <strong>in</strong> f<strong>in</strong>ite state mach<strong>in</strong>es for m<strong>in</strong>imal<br />
switch<strong>in</strong>g power consumption,” IEE Electron. Lett., vol. 30,<br />
pp. 627-629, 1994.<br />
[21] S. J. Wang, and M. D. Horng, “State assignment of f<strong>in</strong>ite<br />
state mach<strong>in</strong>es for low power applications,” IEE Electron.<br />
Lett., vol. 32, pp2323-2324, 1996.<br />
Meng Yang received Bachelor of<br />
Eng<strong>in</strong>eer<strong>in</strong>g (Honor) degree <strong>in</strong> Electrical<br />
Eng<strong>in</strong>eer<strong>in</strong>g from Shanghai University,<br />
Shanghai, Ch<strong>in</strong>a, <strong>in</strong> 1999. He received<br />
Master of Science with dist<strong>in</strong>ction <strong>in</strong><br />
Electronics and Communication<br />
Eng<strong>in</strong>eer<strong>in</strong>g and Ph.D. <strong>in</strong> Electronics from<br />
School of Eng<strong>in</strong>eer<strong>in</strong>g Ed<strong>in</strong>burgh Napier<br />
University, Ed<strong>in</strong>burgh, UK, <strong>in</strong> 2002 and 2006, respectively.<br />
Currently he is a lecturer of Department of Microelectronics,<br />
School of Information Science and Technology, Fudan<br />
University, Shanghai, Ch<strong>in</strong>a. His research <strong>in</strong>terests <strong>in</strong>clude<br />
algorithms <strong>in</strong> FPGA design automation, logic synthesis, and<br />
dynamic reconfigurable FPGA automation design. He has<br />
published more than 30 research papers.<br />
Dr. Yang is a member of IET and Chairman of Young<br />
Member Section of IET Shanghai Branch.<br />
TABLE II.<br />
EXPERIMENTAL RESULTS SHOWING POWER AND AREA IN COMPARISON<br />
Circuits<br />
NOVA[19] MOGA[7] GA[8] Hong[20] Wang[21] This paper<br />
area Power area power area Power Area power area power area Power<br />
bbara 24 0.495 22 0.49 22 0.317 26 0.295 26 0.279 22 0.277<br />
bbsse 30 1.5 28 0.663 27 0.783 31 0.856 31 0.776 27 0.758<br />
cse 46 0.604 43 0.39 43 0.355 50 0.292 48 0.239 43 0.250<br />
donfile 28 1.75 22 1.375 36 1.6 40 1.083 45 1.125 22 1.458<br />
keyb 48 1.466 46 0.98 46 0.674 52 0.647 58 0.556 46 0.533<br />
modulo12 12 1 10 0.75 12 0.583 12 0.583 12 0.5 10 0.568<br />
planet 87 2.831 81 2.49 86 2.424 101 1.153 103 0.984 81 1.680<br />
s1 80 1.698 43 1.37 66 1.48 85 1.131 91 1.175 43 1.188<br />
sand 97 1.085 94 0.585 89 0.765 110 0.604 109 0.61 92 0.666<br />
styr 94 1.278 78 1.1 88 0.943 101 0.578 99 0.553 78 0.578<br />
ex1 44 1.358 48 0.78 52 0.842 49 0.755 47 1.135 48 0.754<br />
ex4 19 1.316 13 0.568 14 0.421 16 0.495 18 0.957 13 0.476<br />
opus 16 0.812 15 0.49 15 0.556 17 0.524 17 0.712 15 0.471<br />
tra<strong>in</strong>11 9 0.619 10 0.414 10 0.339 9 0.36 10 0.714 10 0.302<br />
Total 634 17.812 553 12.445 606 12.082 699 9.356 714 10.315 550 9.959<br />
Improved% 0% 0% -13% -30% -4% -32% 10% -47% 13% -42% -13.2% -44.1%<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1411<br />
A Rotation-based Data Buffer<strong>in</strong>g Architecture for<br />
Convolution Filter<strong>in</strong>g <strong>in</strong> a Field Programmable<br />
Gate Array<br />
Zhijian Lu<br />
College of Computer Science and Technology Harb<strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g University, Harb<strong>in</strong>, Ch<strong>in</strong>a<br />
Email: luzhijian@hrbeu.edu.cn<br />
Yanxia Wu, Zhenhua Guo, Guochang Gu<br />
College of Computer Science and Technology Harb<strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g University, Harb<strong>in</strong>, Ch<strong>in</strong>a<br />
Email: {wuyanxia, guozhenhua, guguochang}@hrbeu.edu.cn<br />
Abstract—Convolution filter<strong>in</strong>g applications range from<br />
image recognition and video surveillance. Two observations<br />
drive the design of a new buffer<strong>in</strong>g architecture for convolution<br />
filters. First, the convolutional operations are <strong>in</strong>herently<br />
local; hence every pixel of the output feature maps is calculated<br />
by the neighbor<strong>in</strong>g pixels of the <strong>in</strong>put feature maps.<br />
Even though the operation is simple, the convolution filter<strong>in</strong>g<br />
is both computation-<strong>in</strong>tensive and memory-<strong>in</strong>tensive.<br />
For real-time applications, large amounts of on-chip memories<br />
are required to support massively parallel process<strong>in</strong>g<br />
architectures. Second, to avoid access to external memories<br />
directly, the data that are already stored <strong>in</strong> on-chip memories<br />
should be used as many times as possible. Based on these<br />
two observations, we show that for a given throughput<br />
rate and off-chip memory bandwidth, a rotation-based data<br />
buffer<strong>in</strong>g architecture provide the optimum area-utilization<br />
results for a particular design po<strong>in</strong>t, which are commonly<br />
used applications <strong>in</strong> recognition area.<br />
Index Terms—convolution filter<strong>in</strong>g, Field Programmable<br />
Gate Arrays (FPGAs), data buffer<strong>in</strong>g<br />
I. INTRODUCTION<br />
Convolution filters are the computational models that<br />
are widely used <strong>in</strong> recognition and video process<strong>in</strong>g doma<strong>in</strong>s<br />
[1][2][3][4]. The computation of convolution requires<br />
not only the high computational capability but also<br />
large memory bandwidth, especially when high-def<strong>in</strong>ition<br />
images and videos have to be processed <strong>in</strong> real-time. In<br />
these applications, convolution filter<strong>in</strong>g plays an essential<br />
role [5][6]. Generally, external memories are used to conta<strong>in</strong><br />
<strong>in</strong>put image pixels, but the memory bandwidth cannot<br />
satisfy the requirement of the optimal throughput directly.<br />
Hence <strong>in</strong>termediate buffers by means of on-chip<br />
memories are adopted to avoid access to external memories<br />
directly [7][8]. To load as many pixel values as needed<br />
to the convolution filter <strong>in</strong> one cycle, multiple memory<br />
ports are attached to <strong>in</strong>termediate data buffers. Once a<br />
pixel value is loaded, it can be reused for the correspond<strong>in</strong>g<br />
successive convolutions to avoid access<strong>in</strong>g it from<br />
off-chip memories repetitively. As a result, the requirements<br />
for off-chip memory bandwidth are reduced.<br />
Convolution architecture with a complete convolution<br />
architecture is adopted <strong>in</strong> [7], where a set of l<strong>in</strong>ear shift<br />
registers are used to move a w<strong>in</strong>dow over the <strong>in</strong>put<br />
image. The <strong>in</strong>put image is divided <strong>in</strong> rows, each with a<br />
fixed length accord<strong>in</strong>g to the <strong>in</strong>put image row length, and<br />
the height accord<strong>in</strong>g to the convolution w<strong>in</strong>dow height.<br />
Each pixel <strong>in</strong> the <strong>in</strong>put image needs to be loaded only<br />
once to the <strong>in</strong>termediate data buffer and with a fixed m<strong>in</strong>imum<br />
external memory bandwidth. In case the size of<br />
<strong>in</strong>put image or convolution w<strong>in</strong>dow become large, FPGA<br />
implementations become very expensive, which will cost<br />
a significant amount of FPGA resources [7][8].<br />
There are alternative buffer<strong>in</strong>g architectures that <strong>in</strong>ternal<br />
buffers only store a small portion of pixels [7][9].<br />
Each group of shift registers <strong>in</strong> the convolution w<strong>in</strong>dow<br />
receives the pixels belong<strong>in</strong>g to consecutive rows of <strong>in</strong>put<br />
image. Compared with the aforementioned methods, a<br />
great shift register reduction is achieved. However, multiple-dataflow<br />
is needed to feed data to the <strong>in</strong>ternal buffer.<br />
Pixels <strong>in</strong> the <strong>in</strong>put image need to be read repetitively<br />
from external memories depend<strong>in</strong>g on the size of convolution<br />
w<strong>in</strong>dow. And to keep the maximum throughput<br />
rate, this leads to a sharp <strong>in</strong>crease <strong>in</strong> terms of external<br />
memory bandwidth requirement.<br />
In this paper, we are concerned with the implementation<br />
of convolution filters <strong>in</strong> FPGA and we design a alternative<br />
buffer<strong>in</strong>g architecture for convolution filters that<br />
shows good balance between on-chip resource utilization<br />
and external memory bus bandwidth.<br />
II. ROTATION-BASED DATA BUFFERING ARCHITECTURE<br />
Yanxia Wu is the correspond<strong>in</strong>g author.<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1411-1416
1412 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 1. Conceptual view of an convolver and an image<br />
In this section, we will first <strong>in</strong>troduce the convolution<br />
filter<strong>in</strong>g implementation strategy. The advantages and<br />
disadvantages of exist<strong>in</strong>g implementation architectures<br />
will be discussed. Then we will present the rotation-based<br />
data buffer<strong>in</strong>g architecture. In Fig. 1, we show the conceptual<br />
view of a convolution filter mov<strong>in</strong>g over an<br />
<strong>in</strong>put image, which will be used <strong>in</strong> the follow<strong>in</strong>g<br />
sections.<br />
A. Convolution Filter Implementation Strategy<br />
The convolution of an image is def<strong>in</strong>ed by equation<br />
1:<br />
<br />
∑ ∑ , ∙ ,<br />
,<br />
R<br />
S<br />
Input Image<br />
/ /<br />
/ /<br />
(1)<br />
<br />
where , is the convolved pixel on the output image,<br />
, is the pixel value from the <strong>in</strong>put image, and , is<br />
the convolution kernel weight. To calculate the convolution<br />
, , each pixel , from a w<strong>in</strong>dow of <strong>in</strong>put<br />
<br />
image centered on , is multiplied by the correspond<strong>in</strong>g<br />
convolution kernel of weights, and then the<br />
products are accumulated to produce the output value.<br />
<br />
Because the two-dimensional convolution , of each<br />
pixel , requires the values of its 1 immediate<br />
neighbors before be<strong>in</strong>g able to process that pixel, more<br />
columns than needed will be read with<strong>in</strong> the same transaction.<br />
Each output pixel requires multiplyaccumulations,<br />
all of which can be performed <strong>in</strong> parallel.<br />
To accelerate the computation of convolution filter, multiple<br />
data <strong>in</strong> a convolution w<strong>in</strong>dow need to be accessed<br />
simultaneously, so the calculations can be performed <strong>in</strong><br />
parallel.<br />
B. Multiple Dataflow S<strong>in</strong>gle Convolution Architecture<br />
(MDSCA)<br />
In order to elim<strong>in</strong>ate the shift register arrays <strong>in</strong> [7],<br />
multiple dataflow s<strong>in</strong>gle convolution architectures are<br />
adopted <strong>in</strong> [8][10]. In these architectures, small portion of<br />
image pixels are loaded to the convolution filter. However,<br />
with fewer shift register arrays, the pixels can no<br />
longer be loaded to the convolution w<strong>in</strong>dow <strong>in</strong> zigzag<br />
order. Instead of that, pixels belong<strong>in</strong>g to consecutive<br />
rows are read <strong>in</strong>to the shift register simultaneously.<br />
Groups of FIFOs are <strong>in</strong>cluded to feed the pixels to the<br />
shift registers. After one column of pixels are fed <strong>in</strong>to the<br />
convolution filter, the convolution w<strong>in</strong>dow moves to a<br />
next position.<br />
Fig. 2 shows a multiple dataflow s<strong>in</strong>gle convolution<br />
architecture us<strong>in</strong>g an <strong>in</strong>put/output bus, which can completely<br />
elim<strong>in</strong>ate the shift register arrays <strong>in</strong> [7]. The convolution<br />
w<strong>in</strong>dow pixel registers receive the pixels belong<strong>in</strong>g<br />
to consecutive rows of the orig<strong>in</strong>al image through <br />
stacks. Multiple dataflow s<strong>in</strong>gle convolution architecture<br />
requires much larger bandwidth than the s<strong>in</strong>gle dataflow<br />
architecture. The shift register arrays are completely<br />
elim<strong>in</strong>ated. Extra memory bandwidth is used to reduce<br />
the number of shift registers. To compute a s<strong>in</strong>gle cycle<br />
convolution, one new pixel per row is needed at<br />
every cycle. The total of pixels transferred and one<br />
result produced means that a bandwidth of 1 bytes<br />
per cycle is needed.<br />
C. S<strong>in</strong>gle Dataflow Complete Convolution Architecture<br />
(SDCCA)<br />
To avoid directly access to external memories, FPGA<br />
on-chip memories are used as <strong>in</strong>termediate data buffers<br />
[7]. In Fig. 3, a s<strong>in</strong>gle dataflow complete convolution<br />
architecture, makes use of on-chip shift register arrays to<br />
move a w<strong>in</strong>dow over the <strong>in</strong>put image. To extract<br />
pixels from <strong>in</strong>put image, a s<strong>in</strong>gle dataflow strategy has<br />
been adopted. Pixels are fed from external memories <strong>in</strong> a<br />
zigzag order, until 1 complete l<strong>in</strong>es and the first <br />
pixels <strong>in</strong> the next l<strong>in</strong>e are conta<strong>in</strong>ed with<strong>in</strong> a series of<br />
l<strong>in</strong>ear shift registers. From that moment on, all the pixels<br />
belong<strong>in</strong>g to the first convolution w<strong>in</strong>dow are<br />
available for the process<strong>in</strong>g element. Each time a new<br />
pixel is loaded, the convolution w<strong>in</strong>dow moves to a new<br />
position until the entire image has been visited. The<br />
throughput of this architecture is one clock per pixel. In<br />
[7], 1 sets of shift registers with a length of ,<br />
are employed to keep data before mov<strong>in</strong>g them to the<br />
convolution filter, and sets of registers, each with <br />
shift registers, are used for the convolution filter. These<br />
shift registers, which enable arbitrary size convolution<br />
filter to work with a s<strong>in</strong>gle data stream, require no more<br />
than one pixel per clock external memory bandwidth.<br />
Pixels <strong>in</strong> the <strong>in</strong>put image need to be read only once. The<br />
side-effect of this architecture is that <strong>in</strong> order to make this<br />
s<strong>in</strong>gle data stream architecture work, 1 complete<br />
rows must be read from external memory first, therefore<br />
stor<strong>in</strong>g these data with<strong>in</strong> a set of shift registers would be<br />
very expensive <strong>in</strong> FPGA implementation when the size of<br />
<strong>in</strong>put image or the size of convolution filter is large.<br />
D. Rotation-based Multiple dataflow Buffer<strong>in</strong>g Architecture<br />
(RMDBA)<br />
In order to reuse data that are already stored <strong>in</strong> on-chip<br />
buffers as many times as possible, we proposed a rotation-based<br />
data buffer<strong>in</strong>g architecture. Fig.4 illustrates <br />
cont<strong>in</strong>uous convolution filter <strong>in</strong> a row-wise direction,<br />
where the two adjacent filter w<strong>in</strong>dows share 1 columns.<br />
The architecture of these slid<strong>in</strong>g w<strong>in</strong>dows <strong>in</strong>cludes<br />
R contiguous convolution filter w<strong>in</strong>dows, which share<br />
1 columns <strong>in</strong> the row-wise direction. If the calculations<br />
of these convolution kernels are performed at the<br />
same time, a much higher level of data reus<strong>in</strong>g will be<br />
© 2013 ACADEMY PUBLISHER
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F<br />
I<br />
F<br />
O<br />
S<br />
shift<br />
registers<br />
off-chip memory<br />
and FIFO<br />
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.<br />
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F<br />
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shift<br />
registers<br />
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convolution filter array<br />
F<br />
I<br />
F<br />
O<br />
S<br />
shift<br />
registers<br />
Figure 2. Multiple dataflow s<strong>in</strong>gle convolution architecture<br />
off-chip memory and FIFO<br />
S<br />
shift<br />
registers<br />
(N-S) Shift registers<br />
.<br />
.<br />
.<br />
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.<br />
.<br />
.<br />
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S<br />
shift<br />
registers<br />
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convolution filter array<br />
(N-S) Shift registers<br />
S<br />
shift<br />
registers<br />
achieved compared with the multiple dataflow s<strong>in</strong>gle<br />
convolution architecture. Fig. 5 illustrates the rotationbased<br />
multiple dataflow architecture we proposed. The<br />
number of shift register arrays is extended to Y to hold all<br />
the pixels <strong>in</strong> the area as depicted <strong>in</strong> Fig. 4. Unlike<br />
the multiple dataflow s<strong>in</strong>gle convolution architecture and<br />
the s<strong>in</strong>gle dataflow complete convolution architecture, the<br />
pixel data <strong>in</strong> each set of shift register array are not simultaneously<br />
fed to the convolution filter w<strong>in</strong>dow, but <strong>in</strong> a<br />
serial type <strong>in</strong>stead. One register <strong>in</strong> the shift register group<br />
is useable <strong>in</strong> each cycle, and a rotationally self<strong>in</strong>crement<strong>in</strong>g<br />
counter is used to address the register <strong>in</strong> the<br />
output. Consequently, pixels <strong>in</strong> all of a same row <strong>in</strong> the<br />
<strong>in</strong>put, belong<strong>in</strong>g to adjacent w<strong>in</strong>dows <strong>in</strong> the row-wise<br />
direction, are available to the convolution filter <strong>in</strong> each<br />
cycle. After cycles, all the data <strong>in</strong> the place have<br />
Figure 3. S<strong>in</strong>gle dataflow complete convolution architecture<br />
been sent to the convolution filter, and then shift register<br />
arrays will be updated. A new row of data will be moved<br />
<strong>in</strong> from the FIFO and moves the area to next position<br />
effectively. The architecture for the convolution filter<br />
us<strong>in</strong>g rotation-based data buffer<strong>in</strong>g architecture is not the<br />
same as the aforementioned architectures. For each <br />
convolution w<strong>in</strong>dow, <strong>in</strong>put pixels are fed column-bycolumn,<br />
therefore one-column convolution l<strong>in</strong>e can be<br />
calculated, and it will take cycles to complete all the<br />
calculation for each convolution w<strong>in</strong>dow. When neighbor<strong>in</strong>g<br />
w<strong>in</strong>dows are available, entire R one-column convolution<br />
can be processed simultaneously.<br />
In order to achieve the throughput rate of 1 cycle/pixel,<br />
multiple dataflow must be loaded to update the convolution<br />
w<strong>in</strong>dow. Compared with the multiple dataflow s<strong>in</strong>gle<br />
© 2013 ACADEMY PUBLISHER
1414 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 4. R simultaneous convolution w<strong>in</strong>dows <strong>in</strong> a area<br />
off-chip memory<br />
. . . . . .<br />
F<br />
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R . . . 1<br />
R . . . 1<br />
R . . . 1<br />
. . . . . .<br />
convolution filter array<br />
Figure 5. Rotation-based data buffer<strong>in</strong>g architecture<br />
convolution architecture the w<strong>in</strong>dow <strong>in</strong> the rotation-based<br />
architecture is updated every cycle. In this case, shift<br />
registers can move every cycles. pixels <strong>in</strong> all will be<br />
loaded from off-chip memories every cycles. So the<br />
external memory bandwidth is / pixels/clock. This<br />
means that for most convolution filter applications approximately<br />
twice of the external memory bandwidth<br />
requirement is needed.<br />
III. ARCHITECTURE SELECTION<br />
In this section, we will consider an <strong>in</strong>put image size of<br />
© 2013 ACADEMY PUBLISHER
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1280720 with 8 bits/pixel and a convolution kernel size<br />
of 77 as a case study. The operation will fetch image<br />
pixels from external memories, and store back to external<br />
memories after the convolution operation. In addition to<br />
this we will use a memory bus word length of 256-bits<br />
and a burst length (BL) of 8 words (i.e. 16 pixels). In<br />
Table I, we have summarized the ma<strong>in</strong> features of the two<br />
and the proposed architectures: area-utilization measured<br />
<strong>in</strong> terms of register pixels and memory pixels. Flip-flop<br />
count was obta<strong>in</strong>ed by multiply<strong>in</strong>g the number of shift<br />
registers and memory pixels by bit per pixel;<br />
TABLE 1.<br />
FEATURES OF DIFFERENT CONVOLUTION FILTER FOR A WINDOW<br />
architecture<br />
register<br />
pixels<br />
memory pixels<br />
throughput<br />
(cycles/pixel)<br />
ff count<br />
bandwidth (pixels/cycle)<br />
MDSCA 1 5496 7<br />
SDCCA <br />
1 <br />
<br />
1 49336 1<br />
RMDBA 1 2392 1.9<br />
TABLE 2.<br />
AREA UTILIZATION OF DIFFERENT ARCHITECTURES FOR VARIOUS CONVOLUTION FILTER WINDOW SIZE<br />
filter size<br />
MDSCA SDCCA RMDBA<br />
flip-flop count flip-flop count flip-flop count<br />
33 456 16536 760<br />
55 840 32936 1512<br />
77 5496 49336 2392<br />
99 1800 65736 3400<br />
11 11 2376 82136 4536<br />
13 13 3016 98536 5800<br />
15 15 3720 114936 7192<br />
17 17 4488 131336 8712<br />
19 19 5320 147736 10360<br />
throughput, given <strong>in</strong> terms of cycles/pixel; and external<br />
memory bandwidth requirements, given <strong>in</strong> terms of pixels/cycle.<br />
We used different FPGA resources to implement<br />
FIFOs and shift registers depend<strong>in</strong>g on specific<br />
FPGA devices.<br />
For comparison, the area-utilization will be evaluated<br />
<strong>in</strong> terms of flip-flops. The last two columns of Table I<br />
show the results of flip-flop count and external memory<br />
bandwidth requirement for the case study. The SCPB<br />
architecture shows the most area-efficient feature at the<br />
cost of much more requirement of the external memory<br />
bandwidth.<br />
In order to choose the optimum architecture for a particular<br />
design po<strong>in</strong>t, a suitable metric that consists <strong>in</strong><br />
maximiz<strong>in</strong>g the throughput with respect to the amount of<br />
resources will be used. The evaluation metric was proposed<br />
<strong>in</strong> [10] that the product throughput <strong>in</strong> terms of cycles/pixel<br />
times flip-flop number is the metric. For a particular<br />
design po<strong>in</strong>t, the architecture will m<strong>in</strong>imize the<br />
metric value and maximize the degree of area efficiency.<br />
We used the same concept <strong>in</strong> our architecture. Table 2<br />
shows the correspond<strong>in</strong>g product of flip-flop count and<br />
throughput for convolution w<strong>in</strong>dow size from 3 to 19 for<br />
the three architectures. We assumed a same output<br />
memory bandwidth of 1 pixel/cycle. In Fig. 6, we show<br />
the aforementioned metric comparisons and the rema<strong>in</strong><strong>in</strong>g<br />
variable are the same described for the case study. In<br />
the bar diagram <strong>in</strong> Fig. 6, we can observe that RMDBA<br />
architecture is superior to the rest of the architecture for<br />
w<strong>in</strong>dow size 7, and for the other w<strong>in</strong>dow size MDSCA is<br />
superior. W<strong>in</strong>dow size 5 and 7 are the most frequently<br />
used convolution w<strong>in</strong>dow <strong>in</strong> practical applications. As the<br />
size of <strong>in</strong>put image gets larger, tradeoffs must be made,<br />
depend<strong>in</strong>g on different FPGA resources and available offchip<br />
memory bandwidth.<br />
IV. CONCLUSIONS<br />
In this paper, we proposed a rotation-based data buffer<strong>in</strong>g<br />
architecture for convolution filter<strong>in</strong>g <strong>in</strong> FPGA. Compared<br />
with the direct implementation of the prior-arts, the<br />
new technique requires less FPGA resources and lowers<br />
off-chip memory bandwidth and reta<strong>in</strong>s the optimum<br />
throughput for a particular design po<strong>in</strong>t, therefore it is suitable<br />
for low-cost FPGA implementation.<br />
ACKNOWLEDGEMENTS<br />
This work is supported by the National Natural Science<br />
Foundation of Ch<strong>in</strong>a No. 61003036 and the Natural<br />
Science Foundation of Heilongjiang Prov<strong>in</strong>ce of Ch<strong>in</strong>a<br />
under Grant No. QC2010049 and Fundamental Research<br />
Funds for the Central Universities (No. HEUCFT1202,<br />
No. HEUCF100606).<br />
© 2013 ACADEMY PUBLISHER
1416 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 6. Bar diagram compar<strong>in</strong>g the area efficiency metric for different architectures and for w<strong>in</strong>dow sizes from 3x3 to 19x19 us<strong>in</strong>g the parameters of<br />
the case study. The lower the bar, the more efficient.<br />
REFERENCE<br />
[1] Gonzalez, R.C. and R.E. Woods, “Digital Image Process<strong>in</strong>g,”<br />
Prentice Hall Press, 2002<br />
[2] B. S. Wu, C. C. Hsieh and C. C. Lee, “A Distance Computer<br />
Vision Assisted Yoga Learn<strong>in</strong>g System,” Journal of<br />
Computers, 11(6): pp.2382-2388, 2011<br />
[3] Z. Wang and X. Sun, “Orthogonal Maximum Marg<strong>in</strong> Projection<br />
for Face Recognition,” Journal of Computers, 2(7):<br />
pp.377-383, 2012<br />
[4] B. Zhu and W. J<strong>in</strong>, “Radar Emitter Signal Recognition<br />
Based on EMD and Neural Network,” Journal of Computers,<br />
6(7): pp.1413-1420, 2012<br />
[5] Hecht, V. and K. Ronner, “An Advanced Programmable<br />
2D-convolution Chip for Real Time Image Process<strong>in</strong>g,”<br />
IEEE International Sympoisum on Circuits and Systems,<br />
pp.1897-1900, 1991<br />
[6] Leblebici, Y., et al., “A <strong>Full</strong>y Pipel<strong>in</strong>ed Programmable Real-time<br />
(3×3) Image Filter Based on Capacitive Thresholdlogic<br />
gates,” Proceed<strong>in</strong>gs of IEEE International Symposium<br />
on Circuits and Systems, vol.3, pp. 2072-2075, 1997<br />
[7] Bosi, B., G. Bois, and Y. Savaria, “Reconfigurable Pipel<strong>in</strong>ed<br />
2-D Convolvers for Fast Digital Signal Process<strong>in</strong>g,”<br />
IEEE Transactions on Very Large Scale Integration (VLSI)<br />
Systems, 7(3): pp. 299-308, 1999<br />
[8] Liang, X., J. Jean, and K. Tomko, “Data Buffer<strong>in</strong>g and Allocation<br />
<strong>in</strong> Mapp<strong>in</strong>g Generalized Template Match<strong>in</strong>g on<br />
Reconfigurable Systems,” The Journal of Supercomput<strong>in</strong>g,<br />
19(1): pp. 77-91, 2001<br />
[9] Nakajima, M., et al., “A 40GOPS 250mw Massively Parallel<br />
Processor Based on Matrix Architecture,” IEEE International<br />
Solid-State Circuits Conference, pp.1616-1625,<br />
2006<br />
[10] Cardells-Tormo, F. and P.L. Mol<strong>in</strong>et, “Area-efficient 2-D<br />
Shift-variant Convolvers for FPGA-based Digital Image<br />
Process<strong>in</strong>g,” IEEE Workshop on Signal Process<strong>in</strong>g Systems<br />
Design and Implementation, pp. 209-213, 2005<br />
Zhijian Lu is a Ph.D. student <strong>in</strong> College of Computer Science<br />
and Technology of Harb<strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g University, Harb<strong>in</strong>, Ch<strong>in</strong>a.<br />
His current research <strong>in</strong>terest <strong>in</strong>cludes neural network, reconfigurable<br />
comput<strong>in</strong>g and image process<strong>in</strong>g.<br />
Yanxia Wu is Associate Professor <strong>in</strong> College of Computer Science<br />
and Technology of Harb<strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g University, Harb<strong>in</strong>,<br />
Ch<strong>in</strong>a. Her current research <strong>in</strong>terests <strong>in</strong>clude safe compiler, reconfigurable<br />
compiler and computer architecture.<br />
Zhenhua Guo is a Ph.D. student <strong>in</strong> College of Computer Science<br />
and Technology of Harb<strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g University, Harb<strong>in</strong>, Ch<strong>in</strong>a.<br />
His current research <strong>in</strong>terest <strong>in</strong>cludes reconfigurable comput<strong>in</strong>g<br />
and embedded system.<br />
Guochang Gu is Professor <strong>in</strong> College of Computer Science and<br />
Technology of Harb<strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g University, Harb<strong>in</strong>, Ch<strong>in</strong>a. His<br />
ma<strong>in</strong> research <strong>in</strong>terests <strong>in</strong>clude embedded systems and safe compiler.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1417<br />
AT-M<strong>in</strong>e: An Efficient Algorithm of Frequent<br />
Itemset M<strong>in</strong><strong>in</strong>g on Uncerta<strong>in</strong> Dataset<br />
Le Wang a,b ,L<strong>in</strong> Feng a,b, *, and M<strong>in</strong>gfei Wu a,b<br />
a School of Computer Science and Technology, Faculty of Electronic Information and Electrical Eng<strong>in</strong>eer<strong>in</strong>g, Dalian<br />
University of Technology, Dalian, Liaon<strong>in</strong>g, Ch<strong>in</strong>a 116024.<br />
b<br />
School of Innovation and Experiment, Dalian University of Technology, Liaon<strong>in</strong>g, Ch<strong>in</strong>a 116024.<br />
Email: lelewater@gmail.com; fengl<strong>in</strong>@dlut.edu.cn; merphy.wmf@gmail.com<br />
Abstract—Frequent itemset/pattern m<strong>in</strong><strong>in</strong>g (FIM) over<br />
uncerta<strong>in</strong> transaction dataset is a fundamental task <strong>in</strong> data<br />
m<strong>in</strong><strong>in</strong>g. In this paper, we study the problem of FIM over<br />
uncerta<strong>in</strong> datasets. There are two ma<strong>in</strong> approaches for FIM:<br />
the level-wise approach and the pattern-growth approach.<br />
The level-wise approach requires multiple scans of dataset<br />
and generates candidate itemsets. The pattern-growth<br />
approach requires a large amount of memory and<br />
computation time to process tree nodes because the current<br />
algorithms for uncerta<strong>in</strong> datasets cannot create a tree as<br />
compact as the orig<strong>in</strong>al FP-Tree. In this paper, we propose<br />
an array based tail node tree structure (namely AT-Tree) to<br />
ma<strong>in</strong>ta<strong>in</strong> transaction itemsets, and a pattern-growth based<br />
algorithm named AT-M<strong>in</strong>e for FIM over uncerta<strong>in</strong> dataset.<br />
AT-Tree is created by two scans of dataset and it is as<br />
compact as the orig<strong>in</strong>al FP-Tree. AT-M<strong>in</strong>e m<strong>in</strong>es frequent<br />
itemsets from AT-Tree without additional scan of dataset.<br />
We evaluate our algorithm us<strong>in</strong>g sparse and dense datasets;<br />
the experimental results show that our algorithm has<br />
achieved better performance than the state-of-the-art FIM<br />
algorithms on uncerta<strong>in</strong> transaction datasets, especially for<br />
small m<strong>in</strong>imum expected support number.<br />
Index Terms—data m<strong>in</strong><strong>in</strong>g, frequent itemset, frequent<br />
pattern, uncerta<strong>in</strong> dataset<br />
I. INTRODUCTION<br />
Frequent itemsets m<strong>in</strong><strong>in</strong>g (FIM) over transaction<br />
dataset is an important and common topic <strong>in</strong> data m<strong>in</strong><strong>in</strong>g.<br />
The algorithm Apriori [1] was first proposed to discover<br />
frequent itemsets from market basket data. S<strong>in</strong>ce then,<br />
FIM algorithms were constantly proposed for various<br />
application doma<strong>in</strong>s, such as those for complete frequent<br />
itemsets [1, 2, 3, 4, 5, 6, 7], for maximal frequent itemsets<br />
[8, 9, 10, 11, 12], for closed frequent itemsets [13, 14, 15]<br />
and for frequent sequential patterns [16] and high uitlity<br />
itemsets [17, 18, 19, 20]. These algorithms concern<br />
precise transaction datasets, that is, all items can be<br />
described with a certa<strong>in</strong> value. However, many real-world<br />
applications generate or require uncerta<strong>in</strong> transaction<br />
datasets <strong>in</strong> which items can only be described with an<br />
existential probability. For example, some diseases can<br />
Manuscript received January 12, 2013; revised February. 11, 2013;<br />
accepted March 1, 2011.<br />
This work was supported by National Natural Science Foundation of<br />
P.R. Ch<strong>in</strong>a (61173163, 51105052), Program for New Century Excellent<br />
Talents <strong>in</strong> University (NCET-09-0251); and Liaon<strong>in</strong>g Prov<strong>in</strong>cial<br />
Natural Science Foundation of Ch<strong>in</strong>a (Grant No. 201102037).<br />
Correspond<strong>in</strong>g Author: L<strong>in</strong> Feng; E-mail: fengl<strong>in</strong>@dlut.edu.cn.<br />
not be def<strong>in</strong>itely diagnosed by a set of symptons - they<br />
can only be ascerta<strong>in</strong>ed as a probability value; the<br />
locations of a mov<strong>in</strong>g object obta<strong>in</strong>ed through RFID or<br />
GPS devices are not precise [21, 22]; the shopp<strong>in</strong>g habits<br />
m<strong>in</strong>ed from an e-commerce website are also probability<br />
values for predict<strong>in</strong>g what a customer will buy <strong>in</strong> the<br />
future.<br />
TABLE I.<br />
AN EXAMPLE OF UNCERTAIN DATASET<br />
TID Transaction itemset<br />
T 1 (a: 0.8), (b: 0.7), (d: 0.9), (f: 0.5)<br />
T 2 (c: 0.8), (d: 0.85), (e: 0.4)<br />
T 3 (c: 0.85), (d: 0.6), (e: 0.6)<br />
T 4 (a: 0.9) , (b: 0.85), (d: 0.65)<br />
T 5 (a: 0.95), (b: 0.7), (d: 0.8) , (e: 0.7)<br />
T 6 (b: 0.7), (c: 0.65), (f: 0.45)<br />
Table 1 shows an example of uncerta<strong>in</strong> transaction<br />
dataset, each transaction of which represents that a<br />
customer might buy a certa<strong>in</strong> item with a probability. The<br />
value associated with each item is called the existential<br />
probability of the item. For <strong>in</strong>stance, the first transaction<br />
T 1 <strong>in</strong> Table 1 shows that a customer might purchase “a”,<br />
“b”, “d” and “f” with 80%, 70%, 90% and 50% chances<br />
<strong>in</strong> the future respectively.<br />
In recent years, FIM over uncerta<strong>in</strong> datasets has<br />
become an important topic <strong>in</strong> data m<strong>in</strong><strong>in</strong>g [23, 24, 25, 26,<br />
27, 28, 29, 30, 31, 32]. The exist<strong>in</strong>g algorithms can be<br />
classified <strong>in</strong>to two ma<strong>in</strong> categories: the level-wise<br />
approach and the pattern-growth approach. The<br />
algorithms U-Apriori [31], MBP [28] and IMBP [26]<br />
employ the level-wise approach, and all these algorithms<br />
generate candidates and require multiple scans of the<br />
dataset. The algorithms UH-M<strong>in</strong>e [30], UFP-Growth [30],<br />
and UF-Growth [25, 29] employ the pattern-growth<br />
approach. UH-M<strong>in</strong>e is based on the algorithm H-M<strong>in</strong>e [5];<br />
UF-Growth is based on the classical algorithm FP-<br />
Growth [2] and employs the same method as FP-Growth<br />
for m<strong>in</strong><strong>in</strong>g frequent itemsets on uncerta<strong>in</strong> transaction<br />
itemsets. Both UH-M<strong>in</strong>e and UF-Growth cannot create a<br />
tree as compact as FP-Tree for ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g transaction<br />
itemsets, thus they require a large amount of memory and<br />
computational time to process tree nodes, especially on<br />
© 2013 ACADEMY PUBLISHER<br />
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1418 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
large datasets. UFP-Growth [30] also builds the UFP-<br />
Tree <strong>in</strong> the same manner as FP-Growth, and the UFP-<br />
Tree is as compact as the orig<strong>in</strong>al FP-Tree. However<br />
UFP-M<strong>in</strong>e generates candidates, and identifies frequent<br />
itemsets by additional scan of dataset.<br />
So our thought is to build a tree as compact as the<br />
orig<strong>in</strong>al FP-Tree and avoid generat<strong>in</strong>g candidates. To<br />
achieve this goal, we propose a tree structure named AT-<br />
Tree (Array based Tail node Tree) and a new algorithm<br />
named AT-M<strong>in</strong>e. AT-M<strong>in</strong>e needs just two scans of<br />
dataset. In the first scan, it f<strong>in</strong>ds frequent items and<br />
arranges them <strong>in</strong> descend<strong>in</strong>g order of support number. In<br />
the second scan, it constructs an AT-Tree us<strong>in</strong>g<br />
transaction itemsets like the method of FP-Growth, while<br />
ma<strong>in</strong>ta<strong>in</strong>s the probability <strong>in</strong>formation of each transaction<br />
to a tail node and an array. Then AT-M<strong>in</strong>e can directly<br />
m<strong>in</strong>e frequent itemsets from AT-Tree without additional<br />
scan of datasets. The experimental results show that AT-<br />
M<strong>in</strong>e is more efficient than the algorithms MBP, UF-<br />
Growth and CUFP-M<strong>in</strong>e.<br />
The contributions of this paper are summarized as<br />
follows:<br />
(1) We propose a new tree structure named AT-Tree<br />
(Array based Tail node Tree) for ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g<br />
important <strong>in</strong>formation related to an uncerta<strong>in</strong><br />
transaction dataset;<br />
(2) We also give an algorithm named AT-M<strong>in</strong>e for<br />
FIM over uncerta<strong>in</strong> transaction datasets based on<br />
AT-Tree;<br />
(3) Both sparse and dense datasets are used <strong>in</strong> our<br />
experiments to compare the performance of the<br />
proposed algorithm aga<strong>in</strong>st the state-of-the-art<br />
algorithms based on level-wise approach and<br />
pattern-growth approach, respectively.<br />
The rest of this paper is organized as follows: Section<br />
2 is the description of the problem and def<strong>in</strong>itions;<br />
Section 3 describes related works; Section 4 describes our<br />
algorithms AT-M<strong>in</strong>e; Section 5 shows the experimental<br />
results; and Section 6 gives the conclusion and discussion.<br />
II.<br />
PROBLEM DEFINITIONS<br />
Let D = {T 1 , T 2 , …, T n } be an uncerta<strong>in</strong> transaction<br />
dataset which conta<strong>in</strong>s n transaction itemsets and m<br />
dist<strong>in</strong>ct items, i.e. I= {i 1 , i 2 , …, i m }. Each transaction<br />
itemset is represented as {i 1 :p 1 , i 2 :p 2 , …, i v :p v }, where {i 1 ,<br />
i 2 , …, i v } is a subset of I, and p u (1≤u≤v) is the existential<br />
probability of item i u <strong>in</strong> a transaction itemset. The size of<br />
dataset D is the number of transaction itemsets and is<br />
denoted as |D|. An itemset X = {i 1 , i 2 , …, i k }, which<br />
conta<strong>in</strong>s k dist<strong>in</strong>ct items, is called a k-itemset, and k is the<br />
length of the itemset X.<br />
We adopt some def<strong>in</strong>itions similar to those presented<br />
<strong>in</strong> the previous works [1, 23, 28, 29, 30, 31, 32].<br />
Def<strong>in</strong>ition 1: The support number (SN) of an itemset X <strong>in</strong><br />
a transaction dataset is def<strong>in</strong>ed by the number of<br />
transaction itemsets conta<strong>in</strong><strong>in</strong>g X.<br />
Def<strong>in</strong>ition 2: The probability of an item i u <strong>in</strong> transaction<br />
T d is denoted as p(i u ,T d ) and is def<strong>in</strong>ed by<br />
p( i , T ) = p<br />
(1)<br />
u d u<br />
For example, <strong>in</strong> Table 1, p({a},T 1 ) = 0.8, p({b},T 1 ) =<br />
0.7, p({d},T 1 ) = 0.9, p({f},T 1 ) = 0.5.<br />
Def<strong>in</strong>ition 3: The probability of an itemset X <strong>in</strong> a<br />
transaction T d is denoted as p(X, T d ) and is def<strong>in</strong>ed by<br />
p( XT ,<br />
d) = ∏ pi ( , )<br />
iu<br />
X,<br />
X T u<br />
T<br />
∈ ⊂<br />
d<br />
d<br />
(2)<br />
For example, <strong>in</strong> Table 1, p({a, b},T 1 ) = 0.8×0.7 = 0.56,<br />
p({a, b},T 4 ) = 0.9×0.85=0.765, p({a, b},T 5 ) =<br />
0.95×0.7=0.665.<br />
Def<strong>in</strong>ition 4: The expected support number (expSN) of<br />
an itemset X <strong>in</strong> an uncerta<strong>in</strong> transaction dataset is denoted<br />
as expSN(X) and is def<strong>in</strong>ed by<br />
expSN( X ) = ∑ P( X , T )<br />
Td⊇X,<br />
T d<br />
d∈D<br />
(3)<br />
For example, expSN({a, b}) = p({a, b},T 1 ) + p({a,<br />
b},T 4 ) + p({a, b},T 5 ) = 0.56+0.765+ 0.665 = 1.99.<br />
Def<strong>in</strong>ition 5: Given a dataset D, the m<strong>in</strong>imum expected<br />
support threshold η is a predef<strong>in</strong>ed percentage of |D|;<br />
correspond<strong>in</strong>gly, the m<strong>in</strong>imum expected support number<br />
(m<strong>in</strong>ExpSN) is def<strong>in</strong>ed by<br />
m<strong>in</strong>ExpSN = | D | × η<br />
(4)<br />
In the papers [23, 25, 26, 29, 30, 31], an itemset X is<br />
called a frequent itemset if its expected support number is<br />
not less than the value m<strong>in</strong>ExpSN. M<strong>in</strong><strong>in</strong>g frequent<br />
itemsets from an uncerta<strong>in</strong> transaction dataset means<br />
discover<strong>in</strong>g all itemsets whose expected support numbers<br />
are not less than the value m<strong>in</strong>ExpSN.<br />
Def<strong>in</strong>ition 6: The m<strong>in</strong>imum support threshold λ is a<br />
predef<strong>in</strong>ed percentage of |D|; correspond<strong>in</strong>gly, the<br />
m<strong>in</strong>imum support number (m<strong>in</strong>SN) <strong>in</strong> a dataset D is<br />
def<strong>in</strong>ed by<br />
m<strong>in</strong>SN = | D | × λ<br />
(5)<br />
III. RELATED WORK<br />
Most of algorithms of FIM on uncerta<strong>in</strong> datasets can<br />
be classified <strong>in</strong>to two ma<strong>in</strong> categories: the level-wise<br />
approach and the pattern-growth approach. The ma<strong>in</strong> idea<br />
of the level-wise algorithms comes from Apriori [1]<br />
which is the first level-wise algorithm for FIM. It is to<br />
iteratively generate candidate (k+1)-itemsets from<br />
comb<strong>in</strong>ations of frequent k-itemsets (k≥1), and calculate<br />
expected support numbers of candidates by one scan of<br />
dataset. Its ma<strong>in</strong> shortcom<strong>in</strong>g is that it needs multiple<br />
scans of dataset and generates candidate itemsets.<br />
The ma<strong>in</strong> idea of the pattern-growth approach comes<br />
from the algorithm FP-Growth [2] which is the first<br />
pattern-growth algorithm. It is also an iteration approach,<br />
but it does not m<strong>in</strong>e frequent itemsets by the comb<strong>in</strong>ation<br />
method like Apriori. It f<strong>in</strong>ds all frequent items under the<br />
condition of frequent k-itemset X, and generates frequent<br />
(k+1)-itemsets by the union of each one of those frequent<br />
items and X (k≥1). It ma<strong>in</strong>ta<strong>in</strong>s all transaction itemsets to<br />
a FP-Tree [2] with two scans of dataset. It will generate a<br />
conditional tree (which is also called prefix FP-Tree or<br />
sub FP-Tree) for each frequent itemset X. Thus it will<br />
f<strong>in</strong>d all frequent items under the condition of X by<br />
scann<strong>in</strong>g this conditional tree <strong>in</strong>stead of the whole dataset.<br />
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FP-Tree is created by the follow<strong>in</strong>g rules: (1) transaction<br />
itemsets are rearranged <strong>in</strong> descend<strong>in</strong>g order of support<br />
numbers of items and are <strong>in</strong>serted to a FP-Tree; (2)<br />
transaction itemsets will share the same node when the<br />
correspond<strong>in</strong>g items are the same.<br />
A. Level-wise Approach<br />
In 2007, the algorithm U-Apriori was proposed for<br />
discover<strong>in</strong>g frequent itemsets from uncerta<strong>in</strong> datasets<br />
[31]. It is based on the algorithm Apriori. U-Apriori is a<br />
classical level-wise algorithm for FIM on uncerta<strong>in</strong><br />
datasets. It starts by f<strong>in</strong>d<strong>in</strong>g all frequent 1-itemsets with<br />
one scan of dataset. Then <strong>in</strong> each iteration, it first<br />
generates candidate (k+1)-itemsets us<strong>in</strong>g frequent k-<br />
itemsets (k ≥1), and then identifies real frequent itemsets<br />
from candidates with one scan of dataset. The iteration<br />
goes on until there is no new candidate. One important<br />
shortcom<strong>in</strong>g of U-Apriori is that it generates candidates<br />
and requires multiple scans of datasets; and the situation<br />
may become worse with the <strong>in</strong>crease of the number of<br />
long transaction itemsets or decrease of the m<strong>in</strong>imum<br />
expected support threshold.<br />
In 2011, Wang et al. [28] proposed the algorithm<br />
MBP for FIM on uncerta<strong>in</strong> datasets. The authors<br />
proposed one strategy to speed up the calculation of the<br />
expected support number of a candidate itemset: MBP<br />
will stop calculat<strong>in</strong>g the expected support number of a<br />
candidate itemset if the itemset can be determ<strong>in</strong>ed to be<br />
frequent or <strong>in</strong>frequent <strong>in</strong> advance. Thus it can achieve a<br />
better performance than the algorithm U-Apriori.<br />
In 2012, Sun et al. [26] modified the algorithm MBP,<br />
and gave an approximate algorithm (called IMBP) for<br />
FIM on uncerta<strong>in</strong> datasets. The performance of IMBP<br />
outperforms MBP <strong>in</strong> terms of runn<strong>in</strong>g time and memory<br />
usage. However its accuracy is not stable, and becomes<br />
lower on dense datasets.<br />
B. Pattern-growth Approach<br />
In 2007, Leung et al. [29] proposed a tree-based<br />
algorithm UF-Growth for FIM on uncerta<strong>in</strong> transaction<br />
dataset. Firstly, it also constructs a UF-Tree us<strong>in</strong>g<br />
transaction itemsets like the method of FP-Growth;<br />
secondly, it m<strong>in</strong>es frequent itemsets from the UF-Tree by<br />
the pattern-growth approach. It creates a UF-Tree by two<br />
scans of dataset. In the first scan, it f<strong>in</strong>ds all frequent 1-<br />
itemsets, arranges frequent 1-itemsets <strong>in</strong> descend<strong>in</strong>g order<br />
of support numbers and ma<strong>in</strong>ta<strong>in</strong>s them <strong>in</strong> a header table.<br />
In the second scan, removes <strong>in</strong>frequent items from each<br />
transaction itemset, re-arranges the rema<strong>in</strong><strong>in</strong>g items of<br />
each transaction itemset <strong>in</strong> order of the header table, and<br />
<strong>in</strong>serts the sorted itemset to a global UF-Tree. It only<br />
merges nodes that have the same item and the same<br />
probability when transaction itemsets are <strong>in</strong>serted to a<br />
UF-Tree. For example, for two transaction itemsets<br />
{a:0.50, b:0.70, c:0.23} and {a:0.55, b:0.80, c:0.23},<br />
they will not share the node “a” when they are <strong>in</strong>serted to<br />
a UF-Tree by lexicographic order because the<br />
probabilities of item “a” are not equal <strong>in</strong> these two<br />
itemsets. Thus UF-Growth requires a large amount of<br />
memory to store UF-Tree.<br />
Leung et al. [25] improved the algorithm UF-Growth<br />
to reduce the size of UF-Tree. The improved algorithm<br />
considers that the items with the same k-digit value after<br />
the decimal po<strong>in</strong>t have the same probability. For example,<br />
when two transaction itemsets {a:0.50, b:0.70, c:0.23}<br />
and {a:0.55, b:0.80, c:0.23} are <strong>in</strong>serted to a UF-Tree<br />
by lexicographic order, they will share the node “a” if k is<br />
set as 1 because both probability values of the two item<br />
“a” are considered to be 0.5; if k is set as 2, they will not<br />
share the node “a” because the probabilities of “a” are<br />
0.50 and 0.55 respectively. The smaller k is, the lesser<br />
memory the improved algorithm requires. However, the<br />
improved algorithm still cannot build a UF-Tree as<br />
compact as the orig<strong>in</strong>al FP-Tree; moreover, it may lose<br />
some frequent itemsets.<br />
UH-M<strong>in</strong>e [30] is a pattern-growth algorithm. The<br />
ma<strong>in</strong> difference between UH-M<strong>in</strong>e and UF-Growth is<br />
that UF-Growth adopts a prefix tree structure while UH-<br />
M<strong>in</strong>e adopts a hyperl<strong>in</strong>ked array based structure called H-<br />
struct [5] (which can also be considered as a tree). UH-<br />
M<strong>in</strong>e requires two scans of dataset for creat<strong>in</strong>g the<br />
structure H-struct: <strong>in</strong> the first scan, it creates a header<br />
table which ma<strong>in</strong>ta<strong>in</strong>s sorted frequent 1-items; <strong>in</strong> the<br />
second scan, it removes <strong>in</strong>frequent items from each<br />
transaction itemset, re-arranges the rema<strong>in</strong><strong>in</strong>g items <strong>in</strong> the<br />
order of the header table, and <strong>in</strong>serts the sorted<br />
transaction itemset <strong>in</strong>to an H-struct tree without shar<strong>in</strong>g<br />
nodes with other transaction itemsets. The header table<br />
ma<strong>in</strong>ta<strong>in</strong>s the hyperl<strong>in</strong>k of all nodes with the same item<br />
name when the itemsets are <strong>in</strong>serted <strong>in</strong>to an H-struct tree.<br />
It will achieve a good performance on small datasets.<br />
However, the H-struct does not share any node and is not<br />
a compact tree, and this will impact the performance of<br />
FIM, especially for large datasets.<br />
The authors of the paper [30] also extend the classical<br />
algorithm FP-Growth to get the algorithm UFP-Growth<br />
for FIM on uncerta<strong>in</strong> datasets. UFP-Growth firstly<br />
generates candidates by the UFP-Tree, and then identifies<br />
frequent itemsets through additional scan of datasets. Its<br />
performance is also impacted by the generation of<br />
candidate itemsets.<br />
C. The Algorithm CUFP-M<strong>in</strong>e<br />
In 2011, L<strong>in</strong> et al. [23] proposed the algorithm CUFP-<br />
M<strong>in</strong>e for FIM on uncerta<strong>in</strong> transaction datasets. CUFP-<br />
M<strong>in</strong>e creates a tree named CUFP-Tree to ma<strong>in</strong>ta<strong>in</strong><br />
transaction itemsets. A CUFP-Tree is created by two<br />
scans of dataset. In the first scan, it creates a header table<br />
for ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g sorted frequent 1-itemsets; <strong>in</strong> the second<br />
scan, when an item Z i <strong>in</strong> transaction itemset Z ({Z 1 , Z 2 ,…,<br />
Z i ,.., Z m }) is <strong>in</strong>serted <strong>in</strong>to a tree, CUFP-M<strong>in</strong>e generates all<br />
supersets of item Z i us<strong>in</strong>g items Z 1 , Z 2 ,…, Z i , and<br />
ma<strong>in</strong>ta<strong>in</strong>s all supersets and their correspond<strong>in</strong>g<br />
probabilities to a node correspond<strong>in</strong>g to Z i . CUFP-M<strong>in</strong>e<br />
only accumulates the probability of each superset if there<br />
is a correspond<strong>in</strong>g node on the tree for item Z i . The idea<br />
of CUFP-M<strong>in</strong>e is that it f<strong>in</strong>ds frequent itemsets through<br />
scann<strong>in</strong>g supersets of each node and calculat<strong>in</strong>g expected<br />
support number of each superset. CUFP-M<strong>in</strong>e generates<br />
all comb<strong>in</strong>ations of items <strong>in</strong> an itemset, and ma<strong>in</strong>ta<strong>in</strong>s<br />
these comb<strong>in</strong>ations to tree nodes. Thus CUFP-M<strong>in</strong>e<br />
requires a large amount of computation time and memory<br />
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when the length of itemsets is not very short or on large<br />
datasets.<br />
IV. THE ALGORITHM AT-MINE<br />
The proposed algorithm AT-M<strong>in</strong>e ma<strong>in</strong>ly consists of<br />
two procedures: (1) creat<strong>in</strong>g an AT-Tree; (2) m<strong>in</strong><strong>in</strong>g<br />
frequent itemsets from the AT-Tree. We describe the<br />
structure of an AT-Tree <strong>in</strong> Section 4.1, give an example<br />
of the construction of an AT-Tree <strong>in</strong> Section 4.2, and<br />
elaborate the algorithm AT-M<strong>in</strong>e with an example <strong>in</strong><br />
Section 4.3.<br />
A. Structure of an AT-Tree<br />
Def<strong>in</strong>ition 9: Let itemset X = {i 1 , i 2 , i 3 , …, i u } be a sorted<br />
itemset, and the item i u is called tail-item of X. When the<br />
itemset X is <strong>in</strong>serted <strong>in</strong>to a tree T <strong>in</strong> accordance with its<br />
items’ order, the node N on the tree that represents this<br />
tail-item is def<strong>in</strong>ed as tail node of itemset X, and other<br />
nodes that represent items i 1 , i 2 , …, i u-1 are def<strong>in</strong>ed as<br />
normal nodes. The itemset X is called tail-node-itemset<br />
for node N.<br />
Def<strong>in</strong>ition 10: Let an itemset X conta<strong>in</strong> itemset Y. When<br />
itemset X is added to a prefix tree of itemset Y, the<br />
probability of itemset Y <strong>in</strong> itemset X, p(Y, X), is def<strong>in</strong>ed<br />
as the base probability of itemset X on the tree T, and is<br />
denoted as BP(X, Y):<br />
BP YX , = pYX ( , )<br />
(8)<br />
( )<br />
Figure 1. Structure of nodes on an AT-Tree<br />
The node structure on an AT-Tree is illustrated <strong>in</strong><br />
Figure 1. There are two types of nodes: one is normal<br />
node, as shown <strong>in</strong> Figure 1(a), where Name is the item<br />
name of each node; the other type is tail node, as shown<br />
<strong>in</strong> Figure 1(b), where Tail_<strong>in</strong>fo is the supplemental<br />
<strong>in</strong>formation that <strong>in</strong>cludes 4 fields: (1) bp: a list that keeps<br />
base probability values of all tail-node-itemsets; (2) len:<br />
the length of the tail-node-itemset; (3) Arr_<strong>in</strong>d: a list of<br />
<strong>in</strong>dex values of an array each element of which records<br />
probability values of items <strong>in</strong> each sorted transaction<br />
itemset (see Substep 5.2 <strong>in</strong> Section 4.2.1 and Step 5 <strong>in</strong><br />
Section 4.2.2, etc.); (4) Item_<strong>in</strong>d: a list of <strong>in</strong>dex values of<br />
an array that records probability values of each item <strong>in</strong> a<br />
sorted transaction itemset (see Substep 10.5 and 10.7 <strong>in</strong><br />
Section 4.3.2, etc., Item_<strong>in</strong>d is just used <strong>in</strong> a sub AT-<br />
Tree).<br />
B. Construction of an AT-Tree<br />
The structure of AT-Tree is designed to efficiently<br />
store the related <strong>in</strong>formation on tail nodes. It is<br />
constructed by two scans of dataset. In the first scan, a<br />
header table is created to ma<strong>in</strong>ta<strong>in</strong> sorted frequent items.<br />
In the second scan, the probability values of frequent<br />
items <strong>in</strong> each transaction itemsets are stored to a list<br />
accord<strong>in</strong>g to the order of the header table; the list is then<br />
added to an array (and its correspond<strong>in</strong>g sequence<br />
number <strong>in</strong> the array is denoted as ID); the frequent items<br />
<strong>in</strong> each transaction itemset are <strong>in</strong>serted to an AT-Tree<br />
accord<strong>in</strong>g to the order of the header table; the length of<br />
the itemset and the number ID are stored to the<br />
correspond<strong>in</strong>g tail node. When the transaction itemsets<br />
are added to an AT-Tree, they are rearranged <strong>in</strong><br />
descend<strong>in</strong>g order of support numbers of items, and share<br />
the same node/nodes if their prefix items/itemsets are<br />
identical. Thus the AT-Tree is as compact as the orig<strong>in</strong>al<br />
FP-Tree. Moreover, AT-Tree does not lose probability<br />
<strong>in</strong>formation with respect to the dist<strong>in</strong>ct probability values<br />
of the transaction itemsets.<br />
B.1 The construction algorithm of a global AT-Tree<br />
A global AT-Tree is the first AT-Tree that ma<strong>in</strong>ta<strong>in</strong>s<br />
itemset <strong>in</strong>formation of the whole dataset. The<br />
construction algorithm is described as follows:<br />
CreateTree(D, η )<br />
INPUT: An uncerta<strong>in</strong> database D consist<strong>in</strong>g of n<br />
transaction itemsets and a predef<strong>in</strong>ed m<strong>in</strong>imum expected<br />
support threshold η .<br />
OUTPUT: An AT-Tree T.<br />
Step 1: Calculate the m<strong>in</strong>imum expected support number<br />
m<strong>in</strong>ExpSN, i.e. m<strong>in</strong>ExpSN = | D | × η ; count the<br />
expected support number and support number of<br />
each item by one scan of dataset.<br />
Step 2: Put those items whose expected support numbers<br />
are not less than m<strong>in</strong>ExpSN to a header table, and<br />
sort the items <strong>in</strong> the header table accord<strong>in</strong>g to the<br />
descend<strong>in</strong>g order of their support numbers; f<strong>in</strong>ish<br />
the algorithm if the header table is null.<br />
Step 3: Initially set the root node of the AT-Tree T as null.<br />
Step 4: Remove the items that are not <strong>in</strong> the header table<br />
from each transaction itemset, and sort the<br />
rema<strong>in</strong><strong>in</strong>g items of each transaction itemset<br />
accord<strong>in</strong>g to the order of the header table, and get a<br />
sorted itemset X.<br />
Step 5: If the length of itemset X is 0, process the next<br />
transaction itemset; otherwise <strong>in</strong>sert the itemset X<br />
<strong>in</strong>to the AT-Tree T by the follow<strong>in</strong>g substeps:<br />
Substep 5.1: Store the probability value of each<br />
item <strong>in</strong> itemset X sequentially to a list; save the<br />
list to an array (which is denoted as ProArr);<br />
the correspond<strong>in</strong>g sequence number of the list<br />
<strong>in</strong> the array is denoted as ID.<br />
Substep 5.2: If there has not been a tail node for the<br />
itemset X, create a tail node N for this itemset,<br />
where N.Tail_<strong>in</strong>fo.len is the length of itemset X,<br />
and N.Tail_<strong>in</strong>fo.Arr_<strong>in</strong>d={ID}; otherwise,<br />
append the sequence number ID to<br />
N.Tail_<strong>in</strong>fo.Arr_<strong>in</strong>d.<br />
Step 6: Process the next transaction itemset.<br />
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Figure 2. Construction of an AT-Tree<br />
TABLE II.<br />
PROBABILITY LIST (PROARR)<br />
ID probabilities<br />
1 {0.9, 0.7, 0.8}<br />
2 {0.85, 0.8, 0.4}<br />
3 {0.6, 0.85, 0.6}<br />
4 {0.65, 0.85, 0.9}<br />
5 {0.8, 0.7, 0.95, 0.7}<br />
6 {0.7, 0.65}<br />
B.2 An Example of Construct<strong>in</strong>g a Global AT-Tree<br />
The uncerta<strong>in</strong> dataset <strong>in</strong> Table 1 is used as an example<br />
here to illustrate the construction of the AT-Tree. This<br />
dataset concludes 6 transaction itemsets and 6 dist<strong>in</strong>ct<br />
items. The m<strong>in</strong>imum support threshold is set as 20%.<br />
Step 1: Calculate the m<strong>in</strong>imum expected support number<br />
as 1.2 (6*20%); count the expected support number<br />
and support number of each item by one scan of<br />
database.<br />
Step 2: Create a header table, as shown <strong>in</strong> Figure 2(a).<br />
Each l<strong>in</strong>k <strong>in</strong> the header table records all nodes of a<br />
correspond<strong>in</strong>g item on a tree (not shown <strong>in</strong> the<br />
Figures for simplicity).<br />
Step 3: Initially set the root node of an AT-Tree as null.<br />
Step 4: Remove the <strong>in</strong>frequent item “f” from the<br />
transaction itemset T 1 , and sort the rema<strong>in</strong><strong>in</strong>g items<br />
accord<strong>in</strong>g to the order of the header table, the<br />
result<strong>in</strong>g is {d:0.9, b:0.7, a:0.8}.<br />
Step 5: Ma<strong>in</strong>ta<strong>in</strong> probability value of each item to a list<br />
{0.9, 0.7, 0.8}, and append the list to an array ProArr,<br />
as shown <strong>in</strong> Table 2; the correspond<strong>in</strong>g ID of the list <strong>in</strong><br />
the array ProArr is 1; then <strong>in</strong>sert the first sorted<br />
itemset <strong>in</strong>to the AT-Tree, and the result<strong>in</strong>g AT-Tree is<br />
shown <strong>in</strong> Figure 2(b). On the tail node “a”, “3”<br />
represents the length of the tail-node-itemset (len), and<br />
“{1}” represents the <strong>in</strong>dex number of the array<br />
ProArr <strong>in</strong> Table 2.<br />
Step 6: Process the next transaction T 2 , get the sorted<br />
transaction itemset {d:0.85, c:0.8, e:0.4}. S<strong>in</strong>ce the<br />
path “root-d” can be shared, <strong>in</strong>sert a normal node<br />
“c” and a tail node “e”. The result<strong>in</strong>g AT-Tree is<br />
shown <strong>in</strong> Figure 2(c).<br />
Step 7: Process the next transaction T 3 , get the sorted<br />
transaction itemset {d:0.6, c:0.85, e:0.6}. S<strong>in</strong>ce the<br />
path “root-d-c-e” can be shared and the node “e” on<br />
the path is a tail node, just append the correspond<strong>in</strong>g<br />
ID <strong>in</strong> ProArr of Table 2 to the Tail_<strong>in</strong>fo.Arr_<strong>in</strong>d of<br />
the tail node “e”. The result<strong>in</strong>g AT-Tree is shown <strong>in</strong><br />
Figure 2(d).<br />
Step 8: Process the rema<strong>in</strong><strong>in</strong>g transactions one by one.<br />
The result<strong>in</strong>g AT-Tree is shown <strong>in</strong> Figure 2(e).<br />
C. M<strong>in</strong><strong>in</strong>g Frequent Itemsets from a Global AT-Tree<br />
After an AT-Tree is constructed, the algorithm AT-<br />
M<strong>in</strong>e can directly m<strong>in</strong>e frequent itemsets from the tree<br />
without additional scan of dataset. The details of the<br />
m<strong>in</strong><strong>in</strong>g approach are described below.<br />
C.1 The M<strong>in</strong><strong>in</strong>g Algorithm<br />
The algorithm AT-M<strong>in</strong>e is similar to the algorithm<br />
FP-Growth: it creates and processes sub trees (prefix<br />
trees or conditional trees) recursively. But the condition<br />
of generat<strong>in</strong>g frequent itemsets is different from FP-<br />
Growth. The detailed steps of the m<strong>in</strong><strong>in</strong>g algorithm are as<br />
follows:<br />
M<strong>in</strong><strong>in</strong>g (T, H, m<strong>in</strong>ExpSN)<br />
INPUT: An AT-Tree T, a header table H, and a<br />
m<strong>in</strong>imum expected support number m<strong>in</strong>ExpSN.<br />
OUTPUT: The frequent itemsets (FIs).<br />
Step 1: Process the items <strong>in</strong> the header table one by one<br />
from the last item by the follow<strong>in</strong>g steps (denote the<br />
currently processed item as Z).<br />
Step 2: Append item Z to the current base-itemset (which<br />
is <strong>in</strong>itialized as null); each new base-itemset is a<br />
frequent itemset.<br />
Step 3: Let Z.l<strong>in</strong>ks <strong>in</strong> the header table H conta<strong>in</strong> k nodes<br />
whose item name is Z; we denote these k nodes as N 1 ,<br />
N 2 , …, N k ; because item Z is the last one <strong>in</strong> the<br />
header table, all these k nodes are tail nodes, i.e.,<br />
each of these nodes conta<strong>in</strong>s a Tail_<strong>in</strong>fo.<br />
Substep 3.1: Create a sub header table subH by<br />
scann<strong>in</strong>g the k branches from these k nodes to<br />
the root.<br />
Substep 3.2: If the sub header table is null, go to<br />
Step 4.<br />
Substep 3.3: Create sub AT-Tree subTree =<br />
CreateSubTree(Z.l<strong>in</strong>k, subH).<br />
Substep 3.4: M<strong>in</strong><strong>in</strong>g(subTree, subH, m<strong>in</strong>ExpSN).<br />
Step 4: Remove item Z from the base-itemset.<br />
Step 5: For each of these k nodes (which we denote as N i ,<br />
1≤i≤k), modify its Tail_<strong>in</strong>fo by the follow<strong>in</strong>g<br />
substeps:<br />
Substep 5.1: Alter N i .Tail_<strong>in</strong>fo.len values:<br />
N i .Tail_<strong>in</strong>fo.len = N i .Tail_<strong>in</strong>fo.len -1.<br />
Substep 5.2: Move N i .Tail_<strong>in</strong>fo to the parent of<br />
node N i .<br />
Step 6: Process the next item of the header table H.<br />
Subrout<strong>in</strong>e: CreateSubTree(l<strong>in</strong>k, subH)<br />
INPUT: A list l<strong>in</strong>k which records tree nodes with the<br />
same item name, and a header table subH.<br />
OUTPUT: An AT-Tree subT.<br />
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Step 1: Initially set the root node of the tree subT as null.<br />
Step 2: Process each node <strong>in</strong> the list l<strong>in</strong>k by the follow<strong>in</strong>g<br />
steps (denote the currently processed node as N).<br />
Step 3: Get the tail-node-itemset of node N (denote it as<br />
itemset X).<br />
Step 4: Remove those items that are not <strong>in</strong> the header<br />
table subH from itemset X, and sort the rema<strong>in</strong><strong>in</strong>g<br />
items <strong>in</strong> itemset X accord<strong>in</strong>g to the order of the<br />
header table subH.<br />
Step 5: If the length of the sorted itemset (denoted as k)<br />
is 0, process the next node of the list l<strong>in</strong>k; otherwise<br />
<strong>in</strong>sert the sorted itemset X <strong>in</strong>to the AT-Tree subT by<br />
the follow<strong>in</strong>g substeps:<br />
Substep 5.1: Get the orig<strong>in</strong>al sequential ID of each<br />
item of the itemset X <strong>in</strong> the correspond<strong>in</strong>g list<br />
of ProArr: item_<strong>in</strong>d = {d 1 , d 2 , .., d k } (k is the<br />
length of itemset X).<br />
Substep 5.2: Make a copy of N.Tail_<strong>in</strong>fo; denote the<br />
copy as nTail_<strong>in</strong>fo.<br />
Substep 5.3: Alter nTail_<strong>in</strong>fo as the follow<strong>in</strong>g:<br />
(1) nTail_<strong>in</strong>fo.len = k.<br />
(2) nTail_<strong>in</strong>fo. Item_<strong>in</strong>d = item_<strong>in</strong>d.<br />
(3) if nTail_<strong>in</strong>fo.bp is null, set nTail_<strong>in</strong>fo.bp[j]<br />
to be the probability of item Z, i.e.<br />
ProArr[nTail_<strong>in</strong>fo.Arr_<strong>in</strong>d[j]]; otherwise,<br />
set nTail_<strong>in</strong>fo.bp[j] to be the product of<br />
nTail_<strong>in</strong>fo.bp[j] and the probability of item<br />
Z (1 ≤ j ≤ bp.size; the array ProArr is<br />
created when the global tree is created <strong>in</strong><br />
Substep 5.1 <strong>in</strong> Section 4.2.1).<br />
C.2 An Example of M<strong>in</strong><strong>in</strong>g Frequent Itemsets from a<br />
Global AT-Tree<br />
Figure 3. An Example of m<strong>in</strong><strong>in</strong>g frequent itemsets from uncerta<strong>in</strong><br />
dataset<br />
The global AT-Tree <strong>in</strong> Figure 2(e) and its<br />
correspond<strong>in</strong>g header table H <strong>in</strong> Figure 2(a) are used as<br />
an example here to illustrate the detailed processes of<br />
m<strong>in</strong><strong>in</strong>g frequent itemsets. The m<strong>in</strong>imum expected support<br />
number is 1.2.<br />
Step 1: Process the item “e” <strong>in</strong> the header table H by the<br />
follow<strong>in</strong>g steps 2-3.<br />
Step 2: Append item “e” to the current base-itemset<br />
(which is <strong>in</strong>itialized as null), and generates a new<br />
frequent itemset {e}.<br />
Step 3: Scan the branches conta<strong>in</strong><strong>in</strong>g the node “e” to<br />
create sub header table:<br />
Substep 3.1: In Figure 2(e), there are 2 nodes “e”.<br />
From the path “root-d-b-a-e” and Table 2, the<br />
expected support numbers of itemsets {ed}, {eb}<br />
and {ea} are calculated as 0.56 (0.7*0.8), 0.49<br />
(0.7*0.7) and 0.665 (0.7*0.95), respectively;<br />
from the path “root-d-c-e”, the expected<br />
supports of itemset {ed} and {ec} are<br />
calculated as 0.7 (0.4*0.85+0.6*0.6) and 0.83<br />
(0.4*0.8+0.6*0.85).<br />
Substep 3.2: Because the total expected support<br />
numbers of itemset {ed} is bigger than 1.2, the<br />
sub header table is not null, create a sub tree<br />
(prefix tree or conditional tree) for the baseitemset<br />
{e}, and get a new frequent itemset<br />
{ed}.<br />
SubStep 3.3: Remove the item “e” from the baseitemset,<br />
pass the Tail_<strong>in</strong>fo of nodes “e” to their<br />
parents, and modify Tail_<strong>in</strong>fo.len as<br />
Tail_<strong>in</strong>fo.len -1; the result is shown <strong>in</strong> Figure<br />
3(a).<br />
Step 4: Process the next item “c” <strong>in</strong> the header table H by<br />
the follow<strong>in</strong>g steps 5-6.<br />
Step 5: Append item “c” to base-itemset, and get a new<br />
frequent itemset {c}.<br />
Step 6: Scan the branches conta<strong>in</strong><strong>in</strong>g node “c” to create<br />
the sub header table:<br />
Substep 6.1: In Figure 3(a), there are 2 nodes “c”.<br />
From the path “root-d-c” and Table 2, the<br />
expected support numbers of itemset {cd} is<br />
calculated as 1.19 (0.8*0.85+0.85*0.6); from<br />
the path “root-b-c”, the expected support of<br />
itemset {cb} is calculated as 0.455 (0.65*0.7).<br />
Substep 6.2: Because the total expected support<br />
numbers of itemsets {cd} and {cb} are smaller<br />
than 1.2, the sub header table is null.<br />
SubStep 6.3: Remove the item “c” from the baseitemset,<br />
pass the Tail_<strong>in</strong>fo of nodes “c” to their<br />
parents; the result is shown <strong>in</strong> Figure 3(b).<br />
Step 7: Process the next item “a” <strong>in</strong> the header table <strong>in</strong><br />
Figure 2(a) as the follow<strong>in</strong>g steps 8-10.<br />
Step 8: Append item “a” to the base-itemset, and get a<br />
new frequent itemset {a}.<br />
Step 9: Scan the branches conta<strong>in</strong><strong>in</strong>g node “a” to create<br />
the sub header table:<br />
Substep 9.1: In Figure 3(b), there is one node “a”.<br />
From the path “root-d-b-a” and Table 2, the<br />
expected support numbers of itemsets {ad} and<br />
{ab} are calculated as 2.065<br />
(0.8*0.9+0.9*0.65+0.95*0.8) and 1.99<br />
(0.8*0.7+0.9*0.85+0.95*0.7).<br />
Substep 9.2: Because the total expected support<br />
numbers of itemsets {ad} and {ab} are not<br />
smaller than 1.2, the sub header table subH is<br />
{d:2.065:3, b:1.99:3}.<br />
Step 10: Create a sub tree for the base-itemset {a} by the<br />
follow<strong>in</strong>g substeps:<br />
Substep 10.1: Initially set the root node of the sub<br />
tree subT as null.<br />
Substep 10.2: Get the itemset {db} from the tailnode-itemset<br />
of the tail node “a” <strong>in</strong> Figure 3(b).<br />
Substep 10.3: Sort the itemset {db} <strong>in</strong> the order of<br />
the header table subH.<br />
Substep 10.4: Make a copy of Tail_<strong>in</strong>fo.Arr_<strong>in</strong>d,<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1423<br />
and denote it as arr_<strong>in</strong>d={1, 4, 5}.<br />
Substep 10.5: Get the list <strong>in</strong>dexes (orig<strong>in</strong>al<br />
sequential ID <strong>in</strong> a list) of items “d” and “b” <strong>in</strong><br />
the list ProArr[1], which are 1 and 2<br />
respectively, and denote it as item_<strong>in</strong>d={1, 2}.<br />
Substep 10.6: Get the probability values of itemset<br />
{a} <strong>in</strong> ProArr[1] and ProArr[4] and ProArr[5]<br />
respectively, and denote them as bp={0.8, 0.9,<br />
0.95}; this is the correspond<strong>in</strong>g base<br />
probabilities <strong>in</strong> the sub tree subT.<br />
Substep 10.7: Add the sorted itemset {db} to subT;<br />
ma<strong>in</strong>ta<strong>in</strong> arr_<strong>in</strong>d, item_<strong>in</strong>d, bp and the length<br />
of the itemset {db} to the tail node <strong>in</strong> subT; the<br />
result is shown <strong>in</strong> Figure 3(c).<br />
Substep 10.8: Process the tree subT recursively, and<br />
get a new sub tree for the base-itemset {ab}, as<br />
shown <strong>in</strong> Figure 3(d). Lastly, get frequent<br />
itemsets {ab}, {abd} and {ad} when process<strong>in</strong>g<br />
the sub tree of itemset {a}.<br />
Step 11: Go on process<strong>in</strong>g the rema<strong>in</strong><strong>in</strong>g items <strong>in</strong> header<br />
table H.<br />
V. EXPERIMENTAL RESULTS<br />
In this section, we evaluate the performance of the<br />
proposed algorithm AT-M<strong>in</strong>e.<br />
Summariz<strong>in</strong>g the related works <strong>in</strong> Section 3, we can<br />
conclude that the algorithm MBP is the state-of-the-art<br />
algorithm employ<strong>in</strong>g the level-wise approach, UP-<br />
Growth is the state-of-the-art algorithm employ<strong>in</strong>g the<br />
pattern-growth approach and CUFP-M<strong>in</strong>e is a new<br />
proposed algorithm. So we compare AT-M<strong>in</strong>e with the<br />
algorithms UF-Growth, CUFP-M<strong>in</strong>e and MBP on both<br />
types of datasets: the sparse transaction datasets and<br />
dense transaction datasets. All algorithms were written <strong>in</strong><br />
Java programm<strong>in</strong>g language. The configuration of the<br />
test<strong>in</strong>g platform is as follows: W<strong>in</strong>dows XP operat<strong>in</strong>g<br />
system, 2G Memory, Intel(R) Core(TM) i3-2310 CPU @<br />
2.10 GHz; Java heap size is 1G.<br />
TABLE III.<br />
DATASET CHARACTERISTICS<br />
Dataset |D| |I| ML SD (%) Type<br />
T20I6D<br />
300K<br />
300,000 1000 20 2 sparse<br />
kosarak 990,002 41,271 8 0.02 sparse<br />
connect 67,557 129 43 33.33 dense<br />
mushroom 8,124 119 23 19.33 dense<br />
Table 3 shows the characteristics of 4 datasets used <strong>in</strong><br />
our experiments. “|D|” represents the total number of<br />
transactions; “|I|” represents the total number of dist<strong>in</strong>ct<br />
items; “ML” represents the mean length of all transaction<br />
itemsets; “SD” represents the degree of sparsity or<br />
density. The synthetic dataset T20I6D300K came from<br />
the IBM Data Generator [1] and the datasets kosarak,<br />
connect and mushroom were obta<strong>in</strong>ed from FIMI<br />
Repository [33]; These four datasets orig<strong>in</strong>ally do not<br />
provide probability values for each item of each<br />
transaction itemset; as suggested by literatures [23, 25, 28,<br />
29], we assign a existential probability of range (0, 1] to<br />
each item. The runnable programs and test<strong>in</strong>g datasets<br />
can be downloaded from the follow<strong>in</strong>g address:<br />
http://code.google.com/p/at-tree/downloads/list.<br />
A. Evaluation on Sparse Datasets<br />
Tables 4-5 show the total number of tree nodes<br />
generated by AT-M<strong>in</strong>e, UF-Growth and CUFP, and the<br />
number of candidate itemsets generated by MBP,<br />
respectively, on the sparse datasets. As shown <strong>in</strong> Tables<br />
4-5, UF-Growth creates much more tree nodes than AT-<br />
M<strong>in</strong>e. This is because that UF-Growth just merges the<br />
nodes that have the same item name and the same<br />
probability. CUFP-M<strong>in</strong>e is out of memory on these two<br />
sparse datasets because it generates too many supersets;<br />
UF-Growth is out of memory on kosarak when the<br />
threshold is set 0.01% because it generates too many tree<br />
nodes; MBP is out of memory when the threshold is set<br />
0.03% because it generates too many candidates. Thus we<br />
can <strong>in</strong>fer that AT-M<strong>in</strong>e has a better performance than<br />
other three algorithms <strong>in</strong> terms of memory usage.<br />
TABLE IV.<br />
DETAILS ANALYSIS ON THE DATASET T20I6D300K<br />
η (%)<br />
trees nodes (#) candidates (#)<br />
AT-M<strong>in</strong>e UF-Growth MBP<br />
0.15 4,978,327 7,556,250 374,271<br />
0.13 5,101,077 8,629,034 391,413<br />
0.11 5,438,410 10,282,811 419,770<br />
0.09 6,310,746 12,978,032 467,217<br />
0.07 8,474,124 17,477,552 594,050<br />
0.05 13,189,900 24,946,139 999,799<br />
Runn<strong>in</strong>g time (s)<br />
TABLE V.<br />
DETAILS ANALYSIS ON THE DATASET KOSARAK<br />
η (%)<br />
trees nodes (#) candidates (#)<br />
AT-M<strong>in</strong>e UF-Growth MBP<br />
0.1 2,020,568 14,471,137 172,399<br />
0.09 2,208,231 15,724,272 252,348<br />
0.07 2,542,835 19,210,453 419,272<br />
0.05 3,058,380 24,651,644 793,554<br />
0.03 4,580,785 38,083,667<br />
0.01 18,829,877<br />
Memory<br />
Overflow<br />
Memory<br />
Overflow<br />
10000<br />
1000<br />
100<br />
AT-M<strong>in</strong>e<br />
MBP<br />
UF-Growth<br />
CUFP-M<strong>in</strong>e (Memory Overflow)<br />
10<br />
0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05<br />
M<strong>in</strong>imum expected support threshold (%)<br />
© 2013 ACADEMY PUBLISHER
1424 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
(a)<br />
On the dataset T20I6D300K<br />
Runn<strong>in</strong>g time (s)<br />
1000<br />
100<br />
10<br />
AT-M<strong>in</strong>e<br />
MBP<br />
UF-Growth<br />
CUFP-M<strong>in</strong>e (Memory Overflow)<br />
0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01<br />
(b)<br />
M<strong>in</strong>imum expected support threshold (%)<br />
On the dataset kosarak<br />
Figure 4. Runn<strong>in</strong>g time comparison on sparse datasets<br />
Figure 4 shows the runn<strong>in</strong>g time of three algorithms<br />
on two sparse datasets. CUFP-M<strong>in</strong>e is out of memory on<br />
these two sparse datasets. As shown <strong>in</strong> Figure 4, the time<br />
performance of our algorithm outperforms UF-Growth,<br />
MBP and CUFP-M<strong>in</strong>e under different m<strong>in</strong>imum expected<br />
support thresholds. This is because that CUFP-M<strong>in</strong>e<br />
generates too many supersets and UF-Growth generates<br />
too many tree nodes and MBP generates many candidates,<br />
as shown <strong>in</strong> Tables 4-5. The time performance of MBP is<br />
dependent on the length of candidate itemsets, the length<br />
of transaction itemsets, and the size of dataset: the higher<br />
these values are, the lower the time performance of MBP<br />
will be. Thus the time performance of MBP decreases<br />
sharply with the decreas<strong>in</strong>g of the threshold. Figure 4<br />
<strong>in</strong>dicates that AT-M<strong>in</strong>e has achieved a better time<br />
performance; moreover, its time performance is more<br />
stable on sparse dataset.<br />
B. Evaluation on Dense Datasets<br />
In this section, we test the performance of our<br />
proposed algorithm on dense datasets connect and<br />
mushroom.<br />
TABLE VI.<br />
DETAILS ANALYSIS ON THE DATASET CONNECT<br />
η (%)<br />
trees nodes (#) candidates (#)<br />
AT-M<strong>in</strong>e UF-Growth MBP<br />
15.0 36,823 32,204,274 5,981<br />
14.0 89,118 33,739,243 6,962<br />
13.0 98,842 35,332,360 7,786<br />
12.0 116,290 48,046,639 8,565<br />
11.0 130,423 106,626,725 12,754<br />
10.0 153,913 163,809,762 19,162<br />
Tables 6-7 show the total number of tree nodes<br />
generated by AT-M<strong>in</strong>e and UF-Growth, and the number<br />
of candidate itemsets generated by MBP, on the dense<br />
datasets. As shown <strong>in</strong> Tables 6-7, UF-Growth creates too<br />
many tree nodes. For example, on the dataset connect,<br />
UF-Growth generates 163,809,762 nodes while AT-M<strong>in</strong>e<br />
generates 153,913 nodes when the m<strong>in</strong>imum expected<br />
support threshold is 10%. This is because that UF-<br />
Growth just merges the nodes that have the same item<br />
name as well as the same probability, and it is a very<br />
dense and long dataset. Thus we can <strong>in</strong>fer that our<br />
algorithm has achieved better performance than UF-<br />
Growth <strong>in</strong> terms of memory usage. MBP not only<br />
ma<strong>in</strong>ta<strong>in</strong>s candidates, but also ma<strong>in</strong>ta<strong>in</strong> the dataset while<br />
our algorithms only ma<strong>in</strong>ta<strong>in</strong> tree nodes us<strong>in</strong>g compact<br />
trees.<br />
Figure 5 shows the runn<strong>in</strong>g time of three algorithms<br />
on the dense datasets connect and mushroom. CUFP-<br />
M<strong>in</strong>e is out of memory on these two dense datasets. As<br />
shown <strong>in</strong> Figure 5, the time performance of our algorithm<br />
prevails over UF-Growth, MBP and CUFP-M<strong>in</strong>e under<br />
different m<strong>in</strong>imum expected support thresholds. This is<br />
because that CUFP-M<strong>in</strong>e generates too many supersets<br />
and UF-Growth generates too many tree nodes and MBP<br />
generates many candidates, as shown <strong>in</strong> Tables 6-7.<br />
Figure 5 shows that the time performance of AT-M<strong>in</strong>e<br />
obviously outperforms that of other algorithms on these<br />
two dense datasets; moreover, our time performance is<br />
also more stable on the dense datasets.<br />
Runn<strong>in</strong>g time (s)<br />
TABLE VII.<br />
DETAILS ANALYSIS ON THE DATASET MUSHROOM<br />
η (%)<br />
trees nodes (#) candidates(#)<br />
AT-M<strong>in</strong>e UF-Growth MBP<br />
7.0 12,041 1,011,721 1,917<br />
6.0 14,420 1,344,369 2,501<br />
5.0 16,243 1,947,609 3,460<br />
4.0 18,685 2,760,249 5,024<br />
3.0 25,884 4,125,745 8,222<br />
2.0 37,395 8,076,099 16,764<br />
10000<br />
1000<br />
100<br />
AT-M<strong>in</strong>e<br />
MBP<br />
UF-Growth<br />
CUFP-M<strong>in</strong>e (Memory Overflow)<br />
10<br />
15.0 14.5 14.0 13.5 13.0 12.5 12.0 11.5 11.0 10.5 10.0<br />
M<strong>in</strong>imum expected support threshold (%)<br />
(a)<br />
On the dataset connect<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1425<br />
Runn<strong>in</strong>g time (s)<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
AT-M<strong>in</strong>e<br />
MBP<br />
UF-Growth<br />
CUFP-M<strong>in</strong>e (Memory Overflow)<br />
7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0<br />
(b)<br />
M<strong>in</strong>imum expected support threshold (%)<br />
On the dataset mushroom<br />
Figure 5. Runn<strong>in</strong>g time comparison on dense datasets<br />
VI. CONCLUSION AND DISCUSSION<br />
In this paper, we propose a novel tree structure named<br />
AT-Tree to ma<strong>in</strong>ta<strong>in</strong> transaction itemsets of an uncerta<strong>in</strong><br />
dataset, and a correspond<strong>in</strong>g algorithm named AT-M<strong>in</strong>e<br />
to m<strong>in</strong>e frequent itemsets. AT-M<strong>in</strong>e requires two scans of<br />
dataset to create an AT-Tree. In the first scan, it creates a<br />
header table to ma<strong>in</strong>ta<strong>in</strong> sorted frequent items <strong>in</strong> the<br />
descend<strong>in</strong>g order of support numbers of items. In the<br />
second scan, it ma<strong>in</strong>ta<strong>in</strong>s probability values of frequent<br />
items <strong>in</strong> each transaction itemsets to an array; it <strong>in</strong>serts<br />
frequent items <strong>in</strong> each transaction itemsets to an AT-Tree;<br />
it ma<strong>in</strong>ta<strong>in</strong>s probability <strong>in</strong>formation of each transaction<br />
itemsets to the tail node. So the AT-Tree is as compact as<br />
the orig<strong>in</strong>al FP-Tree, and it does not lose the probability<br />
<strong>in</strong>formation of each transaction itemsets. Thus, AT-M<strong>in</strong>e<br />
can f<strong>in</strong>d frequent itemsets from AT-Tree without<br />
additional scan of dataset.<br />
Experiments were performed on sparse and dense<br />
datasets. We compared our proposed algorithm with<br />
some state-of-the-art level-wise and pattern-growth<br />
algorithms. The experimental results show that the<br />
proposed algorithm has better performance on dense<br />
datasets and large sparse datasets, and their time<br />
performance is stable on both dense and sparse datasets<br />
along with the decreas<strong>in</strong>g of the m<strong>in</strong>imum expected<br />
support threshold.<br />
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© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1427<br />
A Solution for Privacy-Preserv<strong>in</strong>g Data<br />
Manipulation and Query on NoSQL Database<br />
Guo Yub<strong>in</strong> a , Zhang Liankuan b , L<strong>in</strong> Fengren a , Li Xim<strong>in</strong>g a,∗<br />
a College of Informatics, South Ch<strong>in</strong>a Agricultural University, Guangzhou 510640, Ch<strong>in</strong>a<br />
Email: {guoyub<strong>in</strong>,l<strong>in</strong>fengren,lixim<strong>in</strong>g}@scau.edu.cn<br />
b College of Science, South Ch<strong>in</strong>a Agricultural University, Guangzhou 510640, Ch<strong>in</strong>a<br />
Email: zhangliankuan@scau.edu.cn<br />
Abstract— Privacy of data owners and query users is vital <strong>in</strong><br />
modern cloud<strong>in</strong>g data management. Many researches have<br />
been done on cloud security, but most of them are focused on<br />
the privacy of data owners or of query users separately. How<br />
to protect the privacy of the data owners and users simultaneously<br />
is a great challenge. In this paper, a solution of data<br />
storage and query protocol based on classical homomorphic<br />
encryption scheme is given to preserve privacy of both data<br />
owners and query users. Our ma<strong>in</strong> efforts are put on NoSQL<br />
database which is less structural than relational database.<br />
Storage and <strong>in</strong>dex<strong>in</strong>g structure on NoSQL database, query<br />
protocol are proposed, and algorithms for updat<strong>in</strong>g and<br />
query<strong>in</strong>g are also given. To implement our solution, Berkley<br />
DB, an excellent storage solution for NoSQL database is<br />
chosen and data are encrypted/decrypted us<strong>in</strong>g Elgamal<br />
and Paillier encryption system, us<strong>in</strong>g basic Java package.<br />
Experiments are done under different parameters <strong>in</strong> order<br />
to achieve better efficiency.<br />
Index Terms— NoSQL; cloud data management; privacy<br />
preserv<strong>in</strong>g<br />
need to query data from cloud, but the query might<br />
disclose sensitive <strong>in</strong>formation, behavior patterns of the<br />
user. For example, when Alice searches a website, such as<br />
Facebook, for friends who share the similar backgrounds<br />
(e.g., age, education, home address) with her, she should<br />
not disclose the query that <strong>in</strong>volves her own details to the<br />
cloud. Privacy of data owners and query users are def<strong>in</strong>ed<br />
as data privacy and user privacy respectively.<br />
I. INTRODUCTION<br />
Today cloud comput<strong>in</strong>g and data outsourc<strong>in</strong>g provide<br />
much convenience for k<strong>in</strong>ds of enterprises. For <strong>in</strong>stance,<br />
enterprises can concentrate on their ma<strong>in</strong> bus<strong>in</strong>ess while<br />
outsourc<strong>in</strong>g their complex data management and query<br />
service to service providers <strong>in</strong> cloud. These service<br />
providers <strong>in</strong> cloud focus on data management, and provide<br />
high quality service. But <strong>in</strong> such k<strong>in</strong>d of comput<strong>in</strong>g<br />
pattern, a bottleneck, privacy preserv<strong>in</strong>g of data owners<br />
and query users, seriously restricts progress of cloud<br />
comput<strong>in</strong>g.<br />
Consider environment illustrated <strong>in</strong> Fig. 1, data owners<br />
outsource their data and query services, but the data is<br />
private assets of them and should be protected aga<strong>in</strong>st<br />
the service providers and query<strong>in</strong>g users <strong>in</strong> some extent.<br />
On one hand, data owner can update, query and authorize<br />
access of data, while the service providers <strong>in</strong> cloud should<br />
know noth<strong>in</strong>g about especially detailed data, and query<br />
users should know not more than the exact answers for<br />
what she/he is query<strong>in</strong>g. On the other hand, query users<br />
Partially supported by National Science Foundation of Ch<strong>in</strong>a<br />
(61103232, 61272402, 61202294),Guangdong Provice Nature Science<br />
Foundation (10351806001000000, 10151064201000028), Guangdong<br />
Science Technology Plan Project (2010B010600046, 2011B090400325),<br />
Guangzhou Science Technology Plan Project (12C42101606).<br />
* Contact author.<br />
Figure 1: Architecture of Data Service on Cloud<br />
A. Related works<br />
For data privacy, the most general solution <strong>in</strong> recently<br />
research papers are encryption that means data deposited<br />
to service provider must be encrypted to avoid <strong>in</strong>formation<br />
leakage. Agrawal et al [5] proposed an order<br />
preserv<strong>in</strong>g encryption scheme (OPES) by which <strong>in</strong>dexes<br />
can be built directly on ciphertext. OPES can handle<br />
directly (without decryption) any <strong>in</strong>terest<strong>in</strong>g SQL query<br />
types, except SUM and AVG. But order preserv<strong>in</strong>g would<br />
leak <strong>in</strong>formation about data, and is not a good solution<br />
to privacy preserv<strong>in</strong>g. Hacigumus et al [9] proposed to<br />
handle SUM and AVG us<strong>in</strong>g homomorphic encryption<br />
function <strong>in</strong> the database context. Ayman Mousa et al. [14]<br />
uses classic REA, a symmetric encryption algorithm, to<br />
encrypted data respectively, and <strong>in</strong> this way the query process<strong>in</strong>g<br />
performance is assured, but <strong>in</strong>formation leakage<br />
and query privacy are not considered. Privacy homomorphism<br />
[17] is encryption transformations which map a<br />
set of operations on cleartext to another set of operations<br />
on ciphertext. In essence, privacy homomorphism enables<br />
complex computations (such as distances) based solely on<br />
ciphertext, without decryption. Unfortunately, as po<strong>in</strong>ted<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1427-1432
1428 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
out by Mykletun and Tsudik [15], its encryption scheme<br />
is <strong>in</strong>secure, demonstrated by its vulnerability to a basic<br />
ciphertext-only attack. However, for encrypted database,<br />
efficiency of query process<strong>in</strong>g is a great challenge.<br />
In [8], [10], [11], user privacy is considered together<br />
with data privacy. Yonghong Yu and Wenyang Bai discussed<br />
how to enforce data privacy and user privacy<br />
over outsourced database service <strong>in</strong> [18]. Hu et al. [11]<br />
proposed a solution based on secure traversal framework<br />
and privacy homomorphism based encryption scheme.<br />
Yong Hu et.al <strong>in</strong> [12] constructed an <strong>in</strong>telligent analysis<br />
model for outsourced software. And secure protocols<br />
for process<strong>in</strong>g k-nearest-neighbor queries (kNN) on R-<br />
tree <strong>in</strong>dex is given. In the authors follow<strong>in</strong>g work [10],<br />
they <strong>in</strong>tegrated <strong>in</strong>dex<strong>in</strong>g techniques with secure multiparty<br />
computation (SMC) based protocols to construct<br />
a secure <strong>in</strong>dex traversal framework. In this framework,<br />
the service provider cannot trace the <strong>in</strong>dex traversal path<br />
of a query dur<strong>in</strong>g evaluation, and thus keep privacy of<br />
users. Their protocols for query are complex, and hard<br />
to implement. The thought of composed key <strong>in</strong> <strong>in</strong>dex is<br />
directly prompted by T<strong>in</strong>gjian Ge’s work [8]. In his paper,<br />
keyword are composed together to improve the efficiency<br />
of aggregation operations <strong>in</strong> database. It is <strong>in</strong>tuitively that<br />
addition of keywords <strong>in</strong> block is dramatically efficient<br />
than add<strong>in</strong>g them one by one. But the authors have not<br />
considered range or s<strong>in</strong>gle key search. As to protect<strong>in</strong>g<br />
data privacy and user privacy, we use the block structure<br />
to hide real structure of keys <strong>in</strong> <strong>in</strong>dex. And key search is<br />
efficient for key comparison can be done k−<strong>in</strong>−1 where<br />
the k is key number <strong>in</strong> a s<strong>in</strong>gle block, that is decided by<br />
block and key size.<br />
B. Our contribution<br />
For data privacy and user privacy, a solution of data<br />
storage, manipulation and query is presented <strong>in</strong> this paper.<br />
In ma<strong>in</strong> database files, data are stored <strong>in</strong> key/value pair<br />
which is a typical NoSQL storage structure and are encrypted<br />
with Elgamal homomorphic encryption scheme.<br />
Keys <strong>in</strong> <strong>in</strong>dex are ciphertext of comb<strong>in</strong>ations of real keys<br />
<strong>in</strong> big blocks (<strong>in</strong> our experiments, one block is set to<br />
1024 bits), which are encrypted with Paillier encryption<br />
scheme [16] which is an additive homomorphic cryptosystem.<br />
When a key is queried, comparison can be done<br />
on ciphertext <strong>in</strong> blocks that improves efficiency of query.<br />
Protocols of data manipulation and query among data<br />
owner, service provider and query<strong>in</strong>g user is given. Algorithm<br />
for data updat<strong>in</strong>g and query<strong>in</strong>g are implemented to<br />
verify usefulness of the solution. As to implementation of<br />
our solution, Berkley DB, a typical key/value pair model<br />
database, is chosen to construct a prototype system. It is<br />
an excellent storage solution for NoSQL database for its<br />
high efficiency and convenience.<br />
C. Outl<strong>in</strong>e of the paper<br />
The rest of the paper is organized as follows. Section<br />
II provides background <strong>in</strong>formation on homomorphic<br />
encryption scheme, NoSQL database and <strong>in</strong>dex. Section<br />
III describes the query protocol and ma<strong>in</strong> algorithms,<br />
security analysis is also given <strong>in</strong> the section. Performance<br />
and analysis of experiments results are shown <strong>in</strong> section<br />
IV. F<strong>in</strong>ally, section V gives conclusions and future works.<br />
II. PRELIMINARY<br />
A. Homomorphic Encryption<br />
Homomorphic encryption allows specific types of computations<br />
to be carried out on ciphertext and obta<strong>in</strong>s<br />
an encrypted result which is ciphertext of the result<br />
of operations performed on the pla<strong>in</strong> text. The additive<br />
homomorphic property of a homomorphic cryptosystem<br />
is Enc(a) × Enc(b) = Enc(a + b) , where a and<br />
b are two pla<strong>in</strong> text message blocks, and Enc is the<br />
encryption function that takes a pla<strong>in</strong>text message block<br />
(and an encryption key) and returns the ciphertext block.<br />
Thus, <strong>in</strong> the above equation, + operates on the pla<strong>in</strong><br />
text, and × operates on the ciphertext. An example of<br />
such an encryption scheme is the Paillier system. Elgamal<br />
encryption scheme [6], [7] is multiplicative homomorphic<br />
with Enc(a) × Enc(b) = Enc(a ∗ b) where a, b, Enc<br />
and × share the same mean<strong>in</strong>gs with formula above,<br />
and operation + is multiple operation on the pla<strong>in</strong>text.<br />
The Legion of the Bouncy Castle [1] provided open<br />
source libraries of Java and c# Cryptography Architecture.<br />
Both Paillier and ElGamal encryption scheme have<br />
great practical implications on the outsourc<strong>in</strong>g of private<br />
computations, such as, <strong>in</strong> the context of cloud comput<strong>in</strong>g<br />
and outsourc<strong>in</strong>g [13].<br />
B. NoSQL database and <strong>in</strong>dex<br />
NoSQL database is def<strong>in</strong>ed as the next Generation<br />
Databases mostly because of the follow<strong>in</strong>g characteristics:<br />
be<strong>in</strong>g non-relational, distributed, open-source and horizontally<br />
scalable [2]. The concept NoSQL is prompted<br />
by Carlo Strozzi <strong>in</strong> 1998 [3], and the current NoSQL<br />
movement beg<strong>in</strong>n<strong>in</strong>g from 2009 often more characteristics<br />
apply such as: schema-free, easy replication support,<br />
simple API, eventually consistent / BASE (not ACID),<br />
a huge amount of data and more. From NoSQL Data<br />
Model<strong>in</strong>g Techniques [4] data model for NoSQL Database<br />
can be cataloged <strong>in</strong>to key/value or tuple store, Bigtable<br />
style databases, Document databases, and graph<br />
databases. Berkeley DB is a robust solution on which<br />
to build a NoSQL system, and the storage system of its<br />
key/value pair is more efficient than other database. That<br />
is the reason for us to choose it as our base database <strong>in</strong><br />
our experiments.<br />
III. SOLUTION FOR STORAGE AND UPDATING<br />
In this section some symbols are def<strong>in</strong>ed for simplification.<br />
owner means data owner, sp is service provider<br />
<strong>in</strong> cloud, and user data user for query. We use Paillier<br />
crypto-system to encrypt keys and values <strong>in</strong> NoSQL<br />
database. System parameter is taken as n. Enc(m, pk)<br />
is the function to encrypt pla<strong>in</strong>text m with public key<br />
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pk, and Dec(c, sk) function to decrypt ciphertext c with<br />
private key sk. Denote the public key and secret key of<br />
data owner as (pk owner , sk owner ). Denote the public key<br />
and secret key of user user i as (pk useri , sk useri ). All data<br />
are encrypted us<strong>in</strong>g homomorphic encryption algorithm,<br />
each one of owner, sp and user publishes his public key<br />
and uses the private key to decrypt ciphers.<br />
A. data storage<br />
In our solution, data are stored <strong>in</strong> database, and <strong>in</strong><br />
key/data model. That means each tuple is composed of<br />
one key and one data, the key and data are encrypted<br />
respectively. To construct <strong>in</strong>dices of data, several keys<br />
are composited together to form a 1024 b<strong>in</strong>ary bits block.<br />
Number of keys <strong>in</strong> one block is determ<strong>in</strong>ed by length of<br />
key. Let l be length of key, then the number of keys <strong>in</strong> one<br />
block is ⌊(1024)/(l+1)⌋ and one bit is added to each key<br />
to deal with overflow.. Let k 1 , k 2 , . . . , k m be keys which<br />
will be comb<strong>in</strong>ed together, then the key block <strong>in</strong> <strong>in</strong>dex k<br />
can be computed as follows:<br />
Algorithm 1: Index construct<strong>in</strong>g algorithm<br />
Input: key, po<strong>in</strong>ter*<br />
Output: <strong>in</strong>dex file f<br />
1 f= New(file );<br />
2 l= length of key;<br />
3 n = <strong>in</strong>t(1024/(l + 1));<br />
4 while not end of <strong>in</strong>put do<br />
5 i = 0;<br />
6 m 1 = m 2 = 0;<br />
7 while i
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Algorithm 2: Data <strong>in</strong>sert<strong>in</strong>g algorithm<br />
Input: < key, value > //a new tuple that is <strong>in</strong>sert<strong>in</strong>g<br />
<strong>in</strong>to the database<br />
Output:<br />
1 //Insert a new tuple<br />
< Enc(key, pk owner ), Enc(key, pk owner ) > <strong>in</strong>to<br />
database.;<br />
2 T =< Enc(key, pk owner ), Enc(value, pk owner ) >;<br />
3 Attach<br />
T =< Enc(key, pk owner ), Enc(value, pk owner ) ><br />
to the end of ma<strong>in</strong> database file;<br />
4 //<strong>in</strong>dex ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g;<br />
5 for each <strong>in</strong>dex do<br />
6 Construct its new keys key ′ ;<br />
7 t =<<br />
Enc(key ′ , pk owner ), Enc(key, pk owner ) >;<br />
8 if the last data block of <strong>in</strong>dex file is not full then<br />
9 (c key , c value )= ciphertext of last block ;<br />
10 c key = c l+1<br />
key + Enc(key, pk owner) mod n 2 ;<br />
11 c value = c l+1<br />
value + Enc(value, pk owner)<br />
mod n 2 ;<br />
12 Write (c key , c value ) back to file;<br />
13 else<br />
14 Attach T =<<br />
Enc(key, pk owner ), Enc(value, pk owner ) ><br />
to the end of <strong>in</strong>dex file.<br />
15 Send the <strong>in</strong>dex back to sp and replace old one ;<br />
Algorithm 3: Data delet<strong>in</strong>g algorithm<br />
Input: t =<<br />
Enc(key, pk owner ), Enc(value, pk owner ) >,<br />
database(ma<strong>in</strong> file and <strong>in</strong>dices)<br />
Output: database(ma<strong>in</strong> file and <strong>in</strong>dices) after<br />
deletion<br />
1 Select<br />
t =< Enc(key, pk owner ), Enc(value, pk owner )) ><br />
<strong>in</strong> ma<strong>in</strong> file and <strong>in</strong>dices.;<br />
2 //delet<strong>in</strong>g from ma<strong>in</strong> database file, is done by sp;<br />
3 Select the last tuple of ma<strong>in</strong> database file as t 1 ;<br />
4 Replace t with t 1 ;<br />
5 //delet<strong>in</strong>g from <strong>in</strong>dex;<br />
6 for each <strong>in</strong>dex do<br />
7 Construct key key ′ ;<br />
8 Let t =<<br />
Enc(key ′ , pk owner ), Enc(key, pk owner ) >;<br />
9 F<strong>in</strong>d the block b t <strong>in</strong> which t is the ith key;<br />
10 F<strong>in</strong>d the last key block b l <strong>in</strong> <strong>in</strong> which key t l is<br />
<strong>in</strong> b l ;<br />
11 b t = b t /t i∗(l+1) ∗ t i∗(l+1)<br />
l<br />
mod n 2 ;<br />
12 b l = b l /t l mod n 2 ;<br />
13 Send the <strong>in</strong>dex file to sp and replace old one;<br />
Figure 3: An example of query<strong>in</strong>g<br />
We know, the query algorithm is oblivious for data user.<br />
The data user encrypted additive reverse of queried key<br />
at first, and send it to service provider. Then the service<br />
provider extends it <strong>in</strong>to queried block, and chooses proper<br />
<strong>in</strong>dex to multiple the queried block with a key block, and<br />
as follows, the product is sent to data owner one by one.<br />
When the data owner receives the product, it decrypts<br />
the cipher and decomposes the pla<strong>in</strong>text to f<strong>in</strong>d which<br />
one is 0, which means the accord<strong>in</strong>g key <strong>in</strong> the block<br />
is equal to queried key. The serial numbers of the key<br />
are sent back to the service provider, service provider<br />
can get the key <strong>in</strong> ma<strong>in</strong> data file and get queried data<br />
for the data owner. This process will term<strong>in</strong>ated when the<br />
queried key is found or all blocks <strong>in</strong> the <strong>in</strong>dex is searched.<br />
To database applications, query<strong>in</strong>g is the most common<br />
operation. In our solution, all of the three roles, service<br />
provider, data owner and data user must participant <strong>in</strong><br />
the query<strong>in</strong>g process. To preserve both data owner and<br />
user privacy, query<strong>in</strong>g process is more complex than <strong>in</strong><br />
traditional database system. Fig. 4 presents the query<strong>in</strong>g<br />
protocol <strong>in</strong> detail.<br />
D. Security analysis<br />
Figure 4: Query protocol<br />
In this protocol, data user prompts a query by encrypt<strong>in</strong>g<br />
additive <strong>in</strong>verse of queried key with public key of data<br />
owner and sends it to the service provider. The second<br />
step starts when the service provider receives a query<br />
request. The service provider chooses proper <strong>in</strong>dex, and<br />
then a 1024 bits big <strong>in</strong>teger M is composed by repeat<strong>in</strong>g<br />
the queried key several times. Then multiplies M by each<br />
key block respectively, and sends the results to data owner.<br />
When the data owner receives the products, he decrypts<br />
the cipher and decomposes the pla<strong>in</strong>text to f<strong>in</strong>d 0 <strong>in</strong> each<br />
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product. This procedure can be ended when the key is<br />
found or all products are searched. Then the serial number<br />
of equal key is sent back to the service provider, and all<br />
the queried data are sent to the data owner. At last step,<br />
the data owner decrypts the data with his owner private<br />
key and encrypts it with public key of the data user and<br />
sent the result to him.<br />
Dur<strong>in</strong>g the query process, additive reverse of the<br />
queried keyword is encrypted before send<strong>in</strong>g to the service<br />
provider, and the queried data is sent by data owner,<br />
therefore the service provider can get no <strong>in</strong>formation<br />
about what the data user is query<strong>in</strong>g on the database.<br />
Security can also be enforced by add<strong>in</strong>g disturb<strong>in</strong>g data<br />
when the data owner requests query data from service<br />
provider. And as to the data owner, dur<strong>in</strong>g the query<br />
process, only product of the queried block and <strong>in</strong>dex key<br />
blocks are received and decrypted to f<strong>in</strong>d the order of<br />
equal ones, while the queried key is kept <strong>in</strong>visible. The<br />
data owner do not know which <strong>in</strong>dex is chosen and cannot<br />
deduce what the data user is query<strong>in</strong>g. It is obvious that<br />
we cannot complete query without leak<strong>in</strong>g no <strong>in</strong>formation<br />
about the user and what she is query<strong>in</strong>g. At least, queried<br />
result must be sent back to her. What we really want to do<br />
and can do is to limit the <strong>in</strong>formation leakage as much as<br />
possible. From the analysis above, we can see, confidence<br />
of data owner can surely be protected for homomorphic<br />
encryption scheme is used. Data privacy and user privacy<br />
are all kept by the scheme we propose to some extent.<br />
Figure 5: Query efficiency on data quantity, and length of<br />
key<br />
length. In this figure thread number is x axis, and there<br />
3 curves are with different key length. It is oblivious<br />
that the best value of thread number is 4. When thread<br />
is few, comput<strong>in</strong>g power of CPU cannot be fully used.<br />
And when threads are too much, communication and<br />
context change decrease the efficiency of the solution.<br />
Thread number is vital for most service providers <strong>in</strong><br />
clouds. And parallel process of key words comparison can<br />
improve query performance drastically. In our prototype<br />
system, block comparison is divided <strong>in</strong>to several parts<br />
simply, query efficiency can be heightened further with<br />
sophisticated technology of parallel programm<strong>in</strong>g. Note<br />
that thread number is a hardware-depended parameter.<br />
A. Setup<br />
IV. EXPERIMENTS<br />
Our experiments are conducted on BDB database<br />
system on W<strong>in</strong>dows 7. We implements the generalized<br />
Paillier system with basic Java package, and the Elgamal<br />
scheme is from open source library of bouncy castle<br />
[1]. All experiments of the solution are implemented <strong>in</strong><br />
Java with JDK 1.7 and the prototype system are run on<br />
personal computer with Intel 2Ghz processor and 2GB<br />
memory.<br />
B. Experiments design and analysis<br />
A series of experiments have been done to test efficiency<br />
of our solution. Some vital parameters, like<br />
quantity of data, thread number, and length of key, have<br />
been changed to f<strong>in</strong>d difference. Fig. 5 illustrates query<br />
efficiency of our solution. In this figure, x axis is number<br />
of tuples which is set to be 20000, 30000, 40000, 50000,<br />
75000 and 100000, while y axis is average time used<br />
for a s<strong>in</strong>gle value query. And we can get 3 curves when<br />
the length of key is set to 5, 10 and 20 decimal bits<br />
respectively. (as <strong>in</strong> b<strong>in</strong>ary, it should be 1, 2, and 4 bytes<br />
approximately.) On the whole, query efficiency is much<br />
better when length of key is not so long. The reason<br />
lies <strong>in</strong> that when the key is short, more keys can be put<br />
<strong>in</strong>to one s<strong>in</strong>gle block, therefore a comparison on block is<br />
equivalent to much more comparisons on s<strong>in</strong>gle key.<br />
In Fig. 6, tuple number is set to 50,000, to illustrate<br />
query efficiency variation on thread number and key<br />
Figure 6: Query efficiency on thread number and key<br />
length<br />
Fig. 7 illustrates efficiency variation accord<strong>in</strong>g to thread<br />
number and tuple number when the key size is fixed to 10.<br />
From the figure, we can see, query time <strong>in</strong>creases more<br />
quickly when tuples are more than 50,000. And it means<br />
performance of our solution is more better to middle scale<br />
database.<br />
V. CONCLUSION<br />
Homomorphic encryption scheme provides a good solution<br />
to privacy preservation for database system. We<br />
present a storage solution for NoSQL database us<strong>in</strong>g homomorphic<br />
encryption algorithms. Protocol of data query<strong>in</strong>g<br />
is proposed, and algorithms for data manipulation are<br />
given also. In <strong>in</strong>dices, keys are composed <strong>in</strong>to big blocks<br />
to improve the performance of encryption and decryption,<br />
therefore accelerate the process of data manipulation and<br />
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1432 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 7: Query efficiency on thread number and tuple<br />
number<br />
query. Although Paillier and Elgamal encryption scheme<br />
is not so efficient compar<strong>in</strong>g to symmetric encryption<br />
schemes like DES and SHA. But it is good enough for<br />
some cases that users pay more attention on <strong>in</strong>formation<br />
security than computation performance.<br />
Future work <strong>in</strong>cludes improv<strong>in</strong>g efficiency of the system<br />
and extend<strong>in</strong>g system functionality, such as extended<br />
query on range, aggregation, and jo<strong>in</strong>.<br />
REFERENCES<br />
[1] The legion of the bouncy castle. http://www.<br />
bouncycastle.org/, 2013. [Onl<strong>in</strong>e; accessed 10-Jan-<br />
2013].<br />
[2] Non - relational universe. http://nosql-database.<br />
org/, 2013. [Onl<strong>in</strong>e; accessed 10-Jan-2013].<br />
[3] Nosql, a relational database management system.<br />
http://www.strozzi.it/cgi-b<strong>in</strong>/CSA/tw7/<br />
I/en US/nosql/Home\%20Page, 2013. [Onl<strong>in</strong>e;<br />
accessed 10-Jan-2013].<br />
[4] Nosql data model<strong>in</strong>g techniques. http:<br />
//highlyscalable.wordpress.com/2012/<br />
03/01/nosql-data-model<strong>in</strong>g-techniques/,<br />
2013. [Onl<strong>in</strong>e; accessed 10-Jan-2013].<br />
[5] Rakesh Agrawal, Jerry Kiernan, Ramakrishnan Srikant,<br />
and Yirong Xu. Order preserv<strong>in</strong>g encryption for numeric<br />
data. In Proceed<strong>in</strong>gs of the 2004 ACM SIGMOD <strong>in</strong>ternational<br />
conference on Management of data, SIGMOD ’04,<br />
pages 563–574, New York, NY, USA, 2004. ACM.<br />
[6] Haipeng Chen, Xuanj<strong>in</strong>g Shen, and Y<strong>in</strong>gda Lv. An implicit<br />
elgamal digital signature scheme. JSW, 6(7):1329–1336,<br />
2011.<br />
[7] Taher El Gamal. A public key cryptosystem and a signature<br />
scheme based on discrete logarithms. In CRYPTO, pages<br />
10–18, 1984.<br />
[8] T<strong>in</strong>gjian Ge, Stanley B. Zdonik, and Stanley B. Zdonik.<br />
Answer<strong>in</strong>g aggregation queries <strong>in</strong> a secure system model.<br />
In VLDB, pages 519–530, 2007.<br />
[9] Hakan Hacgm, Bala Iyer, and Sharad Mehrotra. Efficient<br />
execution of aggregation queries over encrypted relational<br />
databases. In YoonJoon Lee, Jianzhong Li, Kyu-Young<br />
Whang, and Doheon Lee, editors, Database Systems for<br />
Advanced Applications, volume 2973 of Lecture Notes<br />
<strong>in</strong> Computer Science, pages 125–136. Spr<strong>in</strong>ger Berl<strong>in</strong><br />
Heidelberg, 2004.<br />
[10] Haibo Hu and Jianliang Xu. Non-exposure location<br />
anonymity. In Yannis E. Ioannidis, Dik Lun Lee, and<br />
Raymond T. Ng, editors, ICDE, pages 1120–1131. IEEE,<br />
2009.<br />
[11] Haibo Hu, Jianliang Xu, Chushi Ren, Byron Choi, and<br />
Byron Choi. Process<strong>in</strong>g private queries over untrusted data<br />
cloud through privacy homomorphism. In ICDE, pages<br />
601–612, 2011.<br />
[12] Yong Hu, Xizhu Mo, Xiangzhou Zhang, Yuran Zeng,<br />
Jianfeng Du, and Kang Xie. Intelligent analysis model<br />
for outsourced software project risk us<strong>in</strong>g constra<strong>in</strong>t-based<br />
bayesian network. JSW, 7(2):440–449, 2012.<br />
[13] Daniele Micciancio. A first glimpse of cryptography’s holy<br />
grail. page 96, 2010.<br />
[14] Ayman Mousa, Elsayed Nigm, El-Sayed El-Rabaie,<br />
Osama S. Faragallah, and Osama S. Faragallah. Query<br />
process<strong>in</strong>g performance on encrypted databases by us<strong>in</strong>g<br />
the rea algorithm. pages 280–288, 2012.<br />
[15] E<strong>in</strong>ar Mykletun and Gene Tsudik. Aggregation queries<br />
<strong>in</strong> the database-as-a-service model. In Ernesto Damiani<br />
and Peng Liu, editors, Data and Applications Security XX,<br />
volume 4127 of Lecture Notes <strong>in</strong> Computer Science, pages<br />
89–103. Spr<strong>in</strong>ger Berl<strong>in</strong> / Heidelberg, 2006.<br />
[16] Pascal Paillier. Public-key cryptosystems based on composite<br />
degree residuosity classes. In EUROCRYPT, pages<br />
223–238, 1999.<br />
[17] R. Rivest, L. Adleman, and M. Dertouzos. On data banks<br />
and privacy homomorphisms. pages 169–177. Academic<br />
Press, 1978.<br />
[18] Yonghong Yu and Wenyang Bai. Enforc<strong>in</strong>g data privacy<br />
and user privacy over outsourced database service. JSW,<br />
6(3):404–412, 2011.<br />
GuoYub<strong>in</strong> Received Ph. D. from South Ch<strong>in</strong>a University of<br />
Technology <strong>in</strong> 2007. She is now lecturer <strong>in</strong> South Ch<strong>in</strong>a<br />
Agricultural University. Her research <strong>in</strong>terests <strong>in</strong>clude Database<br />
theory and technology, cryptography and network comput<strong>in</strong>g.<br />
Zhang Liankuan Received Ph. D. from South Ch<strong>in</strong>a Agricultural<br />
University <strong>in</strong> 2012. He is now lecturer <strong>in</strong> South Ch<strong>in</strong>a<br />
Agricultural University. His research <strong>in</strong>terests <strong>in</strong>clude Database<br />
theory, technology and network comput<strong>in</strong>g.<br />
L<strong>in</strong> Fengren He is now Bachelor student <strong>in</strong> South Ch<strong>in</strong>a<br />
Agricultural University. His research <strong>in</strong>terests <strong>in</strong>clude Database<br />
theory and technology.<br />
Li Xim<strong>in</strong>g Received Ph.D. degree from College of Informatics,<br />
South Ch<strong>in</strong>a Agricultural University, Guangzhou, Guangdong,<br />
Ch<strong>in</strong>a, <strong>in</strong> 2011. His current research <strong>in</strong>terests <strong>in</strong>clude computer<br />
theory and cryptography.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1433<br />
Predicate Formal System based on 1-level<br />
Universal AND Operator and its Soundness<br />
Y<strong>in</strong>gcang Ma<br />
School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi, 710048, Ch<strong>in</strong>a<br />
School of Electronics and <strong>in</strong>formation, Northwestern Polytechnical University, Xi’an, Shaanxi, 710048, Ch<strong>in</strong>a<br />
Email: may<strong>in</strong>gcang@126.com<br />
Huacan He<br />
School of Computer Science, Northwestern Polytechnical University, Xi’an, Shaanxi, 710048, Ch<strong>in</strong>a<br />
Email: hehuac@nwpu.edu.cn<br />
Abstract—The aim of this paper is solv<strong>in</strong>g the predicate<br />
calculus formal system based on 1-level universal AND<br />
operator. Firstly, universal logic and propositional calculus<br />
formal deductive system UL − h∈ (0, 1] are <strong>in</strong>troduced. Secondly,<br />
a predicate calculus formal deductive system ∀ UL − h∈ (0,<br />
1]<br />
based on 1-level universal AND operator is built. Thirdly,<br />
the soundness theorem and deduction theorem of system<br />
∀ UL − h∈ (0,<br />
1] are given, which ensure that the theorems are<br />
tautologies and the reason<strong>in</strong>g rules are valid <strong>in</strong><br />
system ∀ h (0 1] .<br />
UL − ∈ ,<br />
Index Terms—universal logic, predicate calculus formal<br />
system, universal AND operator<br />
I. INTRODUCTION<br />
How to deal with various uncerta<strong>in</strong>ties and evolution<br />
problems have been critical issues for further<br />
development of artificial <strong>in</strong>telligence [1,2]. Mathematical<br />
logic is too rigid and it can only solve certa<strong>in</strong>ty problems,<br />
therefore, non-classical logic and modern logic develop<br />
rapidly, for example, fuzzy logic and universal logic.<br />
Considerable progresses have been made <strong>in</strong> logical<br />
foundations of fuzzy logic <strong>in</strong> recent years, especially for<br />
logic system based on t-norm and its residua [3]. Some<br />
well-known logic systems have been built up, such as, the<br />
basic logic (BL) [4, 5] <strong>in</strong>troduced by Hajek; the monoidal<br />
t-norm based logic [6, 7] <strong>in</strong>troduced by Esteva and Godo;<br />
a formal deductive system L* <strong>in</strong>troduced by Wang [8-10],<br />
Universal logic proposed by He [11], and so on.<br />
Universal logic is a new cont<strong>in</strong>uous-valued logic<br />
system <strong>in</strong> study<strong>in</strong>g flexible world’s logical rule, which<br />
uses generalized correlation and generalized<br />
autocorrelation to describe the relationship between<br />
propositions, more studies can be found <strong>in</strong> [12-14]. For a<br />
logic system, the formalization’s studies are very<br />
important, which <strong>in</strong>clude propositional calculus and<br />
predicate calculus. The propositional calculus formal<br />
systems are studied <strong>in</strong> [15-18]. But the studies of<br />
predicate calculus formal systems of universal logic are<br />
relatively rare, so we will ma<strong>in</strong>ly study the predicate<br />
calculus formal system <strong>in</strong> this paper, which can enrich the<br />
formalization’s studies of universal logic.<br />
Some predicate calculus formal deductive systems are<br />
built for fuzzy logic systems, for example, the predicate<br />
calculus formal deductive systems of Schweizer-Sklar t-<br />
norm <strong>in</strong> [19, 20]. The predicate calculus formal deductive<br />
systems of universal logic have been studies <strong>in</strong> [21-24],<br />
which ma<strong>in</strong>ly focus on the 0-level universal AND<br />
operator. In this paper, we focus on the formal system of<br />
universal logic based on 1-level universal AND operator.<br />
We will build predicate formal system ∀UL − h∈ (0,<br />
1] for 1-<br />
level universal AND operator, and its soundness and<br />
deduction theorem are given.<br />
The paper is organized as follows. After this<br />
<strong>in</strong>troduction, Section II conta<strong>in</strong>s necessary background<br />
knowledge about BL and UL. Section III we will build the<br />
predicate calculus formal deductive system ∀ UL − h∈ (0,<br />
1] for<br />
1-level universal AND operator. In Section IV the<br />
soundness and deduction theorem of system ∀ UL − h∈ (0,<br />
1]<br />
will be given. The f<strong>in</strong>al section offers the conclusion.<br />
II. PRELIMINARIES<br />
A. The Basic Fuzzy Logic BL and BL-algebra<br />
The languages of BL [3] <strong>in</strong>clude two basic connectives<br />
→ and & , one truth constant 0 . Further connectives are<br />
def<strong>in</strong>ed as follows:<br />
ϕ ∧ ψ is ϕ & ( ϕ → ψ)<br />
,<br />
ϕ ∨ ψ is (( ϕ →ψ) →ψ) ∧( ψ →ϕ) → ϕ)<br />
,<br />
¬ ϕ is ϕ → 0 ,<br />
ϕ ≡ ψ is ( ϕ →ψ) & ( ψ → ϕ)<br />
.<br />
The follow<strong>in</strong>g formulas are the axioms of BL:<br />
(i) ( ϕ →ψ) →(( ψ → χ)( ϕ → χ))<br />
(ii) ( ϕ & ψ)<br />
→ ϕ<br />
(iii) ( ϕ & ψ) → ( ψ & ϕ)<br />
(iv) ϕ &( ϕ →ψ) →( ψ &( ψ → ϕ))<br />
(v) ( ϕ →( ψ → χ)) →(( ϕ&<br />
ψ) → χ)<br />
(vi) (( ϕ & ψ) → χ) →( ϕ →( ψ → χ))<br />
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(vii) (( ϕ →ψ) → χ) →((( ψ →ϕ) → χ) → χ)<br />
(viii) 0 → ϕ<br />
The deduction rule of BL is modus ponens.<br />
Def<strong>in</strong>ition 1 [3] A BL-algebra is an algebra<br />
L = ( L,∩,∪,∗,⇒, 01) , with four b<strong>in</strong>ary operations and<br />
two constants such that ( L,∩,∪, 01) , is a lattice with the<br />
greatest element 1 and the least element 0 (with respect to<br />
the lattice order<strong>in</strong>g ≤ ), ( L,∗, 1) is a commutative<br />
semigroup with the unit element 1, i.e. ∗ is commutative,<br />
associative and 1∗ x = x for all x, the follow<strong>in</strong>g<br />
conditions hold for all x, yz , :<br />
(i) z ≤( x⇒ y)<br />
iff x ∗z ≤ y<br />
(ii) x ∩ y = x∗( x⇒<br />
y)<br />
(iii) ( x⇒ y) ∪( y⇒ x) = 1.<br />
B. Universal Logic<br />
Universal logic was proposed by He [11], which th<strong>in</strong>ks<br />
that all th<strong>in</strong>gs <strong>in</strong> the world are correlative, that is, they are<br />
either mutually exclusive or mutually consistent, and we<br />
call this k<strong>in</strong>d of relation generalized correlation.<br />
The basic pr<strong>in</strong>ciples of universal logic show as follows:<br />
A core objective. The objective is that any one of<br />
modern logics should <strong>in</strong>clude one or some dialectical<br />
contradictions, and which should exclude the logical<br />
contradictions. And different advanced logics have<br />
different dialectical contradictions.<br />
Two basic methods. There are two ways to <strong>in</strong>clude<br />
dialectical contradictions (or uncerta<strong>in</strong>ty) <strong>in</strong> general.<br />
Firstly, the logical scope narrows to the sub-space that<br />
adapts to just <strong>in</strong>clude the dialectical contradictions (or<br />
uncerta<strong>in</strong>ty). Secondly, the logic system express the<br />
impact of the dialectical contradictions (or uncerta<strong>in</strong>ties)<br />
through cont<strong>in</strong>uously variable flexible parameters and<br />
functions <strong>in</strong> the logic operation model.<br />
Three Break directions. There are three different<br />
break directions for the constra<strong>in</strong>ts of various modern<br />
logics relative to that of standard logic: the number of<br />
truth value of proposition, the dimension of truth value<br />
space, and the completeness of <strong>in</strong>formation reason<strong>in</strong>g.<br />
Four logical elements. There are four logical elements<br />
to construct a logical system: doma<strong>in</strong>, propositional<br />
connectives, quantifiers and reason<strong>in</strong>g rules. Universal<br />
logic discussed the possible forms of these elements, and<br />
put forward their general expression.<br />
Universal logic <strong>in</strong>cludes four ways to conta<strong>in</strong><br />
dialectical contradictions (uncerta<strong>in</strong>ties) as follows:<br />
1) The establishment of flexible doma<strong>in</strong>.<br />
The uncerta<strong>in</strong>ty firstly presents <strong>in</strong> the uncerta<strong>in</strong>ty of<br />
truth value of proposition. From the view of truth value<br />
doma<strong>in</strong> and space dimension of proposition variable, the<br />
scope of uncerta<strong>in</strong>ty is fraction dimension space [0, 1] n ,<br />
n>0, which can <strong>in</strong>clude <strong>in</strong>teger dimension space [0, 1] n ,<br />
n=2, 3, …, and which can also <strong>in</strong>clude 1-dimension<br />
cont<strong>in</strong>uous value space [0, 1]. This gives the possible to<br />
break the limitations of truth value doma<strong>in</strong> of 1-<br />
dimaention two-valued logic.<br />
The classical logic is a s<strong>in</strong>gle granularity from the view<br />
of <strong>in</strong>dividual variable doma<strong>in</strong>, that is, the logical<br />
properties of whole doma<strong>in</strong> are identical. The future<br />
development trend of modern logic is <strong>in</strong>troduced the<br />
concept of granularity comput<strong>in</strong>g <strong>in</strong>to the logic. The<br />
doma<strong>in</strong> is divided <strong>in</strong>to different sub-doma<strong>in</strong>s accord<strong>in</strong>g to<br />
some k<strong>in</strong>d of equivalence relations, and the logical<br />
properties of different sub-doma<strong>in</strong> may be different to<br />
express the uncerta<strong>in</strong>ty of doma<strong>in</strong>. This gives the possible<br />
to break the limitations of s<strong>in</strong>gle granularity of 1-<br />
dimension two-valued logic.<br />
From the model doma<strong>in</strong>, the classical logic is the<br />
s<strong>in</strong>gle-mode. There are many different modes <strong>in</strong> the<br />
current modal logic. In the future cont<strong>in</strong>uous variable<br />
mode may be build, which can accurately describe the<br />
effect of modal area <strong>in</strong> uncerta<strong>in</strong>ty. This gives the<br />
possible to break the limitations of s<strong>in</strong>gle mode of 1-<br />
dimension two-valued logic.<br />
2) The def<strong>in</strong>ition of <strong>in</strong>tegrity cluster of operation<br />
model<br />
The effect of all k<strong>in</strong>ds of uncerta<strong>in</strong>ties on logic<br />
operations results can be expressed by all k<strong>in</strong>ds of<br />
cont<strong>in</strong>uous-valued proposition conjunction <strong>in</strong>tegrity<br />
cluster of operation model. For example, <strong>in</strong> the<br />
propositional universal logics, Firstly, we narrow the<br />
logical scope to <strong>in</strong>clude fitness subspace of the<br />
contradictions of enemy/friends, loose/strict, light/heavy<br />
(<strong>in</strong>clude one, two or three) through time and space;<br />
secondly, we <strong>in</strong>troduce two cont<strong>in</strong>uous variable flexible<br />
parameters k, h∈[0, 1] <strong>in</strong>to the logical operation models,<br />
and use the correspond<strong>in</strong>g adjustment function to<br />
describe the full impact of the dialectical contradictions<br />
(or uncerta<strong>in</strong>ty) for the proposition conjunction<br />
comput<strong>in</strong>g model. F<strong>in</strong>ally, we get the various types of<br />
propositional logics. It is obvious that if we can reduce<br />
the scope of logic to adapt to accommodate just a<br />
dialectical contradiction (or uncerta<strong>in</strong>ty) of the sub-space<br />
by time and space, then cont<strong>in</strong>uously variable flexible<br />
parameters and adjustment functions are <strong>in</strong>troduced <strong>in</strong>to<br />
the logic operation model, which can <strong>in</strong>clude effectively<br />
and deal with the dialectical contradictions (or<br />
uncerta<strong>in</strong>ties) <strong>in</strong> mathematics dialectical logic. This is<br />
foundation for cont<strong>in</strong>uous-valued logical algebra that will<br />
discuss below.<br />
3) Def<strong>in</strong><strong>in</strong>g a variety of flexible quantifiers to express<br />
the uncerta<strong>in</strong>ty of constra<strong>in</strong>ts (ranges).<br />
The flexible quantifiers are: the universal quantifier ∀; the<br />
existential quantifier ∃; the threshold quantifier ♂ k<br />
symboliz<strong>in</strong>g the threshold of propositional truth; the<br />
hypothesis quantifier $ k symboliz<strong>in</strong>g hypothesis<br />
proposition; the scope quantifier ∮ k constra<strong>in</strong><strong>in</strong>g the<br />
scope of <strong>in</strong>dividual variables; the position quantifier ♀ k<br />
<strong>in</strong>dicat<strong>in</strong>g the relative position of an <strong>in</strong>dividual variable<br />
and a specific po<strong>in</strong>t; the transition quantifier ∫ k chang<strong>in</strong>g<br />
the distribution transitional feature of the predicate truth.<br />
k∈[0, 1] is a variable parameter, which express the<br />
change of constra<strong>in</strong>ts. When k=1, the constra<strong>in</strong>ts are the<br />
largest (strong), and when k=0, the constra<strong>in</strong>ts are the<br />
smallest (weak). So <strong>in</strong> this way the logic not only<br />
describe the uncerta<strong>in</strong>ty of constra<strong>in</strong>ts, but also control<br />
the degree of reason<strong>in</strong>g rules by adjust<strong>in</strong>g the degree of k<br />
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value. For example, <strong>in</strong> the scope quantifier ∮ k , k can be<br />
changed cont<strong>in</strong>uously to express the uncerta<strong>in</strong>ty of the<br />
scope of <strong>in</strong>dividual variables. In special case, k=1<br />
<strong>in</strong>dicates the universal quantifier∀; k>0 <strong>in</strong>dicates<br />
existential quantifier ∃, k=! <strong>in</strong>dicates the only existential<br />
quantifier ∃!; k=0 <strong>in</strong>dicates the constra<strong>in</strong>ts of no scope<br />
quantifier.<br />
4) All k<strong>in</strong>ds of cont<strong>in</strong>uous-valued reason<strong>in</strong>g model<br />
Because the truth value of flexible proposition,<br />
comput<strong>in</strong>g model and quantifiers of proposition<br />
conjunction are flexible, the reason<strong>in</strong>g rules based on<br />
them such as deductive reason<strong>in</strong>g, <strong>in</strong>ductive reason<strong>in</strong>g,<br />
analogical reason<strong>in</strong>g, assum<strong>in</strong>g reason<strong>in</strong>g, the evolution<br />
of reason<strong>in</strong>g are also flexible. The flexible reason<strong>in</strong>g<br />
rules are different from standard logic, which can coexist<br />
<strong>in</strong> a reason<strong>in</strong>g process. They transform each other by<br />
chang<strong>in</strong>g flexible parameters, and <strong>in</strong> which deductive<br />
reason<strong>in</strong>g mode is the most basic mode. Therefore, the<br />
theoretical framework can describe the unity of opposites<br />
and transformation process of contradictions, which<br />
provides the possibility to the symbolization and<br />
mathematization of dialectical logic.<br />
The operators of universal logic as follow<strong>in</strong>g:<br />
1) Not operation:<br />
NOT operation model N (x) is unary operation on [0,<br />
1]→[0, 1], which satisfies the follow<strong>in</strong>g Not operation<br />
axiom.<br />
Boundary condition N1: N (0)=1, N (1)=0.<br />
Monotonicity N2: N (x) is monotonously decreas<strong>in</strong>g,<br />
iff ∀x, y∈[0, 1], if x 1 then its value will be 1, if x < 0 , its value<br />
will be 0.<br />
1-level universal AND operators are mapp<strong>in</strong>g<br />
1 mn mn 1/<br />
mn<br />
T :[0, 1] × [0, 1] → [0, 1] T( x, y, h, k) =Γ [( x + y −1) ]<br />
which is usually denoted by<br />
∧<br />
hk ,<br />
. The relation m and h is<br />
as same as (2), the relation of n and k is the same as (1).<br />
There are four special cases of T (x, y, h) (see Figure 2)<br />
as follows:<br />
Zadeh AND operator T (x, y, 1)=T 3 =m<strong>in</strong> (x, y)<br />
Probability AND operator T (x, y, 0.75)=T2=xy<br />
Bounded AND operator T (x, y, 0.5)=T 1 =max (0,<br />
x+y-1)<br />
Drastic AND operator T (x, y, 0)=T 0 =ite{m<strong>in</strong> (x,<br />
y)|max (x, y)=1; 0}<br />
Figure 2. AND operator model figure for special h<br />
3) OR operation:<br />
OR operation model S (x, y) is b<strong>in</strong>ary operation <strong>in</strong> [0,<br />
1] 2 →[0, 1], which satisfies the follow<strong>in</strong>g operation<br />
axioms: x, y, z∈[0, 1].<br />
Boundary condition S (1, y)=1, S (0, y)=y.<br />
Monotonicity S (x, y) <strong>in</strong>creases monotonously along<br />
with x, y.<br />
Association law S (S (x, y), z)=S (x, S (y, z)).<br />
Lower bound S (x, y)≥max (x, y).<br />
The Dualization law holds between S (x, y, k, h) and T<br />
(x, y, k, h).<br />
N (S (x, y, k, h), k)=T (N (x, k), N (y, k), k, h)<br />
N (T (x, y, k, h), k)=S (N (x, k), N (y, k), k, h)<br />
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There are four special cases of S (x, y, h) (see Figure 3)<br />
as follow<strong>in</strong>g:<br />
Zadeh OR operator S (x, y, 1)=S 3 =max (x, y)<br />
Probability OR operator S (x, y, 0.75)=S2=x+yxy<br />
Bounded OR operator S (x, y, 0.5)=S 1 =m<strong>in</strong> (1, x+<br />
y)<br />
Drastic OR operator S (x, y, 0)=S 0 =ite{max (x,<br />
y)|m<strong>in</strong> (x, y)=0;1}<br />
Figure 4. IMPLICATION operator model figure for special h<br />
Figure 3. OR operator model figure for special h<br />
4) IMPLICATION operation<br />
IMPLICATION operation model I (x, y) is b<strong>in</strong>ary<br />
operation <strong>in</strong> [0, 1] 2 →[0, 1], which satisfies the follow<strong>in</strong>g<br />
operation axioms: x, y, z∈[0, 1].<br />
Boundary conditions I1 I (0, y, h, k)=1, I (1, y, h, k)<br />
=y, I (x, 1, h, k)=1.<br />
Monotonicity I2 I (x, y, h, k) is monotone <strong>in</strong>creas<strong>in</strong>g<br />
along with y, and is monotone decreas<strong>in</strong>g along with x.<br />
Cont<strong>in</strong>uity I3 When h, k∈ (0, 1), I (x, y, h, k) is<br />
cont<strong>in</strong>uous along with x, y.<br />
Order-preserv<strong>in</strong>g property I4 I (x, y, h, k)=1, iff x≤y<br />
(except for h=0 and k=1).<br />
Deduction I5 T (x, I (x, y, h, k), h, k)≤y (Hypothetical<br />
consequence).<br />
0-level universal IMPLICATION operators are<br />
mapp<strong>in</strong>g<br />
I :[0, 1] × [0, 1] → [0, 1] , I( x, y, h) = ite{1 | x ≤ y; 0 | m ≤ 0 and<br />
1 m m 1/<br />
m<br />
y = 0 ;Γ [(1 − x + y ) ]}}<br />
, which is usually denoted by<br />
⇒<br />
h<br />
. The relation m and h is the same as (1).<br />
1-level universal IMPLICATION operators are<br />
mapp<strong>in</strong>g I :[0, 1] × [0, 1] → [0, 1] , I( x, y, h) = ite{1 | x≤ y; 0 |<br />
m and y x y<br />
1 mn mn 1/<br />
mn<br />
≤ 0 = 0 ;Γ [(1 − + ) ]}, which is usually<br />
denoted by ⇒<br />
h<br />
. The relation m and h is the same as (1),<br />
the relation of n and k is the same as (2).<br />
There are four special cases of I (x, y, h) (see Figure 4)<br />
as follow<strong>in</strong>g:<br />
Zadeh IMPLICATION operator I (x, y, 1)=I 3 =<br />
ite{1|x≤y; y}<br />
Probability IMPLICATION operator (Goguen<br />
Implication) I (x, y, 0.75)=I2=m<strong>in</strong> (1, y/x)<br />
Bounded IMPLICATION operator (Lukasiewicz<br />
Implication) I (x, y, 0.5)=I 1 =m<strong>in</strong> (1, 1-x+y)<br />
Drastic Implication operator I (x, y, 0)=I 0 =ite{y|x<br />
=1; 1}<br />
C. Universal Logic System ULh∈ (0,<br />
1]<br />
The languages of 0-level UL system ULh∈ (0, 1] are based on<br />
two basic connectives → and & and one truth constant 0 ,<br />
which semantics are 0-level universal AND, 0-level<br />
universal IMPLICATION and 0 respectively (see [15]).<br />
Axioms of the system ULh∈ (0, 1] are as follow<strong>in</strong>g:<br />
(i) ( φ →ψ) →(( ψ → χ)( φ → χ))<br />
(ii) ( φ & ψ)<br />
→ φ<br />
(iii) ( φ & ψ) → ( ψ & φ)<br />
(iv) φ &( φ →ψ) →( ψ &( ψ → φ))<br />
(v) ( φ →( ψ → χ)) →(( φ&<br />
ψ) → χ)<br />
(vi) (( φ & ψ) → χ) →( φ →( ψ → χ))<br />
(vii) (( φ →ψ) → χ) →((( ψ →φ) → χ) → χ)<br />
(viii) 0 → φ<br />
(ix) ( φ →φ& ψ) →(( φ →0) ∨ψ ∨(( φ →φ& φ) ∧( ψ → ψ & ψ)))<br />
.<br />
The deduction rule of ULh∈ (0, 1] is modus ponens.<br />
Def<strong>in</strong>ition 2 [15] A ŁΠG<br />
algebra is a BL-algebra <strong>in</strong><br />
which the identity<br />
( x⇒ x∗y) ⇒(( x⇒0) ∪ y∪(( x⇒ x∗x) ∩( y⇒ y∗ y))) = 1<br />
is valid.<br />
For each h ∈ (0, 1] , ([0, 1] , m<strong>in</strong>, max,∧ h,⇒ h, 0, 1) which is<br />
called ŁΠ G unit <strong>in</strong>terval is a l<strong>in</strong>ear order<strong>in</strong>g ŁΠ G algebra<br />
with its standard l<strong>in</strong>ear order<strong>in</strong>g.<br />
Theorem 1 [16] (Soundness) All axioms of ULh∈ (0, 1] are<br />
1-tautology <strong>in</strong> each PC (h). If φ and ϕ → ψ are 1-tautology<br />
of PC (h) then ψ is also a 1-tautology of PC (h).<br />
Consequently, each formula provable <strong>in</strong> ULh∈ (0, 1] is a 1-<br />
tautology of each PC (h), i.e. Γ φ , then Γ φ .<br />
Theorem 2 [16] (Completeness) The system ULh∈ (0, 1] is<br />
complete, i.e. If φ , then φ . In more detail, for each<br />
formula φ ϕ , the follow<strong>in</strong>g are equivalent:<br />
(i) φ is provable <strong>in</strong> ULh∈ (0, 1] , i.e. φ ;<br />
(ii) φ is an L-tautology for each ŁΠG<br />
-algebra L ;<br />
(iii) φ is an L-tautology for each l<strong>in</strong>early ordered ŁΠG<br />
-<br />
algebra L ;<br />
(iv) φ is a tautology for each ŁΠ G unit <strong>in</strong>terval, i.e.<br />
φ .<br />
D. Universal Logic System UL − h∈ (0,<br />
1]<br />
Def<strong>in</strong>ition 3 [17]Axioms of UL − h∈ (0, 1] are those of ULh∈ (0,<br />
1]<br />
plus<br />
( − −φ)<br />
≡ φ (Involution)<br />
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Δ( φ →ψ) →Δ( −ψ →− φ)<br />
(Order Revers<strong>in</strong>g)<br />
Δφ<br />
∨¬Δ φ<br />
Δ( φ ∨ψ) →( Δφ ∨Δ ψ)<br />
Δφ<br />
→ φ<br />
Δφ<br />
→ΔΔ φ<br />
Δ( φ →ψ) →( Δφ →Δ ψ)<br />
where<br />
¬ φ is φ → 0 . Deduction rules of UL − h∈ (0, 1] are those<br />
of UL Δ h∈ (0,, 1] that is, modus ponens and generalization: from<br />
ϕ derive Δ ϕ .<br />
Def<strong>in</strong>ition 4 [17] A ŁΠG Δ<br />
-algebra is a structure<br />
L =< L,∗,⇒,∩,∪, 01 , ,Δ > which is a ŁΠG<br />
algebra<br />
expanded by an unary operation Δ <strong>in</strong> which the<br />
follow<strong>in</strong>g formulas are true:<br />
Δx∪( Δx⇒ 0) = 1<br />
Δ( x ∪ y)<br />
≤ Δx∪Δ<br />
y<br />
Δx<br />
≤ x<br />
Δx<br />
≤ ΔΔ x<br />
( Δx) ∗( Δ( x⇒ y))<br />
≤ Δ y<br />
Δ 1=<br />
1<br />
Def<strong>in</strong>ition 5 [17] A ŁΠG − -algebra is a structure L<br />
=< L,∗,⇒,∩,∪, 01 , ,Δ,− > which is a ŁΠG Δ<br />
-algebra<br />
expanded by an unary operation -, and satisfy<strong>in</strong>g the<br />
follow<strong>in</strong>g conditions:<br />
(1) −− x = x<br />
(2) Δ( x ⇒ y) =Δ( −y⇒ − x)<br />
(3) Δx<br />
∨¬Δ x = 1<br />
(4) Δ( x ∨ y) ≤( Δx∨Δ<br />
y)<br />
(5) Δx ≤ x<br />
(6) Δx ≤ ΔΔ x<br />
(7) ( Δx) ∗( Δ( x⇒ y))<br />
≤ Δ y<br />
(8) Δ 1=<br />
1<br />
Theorem 3 [17] (Soundness) Each formula provable <strong>in</strong><br />
UL − h∈ (0, 1] is a L-tautology for each ŁΠG − -algebra.<br />
Theorem 4 [17] (Completeness) The system UL − h∈ (0, 1] is<br />
complete, i.e. If φ , then φ . In more detail, for each<br />
formula φ , the follow<strong>in</strong>g are equivalent:<br />
(i) φ is provable <strong>in</strong> UL − h∈ (0,, 1] i.e. ϕ ,<br />
(ii) φ is an L-tautology for each ŁΠG − -algebra L,<br />
(iii)φ is an L-tautology for each l<strong>in</strong>early ordered ŁΠG − -<br />
algebra L.<br />
III. PREDICATE FORMAL SYSTEM ∀ h (0 1]<br />
UL − ∈ ,<br />
In order to build first-order predicate formal deductive<br />
system based on 1-level universal AND operator, we give<br />
the first-order predicate language as follow<strong>in</strong>g:<br />
First-order language J consists of symbols set and<br />
generation rules:<br />
The symbols set of J consist of as follow<strong>in</strong>g:<br />
(1) Object variables: x, yzx , ,<br />
1, y1, z1, x2, y2, z2,;<br />
(2) Object constants: abca , , ,<br />
1, b1, c1,, Truth constants:<br />
01 , ;<br />
(3) Predicate symbols: PQRP , , ,<br />
1, Q1, R1,;<br />
(4) Connectives: &,→, Δ,− ;<br />
(5) Quantifiers: ∀ (universal quantifier), ∃<br />
(existential quantifier);<br />
(6) Auxiliary symbols: (, ), , .<br />
The symbols <strong>in</strong> (1)- (3) are called non-logical symbols<br />
of language J. The object variables and object constants<br />
of J are called terms. The set of all object constants is<br />
denoted by Var (J), The set of all object variables is<br />
denoted by Const (J), The set of all terms is denoted by<br />
Term (J). If P is n-ary predicate symbol, t 1<br />
, t 2<br />
,, t n<br />
are<br />
terms, then Pt (<br />
1, t2,, t n<br />
) is called atomic formula.<br />
The formula set of J is generated by the follow<strong>in</strong>g<br />
three rules <strong>in</strong> f<strong>in</strong>ite times:<br />
(i) If P is atomic formula, then P∈ J ;<br />
(ii) If PQ , ∈ J, then P&Q, P→ Q,ΔP∈ J,−P∈ J ;<br />
(iii) If P∈ J , and x ∈ Var( J ) , then<br />
( ∀ x) P,∃ ( x)<br />
P∈ J .<br />
The formulas of J can be denoted by φ, ϕψ , , φ1, ϕ1, ψ1,.<br />
Further connectives are def<strong>in</strong>ed as follow<strong>in</strong>g:<br />
φ ∧ ψ is φ & ( φ → ψ)<br />
,<br />
φ ∨ ψ is (( φ →ψ) →ψ) ∧( ψ →φ) → φ)<br />
,<br />
¬ φ is φ → 0 ,<br />
φ ≡ ψ is ( φ →ψ) & ( ψ → φ)<br />
.<br />
Def<strong>in</strong>ition 6The axioms and deduction rules of predicate<br />
formal system ∀ UL − h∈ (0,<br />
1] as follow<strong>in</strong>g:<br />
(i)The follow<strong>in</strong>g formulas are axioms of ∀ UL − h∈ (0,<br />
1] :<br />
(U1) ( φ →ψ) →(( ψ → χ) →( φ → χ))<br />
(U2) ( φ & ψ)<br />
→ φ<br />
(U3) ( φ & ψ) → ( ψ & φ)<br />
(U4) φ &( φ →ψ) →( ψ &( ψ → φ))<br />
(U5) ( φ →( ψ → χ)) →(( φ&<br />
ψ) → χ)<br />
(U6) (( φ & ψ) → χ) →( φ →( ψ → χ))<br />
(U7) (( φ →ψ) → χ) →((( ψ →φ) → χ) → χ)<br />
(U8) 0 → φ<br />
(U9) ( φ →φ&<br />
ψ) →(( φ →0) ∨ψ ∨(( φ →φ&<br />
φ)<br />
∧<br />
( ψ → ψ & ψ)))<br />
(U10) ( − −ϕ)<br />
≡ ϕ<br />
(U11) Δ( ϕ →ψ) →Δ( −ψ →− ϕ)<br />
(U12) Δφ ∨¬Δ φ<br />
(U13) Δ( φ ∨ψ) →( Δφ∨Δ<br />
ψ)<br />
(U14) Δφ → φ<br />
(U15) Δφ →ΔΔ φ<br />
(U16) Δ( φ →ψ) →( Δφ →Δ ψ)<br />
(U17) ( ∀x) φ( x) → φ( t)<br />
(t substitutable for x <strong>in</strong> φ ( x)<br />
)<br />
(U18) φ() t →( ∃ x) φ( x)<br />
(t substitutable for x <strong>in</strong> φ ( x)<br />
)<br />
(U19) ( ∀x)( χ →φ) →( χ →( ∀ x) φ)<br />
(x is not free <strong>in</strong><br />
χ )<br />
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1438 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
(U20) ( ∀x)( φ → χ) →(( ∃x) φ → χ)<br />
(x is not free <strong>in</strong><br />
χ )<br />
(U21) ( ∀x)( φ ∨χ) →(( ∀x) φ∨ χ)<br />
(x is not free <strong>in</strong> χ )<br />
Deduction rules of ∀ UL − h∈ (0,<br />
1] are three rules. They are:<br />
Modus Ponens (MP): from φ, φ → ψ <strong>in</strong>fer ψ ;<br />
Necessitation: from φ <strong>in</strong>fer Δ φ ;<br />
Generalization: from φ <strong>in</strong>fer ( ∀ x)<br />
φ .<br />
The mean<strong>in</strong>g of “t substitutable for x <strong>in</strong> φ ( x)<br />
” and “x<br />
is not free <strong>in</strong> χ ” <strong>in</strong> the above def<strong>in</strong>ition have the same<br />
mean<strong>in</strong>g <strong>in</strong> the classical first-order predicate logic,<br />
moreover, we can def<strong>in</strong>e the concepts such as proof,<br />
theorem, theory, deduction from a theory T, T-<br />
consequence <strong>in</strong> the system ∀ UL − h∈ (0,<br />
1] . T φ denotes that<br />
φ is provable <strong>in</strong> the theory T. φ denotes that φ is a<br />
theorem of system ∀ ULh<br />
∈ (0 , 1]<br />
. Let<br />
−<br />
Thm( ∀ UL h∈ (0,<br />
1] ) = { φ ∈ J | φ} , Ded( T) = { φ∈ J | T φ}<br />
.<br />
Be<strong>in</strong>g the axioms of propositional system UL − h∈ (0, 1] are <strong>in</strong><br />
predicate system ∀ UL − h∈ (0,<br />
1] , then the theorems <strong>in</strong><br />
UL h∈ (0, 1] are theorems <strong>in</strong> ∀ UL − h∈ (0,<br />
1] . Accord<strong>in</strong>g the<br />
similar proof <strong>in</strong> [3, 16, 17] we can get the follow<strong>in</strong>g<br />
lemmas.<br />
Lemma 1 The hypothetical syllogism holds <strong>in</strong><br />
∀ , i.e. let Γ= { φ → ψψ , → χ}<br />
, then Γ φ → χ .<br />
UL − h∈ (0,<br />
1]<br />
Lemma 2 ∀ UL − h∈ (0,<br />
1] proves:<br />
(1) φ → φ ;<br />
(2) φ →( ψ → φ)<br />
;<br />
(3) ( φ →ψ) →(( φ →γ) →( ψ → γ))<br />
;<br />
(4) ( φ & ( φ →ψ))<br />
→ ψ ;<br />
(5) Δφ ≡ Δφ&<br />
Δ φ .<br />
Lemma 3 If T = { φ → ψ, χ → γ}<br />
, then<br />
T ( φ & χ) → ( ψ & γ)<br />
.<br />
Let J is first-order predicate language, L is l<strong>in</strong>early<br />
ordered ŁΠG − algebra, M = ( M, ( rP )<br />
P, ( mc) c)<br />
is called a<br />
L-evaluation for first-order predicate language J, which<br />
M is non-empty doma<strong>in</strong>, accord<strong>in</strong>g to each n-ary<br />
predicate P and object constant c, r<br />
P<br />
is L-fuzzy n-ary<br />
n<br />
relation: rP<br />
: M → L, m<br />
c<br />
is an element of M.<br />
Def<strong>in</strong>ition 7 Let J be predicate language, M is L-<br />
evaluation of J, x is object variable, P∈ J .<br />
(i) A mapp<strong>in</strong>g v: Term( J ) → M is called M-<br />
evaluation, if for each c ∈Const (J), vc () = mc<br />
;<br />
(ii)Two M-evaluation vv′ , are called equal denoted<br />
by v ≡<br />
x<br />
v′ if for each y∈<br />
Var( J) \ x , there is<br />
vy ( ) = v′<br />
( y)<br />
.<br />
(iii) The value of a term given by M, v is def<strong>in</strong>ed by:<br />
x = v( x)<br />
; c = mc<br />
. We def<strong>in</strong>e the truth value<br />
M, v<br />
M,<br />
v<br />
L<br />
M v<br />
φ ,<br />
of a formula φ as follow<strong>in</strong>g. Clearly, ∗,⇒,Δ<br />
denote the operations of L .<br />
L<br />
1, 2,, n<br />
=<br />
M v P 1<br />
,,<br />
, M, v n M,<br />
v<br />
L L L<br />
→ = ⇒<br />
M, v M, v M,<br />
v<br />
L L L<br />
& = ∗<br />
M, v M, v M,<br />
v<br />
L<br />
L<br />
Pt ( t t) r( t t )<br />
φ ψ φ ψ<br />
φ ψ φ ψ<br />
0 = 0; 1 = 1<br />
M, v<br />
M,<br />
v<br />
L<br />
L<br />
φ<br />
M, v<br />
M,<br />
v<br />
L<br />
L<br />
φ<br />
M, v M,<br />
v<br />
L<br />
L<br />
φ φ<br />
M, v<br />
M,<br />
v′<br />
L<br />
L<br />
φ φ<br />
M, v<br />
M,<br />
v′<br />
Δ φ = Δ<br />
− φ =−<br />
( ∀ x) = <strong>in</strong>f{ | v ≡ v ′ }<br />
( ∃ x) = sup{ | v ≡ v ′ }<br />
In order to the above def<strong>in</strong>itions are reasonable, the<br />
<strong>in</strong>fimum/supremum should exist <strong>in</strong> the sense of L. So the<br />
structure M is L-safe if all the needed <strong>in</strong>fima and suprema<br />
L<br />
exist, i.e. φ<br />
M ,<br />
is def<strong>in</strong>ed for all φ, v .<br />
v<br />
Def<strong>in</strong>ition 8 Let φ ∈ J , M be a safe L-structure for J.<br />
(i) The truth value of φ <strong>in</strong> M is<br />
L<br />
L<br />
φ = <strong>in</strong>f{ φ ,v<br />
| v M − evaluation} .<br />
M<br />
M<br />
(ii) A formula φ of a language J is an L -tautology if<br />
φ<br />
L<br />
= 1 for each safe L-structure M. i.e. L<br />
M L<br />
φ 1<br />
Mv ,<br />
= for<br />
each safe L-structure M and each M-valuation of object<br />
variables.<br />
Remark For each h∈ (0, 1] , k∈ (0, 1) ,<br />
([0, 1] ,∧<br />
hk ,<br />
,⇒<br />
hk ,<br />
, m<strong>in</strong>, max, 0, 1 ,Δ,−)<br />
is a ŁΠG − -algebra.<br />
So the predicate system ∀ UL − h∈ (0,<br />
1] can be considered the<br />
axiomatization for 1-level universal AND operator.<br />
III. SOUNDNESS OF SYSTEM ∀ h (0 1]<br />
x<br />
x<br />
UL − ∈ ,<br />
Def<strong>in</strong>ition 9 A logic system is soundness if for its each<br />
theorem φ , we can get φ is a tautology.<br />
Theorem 5 (Soundness of axioms) The axioms of<br />
∀ are L-tautologies for each l<strong>in</strong>early ordered<br />
UL − h∈ (0,<br />
1]<br />
G −<br />
ŁΠ -algebra L.<br />
Proof. The axioms of (U1)- (U16) are L-tautologies<br />
can be get as <strong>in</strong> propositional calculus. We verify (U17)-<br />
(U21)<br />
To verify (U17), (U18), let y is substitutable for x to<br />
φ , when v′′ ≡<br />
x<br />
v and v′′ ( x) = v( y)<br />
, there is<br />
L<br />
L<br />
L<br />
L<br />
φ( y) = φ ( x)<br />
So, ( ∀ x) φ( x) = <strong>in</strong>f ( )<br />
M, v<br />
M,<br />
v′′<br />
M v v′≡ v<br />
φ x<br />
, M,<br />
v′<br />
≤<br />
L L L<br />
φ( y) ≤ sup ( ) ( ) ( )<br />
M v v<br />
φ x = ∃ ′<br />
x φ x , then<br />
, ′′ M, v′<br />
M,<br />
v<br />
( ∀ x ) φ( x ) → φ( y ) = ( ∀ x ) φ( x ) → φ( y ) = 1.<br />
M, v M, v M,<br />
v<br />
For (U19), let x not free <strong>in</strong> χ , then for each M-<br />
valuation w, when w≡<br />
x<br />
v , we have v = φ( x)<br />
.<br />
M, w<br />
M,<br />
v<br />
We have to prove<br />
L L L L<br />
<strong>in</strong>f ( v ⇒ φ ) ≤( v ⇒ <strong>in</strong>f φ ) .<br />
w<br />
M, w M, w M, v w M,<br />
w<br />
L<br />
L<br />
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JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1439<br />
L<br />
L<br />
Let v = v = a , φ<br />
M, v M,<br />
w<br />
M ,<br />
= b<br />
w w<br />
, thus we must<br />
prove <strong>in</strong>f<br />
w( a⇒bw) ≤( a⇒ <strong>in</strong>f<br />
wbw)<br />
. On the one hand,<br />
<strong>in</strong>f w<br />
b w<br />
≤ b w<br />
, thus a⇒bw ≥( a⇒ <strong>in</strong>f<br />
wbw)<br />
for each w,<br />
thus <strong>in</strong>f<br />
w( a⇒bw) ≥( a⇒ <strong>in</strong>f<br />
wbw)<br />
. On the other hand if<br />
z ≤( a⇒ b w<br />
) for each w, then z∗a ≤ bw<br />
for each w,<br />
z∗a ≤ <strong>in</strong>f w<br />
b w<br />
, z ≤( a⇒ <strong>in</strong>f<br />
wbw)<br />
. Thus ( a⇒ <strong>in</strong>f<br />
wbw)<br />
is<br />
the <strong>in</strong>fimum of all ( a⇒<br />
b w<br />
). So (U19) holds.<br />
For (U20), we need to verify<br />
<strong>in</strong>f<br />
w( aw ⇒ bw) = (sup<br />
w<br />
aw<br />
⇒ b)<br />
. Indeed, sup w<br />
≥ a w<br />
, thus<br />
(sup<br />
w<br />
aw ⇒b) ≤( aw<br />
⇒ b)<br />
, hence<br />
(sup<br />
w<br />
aw ⇒b) ≤<strong>in</strong>f w( aw<br />
⇒ b)<br />
, If z ≤ aw<br />
⇒ b for all w ,<br />
then aw<br />
≤( z ⇒ b)<br />
for all w, then sup<br />
w<br />
aw<br />
≤( z ⇒ b)<br />
,<br />
z ≤(sup waw<br />
⇒ b)<br />
, so sup w<br />
a w<br />
⇒ b is the <strong>in</strong>fimum. So<br />
(U20) holds.<br />
F<strong>in</strong>ally we verify (U21), we need to verify<br />
<strong>in</strong>f<br />
w( a∨ bw) = a∨ <strong>in</strong>fwbw<br />
. Indeed, a ≤ a∨ bw<br />
, thus<br />
a ≤<strong>in</strong>f w( a∨ bw)<br />
; similarly, <strong>in</strong>fwbw ≤<strong>in</strong>f w( a∨ bw)<br />
, thus<br />
a∨<strong>in</strong>fwbw ≤<strong>in</strong>f w( a∨ b)<br />
. Conversely, let z ≤ a∨ bw<br />
for<br />
all w , we prove z ≤ a∨ <strong>in</strong>f w<br />
b w<br />
.<br />
Case 1: Let a ≤ <strong>in</strong>f w<br />
b w<br />
. Then z ≤ bw<br />
for each w ,<br />
z ≤ <strong>in</strong>f w<br />
b w<br />
and z ≤ a∨ <strong>in</strong>f w<br />
b w<br />
.<br />
Case 2: Let a ≥ <strong>in</strong>f w<br />
b w<br />
. Then for some w 0<br />
, a ≥ b w0<br />
,<br />
thus z ≤ a and z ≤ a∨ <strong>in</strong>f w<br />
b w<br />
.<br />
So we prove the soundness of axioms.<br />
Theorem 6 (Soundness of deduction rules) (1) For<br />
arbitrary formulas φ, ψ , safe-structure M and evaluation<br />
L L L<br />
v , ψ ≥ φ ∗ φ → ψ . In particular, if<br />
M, v M, v M,<br />
v<br />
L<br />
L<br />
L<br />
= → = 1<br />
M, v<br />
M,<br />
v L<br />
then ψ 1<br />
M ,<br />
=<br />
v L<br />
.<br />
L L L<br />
(2) Consequently, ψ φ φ ψ<br />
M M M<br />
φ φ ψ<br />
≥ ∗ → , thus if<br />
φ, φ → ψ are then ψ is 1 L<br />
-true <strong>in</strong> M.<br />
(3) If φ is 1 L<br />
-true <strong>in</strong> M then Δ φ is 1 L<br />
-true <strong>in</strong> M .<br />
(4) If φ is 1 L<br />
-true <strong>in</strong> M then ( ∀ x)<br />
φ is 1 L<br />
-true <strong>in</strong> M.<br />
Proof. (1) is just as <strong>in</strong> propositional calculus.<br />
To prove (2) put φ = aw, ψ = bw, <strong>in</strong>f<br />
w<br />
w<br />
w<br />
aw<br />
= a. We<br />
have to prove <strong>in</strong>f<br />
w( aw ⇒bw) ≤<strong>in</strong>fw aw ⇒ <strong>in</strong>fwbw<br />
.<br />
Observe the follow<strong>in</strong>g:<br />
<strong>in</strong>f( aw ⇒bw) ≤( aw ⇒bw) ≤( a⇒ bw)<br />
,<br />
thus <strong>in</strong>f<br />
w( aw ⇒bw) ≤<strong>in</strong>f w( a⇒ bw)<br />
. It rema<strong>in</strong>s to prove<br />
<strong>in</strong>f<br />
w( a⇒bw) ≤ a⇒ <strong>in</strong>fwbw, this is holds from Theorem<br />
5.<br />
L<br />
(3) If φ is 1 L<br />
-true <strong>in</strong> M then φ<br />
M<br />
= 1L<br />
, so<br />
L<br />
L<br />
Δ φ =Δ φ = . Then (3) holds.<br />
1<br />
M, v<br />
M,<br />
v L<br />
L<br />
M<br />
φ ′<br />
′<br />
,<br />
}<br />
L<br />
M<br />
L<br />
M<br />
(4) Be<strong>in</strong>g φ = <strong>in</strong>f{ φ ,v<br />
| v M − evaluation}<br />
≤ <strong>in</strong>f{<br />
Mv| v ≡ v = ( ∀ x) φ } , So (4) holds.<br />
So we can get the follow<strong>in</strong>g soundness theorem.<br />
L<br />
Theorem 7 (Soundness) Let L is l<strong>in</strong>early ordered<br />
ŁΠG − -algebra and φ is a formula <strong>in</strong> J, if φ , then φ is<br />
L<br />
L-tautology, i.e. φ = 1 . M L<br />
Similarly, we can get the follow<strong>in</strong>g strong soundness<br />
theorem.<br />
Def<strong>in</strong>ition 10 Let T be a theory, L be a l<strong>in</strong>early ordered<br />
ŁΠG − -algebra and M a safe L-structure for the language<br />
of T. M is an L-model of T if all axioms of T are 1 L<br />
-true<br />
<strong>in</strong> M, i.e. φ = 1 L<br />
<strong>in</strong> each φ ∈ T .<br />
Theorem 8 (Strong Soundness) Let T be a theory, L is<br />
l<strong>in</strong>early ordered ŁΠG − -algebra and φ is a formula <strong>in</strong> J,<br />
L<br />
if T φ ( φ is provable <strong>in</strong> T), then φ<br />
M<br />
= 1L<br />
for each<br />
l<strong>in</strong>early ordered ŁΠG − -algebra L and each L-model M<br />
of T.<br />
Proof. In fact, from the proof of Theorem 5, for each<br />
L-model M of T, the axioms are true, and the formulas <strong>in</strong><br />
T are true, from the proof of Theorem 6, the deduction<br />
rules preserve true. So the theorem holds.<br />
Theorem 9 (Deduction Theorem) Let T be a theory,<br />
φ, ψ are closed formulas. Then ( T ∪φ)<br />
ψ iff<br />
T Δφ →ψ<br />
.<br />
Proof. Sufficiency: Let T Δφ →ψ<br />
, from φ<br />
( φ∈ ( T ∪ φ)<br />
), then Δ φ by necessitation, so we can get<br />
ψ by MP rules.<br />
Necessity: Let m is the proof length from T ∪ φ}<br />
to ψ ,<br />
we prove by <strong>in</strong>duction for the length m.<br />
When m = 1 , ψ ∈T<br />
∪φ∪Axm(C ∀ ) , if ψ = φ , The<br />
result holds. If ψ ∈ T or ψ is axiom, from Lemma2 (2),<br />
we have ψ →( Δφ → ψ)<br />
, then by ψψ , →( Δφ→ ψ)<br />
, we<br />
get Δφ → ψ , thus T Δφ →ψ<br />
.<br />
Assume that the result holds when m≤<br />
k , i.e. we get<br />
γ at k step, then T Δφ → γ . Now Let m= k + 1.<br />
If ψ is obta<strong>in</strong>ed from MP rule by the above results<br />
γγ , → ψ <strong>in</strong> the proof sequence, then by <strong>in</strong>duction<br />
hypothesis, we get T Δφ → γ, T Δφ →( γ →ψ)<br />
.<br />
From Lemma 3, we can get<br />
T ( Δφ& Δφ) →( γ &( γ →ψ))<br />
. Be<strong>in</strong>g<br />
T ( Δφ) &( Δφ)<br />
≡ Δφ<br />
, so T Δφ →( γ &( γ →ψ))<br />
.<br />
From lemma 2 (4) we have ( γ & ( γ →ψ)<br />
→ ψ , so we<br />
get T Δφ →ψ<br />
by the hypothetical syllogism.<br />
If ψ is obta<strong>in</strong>ed from necessitation rule by the above<br />
step γ <strong>in</strong> the proof sequence, i.e. Δ γ = ψ , then by<br />
<strong>in</strong>duction hypothesis, we get T Δφ →γ<br />
.<br />
T Δ( Δφ →γ)<br />
, from (U16) we can get T ΔΔφ → Δγ<br />
,<br />
from (U15) we can get Δφ<br />
→ΔΔ φ , thus by the<br />
hypothetical syllogism we can get T Δφ →Δγ<br />
, i.e.<br />
T Δφ →ψ<br />
.<br />
If ψ is obta<strong>in</strong>ed from generalization rule by the above<br />
step γ <strong>in</strong> the proof sequence, i.e. ( ∀ x)<br />
γ = ψ , then by<br />
© 2013 ACADEMY PUBLISHER
1440 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
<strong>in</strong>duction hypothesis, we get T Δφ →γ<br />
, From<br />
generalization rule we can get T ( ∀x)( Δφ →γ)<br />
, be<strong>in</strong>g<br />
Δ φ, γ are closed formula and from (U19), we can get<br />
T Δφ<br />
→( ∀x)<br />
γ , i.e. T Δφ →ψ<br />
.<br />
So the theorem holds.<br />
IV. CONCLUSION<br />
In this paper a predicate calculus formal deductive<br />
system ∀ h (0 1] based on the propositional system<br />
UL − ∈ ,<br />
UL − h∈ (0, 1] for 1-level universal AND operator is built up.<br />
We prove the system ∀ UL − h∈ (0,<br />
1] is sound. The deduction<br />
theorem is also given. Next we will discuss the<br />
completeness of system ∀ h (0 1] .<br />
UL − ∈ ,<br />
ACKNOWLEDGMENT<br />
This work is partially supported Scientific Research<br />
Program Funded by Shaanxi Prov<strong>in</strong>cial Education<br />
Department (Program No. 12JK0878) and Doctor<br />
Scientific Research Foundation Program of Xi'an<br />
Polytechnic University.<br />
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[3] E. P. Klement, R. Mesiar, E. Pap, Triangular Norms,<br />
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[4] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer<br />
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[5] R. Cignoli, F. Esteva, L. Godo, A. Torrens, “Basic fuzzy<br />
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Soft comput<strong>in</strong>g, vol. 4, pp. 106-112, 2000.<br />
[6] F. Esteva, L.Godo, “Monoidal t-normbased logic: towards<br />
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[7] U. Hohle, “Commutative, residuated l-monoids”, <strong>in</strong>: Non-<br />
Classical Logics and Their Applications to Fuzzy Subsets,<br />
U. Hohle, E. P. Klement, (eds.), Kluwer Academic<br />
<strong>Publisher</strong>s, Dordrecht/London, pp. 53-106 , 1995.<br />
[8] G.J. Wang, Non-classical Mathematical Logic and<br />
Approximate Reason<strong>in</strong>g, Science Press (<strong>in</strong> Ch<strong>in</strong>ese),<br />
Beij<strong>in</strong>g, 2000.<br />
[9] D.W. Pei, G. J. Wang, “The completeness and applications<br />
of the formal system L*”, Science <strong>in</strong> Ch<strong>in</strong>a (Series F) vol.<br />
45, pp. 40–50, 2002.<br />
[10] D.W. Pei, “First-order Formal System K* and its<br />
Completeness”, Ch<strong>in</strong>ese Annals of Mathematics (Series A),<br />
vol. 23 (6), pp. 675–684, 2002.<br />
[11] H.C. He, et al, Universal Logic Pr<strong>in</strong>ciple, Science Press (<strong>in</strong><br />
Ch<strong>in</strong>ese), Beij<strong>in</strong>g, 2001.<br />
[12] H.C. He, et al, “Cont<strong>in</strong>uous-valued logic algebra-Studies<br />
on the basic of mathematical dialectical propositional<br />
logic”, IEEE International Conference on GrC, IEEE Press,<br />
pp: 194-199, 2010.<br />
[13] J.L. Chen, H.C. He, C.X. Liu, M.X. Luo. “Integrity studies<br />
on 0-level universal operation models of flexible logic”,<br />
Journal of Beij<strong>in</strong>g University of Posts and<br />
Telecommunications, vol. 34 (4): 10-13, 2011.<br />
[14] Y.F. Fan, H.C. He, L.R. Ai, “N-norm on [0, ∞) and method<br />
for calculat<strong>in</strong>g generalized self-correlation coefficient k”,<br />
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(2): 270-275, 2010.<br />
[15] Y.C. Ma, H.C. He, “A Propositional Calculus Formal<br />
Deductive System ULh<br />
∈ (0 , 1]<br />
of Universal Logic”,<br />
Proceed<strong>in</strong>gs of 2005 ICMLC, IEEE Press, pp: 2716-2721,<br />
2005.<br />
[16] Y.C. Ma, H.C. He, “The Axiomatization for 0-level<br />
Universal Logic”, Lecture Notes <strong>in</strong> Artificial Intelligence,<br />
vol. 3930, pp. 367-37, 2006.<br />
[17] Y.C. Ma, H.C. He, “Axiomatization for 1-level Universal<br />
AND Operator”, The Journal of Ch<strong>in</strong>a Universities of<br />
Posts and Telecommunications, vol. 15 (2), pp. 125-129,<br />
2008.<br />
[18] Y.C. Ma, Q.Y. Li, “A Propositional Deductive System of<br />
Universal Logic with Projection Operator”, Proceed<strong>in</strong>gs of<br />
2006 ISDA, IEEE Press, pp: 993-998, 2006.<br />
[19] Q.Y. Li, Y.C. Ma, “The predicate system based on<br />
schweizer-sklar t-norm and its soundness”, Journal of<br />
Computational Information Systems, vol. 7 (15), p 5600-<br />
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[20] Q.Y. Li, T, Cheng, The Predicate System Based on<br />
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[21] Y.C. Ma, H.C. He, “Predicate Formal System<br />
∀ULh<br />
∈ [0.75 , 1]<br />
and and its completeness”, Computer<br />
Eng<strong>in</strong>eer<strong>in</strong>g and Applications, vol. 46 (34): 17-20, 2010.<br />
[22] Y.C. Ma, H.C. He, “Predicate Formal System<br />
∀ULh<br />
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and its Soundness”, Computer Science, vol.<br />
38 (5): 178-180, 2011.<br />
[23] Y.C. Ma, H.C. He, “Predicate formal system based on 0-<br />
level universal AND operator and its soundness”,<br />
Application Research of Computers, vol. 28 (1): 84-86,<br />
2011.<br />
[24] Y.C. Ma, H.C. He, “Predicate Formal System Based on 0-<br />
level Universal and Operator and its Completeness”,<br />
Journal of Ch<strong>in</strong>ese Computer Systems, vol. 32 (10): 2105-<br />
2108, 2011.<br />
Y<strong>in</strong>gcang Ma, is a professor <strong>in</strong> school<br />
of science, Xi'an Polytechnic University.<br />
He received the PhD. degree from<br />
School of Computer Science,<br />
Northwestern Polytechnical University,<br />
<strong>in</strong> July 2006. His ma<strong>in</strong> research<strong>in</strong>terests<br />
are <strong>in</strong> the areas of fuzzy set, rough set<br />
and non-classical mathematical logic.<br />
Hucan He, male, Professor and Ph.D.<br />
tutor from the Department of Computer<br />
Science and Eng<strong>in</strong>eer<strong>in</strong>g of<br />
Northwestern Polytechnical University,<br />
<strong>in</strong>terested <strong>in</strong> the foundation and<br />
application of AI, universal logic and<br />
uncerta<strong>in</strong>ties reason<strong>in</strong>g.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1441<br />
Analysis of Boolean Networks us<strong>in</strong>g An<br />
Optimized Algorithm of Structure Matrix based<br />
on Semi-Tensor Product<br />
J<strong>in</strong>yu Zhan<br />
University of Electronic Science and Technology of Ch<strong>in</strong>a, Chengdu, Ch<strong>in</strong>a<br />
Email: zhanjy@uestc.edu.cn<br />
Shan Lu and Guowu Yang<br />
University of Electronic Science and Technology of Ch<strong>in</strong>a, Chengdu, Ch<strong>in</strong>a<br />
Email: 617999242@qq.com, guowu@uestc.edu.cn<br />
Abstract—The structure matrix based on semi-tensor<br />
product can provide formulas for analyz<strong>in</strong>g the<br />
characteristics of a Boolean network, such as the number of<br />
fixed po<strong>in</strong>ts, the number of circles of different lengths,<br />
transient period for all po<strong>in</strong>ts to enter the set of attractors<br />
and bas<strong>in</strong> of each attractor. However, the conventional<br />
method of semi-tensor product ga<strong>in</strong>s the structure matrix<br />
through complex matrix operations with high computation<br />
complexity. This paper proposes an optimized algorithm<br />
which ga<strong>in</strong>s the structure matrix through the truth table<br />
reflect<strong>in</strong>g the state transformation of Boolean networks. The<br />
effectiveness and feasibility of our optimized approach are<br />
demonstrated through the analysis of a practical Boolean<br />
network of the mammalian cell.<br />
Index Terms—semi-tensor product, Boolean network,<br />
structure matrix, truth table<br />
I. INTRODUCTION<br />
The Boolean network, <strong>in</strong>troduced firstly by Kauffman<br />
[1], and then developed by [2][3][4][5][6][7][8] and<br />
many others, becomes a powerful tool <strong>in</strong> describ<strong>in</strong>g,<br />
analyz<strong>in</strong>g, and simulat<strong>in</strong>g the cell network. It was shown<br />
that the Boolean network plays an important role <strong>in</strong><br />
model<strong>in</strong>g cell regulation, because they can represent<br />
important features of liv<strong>in</strong>g organisms [9][10]. It has<br />
received the most attention, not only from the biology<br />
community, but also physics, system science, etc.<br />
The structure of a Boolean network is described <strong>in</strong><br />
terms of its cycles and the transient states that lead to<br />
them. Several useful Boolean networks have been<br />
analyzed and their circles have been revealed [11][12]. It<br />
was po<strong>in</strong>ted <strong>in</strong> [13] that f<strong>in</strong>d<strong>in</strong>g fixed po<strong>in</strong>ts and circles<br />
of a Boolean network is an NP hard problem. Semi-tensor<br />
Manuscript received May 24, 2012; revised June 1, 2012; accepted<br />
July 1, 2012.<br />
This work was supported by the Fundamental Research Funds for<br />
the Central Universities of Ch<strong>in</strong>a under Grant No. ZYGX2009J062 and<br />
the National Natural Science Foundation of Ch<strong>in</strong>a under Grant No.<br />
60973016.<br />
Correspond<strong>in</strong>g author: J<strong>in</strong>yu Zhan, email: zhanjy@uestc.edu.cn<br />
product of matrix (STP), presented by Cheng [14]. Us<strong>in</strong>g<br />
STP, a Boolean network equation can be expressed as a<br />
conventional discrete time l<strong>in</strong>ear system which conta<strong>in</strong>s<br />
complete <strong>in</strong>formation of the dynamics of a Boolean<br />
network. Analyz<strong>in</strong>g the structure matrix of a Boolean<br />
network, precise formulas are obta<strong>in</strong>ed to determ<strong>in</strong>e the<br />
number of fixed po<strong>in</strong>ts and numbers of all possible<br />
circles of different lengths.<br />
But the conventional method to calculate the structure<br />
matrix of a Boolean network, presented <strong>in</strong><br />
[15][18][19][21], is very complex. In this paper, a<br />
optimized algorithm is proposed to calculate the structure<br />
matrix. Unlike exist<strong>in</strong>g methods, our approach gets the<br />
structure matrix of a Boolean network not through the<br />
complex matrix operations but through the truth table<br />
which reflects the state transformation of the Boolean<br />
network. Compared with the conventional method, our<br />
approach can greatly reduce the calculation complexity.<br />
The methods for analyz<strong>in</strong>g the characteristics of a<br />
Boolean network are given. The analysis of a practical<br />
Boolean network of the mammalian cell shows that our<br />
approach is effective and efficient.<br />
The rest of the paper is organized as follows. Section II<br />
gives a brief <strong>in</strong>troduction to semi-tensor product of<br />
matrices, matrix expression of logic and dynamics of<br />
Boolean network. The conventional method to calculate<br />
the structure Matrix of a Boolean Network is given <strong>in</strong><br />
Section III and our approach is proposed <strong>in</strong> Section IV.<br />
Section V gives the methods to analyze the characteristics<br />
of Boolean networks through the structure matrix.<br />
Section VI gives a practical Boolean network of the<br />
mammalian cell to show the effectiveness and feasibility<br />
of our approach. F<strong>in</strong>ally, some conclusions are drawn <strong>in</strong><br />
Section VII.<br />
II. EXPRESSION OF BOOLEAN NETWORKS IN SEMI-TENSOR<br />
PRODUCT<br />
A. Semi-tensor Product<br />
This section is a brief <strong>in</strong>troduction to semi-tensor<br />
product (STP) of matrices. STP of matrices is a<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1441-1448
1442 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
generalization of conventional matrix product, which<br />
extends the conventional matrix product to any two<br />
matrices. It plays a fundamental rule <strong>in</strong> the follow<strong>in</strong>g<br />
discussion. We restrict it to some concepts and basic<br />
properties used <strong>in</strong> this paper. In addition, only left semitensor<br />
product for multiply<strong>in</strong>g dimension case is <strong>in</strong>volved<br />
<strong>in</strong> the paper. We refer to [14][15][16][17] for right semitensor<br />
product, arbitrary dimensional case and much<br />
more details. Throughout this paper “semi-tensor<br />
product” means the left semi-tensor product for<br />
multiply<strong>in</strong>g dimensional case.<br />
Def<strong>in</strong>ition 1: 1. Let X be a row vector of dimension<br />
np , and Y be a column vector with dimension p . Then<br />
we split X <strong>in</strong>to p equal-size blocks as 1 , 2 p<br />
X X , , X ,<br />
which are 1× n rows. Def<strong>in</strong>e the STP, denoted by × , as<br />
<strong>in</strong> (1).<br />
p<br />
⎧<br />
⎪X<br />
× Y = ∑ X<br />
i=<br />
1<br />
⎨<br />
p<br />
⎪<br />
T T<br />
Y × X =<br />
⎪⎩<br />
i=<br />
i<br />
∑<br />
1<br />
y ∈ R<br />
i<br />
y ( X<br />
i<br />
i<br />
n<br />
)<br />
T<br />
∈ R<br />
2. Let A ∈ M m × n<br />
and B∈<br />
M<br />
p × q<br />
. If either n is a<br />
factor of p , say nt = p and denote it as A ≺<br />
t<br />
B , or<br />
p is a factor of n , say n = pt and denote is as<br />
A t<br />
B , then we def<strong>in</strong>e the STP of A and B , denoted<br />
by C = A× B , as the follow<strong>in</strong>g: C consists of m × q<br />
ij<br />
blocks as C = ( C ) and each block is <strong>in</strong> (2).<br />
where<br />
ij i<br />
C A B j<br />
n<br />
(1)<br />
= × , i = 1, , m, j = 1, , q . (2)<br />
i<br />
A is the i-th row of A and<br />
B<br />
j<br />
is the j-th column<br />
of B .<br />
We use some simple numerical examples to describe it.<br />
Example 1. Let X = [1 2 3 − 1] and<br />
Then<br />
Example 2. Let<br />
X × Y = [1 2] ⋅ 1 + [3 −1] ⋅ 2 = [7 0]<br />
⎡1 2 1 1⎤<br />
A =<br />
⎢<br />
2 3 1 2<br />
⎥<br />
⎢ ⎥<br />
⎢⎣3 2 1 0⎥⎦<br />
⎡1<br />
− 2⎤<br />
, B = ⎢ ⎥ . Then<br />
⎣2<br />
−1<br />
⎦<br />
⎡1⎤<br />
Y = ⎢<br />
2 ⎥<br />
⎣ ⎦ .<br />
⎡ ⎛1⎞ ⎛−2⎞<br />
⎤<br />
⎢ ( 1 2 1 1 ) ⎜ ⎟ (1 2 1 1) ⎜ ⎟ ⎥<br />
⎢<br />
⎝2⎠ ⎝−1⎠<br />
⎥<br />
⎢<br />
⎛1⎞ ⎛−2⎞⎥<br />
A× B = ⎢( 2 3 1 2) ⎜ ⎟ ( 2 3 1 2)<br />
⎜ ⎟⎥<br />
⎢<br />
⎝2⎠ ⎝−1⎠⎥<br />
⎢<br />
⎥<br />
⎢<br />
⎛1⎞ ⎛−2⎞<br />
( 3 2 1 0) ( 3 2 1 0)<br />
⎥<br />
⎢<br />
⎜ ⎟ ⎜ ⎟<br />
⎝2⎠ ⎝−1⎠<br />
⎥<br />
⎣<br />
⎦<br />
⎡3 4 −3 −5⎤<br />
=<br />
⎢<br />
4 7 5 8<br />
⎥<br />
⎢<br />
− −<br />
⎥<br />
⎢⎣<br />
5 2 −7 −4⎥⎦<br />
B. Matrix Expression of Logic<br />
In this section, the matrix expression of logic will be<br />
given. In a logical doma<strong>in</strong>, we usually set "true" as "1"<br />
and "false" as "0". Then a logical variable is def<strong>in</strong>ed as<br />
x∈ D = {0,1} . There are several fundamental b<strong>in</strong>ary<br />
functions such as ¬ , ∧ , ∨ , ↔ , → , ∨ , ↑ and ↓ .<br />
Their truth table is as TABLE I.<br />
To use matrix expression each element can be<br />
2<br />
0 ~ δ ,<br />
1<br />
identified <strong>in</strong> D with a vector as 1~δ<br />
2<br />
and<br />
2<br />
i<br />
where δ = Col( I ) . Therefore, That a n-ary logical<br />
n<br />
n<br />
n<br />
operator (or function) is a mapp<strong>in</strong>g: f : D → D can be<br />
formed as f : Δ n →Δ.<br />
2<br />
Theorem 1: Let f ( x1<br />
, , x n<br />
) be a logical function <strong>in</strong><br />
vector form as f : Δ n →Δ. Then there exists a unique<br />
2<br />
, called the structure matrix of f , such that<br />
∈L<br />
M<br />
f 2×<br />
2 n<br />
<strong>in</strong> (3).<br />
n<br />
f ( x1<br />
, , xn)<br />
= M<br />
f<br />
× x, where x =×<br />
i=<br />
1<br />
xi<br />
(3)<br />
Therefore, the structure matrix of Negation,<br />
Conjunction, Disjunction, Equivalence and Implication<br />
are as <strong>in</strong> (4) - (11).<br />
¬<br />
= δ 2<br />
[ 2 1]<br />
[ 1 2 2 2]<br />
M (4)<br />
M<br />
∧<br />
= δ 2<br />
(5)<br />
M = δ 2 [ 1 1 1 2<br />
∨ ]<br />
(6)<br />
M = δ 2 [ 1 2 2 1<br />
↔ ]<br />
(7)<br />
M = δ 2 [ 1 2 1 1<br />
→ ]<br />
(8)<br />
p q ¬ p p∧ q p ∨ q<br />
TABLE I.<br />
TRUTH TABLE OF ¬ , ∧ , ∨ , ↔ , → , ∨ , ↑ AND ↓<br />
p ↔ q p → q<br />
p ∨ q p↑ q p ↓ q<br />
0 0 1 0 0 1 1 0 1 1<br />
0 1 1 0 1 0 1 1 1 0<br />
1 0 0 0 1 0 0 1 1 0<br />
1 1 0 1 1 1 1 0 0 0<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1443<br />
M = δ 2 [ 2 1 1 2<br />
∨ ]<br />
(9)<br />
M = δ 2 [ 2 1 1 1<br />
↑<br />
]<br />
(10)<br />
M = δ 2 [ 2 2 2 1<br />
↓<br />
]<br />
(11)<br />
n k<br />
Theorem 2: Let F( x1<br />
, , xn<br />
): D → D be a logical<br />
mapp<strong>in</strong>g: F : Δ n →Δ k .Then there exists a unique<br />
2 2<br />
k n called the structure matrix of F , such <strong>in</strong><br />
∈L<br />
M<br />
F 2 × 2<br />
(12).<br />
F( x , , x ) = M × x<br />
(12)<br />
1<br />
C. Dynamics of Boolean Networks<br />
The Boolean networks play an important role <strong>in</strong><br />
model<strong>in</strong>g cell regulation, because they can represent<br />
important features of liv<strong>in</strong>g organisms. The dynamics of<br />
the Boolean networks will be given <strong>in</strong> this section.<br />
Def<strong>in</strong>ition 2[15][18][20]: A Boolean network is a set<br />
of nodes A , A , 1 2<br />
, An<br />
, which <strong>in</strong>teract with each other<br />
<strong>in</strong> a synchronous manner. At each given time t=0, 1, 2, …,<br />
a node has only one of two different values: 1 or 0. Thus<br />
the network can be described by a set of equations as <strong>in</strong><br />
(13).<br />
⎧ A1( t+ 1) = f1( A1( t), A2( t), , An<br />
( t))<br />
⎪A2( t+ 1) = f2( A1( t), A2( t), , An<br />
( t))<br />
⎨<br />
(13)<br />
⎪<br />
<br />
⎪<br />
⎩An( t+ 1) = fn( A1( t), A2( t), , An( t))<br />
Where<br />
i<br />
n<br />
f , ( i = 1,2, , n)<br />
, are n-ary logic functions.<br />
Note that <strong>in</strong> Boolean networks each function f i<br />
has<br />
only constant, l<strong>in</strong>ear, or product terms [12].<br />
F<br />
Example 3: Consider a Boolean network which<br />
dynamics is described as <strong>in</strong> (15).<br />
⎧ A1( t + 1) = A2( t) ∧ A3( t) ∧ A1( t)<br />
⎪<br />
⎨A2( t + 1) = ( A1() t ∧ A2()) t ∨( A1() t ∧ A3() t ∧ A2())<br />
t<br />
⎪<br />
⎪⎩<br />
A3( t + 1) = ( A1() t ∧ A2() t ∧ A3()) t ∨( A2() t ∧ A3())<br />
t<br />
(15)<br />
In algebraic form (the notation " × " is omitted), we can<br />
have as <strong>in</strong> (16).<br />
⎧A1( t+ 1) = M∧( M A2() t A3()) t A1()<br />
t<br />
↑<br />
⎪<br />
⎪A2( t+ 1) = M∨(( M∧ A1( t)( M¬<br />
A2( t))<br />
⎪ ( M<br />
∧( M A1() t A3()) t A2()))<br />
t<br />
↓<br />
⎨<br />
⎪A3( t+ 1) = M∨(( M∧( M∧A1() t A2())<br />
t<br />
⎪ ( M<br />
¬<br />
A3( t)))( M∧ ( M¬<br />
A2( t))<br />
⎪<br />
⎪⎩ A3<br />
()) t<br />
(16)<br />
There are some propositions <strong>in</strong> [15][18] to calculate the<br />
structure matrix L.<br />
t<br />
Proposition 1: Let Z ∈ R be a column. Then there exists <strong>in</strong><br />
(17).<br />
ZA= ( I ⊗ A)<br />
Z<br />
(17)<br />
Proposition 2: There exists an unique matrix<br />
W ∈ M ×<br />
, called the swap matrix, such that for any<br />
[ mn , ]<br />
mn mn<br />
two column vectors . X ∈ R<br />
m<br />
t<br />
n<br />
. and Y ∈ R .<br />
W[ mn , ]<br />
XY = YX<br />
(18)<br />
We refer to [15][18] for construct<strong>in</strong>g swap matrix.<br />
Proposition 3: Let X . Then we have (19).<br />
X<br />
2<br />
∈ Δ<br />
= M X ,<br />
r<br />
M r<br />
⎡1 0⎤<br />
⎢<br />
0 0<br />
⎥<br />
= ⎢ ⎥<br />
⎢ 0 0 ⎥<br />
⎢ ⎥<br />
⎣0 1⎦<br />
(19)<br />
III. CONVENTIONAL CALCULATION OF STRUCTURE<br />
MATRIX<br />
Us<strong>in</strong>g Theorem 1 and 2, the dynamics of Boolean<br />
networks can be expressed as <strong>in</strong> (14).<br />
A( t+ 1) = LA( t)<br />
(14)<br />
l<br />
l<br />
where At ( + 1) =×<br />
i=<br />
1<br />
Ai( t+ 1) , A( t)<br />
= × i= 1<br />
Ai<br />
( t)<br />
, L is the<br />
structure matrix of F , L l l ∈L . 2 × 2<br />
By means of the STP, the dynamics of Boolean<br />
networks can be converted <strong>in</strong>to the equivalent algebraic<br />
forms. Through the analysis of the structure matrix L ,<br />
we can get the characteristics of the Boolean networks<br />
such as: (1) fixed po<strong>in</strong>ts; (2) circles of different lengths;<br />
(3) transient period; (4) bas<strong>in</strong> of each attractor[15][18].<br />
Therefore, how to get the structure matrix L easily is<br />
very important. The conventional method to get the<br />
structure matrix L is as follows.<br />
Firstly, a simple example is given to show the structure<br />
of a Boolean network.<br />
Where<br />
M<br />
r<br />
is the power-reduc<strong>in</strong>g matrix.<br />
L = M∨M∧M∧ ( I2 ⊗( I2 ⊗M¬<br />
( I2<br />
⊗<br />
M∧ M¬ ( I2 ⊗( I2 ⊗M∨M∧ ( I2<br />
⊗M¬<br />
( I2 ⊗M∧M ( I2 ⊗( I2 ⊗(<br />
I2<br />
⊗M<br />
↓ ↓<br />
M∧)))))))))) W[2] ( I2 ⊗W[2] )( I4 ⊗W[2]<br />
)<br />
( I8 ⊗W[2] )( I32 ⊗W[2] )( I128 ⊗W[2]<br />
)<br />
( I256 ⊗W[2] )( I512 ⊗W[2] )( I1024 ⊗W[2]<br />
)<br />
W[2] ( I4 ⊗W[2] )( I16 ⊗W[2] )( I64 ⊗W[2]<br />
)<br />
( I1<br />
28<br />
⊗W[2] )( I256 ⊗W[2] )( I512 ⊗W[2]<br />
)<br />
( I2 ⊗W[2] )( I32 ⊗W[2] )( I64 ⊗W[2]<br />
)<br />
( I128 ⊗W[2] )( I256 ⊗W[2] )( I16 ⊗W[2]<br />
)<br />
( I128 ⊗W[2] )( I8 ⊗W[2] )( I64 ⊗W[2]<br />
)<br />
( I4 ⊗W[2] )( I32 ⊗W[2] )( I16 ⊗W[2]<br />
)<br />
( I8 ⊗W[2] ) MMM<br />
r r r( I2<br />
⊗(<br />
MM<br />
r r<br />
MM( I ⊗ MMM))<br />
r r 2 r r r<br />
(20)<br />
© 2013 ACADEMY PUBLISHER
1444 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
⎡0 0 0 0 0 0 0 0⎤<br />
1 0 1 [0 0 1 0 0 0 0 0] T<br />
⎢<br />
0 0 1 0 0 0 0 0<br />
⎥<br />
1 1 0 [0 1 0 0 0 0 0 0] T<br />
⎢<br />
⎥<br />
1 1 1 [1 0 0 0 0 0 0 0] T<br />
⎢0 0 0 1 0 0 0 0⎥<br />
⎢<br />
⎥<br />
⎢0 0 0 0 1 0 0 0<br />
=<br />
⎥<br />
Then, we can get the present-state matrix and nextstate<br />
matrix as <strong>in</strong> (21) and (22).<br />
⎢ 0 0 0 0 0 1 0 0 ⎥<br />
⎢<br />
⎥<br />
⎢0 0 0 0 0 0 1 0⎥<br />
⎡1 0 0 0 0 0 0 0⎤<br />
⎢<br />
0 0 0 0 0 0 0 1<br />
⎥<br />
⎢<br />
⎢<br />
⎥<br />
0 1 0 0 0 0 0 0<br />
⎥<br />
⎢<br />
⎥<br />
⎢⎣1 1 0 0 0 0 0 0⎥⎦<br />
⎢0 0 1 0 0 0 0 0⎥<br />
⎢<br />
⎥<br />
0 0 0 1 0 0 0 0<br />
Us<strong>in</strong>g some theorems <strong>in</strong> [15][18][23][24] and<br />
Qt () =<br />
⎢<br />
⎥<br />
⎢<br />
A( t + 1) = LA( t)<br />
, the structure matrix L is as <strong>in</strong> (20).<br />
0 0 0 0 1 0 0 0 ⎥<br />
(21)<br />
⎢<br />
⎥<br />
We can get the structure matrix by the conventional<br />
⎢0 0 0 0 0 1 0 0⎥<br />
⎢<br />
method. But the process is very complex and the biggest<br />
0 0 0 0 0 0 1 0<br />
⎥<br />
⎢<br />
⎥<br />
order of the matrices <strong>in</strong> the equation (20) is more than<br />
⎢⎣<br />
0 0 0 0 0 0 0 1⎥⎦<br />
1024.<br />
⎡0 0 0 0 0 0 0 0⎤<br />
IV. NEW METHOD FOR CALCULATION OF STRUTURE<br />
⎢<br />
0 0 1 0 0 0 0 0<br />
⎥<br />
⎢<br />
⎥<br />
MATRIX<br />
⎢0 0 0 1 0 0 0 0⎥<br />
The conventional method to calculate the structure<br />
⎢<br />
⎥<br />
0 0 0 0 1 0 0 0<br />
matrix L is very complex. A new method will be<br />
Qt ( + 1) =<br />
⎢<br />
⎥<br />
(22)<br />
⎢ 0 0 0 0 0 1 0 0 ⎥<br />
proposed <strong>in</strong> this section.<br />
⎢<br />
⎥<br />
Def<strong>in</strong>ition 3: Form a square matrix by all the presentstate<br />
vectors A() t =×<br />
⎢0 0 0 0 0 0 1 0⎥<br />
l<br />
i=<br />
1<br />
Ai()<br />
t , the matrix is called presentstate<br />
matrix, denoted by Qt ().There is another matrix<br />
⎢⎣<br />
1 1 0 0 0 0 0 0⎥⎦<br />
correspond to Qt (), called next-state matrix, denoted by<br />
⎢0 0 0 0 0 0 0 1⎥<br />
⎢<br />
⎥<br />
Therefore, we can get the structure matrix L = Q( t+<br />
1)<br />
Qt+ ( 1) .<br />
<strong>in</strong> (23).<br />
As A ( t + 1) = LA ( t)<br />
, we can derive<br />
⎡0 0 0 0 0 0 0 0⎤<br />
Q ( t + 1) = LQ ( t)<br />
. It is easy to know that<br />
⎢<br />
0 0 1 0 0 0 0 0<br />
⎥<br />
Qt () l l ∈L , and Qt () is a <strong>in</strong>vertible matrix. Then the<br />
⎢<br />
⎥<br />
2 × 2<br />
⎢0 0 0 1 0 0 0 0⎥<br />
−1<br />
structure matrix L = Q( t+ 1)[ Q( t)]<br />
. Further simplify the<br />
⎢<br />
⎥<br />
0 0 0 0 1 0 0 0<br />
calculation, Qt () can be arrayed to 2 l -order identity<br />
L = Q( t+ 1) =<br />
⎢<br />
⎥<br />
(23)<br />
⎢ 0 0 0 0 0 1 0 0 ⎥<br />
matrix. Therefore, L = Q( t+ 1) .<br />
⎢<br />
⎥<br />
⎢0 0 0 0 0 0 1 0⎥<br />
For the example 3, we have the truth table as TABLE<br />
⎢0 0 0 0 0 0 0 1⎥<br />
II.<br />
⎢<br />
⎥<br />
⎢⎣<br />
1 1 0 0 0 0 0 0⎥⎦<br />
TABLE II.<br />
TRUTH TABLE OF EXAMPLE 3<br />
We can compare the two structure matrix L ga<strong>in</strong>ed <strong>in</strong><br />
Section 3 and our method. And the structure matrix<br />
A 3 (t) A 2 (t) A 1 (t) A 3 (t+1) A 2 (t+1) A 1 (t+1)<br />
which is ga<strong>in</strong>ed by our approach is correct.<br />
0 0 0 0 0 1<br />
0 0 1 0 1 0 By our method, it is easy to get the structure matrix<br />
0 1 0 0 1 1 through the truth table which reflects the transformation<br />
0 1 1 1 0 0 of the states. Our method to get the structure matrix is<br />
1 0 0 1 0 1<br />
simpler than the conventional method.<br />
1 0 1 1 1 0<br />
1 1 0 0 0 0<br />
1 1 1 0 0 0 V. APPLICATION OF STUCTURE MATRIX ON ANALYSIS OF<br />
BOOLEAN NETWORKS<br />
The state vectors’ table is as TABLE III.<br />
S<strong>in</strong>ce a Boolean network has only f<strong>in</strong>ite states, a<br />
trajectory will eventually enter <strong>in</strong>to a fixed po<strong>in</strong>t or a<br />
TABLE III.<br />
STATE VECTORS’ TABLE<br />
cycle. The fixed po<strong>in</strong>ts and cycles form the most<br />
important topological structure of a Boolean network.<br />
A 3 (t) A 2 (t) A 1 (t) A (t)<br />
Therefore, there are many methods to analyze the fixed<br />
0 0 0 [0 0 0 0 0 0 0 1] T<br />
0 0 1 [0 0 0 0 0 0 1 0] T po<strong>in</strong>ts and cycles of Boolean networks.<br />
0 1 0 [0 0 0 0 0 1 0 0] T<br />
Analyz<strong>in</strong>g the structure matrix of the system, easily<br />
0 1 1 [0 0 0 0 1 0 0 0] T<br />
computable formulas are obta<strong>in</strong>ed to show the number of<br />
1 0 0 [0 0 0 1 0 0 0 0] T fixed po<strong>in</strong>ts, the numbers of circles of different lengths<br />
© 2013 ACADEMY PUBLISHER
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and the states <strong>in</strong> the circles. The follow<strong>in</strong>g is a general<br />
result based on the algebraic form.<br />
Consider the Boolean network equation<br />
A( t+ 1) = LA( t)<br />
, and denote by L<br />
i<br />
, 1, 2, …, 2 n the i-th<br />
column of the network matrix L . Then there are<br />
L ∈Δ [15][18].<br />
i<br />
2 n<br />
Def<strong>in</strong>ition 4: 1. A state x 0<br />
∈ Δ is called a fixed po<strong>in</strong>t<br />
2 n<br />
of Boolean network A( t+ 1) = LA( t)<br />
, if Lx0 = x0.<br />
k −1<br />
2. { x , Lx , , L x } is called a circle of Boolean<br />
0 0 0<br />
k<br />
network A( t+ 1) = LA( t)<br />
with length k , if, Lx0 = x0<br />
,<br />
k −1<br />
and the elements <strong>in</strong> set { x0, Lx0, , L x0}<br />
are dist<strong>in</strong>ct.<br />
L can be used for the matrix and its l<strong>in</strong>ear mapp<strong>in</strong>g.<br />
So x<br />
0<br />
may be <strong>in</strong> an L-<strong>in</strong>variant subspace. In this way, a<br />
circle (or a fixed po<strong>in</strong>t) can be def<strong>in</strong>ed on an L-<strong>in</strong>variant<br />
subspace.<br />
The next two theorems [15][18] show how many fixed<br />
po<strong>in</strong>ts and circles of different lengths a Boolean network<br />
has.<br />
Theorem 3: Consider the Boolean network system (13).<br />
i<br />
δ is its fixed po<strong>in</strong>t, iff <strong>in</strong> its algebraic form (14) the<br />
2 n<br />
diagonal element l ii<br />
of network matrix L equals 1. It<br />
follows that the number of equilibriums of system (13),<br />
denoted by N<br />
e<br />
, equals the number of i , for which l ii<br />
= 1.<br />
Equivalently, <strong>in</strong> (24).<br />
Ne<br />
= Trace( L)<br />
(24)<br />
Theorem 4: The number of length s circles,<br />
<strong>in</strong>ductively determ<strong>in</strong>ed by (25).<br />
N s<br />
, is<br />
⎧N1<br />
= Ne,<br />
⎪<br />
s<br />
⎨ Trace( L ) − ∑ kNk<br />
(25)<br />
k∈P( s)<br />
⎪<br />
n<br />
Ns<br />
= , 2≤ s ≤ 2 .<br />
⎪⎩<br />
s<br />
where Ps () is the set of proper factors of s , s ∈ Z + . For<br />
<strong>in</strong>stance, P (6) = {1, 2, 3} .<br />
i<br />
s<br />
Let x0<br />
= δ . Then { x<br />
2 n<br />
0<br />
, Lx 0<br />
, , L x 0<br />
} is a circle with<br />
length s , iff i∈ Ds<br />
.<br />
Consider the Boolean network of the example 3,<br />
N1 = N2 = N3 = N4 = N5 = N6 = N8 = 0 , N<br />
7<br />
= 1 .<br />
Therefore, there is no fixed po<strong>in</strong>t <strong>in</strong> this network, and<br />
there is only one circle which length is 7. Moreover, note<br />
<strong>in</strong> (26).<br />
⎡0 0 0 0 0 0 0 0⎤<br />
⎢<br />
1 1 0 0 0 0 0 0<br />
⎥<br />
⎢<br />
⎥<br />
⎢0 0 1 0 0 0 0 0⎥<br />
⎢<br />
⎥<br />
7<br />
0 0 0 1 0 0 0 0<br />
L =<br />
⎢<br />
⎥<br />
⎢ 0 0 0 0 1 0 0 0 ⎥<br />
⎢<br />
⎥<br />
⎢0 0 0 0 0 1 0 0⎥<br />
⎢0 0 0 0 0 0 1 0⎥<br />
⎢<br />
⎥<br />
⎢⎣0 0 0 0 0 0 0 1⎥⎦<br />
(26)<br />
Then each diagonal nonzero column can generate the<br />
circle. Choosed Z = [0 0 0 0 0 0 0 1] T , then<br />
2<br />
LZ<br />
LZ = [0 0 0 0 0 0 1 0] T<br />
2<br />
LZ=<br />
3<br />
LZ=<br />
4<br />
LZ=<br />
5<br />
LZ=<br />
6<br />
LZ=<br />
[0 0 0 0 0 1 0 0] T<br />
[0 0 0 0 1 0 0 0] T<br />
[0 0 0 1 0 0 0 0] T<br />
[0 0 1 0 0 0 0 0] T<br />
[0 1 0 0 0 0 0 0] T<br />
= [0 0 0 0 0 0 0 1] T = Z<br />
The vector forms <strong>in</strong> the circle can be got <strong>in</strong> TABLE IV.<br />
TABLE IV.<br />
VECTOR FORMS IN THE CIRCLE<br />
A (t) A 3 (t) A 2 (t) A 1 (t)<br />
[0 0 0 0 0 0 0 1] T 0 0 0<br />
[0 0 0 0 0 0 1 0] T 0 0 1<br />
[0 0 0 0 0 1 0 0] T 0 1 0<br />
[0 0 0 0 1 0 0 0] T 0 1 1<br />
[0 0 0 1 0 0 0 0] T 1 0 0<br />
[0 0 1 0 0 0 0 0] T 1 0 1<br />
[0 1 0 0 0 0 0 0] T 1 1 0<br />
The vector forms can be converted back to the scalar<br />
form of A 1<br />
() t , A () t , and A () t<br />
2 3<br />
. The circle is as<br />
000 → 001 → 010 → 011 → 100 → 101 → 110 → 000.<br />
F<strong>in</strong>ally, the state space graph of the network <strong>in</strong> Example<br />
3 can be ga<strong>in</strong>ed as <strong>in</strong> Figure 1.<br />
Figure 1. The state space graph<br />
VI. CASE STUDY: MAMMALIAN CELL<br />
In this section, a useful example of mammalian cell[22]<br />
is given to show that our new approach is effective and<br />
feasible.<br />
A proper understand<strong>in</strong>g of the structure and temporal<br />
behaviors of biological regulatory networks requires the<br />
<strong>in</strong>tegration of regulatory data <strong>in</strong>to a formal dynamical<br />
model. A logical framework enables a more systematic<br />
and extensive characterization of all the behaviors<br />
compatible with a given regulatory graph. Furthermore,<br />
this framework offers enumerative or analytical means to<br />
identify relevant asymptotical behaviors (stable states,<br />
state transition cycles).<br />
The cell cycle <strong>in</strong>volves a succession of molecular<br />
events lead<strong>in</strong>g to the reproduction of the genome of a cell.<br />
Here, the logical regulatory graph for a mammalian cell<br />
© 2013 ACADEMY PUBLISHER
1446 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
cycle network and logical rules associated with the<br />
regulatory graph (<strong>in</strong> Figure 2) are given.<br />
Each node represents the activity of a key regulatory<br />
element, whereas the edges represent cross-regulations.<br />
Blunt arrows stand for <strong>in</strong>hibitory effects, normal arrows<br />
for activations.<br />
Rb<br />
E2F<br />
UbcH10<br />
CycD<br />
CycE<br />
CycA<br />
Cdc20<br />
CycB<br />
Cdh1<br />
Figure 2. The state space graph<br />
The logical equations, which are called dynamics of<br />
Boolean network <strong>in</strong> STP, are as <strong>in</strong> (27).<br />
⎧CycD<br />
= CycD<br />
⎪<br />
⎪Rb = ( CycD ∧CycE ∧CycA ∧CycB)<br />
⎪<br />
⎪<br />
∨( p27 ∧( CycE ∧CycA)<br />
∧CycB<br />
⎪ ∧ CycD)<br />
⎪<br />
⎪E2 F = ( Rb ∧CycA ∧CycB) ∨( p27∧<br />
⎪<br />
⎪ Rb ∧ CycB)<br />
⎪<br />
⎪CycE = ( E2 F ∧Rb)<br />
⎪<br />
⎪CycA = ( E2F ∧Rb ∧Cdc20∧<br />
⎪<br />
( Cdh1 ∧UbcH10)) ∨(<br />
CycA ∧<br />
⎪<br />
⎨ Rb ∧Cdc20 ∧( Cdh1 ∧UbcH10))<br />
⎪<br />
⎪ p27 = ( CycD ∧CycE ∧CycA ∧CycB)<br />
⎪<br />
∨( p27∧( CycE ∧CycA)<br />
∧<br />
⎪<br />
⎪ CycB ∧ CycD)<br />
⎪<br />
⎪Cdc20<br />
= CycB<br />
⎪<br />
⎪Cdh1 = ( CycA ∧CycB) ∨( Cdc20)<br />
∨<br />
⎪<br />
⎪<br />
( p27 ∧ CycB)<br />
⎪ UbcH10 = ( Cdh1) ∨( Cdch1 ∧UbcH10<br />
⎪<br />
⎪ ∧( Cdc20 ∨CycA ∨CycB))<br />
⎪<br />
(27)<br />
⎪CycB = ( Cdc20∧Cdh1)<br />
⎩<br />
Then we use the methods mentioned above to get<br />
stable states and state transition cycles.<br />
There are 10 nodes, so the complete state transition<br />
graph conta<strong>in</strong>s 1024 vertices. The structure matrix L can<br />
be ga<strong>in</strong>ed by algorithm1.<br />
p27<br />
Algorithm1 Algorithm for comput<strong>in</strong>g structure matrix L<br />
L=zeros[1024][1024]<br />
A=zeros[10]<br />
beg<strong>in</strong><br />
for k=0 to 1023 do<br />
A=<strong>in</strong>t_to_b<strong>in</strong>ary (k, 10)<br />
/*convert k to b<strong>in</strong>ary number of 10 bit, */<br />
CycD=A[1];<br />
Rb=A[2];<br />
E2F=A[3];<br />
CycE=A[4];<br />
CycA=A[5];<br />
p27=A[6];<br />
Cdc20=A[7];<br />
Cdh1=A[8];<br />
UbcH10=A[9];<br />
CycB=A[10];<br />
/*assignment each bit to the variables,<br />
from high bit to low bit, A[1] is the highest bit*/<br />
CycD=CycD;<br />
Rb= ( (!CycD) && (!CycE) && (!CycA) && (!CycB))<br />
|| (p27&& (!CycD) && (!CycB)) ;<br />
E2F= ( (!Rb) && (!CycA) && (!CycB)) || (p27&& (!Rb)<br />
&& (!CycB)) ;<br />
CycE= (E2F&& (!Rb)) ;<br />
CycA= (E2F&& (!Rb) && (!Cdc20) && (! (Cdh1<br />
&&UbcH10))) || (CycA&& (!Rb) && (!Cdc20)<br />
&& (! (Cdh1&&UbcH10))) ;<br />
p27= ( (!CycD) && (!CycE) && (!CycA) && (!CycB)) || (p27<br />
&& (! (CycE&&CycA)) && (!CycD) && (!CycB)) ;<br />
Cdc20=CycB;<br />
Cdh1= ( (!CycA) && (!CycB)) || (Cdc20) || (p27&& (!CycB)) ;<br />
UbcH10= (!Cdh1) || ( (Cdh1) && (UbcH10) && ( (Cdc20) ||<br />
(CycA)<br />
|| (CycB))) ;<br />
CycB= ( (!Cdc20) && (!Cdh1)) ;<br />
/* substitute <strong>in</strong>to the logical equations */<br />
i=1024- (CycD*512 + Rb*256 + E2F*128 + CycE*64 +<br />
CycA*32<br />
+ p27*16 + Cdc20*8+Cdh1*4 + UbcH10*2 + CycB*1) ;<br />
j=1024-k;<br />
L[i][j]=1;<br />
return L<br />
end<br />
Accord<strong>in</strong>g to Theorem 3, the characteristics of the<br />
mammalian cell example, such as the number of fixed<br />
po<strong>in</strong>ts, the numbers of circles of different lengths and the<br />
states <strong>in</strong> the circles, can be analyzed by algorithms2.<br />
Through Algorithm1 and Algorithm2, the number of<br />
stable states or fixed po<strong>in</strong>t <strong>in</strong> the example of mammalian<br />
cell is 1. The state or fixed po<strong>in</strong>t is 0100010100, which<br />
means only Rb, p27 and Cdh1 active, <strong>in</strong> the absence of<br />
CycD. And there is 1 circle with the length of 7 <strong>in</strong> the<br />
example of mammalian cell. The states on the circle<br />
<strong>in</strong>clude 1011100100, 1001100000, 1000100011,<br />
1000101011, 1000001110, 1010000110, and 1011000100.<br />
Algorithm2 Algorithm for comput<strong>in</strong>g the number of stable states;<br />
the numbers of circles of different lengths;<br />
Input: structure matrix L<br />
N=zeros[1024]<br />
beg<strong>in</strong><br />
N[1]=trace (L)<br />
if N[1]≠0 then<br />
report the number of stable states is N[1]<br />
for i=2 to 1024 do<br />
T=0<br />
for j=1 to i/2 do<br />
if mod (i, j) =0 then<br />
T=T+j*N[j];<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1447<br />
return T<br />
N[i]= (trace (L^i) -T) /i;<br />
if N[i]>0 then<br />
report the number of circle length of i is N[i]<br />
end<br />
The fixed po<strong>in</strong>t and the circle of the mammalian cell<br />
example are as <strong>in</strong> Figure 3.<br />
0100010100<br />
1 fix po<strong>in</strong>t<br />
1011100100 1001100000 1000100011 1000101011<br />
1011000100 1010000110 1000001110<br />
1 circle with the length of 7<br />
Figure 3. The state space graph<br />
The algorithms <strong>in</strong> the mammalian cell example <strong>in</strong> this<br />
section seem difficult. In fact, it can be easily done <strong>in</strong><br />
computer. We have created a program to handle them.<br />
VII. CONCLUSION<br />
Semi-tensor product is an efficient tool for analyz<strong>in</strong>g<br />
the characteristics of Boolean networks which are<br />
determ<strong>in</strong>ed by the structure matrix. Unlike exist<strong>in</strong>g<br />
methods which calculates the structure matrix through<br />
matrix operations with high computation complexity, an<br />
optimized approach is proposed <strong>in</strong> this paper. The<br />
approach gets the structure matrix of Boolean network<br />
through the truth table which reflects the state<br />
transformation of the Boolean network. Compared with<br />
the conventional methods, our method can greatly reduce<br />
the calculation complexity. A practical Boolean network<br />
of mammalian cell shows our approach is effective and<br />
efficient.<br />
The structure matrix which is ga<strong>in</strong>ed <strong>in</strong> semi-tensor<br />
product is a sparse matrix. On the other hand, with the<br />
number of variables <strong>in</strong> a Boolean network <strong>in</strong>creas<strong>in</strong>g, the<br />
size of the structure matrix will become larger and larger.<br />
These cause higher computation complexity. To optimize<br />
the algorithms <strong>in</strong> section VI, we need to solve the<br />
follow<strong>in</strong>g problems: How to express the structure matrix<br />
<strong>in</strong> sparse matrix How to analyze the fixed po<strong>in</strong>ts and<br />
circles <strong>in</strong> the sparse matrix They are our future work.<br />
ACKNOWLEDGMENT<br />
This work was supported by the Fundamental<br />
Research Funds for the Central Universities of Ch<strong>in</strong>a<br />
under Grant No. ZYGX2009J062 and the National<br />
Natural Science Foundation of Ch<strong>in</strong>a under Grant No.<br />
60973016.<br />
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pp. 6–17, 2011.<br />
J<strong>in</strong>yu Zhan was born <strong>in</strong> Heilongjiang Prov<strong>in</strong>ce of Ch<strong>in</strong>a <strong>in</strong><br />
1978. She received the Ph.D. degree <strong>in</strong> computer applications<br />
from the University of Electronic Science and Technology of<br />
Ch<strong>in</strong>a <strong>in</strong> 2006.<br />
Currently, she is an associate professor at the University of<br />
Electronic Science and Technology of Ch<strong>in</strong>a. Her research<br />
<strong>in</strong>terests <strong>in</strong>clude formal co-verification of SoC, model check<strong>in</strong>g,<br />
real time embedded systems, and VLSI design and verification.<br />
Shan Lu was born <strong>in</strong> Hunan Prov<strong>in</strong>ce of Ch<strong>in</strong>a <strong>in</strong> 1989. He<br />
received the Bachelor degree <strong>in</strong> <strong>in</strong>formation and computation<br />
science from Chongq<strong>in</strong>g Three Gorges University <strong>in</strong> 2011.<br />
Currently, he is a graduate student at the University of<br />
Electronic Science and Technology of Ch<strong>in</strong>a. His research<br />
<strong>in</strong>terests <strong>in</strong>clude formal verification and model check<strong>in</strong>g.<br />
Guowu Yang was born <strong>in</strong> Hubei Prov<strong>in</strong>ce of Ch<strong>in</strong>a <strong>in</strong> 1966. He<br />
received the Ph.D. degree at Electrical and Computer<br />
Eng<strong>in</strong>eer<strong>in</strong>g department of Portland State University <strong>in</strong> USA <strong>in</strong><br />
2005. He was a research associate at Computer Science<br />
department of Portland State University from 2005 to 2006.<br />
Currently, he is a professor of College of Computer Science<br />
and Eng<strong>in</strong>eer<strong>in</strong>g at University of Electronic Science and<br />
Technololgy of Ch<strong>in</strong>a. His research <strong>in</strong>terests <strong>in</strong>clude formal<br />
verification and develop<strong>in</strong>g correspond<strong>in</strong>g program package,<br />
theoretical study of synthesis algorithms <strong>in</strong> quantum comput<strong>in</strong>g,<br />
and non-l<strong>in</strong>ear control theory.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1449<br />
Adaptive Chaotic Prediction Algorithm of RBF<br />
Neural Network Filter<strong>in</strong>g Model based on Phase<br />
Space Reconstruction<br />
Lisheng Y<strong>in</strong>, Yigang He, Xuep<strong>in</strong>g Dong, Zhaoquan Lu<br />
School of Electrical and Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of Technology, Hefei, Ch<strong>in</strong>a<br />
E-mail: yls20000@163.com, hyghnu@yahoo.com.cn, hfdxp@126.com, luzhquan@126.com<br />
Abstract—With the analysis of the technology of phase space<br />
reconstruction, a model<strong>in</strong>g and forecast<strong>in</strong>g technique based<br />
on the Radial Basis Function (RBF) neural network for<br />
chaotic time series is presented <strong>in</strong> this paper. The predictive<br />
model of chaotic time series is established with the adaptive<br />
RBF neural networks and the steps of the chaotic learn<strong>in</strong>g<br />
algorithm with adaptive RBF neural networks are expressed.<br />
The network system can enhance the stabilization and<br />
associative memory of chaotic dynamics and generalization<br />
ability of predictive model even by imperfect and variation<br />
<strong>in</strong>puts dur<strong>in</strong>g the learn<strong>in</strong>g and prediction process by<br />
select<strong>in</strong>g the suitable nonl<strong>in</strong>ear feedback term. The<br />
dynamics of network become chaotic one <strong>in</strong> the weight space.<br />
Simulation experiments of chaotic time series produced by<br />
Lorenz equation are proceeded by a RBF neural<br />
network.The experimental and simulat<strong>in</strong>g results <strong>in</strong>dicated<br />
that the forecast method of the adaptive RBF neutral<br />
network compared with the forecast method of back<br />
propagation (BP) neutral network based on the chaotic<br />
learn<strong>in</strong>g algorithm has faster learn<strong>in</strong>g capacity and higher<br />
accuracy of forecast.The method provides a new way for<br />
the chaotic time series prediction.<br />
Index Terms—Chaos Theory, Phase Space Reconstruction,<br />
Time Series Prediction, RBF Neural network, Algorithm<br />
I. INTRODUCTION<br />
S<strong>in</strong>ce the phase space reconstruction theory proposed<br />
by Packard et al. <strong>in</strong> 1980, many scholars at home and<br />
abroad to set off a climax of chaotic time series<br />
prediction. Prediction for chaotic time series is to<br />
approximate the unknown nonl<strong>in</strong>ear functional mapp<strong>in</strong>g<br />
of a chaotic signal. The laws underly<strong>in</strong>g the chaotic time<br />
series can be expressed as a determ<strong>in</strong>istic dynamical<br />
system. Farmer and Sidorowich suggest reconstruct<strong>in</strong>g<br />
the dynamics <strong>in</strong> phase space by choos<strong>in</strong>g a suitable<br />
embedd<strong>in</strong>g dimension and time delay [1]. Takens’<br />
theorem ensures that the method is reliable, based on the<br />
fact that the <strong>in</strong>teraction between the variables is such that<br />
every component conta<strong>in</strong>s <strong>in</strong>formation on the complex<br />
dynamics of the system [2].<br />
The neural network [3-6]. not only has the selfadaptive,<br />
parallelism and fault tolerance characteristics,<br />
but also has the ability to approximate any nonl<strong>in</strong>ear<br />
function. Based on these advantages, the neural network<br />
model of the nonl<strong>in</strong>ear system has a very wide range of<br />
applications [7-10]. In recent years, particular <strong>in</strong>terest has<br />
been put <strong>in</strong>to predict<strong>in</strong>g chaotic time series us<strong>in</strong>g neural<br />
networks because of their universal approximation<br />
capabilities. Most applications <strong>in</strong> this field are based on<br />
feed-forward neural networks, such as the Back<br />
Propagation (BP) network [11-13], Radial Basis Function<br />
(RBF) network [14-15], Recurrent neural networks<br />
(RNNs) [16-18], FIR neural networks [19-20] and so on.<br />
It is widely used tool for the prediction of time series [21-<br />
23].<br />
The RBF neural network model structure is easy to<br />
understand, tra<strong>in</strong><strong>in</strong>g process stability, tra<strong>in</strong><strong>in</strong>g speed is<br />
fast, tra<strong>in</strong><strong>in</strong>g result is high accuracy and generalization<br />
ability is strong. In this paper, the chaotic algorithm is<br />
proposed to a RBF neural network filter<strong>in</strong>g predictive<br />
model and the model is proposed to make prediction of<br />
chaotic time series. The network system can enhance the<br />
stabilization and associative memory of chaotic dynamics<br />
and generalization ability of predictive model even by<br />
imperfect and variation <strong>in</strong>puts by select<strong>in</strong>g the suitable<br />
nonl<strong>in</strong>ear feedback term. The dynamics of network<br />
become chaotic one <strong>in</strong> the weight space. The model is<br />
tested for the chaotic time series which venerated with<br />
Lorentz system by on-l<strong>in</strong>e method. The experimental and<br />
simulation results <strong>in</strong>dicated that the adaptive filter<strong>in</strong>g has<br />
a good self-suitable prediction performance and can be<br />
successfully used to predict chaotic time series.<br />
II. ESTABLISHMENT OF ADAPTIVE RBF NEURAL<br />
NETWORK FILTERING PREDICTIVE MODEL BASED ON<br />
CHAOTIC ALGORITHM<br />
A. Model of Chaotic Time Series Prediction<br />
Takens theorem considers evolution of any component<br />
of the system is decided by other components <strong>in</strong>teract<strong>in</strong>g<br />
with this component, therefore, the <strong>in</strong>formation of<br />
relevant component imply <strong>in</strong> the development process of<br />
this component, so the orig<strong>in</strong>al rules of the system can be<br />
extracted and restored from a group of time-series data of<br />
a certa<strong>in</strong> component. The one-dimensional time series is<br />
embedded to multi-dimensional phase space through<br />
reconstruction and the new system with same dynamic<br />
characteristics as orig<strong>in</strong>al system can be obta<strong>in</strong>ed through<br />
the selection of a suitable embedd<strong>in</strong>g dimension m and<br />
time delayτ . The usual method of select<strong>in</strong>g time delay<br />
© 2013 ACADEMY PUBLISHER<br />
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1450 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
τ <strong>in</strong>cludes autocorrelation function method, multiple<br />
correlation function method, mutual <strong>in</strong>formation method.<br />
Embedd<strong>in</strong>g dimension m is calculated by the methods of<br />
GP algorithm, pseudo-nearest-po<strong>in</strong>t method, correlation<br />
<strong>in</strong>tegral method and Cao method.<br />
The chaotic time series prediction is based on the<br />
Takens' delay-coord<strong>in</strong>ate phase reconstruct theory. If the<br />
time series of one of the variables is available, based on<br />
the fact that the <strong>in</strong>teraction between the variables is such<br />
that every component conta<strong>in</strong>s <strong>in</strong>formation on the<br />
complex dynamics of the system, a smooth function can<br />
be found to model the portraits of time series. If the<br />
chaotic time series are{ x()<br />
t }, then the reconstruct state<br />
vector is<br />
x( t) = ( x( t), x( t+ τ ), , x( t+ ( m−1) τ ))<br />
where m ( m = 2,3, ) is called the embedd<strong>in</strong>g<br />
dimension ( m= 2d<br />
+ 1 , d is called the freedom of<br />
dynamics of the system), and τ is the delay time. The<br />
predictive reconstruct of chaotic series is a <strong>in</strong>verse<br />
problem to the dynamics of the system essentially. There<br />
exists a smooth function def<strong>in</strong>ed on the reconstructed<br />
m<br />
manifold <strong>in</strong> R to <strong>in</strong>terpret the<br />
dynamics x( t+ T) = F( x( t))<br />
, where T ( T > 0) is forward<br />
predictive step length, and F()<br />
⋅ is the reconstructed<br />
predictive model.<br />
B. RBF Neural Network Function Approximation Theory<br />
Takens embedd<strong>in</strong>g theorem states that there is a<br />
smooth mapp<strong>in</strong>g F of the F makes:<br />
x( t+ τ ) = F( x( t))<br />
(1)<br />
that is,<br />
xt ( + τ), xt (), , xt ( −( m− 2) τ) = F{[ xt (), xt ( −τ), , xt ( −( m−1) τ]}<br />
For purposes of calculation, equation (1) can be rewritten<br />
as:<br />
xt ( + τ ) = Fxt [ ( ), xt ( −τ), , xt ( −( m−1) τ]<br />
(2)<br />
where, f is the mapp<strong>in</strong>g from R M to R L . Chaos theory<br />
suggests that the chaotic time series is short-term forecast,<br />
and the essence of prediction is how to get a good<br />
approximation f on the function f . Chaotic time series<br />
determ<strong>in</strong>ed by the <strong>in</strong>ternal regularity, this regularity<br />
comes from the non-l<strong>in</strong>ear, it exhibits the time series <strong>in</strong><br />
the time delay state, this feature makes the system seem<br />
to have some k<strong>in</strong>d of memory capacity. The same time, it<br />
is difficult to demonstrate such a regularity by us<strong>in</strong>g the<br />
analytic methods; this type of <strong>in</strong>formation process<strong>in</strong>g<br />
happens to be the neural network, and the Kolmogorov<br />
cont<strong>in</strong>uity theorem <strong>in</strong> the neural networks theory<br />
provides a theoretical guarantee for the neural network<br />
nonl<strong>in</strong>ear function approximation.<br />
Theorem (Kolmogorov cont<strong>in</strong>uity theorem) Let ϕ ( x)<br />
be a non-constant and bounded monotonically <strong>in</strong>creas<strong>in</strong>g<br />
a cont<strong>in</strong>uous function; M is a compact sub-set of R n ,<br />
and f( x) = f( x1, x2, , x n<br />
) is the cont<strong>in</strong>uous real value<br />
function on M , then for ∀ ε > 0 , exists a positive <strong>in</strong>teger<br />
N and real numbers C , makes:<br />
<br />
N n<br />
f( x , x , , x ) = Cϕ( ϖ x −θ<br />
) (3)<br />
1 2<br />
∑<br />
∑<br />
n i ij j j<br />
i= 1 j=<br />
1<br />
meet:<br />
<br />
max f( x , x , , x ) − f( x , x , , x ) < ε (4)<br />
M<br />
1 2 n 1 2<br />
By the above theorem, the nonl<strong>in</strong>ear time series<br />
prediction process us<strong>in</strong>g neural network can be<br />
considered as dynamic reconfiguration, which is an<br />
<strong>in</strong>verse process. Namely, the existence of a three-layer<br />
network, the hidden unit output function, the network<br />
<strong>in</strong>put and output function is l<strong>in</strong>ear, three-layer network<br />
<strong>in</strong>put and output relation f can approximate p.<br />
Therefore, the theorem from mathematics is to ensure<br />
the feasibility of chaotic time series prediction by neural<br />
network.<br />
C. Realized Architecture of Adaptive RBF Neural<br />
Network Filter<strong>in</strong>g Predictive Model<br />
After reconstruct<strong>in</strong>g the phase space, the RBF neural<br />
networks adopt three layers networks of Figure 1. Where<br />
the <strong>in</strong>put layer has m nerve cells, the first layer feed to<br />
the second layer directly and it do not need the power<br />
process<strong>in</strong>g. r i<br />
( i = 1, 2, , L ) is the reference vector and<br />
ϖ<br />
k<br />
( i = 1, 2, , L ) is the adjustable parameters <strong>in</strong> the<br />
adaptive RBF neural network filter<strong>in</strong>g. Thus, the adaptive<br />
RBF neural network filter<strong>in</strong>g is more flexible <strong>in</strong> study<strong>in</strong>g<br />
the nonl<strong>in</strong>ear functions. The differentiation between the<br />
networks and the traditional neural networks is that the<br />
activation function is a RBF function but not the Sigmoid<br />
function. The activation function usually choose the<br />
Gauss function, the spl<strong>in</strong>e function f ( di<br />
( k )) ,<br />
where d ( k) = x( k) − r( k)<br />
. In the adaptive RBF neural<br />
i<br />
network filter<strong>in</strong>g, yk ( ) is expressed as<br />
i<br />
2<br />
L−1<br />
yˆ( k) = f ( ∑ ϖ ( k) f( d ( k)))<br />
,<br />
i=<br />
0<br />
i = 0, 2, , L−1,<br />
where f () 2<br />
⋅ is the activation function of output signal.<br />
i<br />
x(k)<br />
−1<br />
z<br />
−1<br />
z<br />
−1<br />
z<br />
r 0<br />
r 1<br />
r 2<br />
r L<br />
i<br />
ϖ 0<br />
( k)<br />
ϖ 1<br />
( k)<br />
ϖ 2<br />
( k)<br />
(k) ϖ L<br />
n<br />
∑<br />
yˆ ( k)<br />
<strong>in</strong>put hidden layer output<br />
Figure 1. Structure of adaptive RBF neural network filter<strong>in</strong>g<br />
Generally, the learn<strong>in</strong>g of the RBF neural network<br />
filter<strong>in</strong>g has three steps. If the gradient method and the<br />
Gauss activation function are adopted, the regulate<br />
formulas of RBF are shown as:<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1451<br />
⎧ϖi( k+ 1) = ϖi( k) + 2 μϖ<br />
e( k) f( di( k))<br />
⎪<br />
2<br />
⎪ di<br />
( k)<br />
σi( k+ 1) = σi( k) + 2 μϖ<br />
e( k) f( di( k)) ϖi( k)<br />
⎪<br />
3<br />
σ<br />
i<br />
( k)<br />
⎪<br />
⎨<br />
x( k) − ri<br />
( k)<br />
(5)<br />
⎪ri( k + 1) = ri( k) + 2 μre( k) f( di( k)) ϖi( k)<br />
2<br />
σ<br />
i<br />
( k)<br />
⎪<br />
⎪<br />
x( k) − ri<br />
( k)<br />
⎪ri( k + 1) = ri( k) + 2 μre( k) f( di( k)) ϖi( k)<br />
2<br />
⎩<br />
σ<br />
i<br />
( k)<br />
i = 0, 2, , L−1.<br />
The RBF neural network system can enhance the<br />
stabilization and associative memory of chaotic dynamics<br />
and generalization ability of predictive model even by<br />
imperfect and variation <strong>in</strong>puts by select<strong>in</strong>g the suitable<br />
nonl<strong>in</strong>ear feedback term. The dynamics of network<br />
become chaotic one <strong>in</strong> the weight space. Thus, the<br />
regulate formula ϖ ( k)<br />
is shown as<br />
ϖ<br />
i( k + 1) = ϖi( k) + 2 μϖ<br />
e( k) f( di( k)) + g( ϖi( k) −ϖI( k−1))<br />
(6)<br />
2<br />
where g( x) = tanh( ax)exp( − bx ), x = ϖ ( k) −ϖ<br />
( k− 1) .<br />
That the feedback function g( x ) is chose is because<br />
that g( x)<br />
can get the difference feedback function<br />
correspond<strong>in</strong>g to the dissimilar parameter, such as the<br />
staircase function, δ function and so on. If the feedback<br />
function is seen as the motion-promot<strong>in</strong>g force, the<br />
different feedback parameters a and b correspond<strong>in</strong>g to<br />
the amplitude and width of the motion-promot<strong>in</strong>g force.<br />
The paper [18] was detailed to discuss the <strong>in</strong>fluences by<br />
select<strong>in</strong>g the suitable learn<strong>in</strong>g and predictive process. The<br />
simulation results <strong>in</strong>dicated that the network system can<br />
enhance the stabilization and associative memory of<br />
chaotic dynamics and generalization ability of predictive<br />
model even by imperfect and variation <strong>in</strong>puts dur<strong>in</strong>g the<br />
learn<strong>in</strong>g and prediction process by select<strong>in</strong>g the suitable<br />
nonl<strong>in</strong>ear feedback term.<br />
III. DETERMINATION METHOD OF THE OPTIMAL DELAY<br />
TIME AND MINIMUM EMBEDDING DIMENSION<br />
A. Determ<strong>in</strong>ation Method of the Optimal Delay Time τ<br />
Dur<strong>in</strong>g Phase Space Reconstruction <strong>in</strong> the Takens<br />
embedd<strong>in</strong>g theorem does not make limited to the delay<br />
time τ .In theory, when the observational data po<strong>in</strong>t is an<br />
<strong>in</strong>f<strong>in</strong>itely long, the effect of embedded not too large.<br />
However, <strong>in</strong> actual operation, τ is caused a great impact.<br />
If τ is too small, the chaotic attractor cannot be fully<br />
expanded, redundant error is larger; if τ is too large, the<br />
no related error is larger. Therefore, <strong>in</strong> order for complex<br />
nonl<strong>in</strong>ear systems, us<strong>in</strong>g the mutual <strong>in</strong>formation method<br />
to determ<strong>in</strong>e the optimal delay time τ , the mutual<br />
<strong>in</strong>formation method us<strong>in</strong>g a m<strong>in</strong>imal value of the mutual<br />
<strong>in</strong>formation function to determ<strong>in</strong>e the optimal delay time<br />
τ , its expression is as follows:<br />
P,<br />
() r<br />
M( x , )<br />
,<br />
( )ln i j<br />
t<br />
xt− τ<br />
= ∑ Pi j<br />
r<br />
(7)<br />
PP<br />
i,<br />
j i j<br />
i<br />
i<br />
where, P<br />
i<br />
is the probability of po<strong>in</strong>t x t<br />
<strong>in</strong> the i time<br />
<strong>in</strong>terval; Pi, j()<br />
r is the jo<strong>in</strong>t probability of the po<strong>in</strong>t x t<br />
<strong>in</strong><br />
t moment fall <strong>in</strong>to the i time <strong>in</strong>terval and the t + τ<br />
moment fall <strong>in</strong>to the j time <strong>in</strong>tervals.<br />
B. Determ<strong>in</strong>ation Method of the M<strong>in</strong>imum Embedd<strong>in</strong>g m<br />
In this paper, the commonly used pseudo-near-po<strong>in</strong>t<br />
method to calculate the m<strong>in</strong>imum embedd<strong>in</strong>g dimension<br />
m , set the number of attractor dimension d , then m is<br />
just the m<strong>in</strong>imum embedd<strong>in</strong>g dimension when the<br />
attractor is fully open. When m< d , the attractor <strong>in</strong> the<br />
phase space cannot be completely open, the attractor will<br />
produce some projection po<strong>in</strong>t <strong>in</strong> the embedded space,<br />
the projection po<strong>in</strong>t and the other po<strong>in</strong>ts <strong>in</strong> the phase<br />
space will form the closest po<strong>in</strong>t. In the orig<strong>in</strong>al system,<br />
the 2 po<strong>in</strong>ts are not true nearest neighbors, so called<br />
pseudo adjacent po<strong>in</strong>ts. Assume that any po<strong>in</strong>t yt () <strong>in</strong> the<br />
phase space, the criterion of false neighbor<strong>in</strong>g po<strong>in</strong>ts are<br />
as follows:<br />
1<br />
2 2<br />
D () () 2<br />
m+ 1<br />
t − Dm<br />
t xt ( + mτ) − xt ( ′ + mτ)<br />
= > ρm<br />
(8)<br />
D () t D () t<br />
m<br />
Where D () t is the Euclidean distance between the<br />
m<br />
N<br />
po<strong>in</strong>ts of yt () with its nearest neighbor y () t <strong>in</strong> the<br />
phase space when the embedd<strong>in</strong>g dimension is m .<br />
Accord<strong>in</strong>g to this criterion, the calculation pseudo-nearest<br />
neighbor number N when m from small to large, and<br />
then calculate the change amount Δ N when the<br />
embedd<strong>in</strong>g dimension from m to m + 1. Draw the curve<br />
ΔN<br />
Δ<br />
from to m ; when Δ N = 0 , just N dropped to 0,<br />
N<br />
N<br />
the value m * of m is seek<strong>in</strong>g the m<strong>in</strong>imum embedd<strong>in</strong>g<br />
dimension.<br />
IV. ADAPTIVE RBF NEURAL NETWORK RAPID LEARNING<br />
ALGORITHM<br />
On the establishment of chaotic time series RBF,<br />
Network <strong>in</strong>put the number of neurons, hidden layers and<br />
the number of neurons <strong>in</strong> the hidden layer are to be<br />
considered.The follow<strong>in</strong>g chaotic time series used are<br />
from Lorenz chaotic sampl<strong>in</strong>g time series. The Lorenz<br />
chaotic sampl<strong>in</strong>g time series RBF neural network can be<br />
constructed: RBF neural network is designed to be three<br />
layers: <strong>in</strong>put layer, s<strong>in</strong>gle hidden layer and output layer;<br />
the number of hidden layer wavelet neural taken as 9 by<br />
Kolmogorov Theorem, the number of <strong>in</strong>put layer neurons<br />
equal to the m<strong>in</strong>imum embedd<strong>in</strong>g dimension, the number<br />
of output layer is 1, so that the 4-9-1 structure of Lorenz<br />
chaotic sampl<strong>in</strong>g time series RBF was obta<strong>in</strong>ed,<br />
specifically shown <strong>in</strong> Figure 1.<br />
Algorithm The steps of the chaotic time series learn<strong>in</strong>g<br />
and prediction of the adaptive RBF neural network<br />
filter<strong>in</strong>g predictive model are showed:<br />
Step1) Based on the Takens' delay-coord<strong>in</strong>ate phase<br />
reconstruct theory, the number of the <strong>in</strong>put nerve cells<br />
m<br />
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1452 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
M of the adaptive RBF neural network filter<strong>in</strong>g is<br />
determ<strong>in</strong>ed.<br />
The dimension m of chaotic time series is<br />
calculated by the way of G- P algorithms, and<br />
the delay time τ is calculated by the selfcorrelation<br />
method. For the overall description<br />
of the dynamics characteristic of the orig<strong>in</strong>al<br />
system by the Takens' delay-coord<strong>in</strong>ate phase<br />
reconstruct theory, a chaotic series demand<br />
m≥ 2d<br />
+ 1 variances at least, so the number of<br />
the <strong>in</strong>put nerve cells of the adaptive RBF neural<br />
network filter<strong>in</strong>g is M = m ; The reconstruction<br />
phase space vector number is 200, Then, the<br />
200 phase space vectors to make a simple<br />
normalized, the normalized as<br />
[ x() t −mean( x())]/[max( t x()) t − m<strong>in</strong>( x())]<br />
t<br />
,<br />
t = 1, 2, 200 , and mak<strong>in</strong>g the value is owned by a range<br />
of -1 / 2 to 1/2.<br />
Step2) The adaptive filter<strong>in</strong>g is <strong>in</strong>itialized and the<br />
weights are vested the <strong>in</strong>itial values. RBF neural network<br />
vector weight<strong>in</strong>g parameters w is <strong>in</strong>itialized, where the<br />
weight vector w <strong>in</strong> each component take random function<br />
between 0 and 1; and the learn<strong>in</strong>g rate η is <strong>in</strong>itialized at<br />
the same time, where η = 0.0002 . β and γ are the<br />
learn<strong>in</strong>g rate adjustment factors, 0< β < 1, γ > 1 , for<br />
example, β = 0.75, γ = 1.05 .<br />
Step3) Us<strong>in</strong>g the above the <strong>in</strong>itialization network and<br />
the pretreatment traffic flow time series, the first tra<strong>in</strong><strong>in</strong>g<br />
network is carried out.<br />
Step4) The error is calculated. If the error is <strong>in</strong> the<br />
scope of the permission, the error is calculated and it<br />
turns <strong>in</strong>to Step4), otherwise it cont<strong>in</strong>ues; the error<br />
function formula:<br />
200<br />
1 2<br />
E( θ ) = ( y( t) − y( t))<br />
(9)<br />
∑<br />
2 t = 1<br />
Set the maximum error is E max<br />
= 0.035 , if E < Emax<br />
,<br />
the storage RBF neural network parameter use w ;<br />
otherwise, then a second tra<strong>in</strong><strong>in</strong>g network will be<br />
required.<br />
Step5) Adjust the adaptive learn<strong>in</strong>g rate If A previous<br />
tra<strong>in</strong><strong>in</strong>g error is recorded as En<br />
− 1<br />
, the current error is<br />
recorded as E n<br />
, then Calculate the ratio of E<br />
n<br />
to En<br />
− 1<br />
,<br />
En<br />
Sett<strong>in</strong>g constants k = 1.04 , if > k = 1.04 , then<br />
En<br />
− 1<br />
substitute βη for η to reduce learn<strong>in</strong>g rate; otherwise,<br />
replace η with γη to <strong>in</strong>crease learn<strong>in</strong>g rate.<br />
Step6) In the adaptive RBF neural network filter<strong>in</strong>g for<br />
the chaotic time series prediction <strong>in</strong> Figure 1,<br />
x( k) = x( t)<br />
t = 1, 2, , N is the <strong>in</strong>put, yk ˆ( ) = xt ˆ( ) is the<br />
output.<br />
Introduce nonl<strong>in</strong>ear feedback <strong>in</strong>to the weight<strong>in</strong>g<br />
formal to adopt Chaos Mechanisms, due to the nonl<strong>in</strong>ear<br />
feedback is vector form of weight<strong>in</strong>g variables. In order<br />
to facilitate understand<strong>in</strong>g, respectively, gives the vector<br />
w and its weight<strong>in</strong>g formal, as follows.<br />
Note<br />
Δ w l ( t+ 1) = w l ( t+ 1) −w l ( t)<br />
,<br />
ji ji ji<br />
which represents the current value of weight<strong>in</strong>g variables,<br />
then<br />
1<br />
Δ w l ( t+ 1) = w l ( t+ 1) − w l () t = −ηδ l+<br />
() t x<br />
l () t<br />
ji ji ji j i<br />
In order to speed up the learn<strong>in</strong>g process, <strong>in</strong> the right to<br />
l<br />
jo<strong>in</strong> a momentum term αΔw () t , then<br />
l 1<br />
( 1) l +<br />
( ) l ( ) l<br />
ji<br />
t ηδ<br />
j<br />
t<br />
i<br />
t α<br />
ji<br />
( t)<br />
ji<br />
Δ w + = − x + Δw (10)<br />
where α is <strong>in</strong>ertia factor. As a constant, the weight of<br />
amendments is l<strong>in</strong>ear, not <strong>in</strong>troduce chaos mechanism.<br />
then we Introduce a nonl<strong>in</strong>ear feedback (chaos<br />
mechanism on the right):<br />
1<br />
Δ w l ( t+ 1) = − ηδ l+<br />
( t) x l ( t) + g( Δ w l ( t+<br />
1)) (11)<br />
ji j i ji<br />
Expand this equation <strong>in</strong>to scalar form as follow:<br />
l l+<br />
1 l l<br />
⎧Δ wji ( t+ 1) = − ηδ<br />
j<br />
( t) xi ( t) + g( Δwji<br />
( t))<br />
⎪<br />
l l+<br />
1<br />
l l<br />
⎪Δ wji ( t+ 1 + τ) =− ηδ<br />
j<br />
( t+ τ) xi ( t+ τ) + g( Δ wji<br />
( t+<br />
τ))<br />
⎪<br />
l l+<br />
1<br />
l l<br />
⎪Δ wji ( t+ 1+ 2 τ ) = − ηδ<br />
j<br />
( t+ 2) xi ( t+ 2 τ ) + g( Δ wji<br />
( t+<br />
2 τ ))<br />
⎨<br />
⎪<br />
⎪ l l+<br />
1<br />
l<br />
⎪<br />
Δ wji ( t+ 1 + ( m− 1) τ ) =− ηδ<br />
j<br />
( t+ ( m− 1) τ ) xi<br />
( t+ ( m−1) τ )<br />
⎪ l<br />
⎩<br />
+ g(<br />
Δwji<br />
( t+ ( m−1) τ ))<br />
(12)<br />
where, feedback can take a variety of vector functions,<br />
for example:<br />
2<br />
g( x) = tanh( px)exp( − qx )<br />
or<br />
g( x) = pxexp( − q x)<br />
,<br />
<strong>in</strong> the study, p = 0.7 , q = 0.1.<br />
Step7) Us<strong>in</strong>g the new learn<strong>in</strong>g rate <strong>in</strong> Step5) and RBF<br />
network parameters with nonl<strong>in</strong>ear feedback <strong>in</strong> Step6) to<br />
calculate the new value, and tra<strong>in</strong> network aga<strong>in</strong>, then get<br />
the error and enter <strong>in</strong>to Step4), repeated tra<strong>in</strong><strong>in</strong>g until the<br />
relative error <strong>in</strong> traffic meet E < Emax<br />
.<br />
Step8) Output of each stored network parameters and<br />
tra<strong>in</strong><strong>in</strong>g error curve.<br />
V. EXAMPLE ANALYSIS AND CONCLUSIONS<br />
A. Model and Data<br />
In this paper, the chaotic time series is the object of<br />
study of the numerical simulation <strong>in</strong> Lorenz dynamic<br />
system. In 1963, the meteorologist Lorenz describe the<br />
evolution of the weather by three-dimensional<br />
autonomous equations; when the parameter σ = 10 ,<br />
8<br />
r = 28 , b = , the long-term changes <strong>in</strong> the weather<br />
3<br />
unpredictable, that is, the system presents a chaotic state,<br />
and for the first time given a strange attractor. The<br />
attractors are shown <strong>in</strong> Figure 2 (a), Figure 2 (b), Figure 2<br />
(c) and Figure 2 (d):<br />
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z(t)<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
-30<br />
20<br />
10<br />
0<br />
y(t)<br />
-10<br />
attractor of Lorenz<br />
-20 -20<br />
(a) three-dimensional map of Lorenz attractor<br />
y(t)<br />
20<br />
15<br />
10<br />
5<br />
0<br />
-5<br />
-10<br />
-15<br />
attractor of Lorenz<br />
-20<br />
-10 0 10 20 30 40 50<br />
x(t)<br />
(b) two-dimensional map of Lorenz attractor <strong>in</strong> the x-y-plan<br />
z(t)<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
attractor of Lorenz<br />
-30<br />
-10 0 10 20 30 40 50<br />
x(t)<br />
(c) two-dimensional map of Lorenz attractor <strong>in</strong> the x-z-plan<br />
y(t)<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
attractor of Lorenz<br />
-30<br />
-20 -15 -10 -5 0 5 10 15 20<br />
z(t)<br />
(d) two-dimensional map of Lorenz attractor <strong>in</strong> the z-y-plan<br />
0<br />
x(t)<br />
20<br />
40<br />
60<br />
Lorenz map:<br />
•<br />
⎧<br />
⎪<br />
x = σ ( y − x)<br />
⎪ •<br />
⎨ y = rx − y − xz<br />
(13)<br />
⎪ •<br />
⎪ z =− bz+<br />
xy<br />
⎩<br />
8<br />
Where σ = 10 , r = 28 , b = .The <strong>in</strong>itial value is<br />
3<br />
x (0) = 0 , y (0) = 5 , z (0) = − 5 ; and the fix<strong>in</strong>g step length<br />
of <strong>in</strong>itial value is 0.05s . Time series to the branch x with<br />
70s is produced by the Runge-Kutta algorithms and the<br />
total data is 1200. The embedded dimension of the<br />
sampl<strong>in</strong>g chaotic time series m is 8 by the G- P<br />
algorithms. The delay time is τ= 1 by the self-correlation<br />
function algorithms and the <strong>in</strong>put dimension of the<br />
adaptive RBF neural network filter<strong>in</strong>g is 8.The former<br />
1200 data is tra<strong>in</strong>ed and other 200 data is predicted by the<br />
adaptive RBF neural network filter<strong>in</strong>g predictive model.<br />
B. Evaluation of the Predictive Ability<br />
The model's predictive ability is generally measure the<br />
follow<strong>in</strong>g three <strong>in</strong>dicators: of MAPE (mean absolute<br />
percentage error), RMSE (root mean square error) and<br />
RMSPE (root mean square percentage error), they are<br />
calculated as follows:<br />
n<br />
1 yi<br />
− yi<br />
MAPE = 100<br />
n<br />
∑ × , (14)<br />
y<br />
i=<br />
1<br />
i<br />
n<br />
1 ⎛ yi<br />
− y ⎞<br />
i<br />
RMSPE = 100× ∑ ⎜ ⎟<br />
n I = 1 ⎝ y<br />
, (15)<br />
i ⎠<br />
n I = 1<br />
i i<br />
1 n<br />
RMSE = y − y<br />
∑( ) 2<br />
(16)<br />
where, y i<br />
is predictive value of the model; y i<br />
is the real<br />
value; n is prediction phases, and MAPE assess the<br />
predictive capability are as follows: less than or equal to<br />
10%, then predictive ability is excellent; 10% -20%, then<br />
the predictive ability is excellent; 20% -50%, more than<br />
50%, then the prediction is <strong>in</strong>accurate. For RMSPE, the<br />
prediction square vulnerable to the impact of outliers, for<br />
the larger error given greater weight, but still can be<br />
modeled on the MAPE to determ<strong>in</strong>e the model of the pros<br />
and cons. RMSPE values range from zero to <strong>in</strong>f<strong>in</strong>ity.<br />
MAPE and RMSPE are the relative <strong>in</strong>dicator, RMSE is<br />
the absolute <strong>in</strong>dicator. The RMSE is the smaller, the<br />
model predictive ability is the stronger.<br />
C. The Simulation Results<br />
That the experimental outcome of Lorenz chaotic<br />
sampl<strong>in</strong>g time series, the true value (real l<strong>in</strong>e) and the<br />
predictive value (star l<strong>in</strong>e) and the predictive error curve<br />
are showed <strong>in</strong> Figure 3., Figure 4. and Figure 5.<br />
2<br />
Figure 2. Lorenz attractor <strong>in</strong> the phase space reconstruction<br />
Consider<strong>in</strong>g Lorenz chaotic system<br />
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1454 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
0 200 400 600<br />
n<br />
800 1000 1200 1400<br />
40<br />
35<br />
30<br />
25<br />
20<br />
15<br />
Figure 3. Lorenz chaotic sampl<strong>in</strong>g time series<br />
10<br />
1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400<br />
n<br />
Figure 4. True value (real l<strong>in</strong>e) and predictive value (star l<strong>in</strong>e)<br />
error<br />
square<br />
0.5<br />
x 10 -3<br />
1<br />
0<br />
1200 1220 1240 1260 1280 1300 1320 1340 136013801400<br />
Figure 5. Predictive error curve<br />
In Figure 3 the sampl<strong>in</strong>g chaotic time series number is<br />
1200 by the Runge-Kutta algorithms.<br />
The former 1200 datum is used to learn and tra<strong>in</strong> the<br />
adaptive wavelet neural networks every 8 datum. After<br />
the learned and tra<strong>in</strong>ed stage, the true value (real l<strong>in</strong>e) and<br />
predictive value (star l<strong>in</strong>e) are shown <strong>in</strong> Figure 4.<br />
The predictive error curve of the true value and the<br />
predictive value is very small <strong>in</strong> Figure 5.<br />
The true value and the predictive value <strong>in</strong> the adaptive<br />
RBF neural network filter<strong>in</strong>g is to f<strong>in</strong>d a <strong>in</strong>ner law <strong>in</strong> the<br />
series itself, which can avoid the disturbance of some<br />
subjective factors and enjoys higher reliability. In this<br />
study, the fusion of chaotic theory with the adaptive RBF<br />
neural network filter<strong>in</strong>g based on chaotic algorithm<br />
provides a new method for chaotic time series prediction.<br />
The experimental <strong>in</strong>dicated that the network system can<br />
enhance the stabilization and associative memory of<br />
chaotic dynamics and generalization ability of predictive<br />
model even by imperfect and variation <strong>in</strong>puts dur<strong>in</strong>g the<br />
learn<strong>in</strong>g and prediction process by select<strong>in</strong>g the suitable<br />
nonl<strong>in</strong>ear feedback term. Simulation results for the<br />
model<strong>in</strong>g and prediction of chaotic time series show<br />
better predictive effectiveness and reliability.<br />
TABLE 1<br />
PREDICTIVE PERFORMANCE COMPARISON TABLE<br />
comparative<br />
<strong>in</strong>dicators<br />
BP neural network<br />
prediction<br />
RBF neural network<br />
prediction<br />
MAPE 5.01% 3.71%<br />
RMSPE 6.13% 4.55%<br />
RMSE 62.50 46.37<br />
From Table 1, the mean absolute percentage error of<br />
Lorenz chaotic sampl<strong>in</strong>g time series prediction and actual<br />
values, BP neural network based on the learn<strong>in</strong>g rate<br />
variable tra<strong>in</strong><strong>in</strong>g algorithm, RBF network based on fast<br />
learn<strong>in</strong>g algorithm, are 5.1% and 3.71%, respectively.<br />
Similarly, for the RMSPE, the results were 6.13% and<br />
4.55%; For RMSE, the results were 62.50 and 46.37. Can<br />
be seen from the data on Lorenz chaotic sampl<strong>in</strong>g time<br />
series RBF network prediction is better than BP neural<br />
network.<br />
VI. CONCLUSIONS<br />
In the paper the chaotic time series RBF neural<br />
network model was designed. A RBF neural network<br />
Adaptive learn<strong>in</strong>g algorithm based on Chaos mechanism<br />
was proposed. The method of model selection and<br />
algorithm design, are considered the chaos of Lorenz<br />
chaotic sampl<strong>in</strong>g time series, which is a theoretical value.<br />
Simulation results show that the method can reduce<br />
MAPE, RMSPE, RMSE, and improve the forecast<br />
accuracy, and show better predictive effectiveness and<br />
reliability.<br />
ACKNOWLEDGMENT<br />
This research is f<strong>in</strong>ancially supported by the National<br />
Natural Science Funds of Ch<strong>in</strong>a for Dist<strong>in</strong>guished Young<br />
Scholar under Grant (50925727), and the Fundamental<br />
Research Funds for the Central Universities, Hefei<br />
University of Technology for Professor He Yigang, the<br />
National Natural Science Foundation of Ch<strong>in</strong>a (NSFC)<br />
for Professor Xue-p<strong>in</strong>g Dong (No. 60974022) and the<br />
Universities Natural Science Foundation of Anhui<br />
Prov<strong>in</strong>ce (No. KJ2012A219) for Professor Y<strong>in</strong> Lisheng.<br />
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Prediction Based on Chaos Time Series Theory”, Journal<br />
of Transportation Systems Eng<strong>in</strong>eer<strong>in</strong>g and Information<br />
Technology, 8 (5), pp. 68-72, 2008.<br />
[2] Ajit Kumar Gautam, A.B. Chelani, V.K. Ja<strong>in</strong>a, S. Devotta,<br />
“A new scheme to predict chaotic time series of air<br />
pollutant concentrations us<strong>in</strong>g artificial neural network and<br />
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Safieva, “Neuralnetwork (ANN) approach to biodiesel<br />
analysis: Analysis of biodiesel density, k<strong>in</strong>ematic viscosity,<br />
methanol and water contents us<strong>in</strong>g near <strong>in</strong>frared (NIR)<br />
spectroscopy”, Fuel, Vol. 90, no. 5, pp. 2007-2015, May<br />
2011.<br />
[4] Yuanp<strong>in</strong>g Zhu, Jun Sun and Satoshi Naoi, “Recogniz<strong>in</strong>g<br />
Natural Scene Characters by Convolutional Neural<br />
Network and Bimodal Image Enhancement, “Lecture<br />
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2012.<br />
[5] Yüksel Özbaya, Rahime Ceylanb, Bekir Karlikc,<br />
“Integration of type-2 fuzzy cluster<strong>in</strong>g and wavelet<br />
transform <strong>in</strong> a neuralnetwork based ECG classifier”,<br />
Expert Systems with Applications, Vol. 38, pp.1004-1010,<br />
January 2011.<br />
[6] Yan Fan, Niall W. Duncan, Moritz de Greck, Georg<br />
Northoff, “Is there a core neuralnetwork <strong>in</strong> empathy An<br />
fMRI based quantitative meta-analysis”, Neuroscience &<br />
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[7] Shunsuke Kobayakawa, Hirokazu Yokoi, “Evaluation of<br />
Prediction Capability of Non-recursion Type 2nd-order<br />
Volterra Neuron Network for Electrocardiogram”, Lecture<br />
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[8] Li-Sheng Y<strong>in</strong>, Xi-Yue Huang, Zu-Yuan Yang, et al,<br />
“Prediction for chaotic time series based on discrete<br />
Volterra neural networks”, Lect Notes Comput SC vol.<br />
3972, pp. 759-764, 2006.<br />
[9] Satoru Murakami, Pham Huu, Anh Ngoc, “On stability and<br />
robust stability of positive l<strong>in</strong>ear Volterra equations <strong>in</strong><br />
Banach lattices”, Central European Journal of<br />
Mathematics, 2010, pp.966-984.<br />
[10] Yu. V. Bibik, “The second Hamiltonian structure for a<br />
special case of the Lotka-Volterra equations”, Mathematics<br />
and Mathematical Physics, 2007, 47, pp.1285-1294.<br />
[11] Zhi Xiao, Shi-Jie Ye, Bo Zhong, Cai-X<strong>in</strong> Sun, “BP neural<br />
network with rough set for short term load forecast<strong>in</strong>g”,<br />
Expert Systems with Applications, 36 (1), pp. 276-279,<br />
2009.<br />
[12] Shiwei Yu, Kejun Zhu, Fengq<strong>in</strong> Diao, “A dynamic all<br />
parameters adaptive BP neural networks model and its<br />
application on oil reservoir prediction”, Applied<br />
Mathematics and Computation, 2008, 195 (1), pp.66-75.<br />
[13] R. Bakker, J. C. Schouten, and C. L. Giles et al., “Learn<strong>in</strong>g<br />
chaotic attractorsby neural networks”, Neural Computer,<br />
12, pp.2355-2383, 2000.”,<br />
[14] H. Leung, T. Lo, and S. Wang, “Prediction of noisy<br />
chaotic time series us<strong>in</strong>g an optimal radial basis function<br />
neural network”, IEEE Trans. Neural Networks, 12,<br />
pp.1163-1172, 2001.<br />
[15] Zhang Yun, Zhou Quan, Sun Caix<strong>in</strong>, Lei Shaolan, Liu<br />
Yum<strong>in</strong>g, Song Yang, “RBF Neural Network and ANFIS-<br />
Based Short-Term Load Forecast<strong>in</strong>g Approach <strong>in</strong> Real-<br />
Time Price Environment”, Power Systems, 23 (3), pp.853-<br />
858, 2008.<br />
[16] Zidong Wang, Yurong Liu, Xiaohui Liu, “State estimation<br />
for jump<strong>in</strong>g recurrent neural networks with discrete and<br />
distributed delays”, Neural Networks, 22 (1), pp.41-48,<br />
2009.<br />
[17] Talebi, H.A., Khorasani, K., Tafazoli, S., “A Recurrent<br />
Neural-Network-Based Sensor and Actuator Fault<br />
Detection and Isolation for Nonl<strong>in</strong>ear Systems With<br />
Application to the Satellite's Attitude Control Subsystem”,<br />
Neural Networks, 2009, 20 (1), pp.45-60.<br />
[18] M<strong>in</strong> Han, Jianhui Xi, Shiguo Xu, and Fuliang Y<strong>in</strong>,<br />
“Prediction of time series based on the recurrent predictor<br />
neural network”, IEEE Transactions on signal process<strong>in</strong>g,<br />
vol.52.no.12.december 2004.<br />
[19] Sirapart Chiewchanwattana, Chidchanok Lurs<strong>in</strong>sap, Chee-<br />
Hung Chu, “Time-series datd prediction based on<br />
reconstruction of miss<strong>in</strong>g samples and selective<br />
ensembl<strong>in</strong>g of FIR neural networks”, Proceed<strong>in</strong>g of the 9th<br />
<strong>in</strong>ternational conference on neural <strong>in</strong>formation<br />
process<strong>in</strong>g.vol.5, 2002.<br />
[20] Dhruba C.Panda, Shyam S.Pattnaik, Rab<strong>in</strong>dra K.Mishra,<br />
“Application of FIR-neural network on f<strong>in</strong>ite difference<br />
time doma<strong>in</strong> technique to calculate <strong>in</strong>put impedance of<br />
microstrip patch antenna”, International Journal of RF and<br />
Microwave Computer-Aided Eng<strong>in</strong>eer<strong>in</strong>g, Vol. 20, pp.158-<br />
162, 2010.<br />
[21] Wu Jian-Da, Hsu Chuang-Ch<strong>in</strong>, Wu Guozhen, “Fault gear<br />
identification and classification us<strong>in</strong>g discrete wavelet<br />
transform and adaptive neuro-fuzzy <strong>in</strong>ference”, Expert<br />
Systems with Applications, vol. 36, pp. 6244-6255, 2009.<br />
[22] Lee Jong Jae, Kim Dookie, Chang Seong Kyu, “An<br />
improved application technique of the adaptive<br />
probabilistic neural network for predict<strong>in</strong>g concrete<br />
strength, “Computational Materials Science, vol. 44, pp.<br />
988-998, 2009.<br />
[23] Hu xiao-jian, wang wei, sheng hui, “Urban Traffic Flow<br />
Prediction with Variable Cell Transmission Model”,<br />
Journal of Transportation Systems Eng<strong>in</strong>eer<strong>in</strong>g and<br />
Information Technology, vol. 4, pp.17-22, 2010.<br />
Lisheng Y<strong>in</strong> (yls20000@163.com) received his doctor’s degree<br />
<strong>in</strong> Control Theory and Control Eng<strong>in</strong>eer<strong>in</strong>g from School of<br />
Automation, Chongq<strong>in</strong>g University, Chongq<strong>in</strong>g Ch<strong>in</strong>a. He is an<br />
associate professor <strong>in</strong> the School of Electrical and Automation<br />
Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of Technology.He conducts<br />
research <strong>in</strong> Modern <strong>in</strong>telligent algorithm, Chaos Theory, Neural<br />
network theory and Fuzzy Theory.<br />
Yigang He (hyghnu@yahoo.com.cn) received his doctor’s<br />
degree <strong>in</strong> Electrical Eng<strong>in</strong>eer<strong>in</strong>g from Electrical Eng<strong>in</strong>eer<strong>in</strong>g,<br />
Xi'an Jiaotong University, Xian Ch<strong>in</strong>a. He is a professor <strong>in</strong> the<br />
School of Electrical and Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei<br />
University of Technology. He conducts research <strong>in</strong> Electrical<br />
science and eng<strong>in</strong>eer<strong>in</strong>g, automatic test and diagnostic<br />
equipment, High-speed low-voltage low-power <strong>in</strong>tegrated<br />
circuits, systems, <strong>in</strong>telligent and real-time <strong>in</strong>formation<br />
process<strong>in</strong>g, Smart grid, electrical measurement techniques and<br />
Circuit theory of massive proportions and Mixed-signal system<br />
test<strong>in</strong>g and diagnosis<br />
Xuep<strong>in</strong>g Dong (hfdxp@126.com) received his doctor’s degree<br />
<strong>in</strong> Control Theory and Control Eng<strong>in</strong>eer<strong>in</strong>g from School of<br />
Automation, Nanj<strong>in</strong>g University Of Science and Technology,<br />
Nangj<strong>in</strong>g Ch<strong>in</strong>a. He is an associate professor <strong>in</strong> the School of<br />
Electrical and Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of<br />
Technology.He conducts research <strong>in</strong> Model<strong>in</strong>g and control of<br />
complex systems, Modern control theory and its application.<br />
Zhaoquan Lu (luzhquan@126.com) received his doctor’s<br />
degree from University of Science and Technology of Ch<strong>in</strong>a,<br />
Hefei Ch<strong>in</strong>a. He is a professor <strong>in</strong> the School of Electrical and<br />
Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of Technology.He<br />
conducts research <strong>in</strong> Large time delay uncerta<strong>in</strong> process and<br />
control, complex systems and controls, <strong>in</strong>telligent control,<br />
wireless communication network and automation systems,<br />
automotive electronics technology research and development,<br />
energy-sav<strong>in</strong>g control system research and development.<br />
© 2013 ACADEMY PUBLISHER
1456 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Intrusion Detection Based on Improved SOM<br />
with Optimized GA<br />
ZHAO Jian-Hua 1, 2<br />
1 College of computer, Northwestern Polytechnical University, Xi’an 710072, Ch<strong>in</strong>a<br />
2 Department of Computer Science, ShangLuo University, ShangLuo 726000, Ch<strong>in</strong>a<br />
E-mail: zhaojh2009@yahoo.com.cn<br />
LI Wei-Hua<br />
College of computer, Northwestern Polytechnical University, Xi’an 710072, Ch<strong>in</strong>a<br />
Abstract—In order to improve the effectiveness of<br />
supervised self-organiz<strong>in</strong>g map (SSOM) neural network, a<br />
k<strong>in</strong>d of genetic algorithm is designed to optimize it. To<br />
improve its classification rate, a real number encod<strong>in</strong>g<br />
genetic algorithm is provided and used to optimize the<br />
learn<strong>in</strong>g rate and neighbor radius of SSOM. To speed up<br />
the model<strong>in</strong>g speed, a b<strong>in</strong>ary encod<strong>in</strong>g genetic algorithm is<br />
provided to optimize <strong>in</strong>put variables of SSOM and reduce<br />
its dimension of <strong>in</strong>put sample. F<strong>in</strong>ally, <strong>in</strong>trusion detection<br />
data set KDD Cup 1999 is used to carry out experiment<br />
based on the proposed model. The results show that the<br />
optimized model has shorter model<strong>in</strong>g time and higher<br />
<strong>in</strong>trusion detection rate.<br />
Index Terms—SOM, <strong>in</strong>trusion detection, classification,<br />
dimension reduction, genetic algorithm<br />
I. INTRODUCTION<br />
Nowadays, network communications become more<br />
and more important to the <strong>in</strong>formation society [1, 2].<br />
Bus<strong>in</strong>ess, e-commerce, onl<strong>in</strong>e shopp<strong>in</strong>g, Internet bank<br />
and other network transactions require more secured<br />
networks. As these operations <strong>in</strong>creases, computer crimes<br />
and attacks become more frequents and dangerous,<br />
compromis<strong>in</strong>g the security and the trust of a computer<br />
system and caus<strong>in</strong>g costly f<strong>in</strong>ancial losses [3, 4].<br />
While a number of effective techniques exist for the<br />
prevention of attacks, it has been approved over and over<br />
aga<strong>in</strong> that attacks and <strong>in</strong>trusions will persist and always<br />
be there [5, 6]. Although <strong>in</strong>trusion prevention is still<br />
important, another aspect of network security, <strong>in</strong>trusion<br />
detection, is just as important [7, 8]. With trenchant<br />
<strong>in</strong>trusion detection techniques, network systems can<br />
make themselves less vulnerable by detect<strong>in</strong>g the attacks<br />
and <strong>in</strong>trusions effectively so the damages can be<br />
m<strong>in</strong>imized while keep<strong>in</strong>g normal network activities<br />
unaffected [2, 9, 10].<br />
The <strong>in</strong>trusion detection system (IDS) is used to detect<br />
<strong>in</strong>trusion action. Collect<strong>in</strong>g and analyz<strong>in</strong>g the <strong>in</strong>formation<br />
This work was sponsored by Scientific Research Program Funded by<br />
Shaanxi Prov<strong>in</strong>cial Education Department (No.12JK0748) and National<br />
m<strong>in</strong>istries foundation <strong>in</strong> Ch<strong>in</strong>a.<br />
of a network or system [11, 12], IDS can f<strong>in</strong>d the actions<br />
of violat<strong>in</strong>g security policy and detect the traces of be<strong>in</strong>g<br />
attacked from the network or system. Accord<strong>in</strong>g to the<br />
network <strong>in</strong>formation, it classifies the network behavior<br />
normal behavior or abnormal behavior [13, 14].<br />
The neural network has the function of pattern<br />
recognition, it may be used <strong>in</strong> the field of the<br />
classification of <strong>in</strong>trusion detection and get very good<br />
results [15, 16]. At the same time, neural network has<br />
self-learn<strong>in</strong>g and adaptive capacity. As long as the system<br />
audit data and the network data packet are provided,<br />
neural network can extract normal user or system feature<br />
model from it and detect the attack mode from the<br />
abnormal activity [25].<br />
The self-organiz<strong>in</strong>g map (SOM) neural network<br />
constitutes an excellent tool for knowledge discovery <strong>in</strong> a<br />
data base, extraction of relevant <strong>in</strong>formation, detection of<br />
<strong>in</strong>herent structures <strong>in</strong> high-dimensional data and mapp<strong>in</strong>g<br />
these data <strong>in</strong>to a two-dimensional representation space. It<br />
has been applied successfully <strong>in</strong> multiple areas. Many<br />
researcher has apply it <strong>in</strong> the field of <strong>in</strong>trusion detection<br />
and got the good test result.<br />
However, the network architecture of SOM has to be<br />
established <strong>in</strong> advance and it requires knowledge about<br />
the problem doma<strong>in</strong>. Moreover, the hierarchical relations<br />
among <strong>in</strong>put data are difficult to represent and it is an<br />
unsupervised network and not easy to determ<strong>in</strong>e the<br />
classification type. Some researcher has improved SOM<br />
and they improved unsupervised SOM to supervised<br />
SOM (name SSOM) and obta<strong>in</strong> good results. However,<br />
there are still some problem exit<strong>in</strong>g for SOM and SSOM.<br />
For example, it is difficult to determ<strong>in</strong>e the parameters of<br />
SOM and SSOM [17, 18].<br />
In light of the disadvantage of SOM and SSOM, this<br />
paper uses genetic algorithm to optimize their parameters<br />
(<strong>in</strong>clud<strong>in</strong>g learn<strong>in</strong>g rate and neighborhood radius). New<br />
neural network model (GA-SOM and New-GA-SSOM)<br />
are proposed and applied <strong>in</strong> the field of <strong>in</strong>trusion<br />
detection.<br />
The rest of the paper is organized as follows: In<br />
Section II we describe the basic def<strong>in</strong>itions and<br />
characteristics of SOM neural network, SSOM neural<br />
network and genetic algorithm. Section III designs a<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1456-1463
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1457<br />
genetic algorithm based on real number encod<strong>in</strong>g, which<br />
is to optimize the learn<strong>in</strong>g rate and neighbor radius of<br />
SSOM and solve the random <strong>in</strong>itialization problem of<br />
learn<strong>in</strong>g rate and neighbor radius. Section IV designs a<br />
genetic algorithm based on b<strong>in</strong>ary encod<strong>in</strong>g to optimize<br />
the <strong>in</strong>put variables and reduce the dimension for SSOM.<br />
In Section V, <strong>in</strong>trusion detection experiment is carried<br />
out based on KDD Cup 1999 data sets to verify the<br />
effectiveness of the provided model.<br />
II. PROPOSED SCHEME<br />
A. SOM Neural Network<br />
Self-organiz<strong>in</strong>g feature map network (SOM) is also<br />
known as Kohonen network, which is proposed by<br />
Holland scholar Teuvo Kohonen <strong>in</strong> 1981. The network is<br />
a no-teachers, self-organization and self-learn<strong>in</strong>g network<br />
consist<strong>in</strong>g of fully connected neurons array.<br />
Adjust the weights of the w<strong>in</strong>n<strong>in</strong>g neuron and its<br />
adjacent neurons, so that the weights can reflect the<br />
relationship between the <strong>in</strong>put samples. Through the<br />
repeated tra<strong>in</strong><strong>in</strong>g and learn<strong>in</strong>g, the neurons are divided<br />
<strong>in</strong>to different regions which have different response<br />
characteristics to <strong>in</strong>put model and implement the<br />
cluster<strong>in</strong>g of <strong>in</strong>put model. And it can realize the<br />
classification of the <strong>in</strong>put samples and can be applied <strong>in</strong><br />
various areas of the classification.<br />
The steps of SOM neural network algorithm are as<br />
follow:<br />
(1) Initialization. Initialize the weights and the<br />
neighbor radius etc.<br />
(2) Distance calculation. Distance can reflect the<br />
similarity degree and closeness degree between samples.<br />
We calculate the distance d between <strong>in</strong>put vector<br />
x<br />
i<br />
= ( x 1<br />
, x 2<br />
,..., xn<br />
) and competitive layer neuron j , which<br />
is shown <strong>in</strong> equation (1).<br />
j<br />
m<br />
2<br />
j<br />
= (<br />
i<br />
− ωij) = 1,2...<br />
i=<br />
1<br />
d ∑ x j n (1)<br />
Figure 1.<br />
The structure diagram of SOM<br />
SOM is an artificial neural network model and it is<br />
proved to be exceptionally successful for data<br />
visualization applications mapp<strong>in</strong>g from a usually very<br />
high-dimensional data space <strong>in</strong>to a two-dimensional<br />
representation space. The remarkable benefit of SOM is<br />
that the similarity between the <strong>in</strong>put data as measured <strong>in</strong><br />
the <strong>in</strong>put data space is preserved as faithfully as possible<br />
with<strong>in</strong> the representation space. Thus, the similarity of<br />
the <strong>in</strong>put data is mirrored to a very large extends <strong>in</strong> terms<br />
of geographical vic<strong>in</strong>ity with<strong>in</strong> the representation space<br />
[19, 20].<br />
The structure of SOM neural network is shown <strong>in</strong><br />
Figure 1, <strong>in</strong>clud<strong>in</strong>g two layers feed forward neural<br />
network structure which is an <strong>in</strong>put layer and a<br />
competitive layer. The first layer is the <strong>in</strong>put layer and its<br />
dimension is equal with the <strong>in</strong>put vector dimension which<br />
is set to m. The second layer is a competitive layer and it<br />
generally shows a two-dimensional array distribution. A<br />
competitive layer node represents a neuron and the<br />
number of competitive layer node is set to n. The<br />
association between <strong>in</strong>put layer and competitive layer is<br />
<strong>in</strong> the form of a full connection; its weight is <strong>in</strong>dicated<br />
byω .<br />
ij<br />
The basic work<strong>in</strong>g pr<strong>in</strong>ciple of SOM neural network is<br />
as follow: dur<strong>in</strong>g the network tra<strong>in</strong> and learn<strong>in</strong>g the<br />
neurons on competitive layer get the response to the <strong>in</strong>put<br />
model by compet<strong>in</strong>g with each other, the neuron hav<strong>in</strong>g<br />
the m<strong>in</strong>imum distance from <strong>in</strong>put sample becomes the<br />
w<strong>in</strong>n<strong>in</strong>g neuron.<br />
(3) The w<strong>in</strong>n<strong>in</strong>g neuron selection on competitive<br />
layer.<br />
F<strong>in</strong>d out neuron c with the m<strong>in</strong>imal distance from the<br />
w<strong>in</strong>n<strong>in</strong>g neuron and calculate the neighborhood N c (t) of<br />
c <strong>in</strong> accordance with equation (2).<br />
N() t = ( t f<strong>in</strong>d( norm( pos , pos ) < r) t = 1,2,.., n (2)<br />
c t c<br />
where posc<br />
represents the position of neuron c<br />
and post<br />
represents the position of neuron t; norm<br />
represents the calculation of Euclidean distance between<br />
two neurons; r represents the neighborhood radius.<br />
(4) Weight adjustment. Adjust the neuron weights of<br />
neuron c and others <strong>in</strong> its neighborhood N c (t) accord<strong>in</strong>g<br />
to equation (3).<br />
ω = ω + η( x − ω )<br />
(3)<br />
ij ij i ij<br />
where ω represents the weight between <strong>in</strong>put layer and<br />
competitive layer, η represents learn<strong>in</strong>g rate, η<br />
decreases with the <strong>in</strong>crease of evolution number<br />
(5) Judge whether the algorithm ends. If not end,<br />
return to (2).<br />
B. SSOM Neural Network<br />
SOM is an unsupervised neural network and it can<br />
effectively classify unlabeled data. However It cannot<br />
determ<strong>in</strong>e the classification types of labeled data more<br />
effectively <strong>in</strong> the help of data labels.. To facilitate the<br />
process<strong>in</strong>g of classification problem and quickly get the<br />
classification type, some researchers improve the<br />
unsupervised SOM to supervised SOM which is named<br />
SSOM.<br />
As shown <strong>in</strong> Figure 2, there are three-layer structures<br />
<strong>in</strong> SSOM <strong>in</strong>stead of two layer structure <strong>in</strong> SOM. They are<br />
<strong>in</strong>put layer, competitive layer and output layer. In this<br />
network, the number of output layer is equal with data<br />
classification category. Each output node represents a<br />
© 2013 ACADEMY PUBLISHER
1458 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
data category, and connection between the output layer<br />
node and the competitive layer node is also full<br />
connection way.<br />
Accord<strong>in</strong>g to different prediction category of <strong>in</strong>put<br />
samples, SSOM selects different weight adjustment<br />
formula to adjust weights and tra<strong>in</strong> network. SSOM not<br />
only adjusts the weight ω ij<br />
between <strong>in</strong>put layer and<br />
competitive layer, but also adjust the weight ω<br />
jk<br />
between<br />
competitive layer and output layer. F<strong>in</strong>ally, the<br />
classification results are generated by the comb<strong>in</strong>ation of<br />
the two weights<br />
Figure 2.<br />
The structure diagram of SSOM<br />
The learn<strong>in</strong>g and tra<strong>in</strong> step of SSOM is as follow:<br />
(1) Initialization. Initialize the weight ω ij<br />
between<br />
<strong>in</strong>put layer and competitive layer, the weight<br />
ω<br />
jk<br />
between competitive layer and output layer, and the<br />
neighbor radius r etc.<br />
(2) The w<strong>in</strong>n<strong>in</strong>g neuron selection on competitive layer.<br />
Compute the distance between <strong>in</strong>put sample x i<br />
and<br />
competitive layer neural j to get the neuron c with the<br />
m<strong>in</strong>imal distance from the w<strong>in</strong>n<strong>in</strong>g neuron. Assume d is<br />
the m<strong>in</strong>imal distance, use c i<br />
to marker output categories<br />
connected to it.<br />
(3) Weight adjustment. Adjust the neuron weights<br />
ω and ω accord<strong>in</strong>g to the predictive value of <strong>in</strong>put<br />
ij<br />
jk<br />
sample x i<br />
. Here we assume the actual output value of x<br />
i<br />
is c<br />
x<br />
. If c i<br />
= c x<br />
, adjust the weights <strong>in</strong> the neighbor area<br />
of Nc (t) accord<strong>in</strong>g to equation (4) and (5).<br />
ω new old ( old )<br />
ij<br />
= ωij + η1 x − ωij<br />
(4)<br />
ω new old ( old )<br />
jk<br />
= ωjk + η2 x − ωjk<br />
(5)<br />
If ci<br />
≠ c x<br />
, adjust the weights accord<strong>in</strong>g to equations<br />
(6) and (7).<br />
ω new old ( old )<br />
ij<br />
= ωij −η1 x − ωij<br />
(6)<br />
ω new old ( old )<br />
jk<br />
= ωjk −η2 x − ωjk<br />
(7)<br />
i<br />
where η<br />
1<br />
and η2<br />
represent the learn<strong>in</strong>g rate, they<br />
decrease with the evolution number <strong>in</strong>creas<strong>in</strong>g.<br />
(5) Judge whether the algorithm ends. If not end,<br />
return it to step (2).<br />
Dur<strong>in</strong>g the tra<strong>in</strong> process of SSOM neural network, The<br />
<strong>in</strong>itial parameters such as weight ω ij<br />
, ω<br />
jk<br />
, learn<strong>in</strong>g rate<br />
η<br />
1<br />
, η2<br />
and neighbor radius r have much <strong>in</strong>fluence on<br />
test<strong>in</strong>g result. These parameters randomly selected will<br />
have a negative effect on test result. In this paper, we use<br />
genetic algorithm to optimize the parameters ( η<br />
1<br />
, η2<br />
and<br />
neighbor radius r ) of SSOM..<br />
Genetic algorithm (GA) is a k<strong>in</strong>d of parallel search<br />
optimization method, which simulates the natural genetic<br />
mechanisms of biological evolution and Darw<strong>in</strong>ian<br />
natural selection. Genetic algorithm simulates the<br />
phenomenon of duplication, crossover and mutation that<br />
occur <strong>in</strong> natural selection and genetic replication.<br />
Start<strong>in</strong>g at a group which is a potential solution set of<br />
problem, it performs selection, crossover and mutation<br />
operation to generate a group of <strong>in</strong>dividuals better<br />
adapted to the environment. Then, group evolves <strong>in</strong>to<br />
better and better areas <strong>in</strong> the search space and cont<strong>in</strong>ues<br />
to evolve through the generations. Eventually they<br />
converge to a group of <strong>in</strong>dividuals best adapted to the<br />
environment and obta<strong>in</strong> the optimal solution.<br />
In recent years, genetic algorithm has been<br />
successfully used <strong>in</strong> the fields of economic management,<br />
traffic transportation, and <strong>in</strong>dustrial design and resolved<br />
many technical problems successfully. For example,<br />
reliability optimization, flow shop schedul<strong>in</strong>g, job shop<br />
schedul<strong>in</strong>g, mach<strong>in</strong>e schedul<strong>in</strong>g, equipment layout design,<br />
image process<strong>in</strong>g and data m<strong>in</strong><strong>in</strong>g etc.<br />
The basic operation of optimization us<strong>in</strong>g genetic<br />
algorithm <strong>in</strong>cludes population <strong>in</strong>itialization, fitness<br />
function calculation, selection, crossover and mutation<br />
operation.<br />
III. OPTIMIZATION OF WEIGHTS AND THRESHOLDS<br />
After tra<strong>in</strong> and learn<strong>in</strong>g SSOM network can quickly<br />
and easily achieves the classification of test<strong>in</strong>g data. It<br />
can be used <strong>in</strong> a variety of classification field for labeled<br />
data such as text classification, <strong>in</strong>trusion detection, fault<br />
detection, etc. However dur<strong>in</strong>g the tra<strong>in</strong> and learn<strong>in</strong>g<br />
process of SSOM neural network, the <strong>in</strong>itialization of<br />
three parameters (learn<strong>in</strong>g rate η 1<br />
andη 2<br />
, neighborhood<br />
radius r ) have much <strong>in</strong>fluence on the experiment result.<br />
If the choice of these parameters is not very good or not<br />
very correct, it will have much negative effect on the test<br />
results and lead to lower correct classification rate.<br />
The real number encod<strong>in</strong>g method is an important<br />
encod<strong>in</strong>g method of genetic algorithm, <strong>in</strong> which each<br />
<strong>in</strong>dividual gene value is real number. The real number<br />
encod<strong>in</strong>g method has follow<strong>in</strong>g advantages:<br />
• Suitable for the scope of the larger number.<br />
• Easy to expand the space of the genetic search.<br />
• It can improve the accuracy requirements of the<br />
genetic algorithm.<br />
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• It can improve the computational complexity and<br />
efficiency of operations.<br />
• Easy to use together with other classical optimization<br />
method.<br />
Here, we design a real encod<strong>in</strong>g genetic algorithm to<br />
optimize the parameters η 1<br />
, η<br />
2<br />
and r of SSOM to<br />
obta<strong>in</strong> the optimal parameters. Us<strong>in</strong>g these optimal<br />
parameters we create a new SSOM network model named<br />
GA-SSOM and perform <strong>in</strong>trusion classification based on<br />
KDD Cup 1999 data set.<br />
To complete the optimization us<strong>in</strong>g GA, we firstly<br />
should <strong>in</strong>itialize the <strong>in</strong>dividual population composed of<br />
parameters η<br />
1<br />
, η<br />
2<br />
and r <strong>in</strong> real cod<strong>in</strong>g, then design a<br />
proper fitness function to perform selection operation,<br />
crossover operation and mutation operation. After many<br />
times repeated iteration, the optimal <strong>in</strong>dividual <strong>in</strong>clud<strong>in</strong>g<br />
the optimal parameters is obta<strong>in</strong>ed. It is what we needed<br />
to create the GA-SSOM model.<br />
The implementation step is shown <strong>in</strong> Figure 3 and the<br />
detailed process is as follows:<br />
Figure 3. The optimization of parameter<br />
(1) Data normalization<br />
Data normalization is a data preprocess<strong>in</strong>g procedure<br />
before tra<strong>in</strong><strong>in</strong>g network; it is accomplished by data<br />
normalized function. Data normalization function is used<br />
to cancel the orders of magnitude difference between the<br />
dimensions of data and avoid large prediction error<br />
caused by differences <strong>in</strong> <strong>in</strong>put and output. In this paper,<br />
the <strong>in</strong>put feature value is normalized to [0, 1] by data<br />
normalization function <strong>in</strong> equation (8).<br />
x = ( x −x )/( x − x ) (8)<br />
k k m<strong>in</strong> max m<strong>in</strong><br />
where x k represents the data sequence, x m<strong>in</strong> and x max<br />
represents the m<strong>in</strong>imum value and maximum value <strong>in</strong><br />
data sequence.<br />
(2) The <strong>in</strong>itialization of population<br />
A population is formed by N <strong>in</strong>dividuals generated<br />
randomly and genetic algorithm starts the iteration from<br />
this population as the <strong>in</strong>itial po<strong>in</strong>t.<br />
In this part, <strong>in</strong>dividual cod<strong>in</strong>g adopts real cod<strong>in</strong>g and<br />
each <strong>in</strong>dividual is a real number series, which consists of<br />
3 components: learn<strong>in</strong>g rate η 1<br />
, learn<strong>in</strong>g rate η 2<br />
and<br />
neighborhood radius r . And N is set to 20 <strong>in</strong> our work.<br />
(3) Fitness function calculation<br />
Fitness value is to measure the excellent degree that<br />
each <strong>in</strong>dividual approach or reach <strong>in</strong> optimization<br />
calculation. The higher fitness value the <strong>in</strong>dividual has,<br />
the larger probability it is genetic to next generation than<br />
others. Fitness value is usually calculated through a<br />
fitness function.<br />
Here, we choose the reciprocal of the square of the<br />
absolute error between forecast output and the desired<br />
output data as the fitness function to judge the quality<br />
level of <strong>in</strong>dividual. The <strong>in</strong>dividual with greater fitness<br />
value will have more opportunity to be selected and<br />
<strong>in</strong>herited to the next generation. The fitness function is<br />
shown <strong>in</strong> equation (9).<br />
F =<br />
1<br />
m<br />
2<br />
∑(ci-c x)<br />
i=<br />
1<br />
Where F represents the fitness value, c i represents the<br />
forecast output and c x represent the desired output of the<br />
first i node, m is the number of output node.<br />
(4) Selection operation<br />
The task of select operation is to select body from the<br />
parent group to <strong>in</strong>herit to the next group. The genetic<br />
algorithm uses selection operator (or copy operation) to<br />
achieve the group <strong>in</strong>dividual survival of the fittest<br />
operation. The probability that high fitness <strong>in</strong>dividual is<br />
<strong>in</strong>herited to the next generation of group is great, and the<br />
probability that small fitness <strong>in</strong>dividual is <strong>in</strong>herited to the<br />
next generation of group is small.<br />
Dur<strong>in</strong>g the process of selection operation, proportional<br />
selection method is used. The basic idea of proportional<br />
selection method is as follow: the probability that<br />
<strong>in</strong>dividuals are selected is proportional to the size of its<br />
fitness.<br />
The selection probability p i which represents the first i<br />
<strong>in</strong>dividual is shown <strong>in</strong> equation (10).<br />
p<br />
i<br />
=<br />
N<br />
F<br />
∑<br />
j = 1<br />
i<br />
F<br />
j<br />
(9)<br />
(10)<br />
where Fi is fitness value of the first i <strong>in</strong>dividual, N is the<br />
population size.<br />
(5) The crossover operation<br />
The crossover operation is a process <strong>in</strong> which the two<br />
paired chromosomes exchange some of its genes <strong>in</strong> a<br />
certa<strong>in</strong> way to form two new <strong>in</strong>dividuals. The crossover<br />
operation is an important feature that the genetic<br />
algorithm is different from other evolutionary algorithms.<br />
It plays a key role <strong>in</strong> the genetic algorithm and is the<br />
ma<strong>in</strong> method to generate new <strong>in</strong>dividual.<br />
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Because we use real number encod<strong>in</strong>g GA, the<br />
crossover operation uses arithmetic crossover which is a<br />
l<strong>in</strong>ear comb<strong>in</strong>ation of the two <strong>in</strong>dividuals to produce a<br />
new <strong>in</strong>dividual. The process is shown <strong>in</strong> equation (11).<br />
In this equation, it shows that the first k chromosome<br />
named a k performs crossover operation with the first l<br />
chromosome named a l , and the crossover bit is at first j<br />
bit. After crossover operation, a new pair of <strong>in</strong>dividual<br />
with good genes is generated.<br />
In this part we use b<strong>in</strong>ary encod<strong>in</strong>g genetic algorithm<br />
to optimize <strong>in</strong>put variable and reduce its dimensionality.<br />
To complete it, first encode the <strong>in</strong>dividual components,<br />
<strong>in</strong>itialize the number of populations and the evolution,<br />
and design the fitness function. Then perform selection<br />
operation, crossover operation and mutation operation to<br />
generate the best <strong>in</strong>dividual which is the optimal<br />
comb<strong>in</strong>ation of <strong>in</strong>dependent variables. The workflow is<br />
shown <strong>in</strong> Figure 4, each part functions as follows:<br />
⎧⎪ akj = akjb+ alj<br />
(1 −b)<br />
⎨<br />
⎪⎩ alj = aljb+ akj<br />
(1 −b)<br />
(11)<br />
where b represents a random number between 0 and 1.<br />
(6) Mutation operation<br />
The so-called mutation operation is a process <strong>in</strong> which<br />
the value of certa<strong>in</strong> genes <strong>in</strong> the <strong>in</strong>dividual encoded str<strong>in</strong>g<br />
is replaced by other genetic value to form a new<br />
<strong>in</strong>dividual. The mutation operation is a helper method to<br />
generate new <strong>in</strong>dividual, but it is essential to a comput<strong>in</strong>g<br />
step. Mutation operation determ<strong>in</strong>es the local search<br />
ability of genetic algorithms.<br />
Equation (12) shows the process of mutation operation<br />
<strong>in</strong> this part. Select a ij , which is the first j gene of the first i<br />
<strong>in</strong>dividual to perform mutation operation. The mutation<br />
operation is as follows:<br />
a<br />
ij<br />
⎧⎪ aij<br />
+ ( aij<br />
− amax<br />
) × r r > 0.5<br />
= ⎨<br />
⎪⎩ aij<br />
+ ( am<strong>in</strong><br />
− aij<br />
) × r r < 0.5<br />
(12)<br />
where a max is the upper bound of a ij , a m<strong>in</strong> is the lower<br />
bound of a ij , r is the random value between 0 and 1.<br />
Through the above steps, we get the optimal<br />
chromosome which is composed of the optimal learn<strong>in</strong>g<br />
rate η<br />
1<br />
and η<br />
2<br />
, the optimal neighborhood radius r . Use<br />
these optimal variables to create SSOM neural network<br />
model named GA-BP. Then we use this model to carry<br />
out <strong>in</strong>trusion detection experiment based on KDD Cup<br />
1999 data set.<br />
IV. OPTIMIZATION OF INPUT VARIABLE FOR<br />
DIMENSIONALITY REDUCTION<br />
Us<strong>in</strong>g SSOM neural network to establish the model,<br />
the excessive <strong>in</strong>put variable is easy to over fitt<strong>in</strong>g, which<br />
leads to the low precision, low rates of detection and<br />
excessive time. So it is necessary to optimize the<br />
selection of <strong>in</strong>put variables, remove the redundancy<br />
variables and reta<strong>in</strong> the variables which can most reflect<br />
the relationship between <strong>in</strong>put and output variables <strong>in</strong> the<br />
model [21].<br />
B<strong>in</strong>ary encod<strong>in</strong>g is one of the most commonly cod<strong>in</strong>g<br />
of genetic algorithm. It has the follow<strong>in</strong>g advantages:<br />
• Encod<strong>in</strong>g, decod<strong>in</strong>g operation is simple.<br />
• The cross and mutation operation is easy to realize.<br />
• Meet<strong>in</strong>g the m<strong>in</strong>imum character set encod<strong>in</strong>g<br />
pr<strong>in</strong>ciple.<br />
• Easy to use schema theorem theoretical to analyze the<br />
algorithm.<br />
Figure 4. The optimization of <strong>in</strong>put variables<br />
(1) Data normalization<br />
Data normalization is a data preprocess<strong>in</strong>g procedure<br />
before the experiment, it is also important for variable<br />
dimension reduction. Here, the <strong>in</strong>put feature value is also<br />
normalized to [0, 1]. Data normalization function also<br />
uses equation (8).<br />
(2) The <strong>in</strong>itialization of population<br />
In this optimization process, the <strong>in</strong>dividual cod<strong>in</strong>g<br />
adopts the b<strong>in</strong>ary cod<strong>in</strong>g mode. As the <strong>in</strong>trusion detection<br />
data has 41 features, the length of cod<strong>in</strong>g is designed to<br />
41 and every <strong>in</strong>dividual is a b<strong>in</strong>ary str<strong>in</strong>g composed of 41<br />
b<strong>in</strong>ary bits. Every chromosome corresponds to an <strong>in</strong>put<br />
feature and every gene can only be 1 and 0. If the value<br />
of a particular chromosome is 1, it means that the <strong>in</strong>put<br />
variable correspond<strong>in</strong>g to this bit takes part <strong>in</strong> the f<strong>in</strong>al<br />
model, otherwise not.<br />
A population is formed by N <strong>in</strong>dividuals generated<br />
randomly and genetic algorithm starts the iteration from<br />
this population as the <strong>in</strong>itial po<strong>in</strong>t.<br />
(3) Fitness function calculation<br />
Here, the reciprocal of the absolute error between<br />
forecast output and the desired output data is chose as the<br />
fitness function and it is shown <strong>in</strong> equation (13).<br />
In the process of calculat<strong>in</strong>g the fitness function, the<br />
learn<strong>in</strong>g rate η 1<br />
and η 2<br />
, neighborhood radius r of<br />
every <strong>in</strong>dividual is optimized by the genetic algorithm <strong>in</strong><br />
Section III, avoid<strong>in</strong>g the impact of its random on fitness<br />
function calculation.<br />
F=<br />
1<br />
m<br />
∑(Ci<br />
-C<br />
x<br />
)<br />
i=1<br />
(13)<br />
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where F represents the fitness function, m is the number<br />
of output node, c i and c x represent respectively forecast<br />
output and the desired output of the first i node.<br />
(4) Selection operation<br />
Dur<strong>in</strong>g this process, we adapt proportion selection<br />
operator and calculate the probability of each <strong>in</strong>dividual's<br />
fitness <strong>in</strong> accordance with the equation (10). The<br />
<strong>in</strong>dividuals with larger probability is selected as the best<br />
<strong>in</strong>dividual to the next generation of genetic population,<br />
the one with smaller probability not.<br />
(5) The crossover operation<br />
Dur<strong>in</strong>g crossover operation, two <strong>in</strong>dividual are selected<br />
randomly from population to generate a new and<br />
outstand<strong>in</strong>g <strong>in</strong>dividual.<br />
As the optimization of this part adopts b<strong>in</strong>ary cod<strong>in</strong>g,<br />
one-po<strong>in</strong>t crossover operator is used dur<strong>in</strong>g the crossover<br />
operation. For a matched pair of <strong>in</strong>dividual, select<br />
randomly the cross-po<strong>in</strong>t and swap the other bit from<br />
cross-po<strong>in</strong>t. The operat<strong>in</strong>g diagram is shown <strong>in</strong> Figure 5.<br />
The b<strong>in</strong>ary str<strong>in</strong>g 1001 <strong>in</strong> <strong>in</strong>dividual A exchanges data<br />
<strong>in</strong>formation with b<strong>in</strong>ary str<strong>in</strong>g 0011 <strong>in</strong> <strong>in</strong>dividual B. After<br />
crossover operation, it generates two new <strong>in</strong>dividual and<br />
<strong>in</strong>creases the diversity of <strong>in</strong>dividual.<br />
Figure 5.<br />
Crossover operation<br />
(6) Mutation operation<br />
Mutation operation can also <strong>in</strong>crease the diversity of<br />
<strong>in</strong>dividual. Here, select a s<strong>in</strong>gle po<strong>in</strong>t mutation operator<br />
and random mutation po<strong>in</strong>t, then 0 and 1 is exchanged.<br />
The pr<strong>in</strong>ciple is shown <strong>in</strong> Figure 6. Two new <strong>in</strong>dividual<br />
generate after this operation.<br />
Figure 6. Mutation operation<br />
(7) The establishment of New-GA-SSOM network<br />
model<br />
After many times evolution, when meet<strong>in</strong>g the<br />
iteration condition, the output of the population is the<br />
optimal solution of the problem. They are the handsome<br />
and the most representative <strong>in</strong>put variable comb<strong>in</strong>ation.<br />
Through the above steps, we get the optimal<br />
chromosome which is composed of the optimal feature.<br />
Extract a set of variables from the best chromosome gene<br />
as the f<strong>in</strong>al <strong>in</strong>put variables to achieve the dimension<br />
reduction of <strong>in</strong>dependent variables. That is the new neural<br />
network model, named New-GA-SSOM. Then we use<br />
this model to tra<strong>in</strong> network, and carry out <strong>in</strong>trusion<br />
detection data based on KDD Cup 1999 data set.<br />
V. EXPERIMENT<br />
KDD Cup 1999 data set is a standard data set for<br />
<strong>in</strong>trusion detection, <strong>in</strong>clud<strong>in</strong>g the tra<strong>in</strong><strong>in</strong>g data set and test<br />
data set. The tra<strong>in</strong><strong>in</strong>g data set <strong>in</strong>cludes 494 021 records<br />
and test<strong>in</strong>g data set <strong>in</strong>cludes 311 029 records. In the<br />
KDD99 data set, each data example represents attribute<br />
values of a class <strong>in</strong> the network data flow, and each class<br />
is labeled either as normal or as an attack with exactly<br />
one specific attack type. There are 22 types of attacks <strong>in</strong><br />
the tra<strong>in</strong><strong>in</strong>g data set and an <strong>in</strong>crease of new 14 k<strong>in</strong>ds of<br />
attacks <strong>in</strong> the test<strong>in</strong>g data set. All the attack types can be<br />
divided <strong>in</strong>to four major categories: Prob<strong>in</strong>g, Denial of<br />
Service (DoS), User-to-Root (U2R) and Remote-to-Local<br />
(R2L). Each complete TCP (transmission control<br />
protocol) connection is considered as a record, <strong>in</strong>clud<strong>in</strong>g<br />
four types of attributes collection: time-based traffic<br />
features, host-based traffic features, content features and<br />
basic features [22, 23, 24].<br />
Our experiment is based on the KDD Cup 1999<br />
<strong>in</strong>trusion detection data set. Tra<strong>in</strong><strong>in</strong>g data set is composed<br />
of 3 000 data of normal type and 3 000 data of attack type,<br />
selected randomly from KDD Cup99 of "10% KDD"<br />
dataset. Test<strong>in</strong>g data set is composed of 2 000 data of<br />
normal type and 2 000 data of attack type, selected<br />
randomly from KDD Cup99 of the "Corrected KDD"<br />
dataset. The selected data set is shown <strong>in</strong> Table I.<br />
Each data has 41 different attributes (32 cont<strong>in</strong>uous<br />
attributes and 9 discrete attributes) used as SSOM <strong>in</strong>put<br />
value and 1 attack type label used as output value of<br />
SSOM. Some of them are the numerical types, and some<br />
are character types, but SSOM can only deal with<br />
numerical data. Therefore, before tra<strong>in</strong><strong>in</strong>g we must make<br />
the <strong>in</strong>put data numerical and normalized. This study used<br />
simple substitution symbols with numerical data types.<br />
The protocol-type, service and flag are replaced by digital<br />
attributes. For example, three k<strong>in</strong>ds of protocol-type (tcp,<br />
udp and icmp) will be expressed with 1, 2, 3. Also, 70<br />
k<strong>in</strong>ds of services are substituted with 1, 2… 70. The<br />
attack types are also numbered with 1, 2, 3 and so on.<br />
Experimental platform is the PC with Intel Core2 Duo<br />
CPU 2.0GHz, memory 2.0GB, W<strong>in</strong>dows XP operat<strong>in</strong>g<br />
system and MATLAB 7.8.0 (R2009.0a) programm<strong>in</strong>g<br />
environment.<br />
Based on the experiment data <strong>in</strong> Table I, tra<strong>in</strong><strong>in</strong>g and<br />
test are carried out respectively us<strong>in</strong>g SSOM (its<br />
parameters are selected randomly), GA-SSOM and New-<br />
GA-SSOM neural network. Accord<strong>in</strong>g to the different<br />
classification number of attack type, experiment is carried<br />
out as follow<strong>in</strong>g two cases.<br />
TABLE I.<br />
TRAINING SET AND TEST SETS<br />
Attack class Attack type Tra<strong>in</strong><strong>in</strong>g set Test set<br />
Normal normal 6000 3000<br />
back 700 400<br />
DOS<br />
neptune 2700 1200<br />
smurf 1600 800<br />
R2L guess_passwd 53 40<br />
U2R buffer_overflow 30 22<br />
ipsweep 350 180<br />
Probe portsweep 350 200<br />
satan 217 158<br />
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TABLE II.<br />
DETECTION RATE AND MODEL TIME (TWO CLASSIFICATION)<br />
Type<br />
Detection rate (%)<br />
Time<br />
Model<br />
normal abnormal<br />
SSOM<br />
93.2 90.2<br />
38.1s<br />
GA-SSOM 98.5 95.3<br />
New-GA-SSOM 13.5s 97.5 95.5<br />
TABLE III.<br />
DETECTION RATE AND MODEL TIME (FIVE CLASSIFICATION)<br />
Model<br />
Model<br />
GA- New-GA-<br />
Type<br />
SSOM<br />
SSOM SSOM<br />
Normal 92.1% 98.4% 96.5%<br />
DOS 89.8% 94.4% 94%<br />
R2L 6.7% 7.7% 7.1%<br />
detection U2R 19.2% 23.4% 22.4%<br />
rate (%) Probe 89.3% 95.1% 96.1%<br />
time (s) 45.4.s 16.5s<br />
Experiment 1: the attack types of selected experiment<br />
data are divided <strong>in</strong>to normal data and attack data, the<br />
normal data is numbered with 1 and the attack data is<br />
numbered with 2. It is a two classification problem and<br />
the experiment result is shown <strong>in</strong> Table II.<br />
Experiment 2: The attack types are classified <strong>in</strong>to<br />
Normal data, DOS, R2L, U2L, Probe. The Normal label<br />
data is numbered with 1, the other four types are<br />
numbered with 2, 3, 4 and 5. It is a multiple classification<br />
problem and the experiment result is shown <strong>in</strong> Table III.<br />
From Table II and Table III, we can know that the<br />
proposed GA-SSOM and New-GA-SSOM have higher<br />
detection than SSOM whose parameters are selected<br />
randomly. Although there is little difference <strong>in</strong> detection<br />
rate between GA-SSOM and New-GA-SSOM, New-GA-<br />
SSOM spends less time than SSOM and GA-SOM <strong>in</strong><br />
model<strong>in</strong>g. So it shows that GA-SSOM has rather higher<br />
<strong>in</strong>trusion detection rate than SSOM, and New-GA-SSOM<br />
has higher <strong>in</strong>trusion detection rate and much shorter<br />
model<strong>in</strong>g time than SSOM.<br />
VI. CONCLUSION<br />
In this paper, we use genetic algorithm to optimize the<br />
SSOM which is an improved and a supervised SOM<br />
neural network. A real encod<strong>in</strong>g genetic algorithm is<br />
applied to optimize the learn<strong>in</strong>g rate η1<br />
and η<br />
2<br />
,<br />
neighborhood radius r of SSOM neural network to<br />
improve detection rate. And a b<strong>in</strong>ary encod<strong>in</strong>g genetic<br />
algorithm is used to reduce the dimension of <strong>in</strong>put<br />
variable of SSOM neural network to improve the<br />
efficiency of model<strong>in</strong>g.<br />
Through optimization, it can quickly and effectively<br />
establish SSOM network model and improve speed of<br />
tra<strong>in</strong><strong>in</strong>g and learn<strong>in</strong>g. Classification experiments based<br />
on KDD Cup 1999 data set was carried out and results<br />
showed that the optimized model has shorter model<strong>in</strong>g<br />
time and higher <strong>in</strong>trusion detection rate.<br />
In the future, we plan to propose a semi-supervised<br />
<strong>in</strong>trusion detection classifier based SOM, and use genetic<br />
algorithm to optimize the <strong>in</strong>put parameters of this semisupervised<br />
classifier.<br />
ACKNOWLEDGMENT<br />
The authors wish to thank the support of ShangLuo<br />
University and Northwestern Polytechnical University.<br />
This work was sponsored by Scientific Research Program<br />
Funded by Shaanxi Prov<strong>in</strong>cial Education Department<br />
(No.12JK0748) and National m<strong>in</strong>istries foundation <strong>in</strong><br />
Ch<strong>in</strong>a.<br />
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no. 13, pp. 3935–3955, 2007.<br />
[9] SWARUP K S, CORTHIS P B, “ANN approach assesses<br />
system security”, Computer Applications <strong>in</strong> Power, vol.15,<br />
no.3, pp.32-38, 2002.<br />
[10] Xiaomei YI, Peng WU, Dan DAI, Lijuan LIU, Xiong HE,<br />
“Intrusion Detection Us<strong>in</strong>g BP Optimized by PSO”, IJACT:<br />
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Technology, vol. 4, no. 2, pp. 268 -274, 2012.<br />
[11] Liu Hui, CAO Yonghui, “The Research of mach<strong>in</strong>e<br />
learn<strong>in</strong>g algorithm for <strong>in</strong>trusion detection techniques”,<br />
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Technology and its Applications, vol. 6, no. 1, pp. 343-347,<br />
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[12] Jie Ma, Zhi Tang Li, B<strong>in</strong>g B<strong>in</strong>g Wang, “Application of<br />
S<strong>in</strong>gular Spectrum Analysis to the Noise Reduction of<br />
Intrusion Detection Alarms”. Journal of Computers, vol. 6,<br />
no. 8, pp. 1715-1722, 2011.<br />
[13] Rauber A., Merkl D., Dittenbach M., “The grow<strong>in</strong>g<br />
hierarchical self-organiz<strong>in</strong>g map: Exploratory analysis of<br />
high-dimensional data”, IEEE Transactions on Neural<br />
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[14] E. J. Palomo, E. Domínguez, R. M. Luque and J. Muñoz,<br />
“An Intrusion Detection System Based on Hierarchical<br />
Self-Organization, “ Advances <strong>in</strong> Soft Comput<strong>in</strong>g, vol. 53,<br />
pp. 139-146, 2009.<br />
[15] Jian Wu, Jie Xia, Jian-m<strong>in</strong>g Chen, Zhi-m<strong>in</strong>g Cui, “Mov<strong>in</strong>g<br />
Object Classification Method Based on SOM and K-means.<br />
Journal of Computers”, vol.6, no.8, pp.1654-1661, 2011.<br />
[16] YANG Ya-hui, JIANG Dian-bo, SHEN Q<strong>in</strong>g-ni, XIA M<strong>in</strong>,<br />
“Research on <strong>in</strong>trusion detection based on an improved<br />
GHSOM”, Journal on Communications, vol.32, no. 1, pp.<br />
121-126. 2011<br />
[17] Zhao Jianhua, LI Weihua, Application of Supervised SOM<br />
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[18] MIYOSHI Tsutomu, “Initial Node Exchange and<br />
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(ISIS2005), pp. 316-319, 2005.<br />
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[21] SHI F, WANG S C, YU L, “Matlab neural network 30<br />
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[22] Mukkamala S, Sung AH, and Abraham A, "Intrusion<br />
dection us<strong>in</strong>g an ensemble of <strong>in</strong>telligent paradigms",<br />
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[23] WANG Hui, ZHANG Guil<strong>in</strong>g, E M<strong>in</strong>gjie, SUN Na, “A<br />
Novel Intrusion Detection Method Based on Improved<br />
SVM by Comb<strong>in</strong><strong>in</strong>g PCA and PSO”, Wuhan University<br />
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2011.<br />
[24] Jim<strong>in</strong> Li, Wei Zhang, KunLun Li, “A Novel Semisupervised<br />
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[25] Hettich S, Bay S D.The UCI KDD Archive [EB/OL]. http:<br />
//kdd.ics.uci.edu/ databases/kddcup99.]<br />
Zhao Jianhua was born <strong>in</strong> 1982. He is currently a lecturer and<br />
seek<strong>in</strong>g for his doctor’s degree. His research <strong>in</strong>terests <strong>in</strong>clude<br />
mach<strong>in</strong>e learn<strong>in</strong>g, network security.<br />
Li Weihua was born <strong>in</strong> 1951. He is currently a professor. His<br />
research <strong>in</strong>terests <strong>in</strong>clude network security and <strong>in</strong>telligent<br />
decision.<br />
© 2013 ACADEMY PUBLISHER
1464 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Fault Diagnosis System for NPC Inverter based<br />
on Multi-Layer Pr<strong>in</strong>cipal Component Neural<br />
Network<br />
Danjiang Chen<br />
Shanghai Maritime University, Shanghai, Ch<strong>in</strong>a<br />
Zhejiang Wanli University, N<strong>in</strong>gbo Zhejiang, Ch<strong>in</strong>a<br />
Email: cdj02@163.com<br />
Y<strong>in</strong>zhong Ye and Rong Hua<br />
Shanghai Institute of Technology, Shanghai, Ch<strong>in</strong>a<br />
Email: yzye@sit.edu.cn, huarong@sit.edu.cn<br />
Abstract—This paper presents a fault diagnosis method for<br />
a neutral po<strong>in</strong>t clamped (NPC) <strong>in</strong>verter us<strong>in</strong>g a multi-layer<br />
artificial neural network (MANN). The considered possible<br />
faults of NPC <strong>in</strong>verter <strong>in</strong>clude the open-circuit fault<br />
occurr<strong>in</strong>g <strong>in</strong> one s<strong>in</strong>gle device or more devices. The upper,<br />
middle and down bridge voltages are adopted the test<br />
signals because of the difficulties <strong>in</strong> isolat<strong>in</strong>g some fault<br />
modes. A novel multi-layer neural network is proposed to<br />
diagnose all possible open-circuit faults. Furthermore, the<br />
pr<strong>in</strong>cipal component analysis (PCA) is utilized to reduce the<br />
<strong>in</strong>put size of neural network. The comparison between<br />
neural network with and without PCA is performed. The<br />
simulation and experimental results prove the feasibility of<br />
the diagnostic method and show that the proposed method<br />
has the advantages of good classification performance and<br />
high reliability.<br />
Index Terms—three level <strong>in</strong>verter, fault diagnosis, MANN,<br />
PCA<br />
I. INTRODUCTION<br />
The multilevel <strong>in</strong>verter could achieve more levels,<br />
lower harmonic distortion <strong>in</strong> the voltage output <strong>in</strong><br />
addition to lower<strong>in</strong>g the voltage stress of the power<br />
devices, as compared with the conventional two-level<br />
<strong>in</strong>verters [1-5] . Due to these advantages, NPC <strong>in</strong>verter has<br />
been widely used <strong>in</strong> high-power <strong>in</strong>dustrial applications.<br />
However, the NPC <strong>in</strong>verter system is composed of many<br />
switch<strong>in</strong>g devices which would reduce the reliability of a<br />
multilevel <strong>in</strong>verter, as a break <strong>in</strong> any one of these devices<br />
will <strong>in</strong>evitably make the entire <strong>in</strong>verter fail to work and<br />
produce the economic losses [6]. Therefore the fault<br />
diagnosis methods would be necessary to ensure the<br />
reliability of the multilevel <strong>in</strong>verter.<br />
Some efforts have been made <strong>in</strong> the problem<br />
mentioned above. For example, the voltage output <strong>in</strong><br />
faulty situation could be analyzed <strong>in</strong> real time mode and<br />
compared with the voltage output <strong>in</strong> normal situation <strong>in</strong><br />
order to f<strong>in</strong>d out the faulty device, see [7]-[10].<br />
Furthermore, it has been shown that the diagnostic<br />
performance could be enhanced if the <strong>in</strong>telligent methods<br />
like neural network, support vector mach<strong>in</strong>e etc. are<br />
<strong>in</strong>troduced <strong>in</strong> recogniz<strong>in</strong>g different fault modes, see [11]-<br />
[14], though only simple applications of the neural<br />
network <strong>in</strong> NPC <strong>in</strong>verter have been proposed [15] .<br />
Investigat<strong>in</strong>g the current research works reveals that<br />
only the simplest fault mode, i.e. the open-circuit<br />
occurr<strong>in</strong>g <strong>in</strong> a s<strong>in</strong>gle device has been taken <strong>in</strong>to account.<br />
In order to improve the reliability of NPC <strong>in</strong>verter, this<br />
paper will focus on a more complicated fault mode, i.e.<br />
the open-circuit fault occurr<strong>in</strong>g <strong>in</strong> two devices<br />
simultaneously, <strong>in</strong> addition to diagnos<strong>in</strong>g the open-circuit<br />
fault mode. Fault features will be extracted from three<br />
bridge voltages by the discrete Fourier transform (DFT)<br />
and a multi-layer artificial neural network (ANN) will be<br />
proposed to accomplish diagnos<strong>in</strong>g all fault modes under<br />
consideration. In additional, the PCA is performed <strong>in</strong> this<br />
paper to reduce the <strong>in</strong>put neural size [16-17]. Figure 1<br />
shows a three level NPC <strong>in</strong>verter.<br />
1<br />
U<br />
2 d<br />
o<br />
1<br />
U<br />
2 d<br />
D a5<br />
D a6<br />
S a1<br />
S a2<br />
S a3<br />
S a4<br />
a<br />
D a1<br />
D a2<br />
D a3<br />
D a4<br />
D b1<br />
D S D<br />
b5 b2<br />
b 2<br />
D b6<br />
S b1<br />
S b3<br />
b<br />
D b3<br />
D c5<br />
D c6<br />
S c1<br />
S c2<br />
S c3<br />
S D b4<br />
S c 4<br />
b4<br />
Figure 1. Ma<strong>in</strong> circuit of a three level NPC <strong>in</strong>verter<br />
II. ANALYSIS OF POSSIBLE FAULT MODE<br />
One s<strong>in</strong>gle bridge leg of NPC <strong>in</strong>verter could be derived<br />
from Figure 1, e.g., as shown <strong>in</strong> Figure 2 for phase a.<br />
There are three bridge voltages <strong>in</strong> Figure 2. The<br />
voltage between po<strong>in</strong>ts a<br />
u<br />
and o V<br />
ao<br />
is named as ‘middle<br />
bridge voltage’, or ‘bridge voltage’ for simplicity. The<br />
voltage between po<strong>in</strong>ts a<br />
u<br />
and o V auo<br />
is named as ‘upper<br />
c<br />
D c1<br />
D c2<br />
D c3<br />
D c4<br />
R a<br />
R b<br />
R c<br />
L a<br />
L b<br />
L c<br />
n<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1464-1471
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1465<br />
bridge voltage’, while V ado<br />
between po<strong>in</strong>ts a<br />
d<br />
and o is<br />
‘down bridge voltage’.<br />
1<br />
U<br />
2 d<br />
D a5<br />
S a1<br />
S a2<br />
D a1<br />
a u<br />
D a2<br />
o<br />
1<br />
U<br />
2 d<br />
D a6<br />
S a3<br />
S a4<br />
a<br />
i a<br />
D a3<br />
a d<br />
D a4<br />
Ra<br />
L a<br />
b<br />
n<br />
Rb<br />
L b<br />
c<br />
Rc<br />
L c<br />
(c) S<br />
a2<br />
open-circuit<br />
Figure 2. S<strong>in</strong>gle bridge leg of NPC <strong>in</strong>verter<br />
A. Open-circuit Fault of S<strong>in</strong>gle Device<br />
Consider the circuit shown <strong>in</strong> Figure 2 which consists<br />
of six devices, namely S<br />
a1<br />
, S<br />
a2<br />
, S<br />
a3<br />
, S<br />
a4<br />
, D<br />
a5<br />
and D<br />
a6<br />
.<br />
Correspond<strong>in</strong>gly, there are six possible fault modes for<br />
the open-circuit fault of s<strong>in</strong>gle device, with each mode<br />
be<strong>in</strong>g denoted by the same symbol of each device. As the<br />
circuit is symmetric <strong>in</strong> configuration, those fault modes<br />
of S<br />
a1<br />
, S<br />
a2<br />
and D<br />
a5<br />
need to be analyzed <strong>in</strong> detail, and<br />
the results apply for the other three fault modes.<br />
Perform<strong>in</strong>g simulation for the NPC <strong>in</strong>verter by the<br />
software PSIM, with the <strong>in</strong>put DC voltage U be<strong>in</strong>g<br />
100V, the load of each phase be<strong>in</strong>g resistance 8Ω and<br />
<strong>in</strong>ductance 20mH <strong>in</strong> series, under the normal (fault free)<br />
condition and each s<strong>in</strong>gle device open-circuit fault mode,<br />
the simulation waveforms of bridge voltage could be<br />
obta<strong>in</strong>ed as shown <strong>in</strong> Figure 3.<br />
(a) Fault free mode<br />
(b) S<br />
a1<br />
open-circuit<br />
d<br />
(d) D<br />
a5<br />
open-circuit<br />
Figure 3. Simulation waveforms of bridge voltage for open-circuit<br />
fault of s<strong>in</strong>gle device<br />
It could be seen obviously from Figure 3 that the<br />
waveform of the bridge voltage is different from one<br />
another and has specific features. By theory of spectrum<br />
analysis [18], each waveform of bridge voltage <strong>in</strong> Figure<br />
3 consists of specific harmonics differ<strong>in</strong>g from the other’s.<br />
Therefore the ‘fault features’ could be extracted from the<br />
bridge voltages. Based on such fault features, it is<br />
possible to isolate the open-circuit fault of s<strong>in</strong>gle device<br />
<strong>in</strong> some proper ways.<br />
B. Open-circuit Fault of Two Devices<br />
Two different situations arise while the case that two<br />
devices malfunction by open-circuit dur<strong>in</strong>g certa<strong>in</strong> period<br />
is taken <strong>in</strong>to account. The first situation arises when two<br />
faulty devices lie <strong>in</strong> the same phase, e.g. S<br />
a1<br />
and S<br />
a3<br />
, and<br />
the second one arises when two faulty devices lie <strong>in</strong><br />
different phases, e.g. S<br />
a1<br />
<strong>in</strong> phase a and S<br />
b1<br />
<strong>in</strong> phase b.<br />
Only the first situation needs to be <strong>in</strong>vestigated because<br />
the second situation could be reduced to the open-circuit<br />
fault of s<strong>in</strong>gle device <strong>in</strong> two phases and then be treated by<br />
the way mentioned above.<br />
Consider<strong>in</strong>g the phase a without loss of generality,<br />
possibly there are six different fault modes as { S<br />
a1<br />
, S<br />
a2<br />
},<br />
{ S<br />
a1<br />
, S<br />
a3<br />
}, { S<br />
a1<br />
, S<br />
a4<br />
}, { S<br />
a2<br />
, S<br />
a3<br />
}, { S<br />
a2<br />
, S<br />
a4<br />
} and<br />
{ S<br />
a3<br />
, S<br />
a4<br />
}. Due to the symmetry <strong>in</strong> the configuration of<br />
NPC <strong>in</strong>verter, for the fault modes { S<br />
a2<br />
, S<br />
a4<br />
} and { S<br />
a3<br />
,<br />
S<br />
a4<br />
}, the bridge voltage would be the same as one for<br />
{ S<br />
a1<br />
, S<br />
a3<br />
} and { S<br />
a1<br />
, S<br />
a2<br />
} respectively, while the phase<br />
is just opposite. Therefore only the other four fault modes<br />
should be analyzed. The bridge voltages’ simulation for<br />
these four faulty modes is given out <strong>in</strong> Figure 4.<br />
© 2013 ACADEMY PUBLISHER
1466 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
(a) { S<br />
a1<br />
, S<br />
a2<br />
}<br />
only one path through D<br />
a1<br />
and D<br />
a2<br />
as shown <strong>in</strong> Figure 5<br />
(c). When the fault { S<br />
a2<br />
} occurs, current flow (3) is<br />
possible while current flow (1) or (2) is impossible. When<br />
the fault { S<br />
a1<br />
, S<br />
a2<br />
} occurs, only current flow (3) is<br />
possible. Hence, no difference exists <strong>in</strong> current flow and<br />
the bridge voltages for the cases { S<br />
a2<br />
} and { S<br />
a1<br />
, S<br />
a2<br />
}.<br />
This reveals that the fault modes { S<br />
a2<br />
} and { S<br />
a1<br />
, S<br />
a2<br />
}<br />
cannot be isolated if only the bridge voltage is used.<br />
1<br />
U<br />
2 d<br />
D a5<br />
S a1<br />
S a2<br />
D a1<br />
a u<br />
D a2<br />
o<br />
a<br />
i a<br />
Ra<br />
b<br />
Rb<br />
c<br />
Rc<br />
(b) { S<br />
a1<br />
, S<br />
a3<br />
}<br />
1<br />
U<br />
2 d<br />
D a6<br />
S a3<br />
S a4<br />
D a3<br />
a d<br />
D a4<br />
L a<br />
n<br />
L b<br />
L c<br />
(a) Current flow (1)<br />
1<br />
U<br />
2 d<br />
D a5<br />
S a1<br />
S a2<br />
D a1<br />
a u<br />
D a2<br />
o<br />
a<br />
i a<br />
R a<br />
b<br />
Rb<br />
c<br />
Rc<br />
(c) { S<br />
a1<br />
, S<br />
a4<br />
}<br />
1<br />
U<br />
2 d<br />
D a6<br />
S a3<br />
S a4<br />
D a3<br />
a d<br />
D a4<br />
L a<br />
n<br />
L b<br />
L c<br />
(b) Current flow (2)<br />
1<br />
U<br />
2 d<br />
D a5<br />
S a1<br />
S a2<br />
D a1<br />
a u<br />
D a2<br />
(d) { S<br />
a2<br />
, S<br />
a3<br />
}<br />
Figure 4. Bridge voltage when two devices malfunction<br />
From Figure 3 and Figure 4 it could be found that the<br />
circuit would have the same bridge voltage for the fault<br />
modes { S<br />
a2<br />
} (see Figure 3 (c)) and { S<br />
a1<br />
, S<br />
a2<br />
} (see<br />
Figure 4 (a)). This will be also the case for the fault<br />
modes { S<br />
a3<br />
} and { S<br />
a3<br />
, S<br />
a4<br />
}.<br />
Consider the current path <strong>in</strong> Figure 2 from a to o<br />
through the upper half bridge where S<br />
a1<br />
, S<br />
a2<br />
, D<br />
a5<br />
,<br />
Da1<br />
and D<br />
a2<br />
are <strong>in</strong>volved, and denote the current of phase<br />
a as i a<br />
. If i<br />
a<br />
> 0 , the current has two possible paths as<br />
shown <strong>in</strong> Figure 5 (a-b), but if i<br />
a<br />
< 0 , the current has<br />
o<br />
1<br />
U<br />
2 d<br />
D a6<br />
S a3<br />
S a4<br />
a<br />
i a<br />
D a3<br />
a d<br />
D a4<br />
Ra<br />
(c) Current flow (3)<br />
L a<br />
b<br />
n<br />
Rb<br />
L b<br />
c<br />
Rc<br />
Figure 5. Diagram of NPC <strong>in</strong>verter work states<br />
In order to isolate all possible fault modes, the voltages<br />
of both the upper bridge and the down bridge as def<strong>in</strong>ed<br />
before are <strong>in</strong>troduced. Figure 6 shows the waveform of<br />
the upper bridge voltage for { S<br />
a2<br />
} and { S<br />
a1<br />
, S<br />
a2<br />
}.<br />
Obviously the waveform is different from each other.<br />
L c<br />
© 2013 ACADEMY PUBLISHER
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Fault free<br />
x 104<br />
4<br />
Sa1 open-circuit<br />
x 104<br />
4<br />
Amp<br />
2<br />
Amp<br />
2<br />
0<br />
0 1 2 3 4<br />
Freq:kHz<br />
Sa2 open-circuit<br />
x 104<br />
4<br />
0<br />
0 1 2 3 4<br />
Freq:kHz<br />
Da5 open-circuit<br />
x 104<br />
4<br />
Amp<br />
2<br />
Amp<br />
2<br />
(a) { S<br />
a2<br />
}<br />
0<br />
0 1 2 3 4<br />
Freq:kHz<br />
{Sa1,Sa2}<br />
x 104<br />
4<br />
Figure 8. DFT result of figure 3<br />
0<br />
0 1 2 3 4<br />
Freq:kHz<br />
{Sa1,Sa3}<br />
x 104<br />
4<br />
Amp<br />
2<br />
Amp<br />
2<br />
0<br />
0 1 2 3 4<br />
Freq:kHz<br />
{Sa1,Sa4}<br />
x 104<br />
4<br />
0<br />
0 1 2 3 4<br />
Freq:kHz<br />
{Sa2,Sa3}<br />
x 104<br />
4<br />
Amp<br />
2<br />
Amp<br />
2<br />
0<br />
0 1 2 3 4<br />
Freq:kHz<br />
Figure 9. DFT result of figure 4<br />
0<br />
0 1 2 3 4<br />
Freq:kHz<br />
(b) { S<br />
a1<br />
, S<br />
a2<br />
}<br />
Figure 6. Waveform of the upper bridge voltage<br />
III. FAULT DIAGNOSIS<br />
A. Structure of Fault Diagnosis System<br />
The structure for a fault diagnosis system is shown <strong>in</strong><br />
Figure 7. The system is composed of three major states:<br />
feature extraction, pr<strong>in</strong>cipal component analysis and<br />
multi-layer neural network. The output of the MNN is<br />
nearly 0 and 1 as b<strong>in</strong>ary code which can be related to<br />
different fault mode.<br />
NPC<br />
Inverter<br />
Bridge Voltage<br />
Feature<br />
Extraction<br />
System<br />
MNN<br />
PCA<br />
Figure 7. Structure of Fault Diagnosis System<br />
B. Feature Extraction<br />
An appropriate selection of the feature extractor is to<br />
provide the MNN with adequate significant details <strong>in</strong><br />
orig<strong>in</strong>al data so that the highest accuracy <strong>in</strong> the MNN<br />
performance can be obta<strong>in</strong>ed. In this paper the DFT<br />
technique is adopted to extract feature from the middle,<br />
upper and down bridge voltages. The transformed signals<br />
of Figure 3 and Figure 4, whose fundamental frequency is<br />
50Hz and carrier frequency is 1.5kHz, are represented <strong>in</strong><br />
Figure 8 and Figure 9 respectively.<br />
Accord<strong>in</strong>g to the spectrum characteristics of PWM<br />
<strong>in</strong>verters [19], and also could be seen from Figure 8 and<br />
Figure 9, obviously, ma<strong>in</strong> harmonics of the bridge<br />
voltage are distributed <strong>in</strong> the fundamental frequency,<br />
carrier frequency and their multiples. Hence, some<br />
components of these ma<strong>in</strong> harmonics are selected as the<br />
fault feature by feature extraction system <strong>in</strong> Figure 7.<br />
The selection of <strong>in</strong>put data for the ma<strong>in</strong> neural network<br />
<strong>in</strong>clude amplitude of DC component, fundamental,<br />
double fundamental, three times of fundamental, carrier<br />
frequency (1.5kHz), side frequency of carrier (1.4kHz<br />
and 1.6kHz) and double carrier frequency. The phase of<br />
DC component, fundamental and double fundamental are<br />
also selected as <strong>in</strong>put data for the ma<strong>in</strong> neural network. It<br />
could be counted that the dimension of the <strong>in</strong>put data for<br />
the ma<strong>in</strong> neural network is 11.<br />
For both auxiliary neural networks, the amplitude of<br />
DC component, fundamental and double fundamental are<br />
selected as the <strong>in</strong>put data with the dimension of three.<br />
C. Pr<strong>in</strong>cipal Component Analysis<br />
It could be seen that the <strong>in</strong>put data of the ma<strong>in</strong> neural<br />
network has high dimension and we don’t know whether<br />
these 11 dimension data are correlated or uncorrelated.<br />
PCA is a statistical technique used to transform a set of<br />
correlated variables to a new lower dimensional set of<br />
variables, which are uncorrelated or orthogonal with each<br />
other. The fundamental PCA used <strong>in</strong> a l<strong>in</strong>ear<br />
transformation is shown as follows:<br />
T = X ⋅ P<br />
(1)<br />
Where T is the m× k score matrix (transformed data),<br />
m is number of observations, k is dimensionality of the<br />
PC space; X is the m× n data matrix, m is number of<br />
observations, n is dimensionality of orig<strong>in</strong>al space; and<br />
P is the n× k load<strong>in</strong>gs matrix (PC coord<strong>in</strong>ates), n is<br />
dimensionality of orig<strong>in</strong>al space, k is number of the PCs<br />
kept <strong>in</strong> the model. The detail equation of Equation (1) is<br />
shown <strong>in</strong> the follow expression:<br />
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1468 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
⎡t11 t12 t1 k ⎤ ⎡x11 x12 x1 n ⎤ ⎡p11 p12 p1k<br />
⎤<br />
⎢<br />
t21 t22 t<br />
⎥ ⎢<br />
2k x21 x22 x<br />
⎥ ⎢<br />
2n p21 p22 p<br />
⎥<br />
⎢<br />
<br />
⎥ ⎢<br />
<br />
⎥ ⎢<br />
<br />
2k<br />
= ⋅<br />
⎥<br />
⎢ ⎥ ⎢ ⎥ ⎢ ⎥<br />
⎢ ⎥ ⎢ ⎥ ⎢ ⎥<br />
t t t x x x p p p<br />
⎣ m1 m2 mk⎦ ⎣ m1 m2 mn⎦ ⎣ n1 n2<br />
nk⎦<br />
Select<strong>in</strong>g a reduced subset of PC space results <strong>in</strong> a<br />
reduced dimension structure with respect to the important<br />
<strong>in</strong>formation available as shown <strong>in</strong> the follow<strong>in</strong>g<br />
expression:<br />
[ t t t ] [ x x x ]<br />
⎡ p11 p12 p1<br />
k ⎤<br />
⎢<br />
p p p<br />
⎥<br />
⎢<br />
<br />
⎥<br />
<br />
⎢<br />
⎥<br />
⎣ pn 1<br />
pn2<br />
pnk⎦<br />
21 22 2k<br />
1 2 k<br />
=<br />
1 2<br />
n<br />
⋅ ⎢ ⎥<br />
D. Artificial Neural Network<br />
ANN is a computer model whose architecture<br />
essentially mimics the knowledge acquisition and<br />
organizational skills of the human bra<strong>in</strong>. Although there<br />
are a variety of ways to construct these models, Back-<br />
Propagated (BP) neural network has become one of the<br />
most widely used ANNs <strong>in</strong> practice. BP neural network<br />
with a s<strong>in</strong>gle hidden layer is selected <strong>in</strong> this paper, which<br />
has been demonstrated to be sufficient to approximate<br />
any cont<strong>in</strong>uous function with<strong>in</strong> the desired accuracy [20].<br />
Figure 10 shows a diagram of neural network with a<br />
s<strong>in</strong>gle hidden layer.<br />
x 1<br />
(2)<br />
(3)<br />
The goal of the tra<strong>in</strong><strong>in</strong>g of ANN is to m<strong>in</strong>imize the<br />
error between predicted and target values by adjust<strong>in</strong>g the<br />
connection weights and biased. The error is given by<br />
Equation (6):<br />
p q<br />
2<br />
E = ∑∑ ( apq<br />
−opq<br />
)<br />
(6)<br />
p= 1 q=<br />
1<br />
Where q is the number of logic units <strong>in</strong> output layer, and<br />
p is the number of tra<strong>in</strong><strong>in</strong>g samples, a pq<br />
and o<br />
pq<br />
are<br />
the predicted and target values, respectively.<br />
E. Multi-layer Neural Network<br />
A new method named as multi-layer neural network is<br />
proposed to diagnose all open-circuit fault modes under<br />
consideration for the NPC <strong>in</strong>verter, as shown <strong>in</strong> Figure 11.<br />
Feature A<br />
Ma<strong>in</strong><br />
Feature<br />
Feature B<br />
Ma<strong>in</strong><br />
ANN<br />
Output<br />
Auxiliary<br />
ANN A<br />
S or { S , S }<br />
a a a<br />
2 1 2<br />
S or { S , S }<br />
a a a<br />
3 3 4<br />
Auxiliary<br />
ANN B<br />
Figure 11. Multi-layer neural network<br />
Output<br />
Output<br />
y 1<br />
x 2<br />
x 3<br />
<br />
x n<br />
<br />
n h q<br />
<br />
<br />
y 2<br />
<br />
y q<br />
Figure 10. Neural network with a s<strong>in</strong>gle hidden layer<br />
The three layers are called the <strong>in</strong>put layer, hidden layer<br />
and output layer, respectively. Each layer consists of<br />
logic units or neurons, as the basic <strong>in</strong>formation<br />
process<strong>in</strong>g units <strong>in</strong> ANN. The relationship of the <strong>in</strong>put<br />
value of the unit i <strong>in</strong> <strong>in</strong>put layer and that of unit j <strong>in</strong><br />
hidden layer is:<br />
n<br />
uj = ∑ ω<br />
ji<br />
xi + bj<br />
(4)<br />
i=<br />
1<br />
Where x<br />
i<br />
is an <strong>in</strong>put value of the logic unit i <strong>in</strong> the <strong>in</strong>put<br />
layer, u<br />
j<br />
an <strong>in</strong>itial output value of the logic unit j <strong>in</strong> the<br />
hidden layer, ω<br />
ji<br />
connection weights between unit j and<br />
i , b<br />
j<br />
<strong>in</strong>put bias of the unit j , n the number of logic<br />
units <strong>in</strong> the <strong>in</strong>put layer.<br />
The <strong>in</strong>itial output value u<br />
j<br />
is further transformed with<br />
the common transfer function <strong>in</strong> a sigmoid form:<br />
1<br />
= (5)<br />
+<br />
O j u j<br />
1 e −<br />
Where O is the f<strong>in</strong>al output value of the logic unit j .<br />
j<br />
TABLE I.<br />
FAULT MODES AND OUTPUT OF MAIN ANN<br />
Fault modes (open-circuit)<br />
Target output<br />
Fault free 000000<br />
S<br />
a1<br />
100000<br />
S<br />
a2<br />
or { S<br />
a1<br />
, S<br />
a2<br />
} 010000<br />
S<br />
a3<br />
or { S<br />
a3<br />
, S<br />
a4<br />
} 001000<br />
S<br />
a4<br />
000100<br />
D<br />
a5<br />
000010<br />
D<br />
a6<br />
000001<br />
{ S<br />
a1<br />
, S<br />
a3<br />
} 101000<br />
{ S<br />
a1<br />
, S<br />
a4<br />
} 100100<br />
{ S<br />
a2<br />
, S<br />
a3<br />
} 011000<br />
{ S<br />
a2<br />
, S<br />
a4<br />
} 010100<br />
TABLE II.<br />
FAULT MODES AND OUTPUT OF AUXILIARY ANN A<br />
Fault modes (open-circuit)<br />
Target output<br />
S<br />
a2<br />
0<br />
{ S<br />
a1<br />
, S<br />
a2<br />
} 1<br />
Ma<strong>in</strong> Feature extracted from the bridge voltage V ao<br />
is<br />
used as <strong>in</strong>put data for ma<strong>in</strong> ANN, which is used to<br />
diagnose eleven fault modes represented <strong>in</strong> Table I<br />
(<strong>in</strong>clud<strong>in</strong>g fault free mode). While Feature A and Feature<br />
B extracted from upper bridge voltage V auo<br />
and down<br />
bridge voltage V ado<br />
are used as the <strong>in</strong>put data for<br />
auxiliary ANN A and B respectively. Table II and Table<br />
© 2013 ACADEMY PUBLISHER
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III represent the fault modes diagnosed by two auxiliary<br />
ANNs and their target output.<br />
TABLE III.<br />
FAULT MODES AND OUTPUT OF AUXILIARY ANN B<br />
Fault modes (open-circuit)<br />
Target output<br />
S 0<br />
{<br />
a3<br />
a3<br />
S , S<br />
a4<br />
} 1<br />
IV. DIAGNOSIS RESULT<br />
To verify the proposed method, an NPC <strong>in</strong>verter us<strong>in</strong>g<br />
MOSFET IRF640 as the switch<strong>in</strong>g device is used to carry<br />
out the three bridge voltages. A DSP chip TMS320F2812<br />
is utilized to generate gate drive signals. The <strong>in</strong>put DC<br />
voltage is 90V to 110V and the three phase wyeconnected<br />
load is 8Ω resistance series with 20mH<br />
<strong>in</strong>ductance. Fault occurrence is created by physically<br />
remov<strong>in</strong>g switch<strong>in</strong>g signal <strong>in</strong> the desired position.<br />
Figure 12 shows the experimental bridge voltage<br />
waveforms for open-circuit fault of s<strong>in</strong>gle device. Figure<br />
13 shows the experimental bridge voltage waveforms<br />
when open-circuit fault occurr<strong>in</strong>g <strong>in</strong> two devices<br />
simultaneously.<br />
Figure 12. Experimental bridge voltage waveforms for open-circuit of<br />
s<strong>in</strong>gle device<br />
Each fault mode from Tab.1 to Tab.3 must cover the<br />
operat<strong>in</strong>g region. Thus, there are three degrees of <strong>in</strong>put<br />
DC voltage <strong>in</strong> the experiment <strong>in</strong>clude 90V, 100V and<br />
110V. Under each DC voltage, the modulation <strong>in</strong>dex is<br />
changed from 0.2 to 1 with step of 0.1. Therefore, 27 sets<br />
orig<strong>in</strong>al data can be obta<strong>in</strong>ed for each fault mode. The<br />
data whose modulation <strong>in</strong>dex is 0.5, 0.7 and 0.9 are<br />
utilized as test sample and the rest data are utilized as<br />
tra<strong>in</strong> sample.<br />
Volt:20/div<br />
Time:5ms/div<br />
(a) { S<br />
a1<br />
, S<br />
a2<br />
}<br />
Volt:20/div<br />
Time:5ms/div<br />
(a) S<br />
a1<br />
open-circuit<br />
Volt:20/div<br />
Time:5ms/div<br />
(b) S<br />
a2<br />
open-circuit<br />
Volt:20/div<br />
Volt:20/div<br />
Time:5ms/div<br />
(b) { S<br />
a1<br />
, S<br />
a3<br />
}<br />
Volt:20/div<br />
Time:5ms/div<br />
(c) { S<br />
a1<br />
, S<br />
a4<br />
}<br />
Volt:20/div<br />
Time:5ms/div<br />
(c) D<br />
a5<br />
open-circuit<br />
Time:5ms/div<br />
(d) { S<br />
a2<br />
, S<br />
a3<br />
}<br />
Figure 13. Experimental bridge voltage waveforms when two devices<br />
malfunction<br />
© 2013 ACADEMY PUBLISHER
1470 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
TABLE IV.<br />
DIAGNOSIS RESULT OF MULTI-LAYER ANN (WITHOUT PCA)<br />
Ma<strong>in</strong> SVM<br />
Auxiliary<br />
SVM A<br />
Auxiliary<br />
SVM B<br />
No noise 98.84% 100% 100%<br />
10% white<br />
nosie 96.31% 100% 100%<br />
Table IV shows diagnosis result of the multi-layer<br />
ANN without PCA and the dimension of the <strong>in</strong>put data of<br />
the ma<strong>in</strong> ANN is 11.<br />
Table V shows diagnosis result of the multi-layer ANN<br />
with PCA. Here, only the <strong>in</strong>put data of the ma<strong>in</strong> ANN is<br />
transformed by the technique of PCA and the dimension<br />
of the new <strong>in</strong>put data of the ma<strong>in</strong> ANN is 8.<br />
TABLE V.<br />
DIAGNOSIS RESULT OF MAIN ANN (WITH PCA)<br />
Ma<strong>in</strong> SVM<br />
No noise 99.24%<br />
10% white nosie 98.43%<br />
It could be seen from Table IV and Table V that the<br />
diagnosis precision of the ma<strong>in</strong> ANN with PCA is higher<br />
than that without PCA. It could be deduced that the ANN<br />
with PCA must be tra<strong>in</strong>ed better than the ANN without<br />
PCA and has better generalization ability.<br />
V. CONCLUSIONS<br />
Additional signals are required <strong>in</strong> order to isolate more<br />
complicated faults of open-circuit occurr<strong>in</strong>g <strong>in</strong> two<br />
devices <strong>in</strong> NPC <strong>in</strong>verter dur<strong>in</strong>g certa<strong>in</strong> period. Note that<br />
this is not just a theoretical problem but a practical one<br />
because some failures have been reported recently, see<br />
[21]-[22]. In this paper, the voltages <strong>in</strong> all the upper,<br />
middle and down bridge are suggested to extract fault<br />
features. A scheme of multi-layer ANN is proposed to<br />
implement fault diagnosis of NPC <strong>in</strong>verter, <strong>in</strong>volv<strong>in</strong>g the<br />
simple open-circuit of one device or more devices. Better<br />
precision could be achieved when the <strong>in</strong>put data is<br />
transformed by PCA.<br />
ACKNOWLEDGMENT<br />
The project is supported by Innovation Project of<br />
Shanghai Municipal Education Commission numbered<br />
12zz191, Graduates’ Innovation Fund of Shanghai<br />
Maritime University numbered YC2011061.<br />
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[16] Foito D., Mart<strong>in</strong>s J.F., Pires V.F., Maia, J., “An<br />
Eigenvalue/Eigenvector 3D Current Reference Method for<br />
Detection and Fault Diagnosis <strong>in</strong> a Voltage Source<br />
Inverter”, 35th Annual Conference of IEEE on Industrial<br />
Electronics, 2009, pp.190-194.<br />
[17] Khomfoi S., Tolbert L.M., “Fault Diagnosis and<br />
Reconfiguration for Multilevel Inverter Drive Us<strong>in</strong>g AI-<br />
Based Techniques”, IEEE Transactions on Industrial<br />
Electronics, vol.54, no.6, 2007, pp.2954-2968.<br />
[18] Hu Guang-shu, “Digital Signal Process<strong>in</strong>g-theory,<br />
Algorithms and Implementation”, Beij<strong>in</strong>g, Ts<strong>in</strong>ghua<br />
University Press, 2003.<br />
[19] L<strong>in</strong> Wei-xun, “Modern Power Electronics Technology”,<br />
Beij<strong>in</strong>g, Mach<strong>in</strong>ery Industry Press, 2006.<br />
[20] U.Ahmad, A.Gavrilov, S.Lee, “Modular Multilayer<br />
Perceptron for WLAN Based Localization”, Proc. of<br />
International Jo<strong>in</strong>t Conference on Neural Networks, 2006,<br />
pp. 3465-3471.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1471<br />
[21] Sun J<strong>in</strong>g, “Fault Recovery Process<strong>in</strong>g for CRH2 Multipleunit<br />
Traction Converter”, Railway Locomotive & Car, vol.<br />
29, no. 6, pp. 64-66, 2009,.<br />
[22] Li Li-jun, Li Pu-m<strong>in</strong>, “Fault Analysis and Recovery<br />
Process<strong>in</strong>g for CRH2 M ultiple-unit Traction Converter”,<br />
Railway Locomotive & Car, vol. 28, no. 4, pp. 69-70, 2008.<br />
Danjiang Chen was born <strong>in</strong> N<strong>in</strong>gbo, Ch<strong>in</strong>a, on Feb 15, 1979.<br />
He received the B.S. and M.S. degrees <strong>in</strong> electrical eng<strong>in</strong>eer<strong>in</strong>g<br />
from Zhejiang University, Hangzhou, Ch<strong>in</strong>a, <strong>in</strong> 2002 and 2005,<br />
respectively. He is currently work<strong>in</strong>g toward the Ph.D. degree <strong>in</strong><br />
Shanghai Maritime University, Shanghai, Ch<strong>in</strong>a.<br />
After received the M.S. degree, he jo<strong>in</strong>ed Zhejiang Wanli<br />
University, where he is a lecturer <strong>in</strong> the faculty of electronic and<br />
<strong>in</strong>formation eng<strong>in</strong>eer<strong>in</strong>g. His current area of research <strong>in</strong>cludes<br />
power electronics and their fault diagnosis system.<br />
Y<strong>in</strong>zhong Ye was born <strong>in</strong> Zhejiang, Ch<strong>in</strong>a, <strong>in</strong> 1964. He<br />
received the B.Sc., M.Sc. and Ph.D. degrees <strong>in</strong> <strong>in</strong>dustrial<br />
automation and electronic eng<strong>in</strong>eer<strong>in</strong>g from East Ch<strong>in</strong>a<br />
University of Science and Technology, Shanghai, Ch<strong>in</strong>a <strong>in</strong> 1982,<br />
1985 and 1989, respectively.<br />
After receiv<strong>in</strong>g the M.Sc. degree, he jo<strong>in</strong>ed the Research<br />
Institute of Automation, East Ch<strong>in</strong>a University of Science and<br />
Technology, Shanghai, Ch<strong>in</strong>a, where he had worked as a<br />
Teach<strong>in</strong>g Assistant, Lecturer and Associate Professor. In 1994<br />
he jo<strong>in</strong>ed Shanghai Maritime University, Shanghai, Ch<strong>in</strong>a, as a<br />
Professor of electrical and automatic control eng<strong>in</strong>eer<strong>in</strong>g. S<strong>in</strong>ce<br />
2009 he has jo<strong>in</strong>ed Shanghai Institute of Technology, Shanghai,<br />
Ch<strong>in</strong>a as Vice President and Professor <strong>in</strong> electrical eng<strong>in</strong>eer<strong>in</strong>g<br />
and automation. His ma<strong>in</strong> research <strong>in</strong>terests and experience<br />
<strong>in</strong>clude fault diagnosis, fault-tolerant control, system simulation,<br />
power electronics, measurement and control of <strong>in</strong>dustrial<br />
processes.<br />
Dr. Ye is a Vice Chairperson of SAFEPROCESS CHINA,<br />
Ch<strong>in</strong>ese Association of Automation.<br />
Rong Hua was born <strong>in</strong> Shanghai, Ch<strong>in</strong>a, on March 26, 1960.<br />
He received the B.S. degrees <strong>in</strong> motor control eng<strong>in</strong>eer<strong>in</strong>g from<br />
Shanghai University, Shanghai, Ch<strong>in</strong>a, <strong>in</strong> July 1982, and the<br />
M.S. degrees <strong>in</strong> control eng<strong>in</strong>eer<strong>in</strong>g from East Ch<strong>in</strong>a University<br />
of Science and Technology, Shanghai, Ch<strong>in</strong>a, <strong>in</strong> March 2008.<br />
At present, he jo<strong>in</strong>ed the Shanghai Institute of Technology,<br />
Shanghai, Ch<strong>in</strong>a, as a Professor and a Master's Supervisor of<br />
electronics Information eng<strong>in</strong>eer<strong>in</strong>g. His ma<strong>in</strong> research <strong>in</strong>terests<br />
and experience <strong>in</strong>clude control eng<strong>in</strong>eer<strong>in</strong>g, signal process<strong>in</strong>g<br />
and power electronics and fault diagnosis system.<br />
© 2013 ACADEMY PUBLISHER
1472 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Pulse Wave K Value Averag<strong>in</strong>g Computation and<br />
Pathological Diagnosis<br />
Li Yang 1, 2 , J<strong>in</strong>xue Sui<br />
1 Shandong Institute of Bus<strong>in</strong>ess and Technology / School of Information and Electronic Eng<strong>in</strong>eer<strong>in</strong>g, Yantai, Ch<strong>in</strong>a<br />
Email: suij<strong>in</strong>xue@163.com<br />
Yunan Hu<br />
2 Department of Control Eng<strong>in</strong>eer<strong>in</strong>g / Naval Aeronautical Eng<strong>in</strong>eer<strong>in</strong>g University, Yantai, Ch<strong>in</strong>a<br />
Email: yangl-2005@163.com<br />
Abstract—Many cardiovascular diseases will lead to changes<br />
<strong>in</strong> pulse wave. Pulse wave’s transmission will play a<br />
significant role <strong>in</strong> promot<strong>in</strong>g the cl<strong>in</strong>ical detection and<br />
diagnosis, one k<strong>in</strong>d pulse wave computational method based<br />
on averag<strong>in</strong>g method is proposed, and comput<strong>in</strong>g<br />
cardiovascular function parameter K accord<strong>in</strong>g to the<br />
waveform area, the K value is associated with pathological<br />
analysis and diagnosis. A large number of cl<strong>in</strong>ical<br />
simulation and experiments proved that the relationship<br />
between the form factor K value and the human<br />
cardiovascular health, the pulse wave of the cerebral<br />
<strong>in</strong>farction matches with the actual cl<strong>in</strong>ical detection, it can<br />
provide theoretical support for the non-<strong>in</strong>vasive detection<br />
and parametric analysis of the cardiovascular function.<br />
Index Terms—pulse wave, averag<strong>in</strong>g computation, cerebral<br />
circulation, pathological diagnosis<br />
I. INTRODUCTION<br />
As the cycle of contraction and relaxation of the heart,<br />
blood pressure, blood flow velocity and blood flow’s<br />
pulsation and vessel wall changes’ expansion spread <strong>in</strong><br />
the vascular network, are known as pulse wave.<br />
Pulse wave transmitt<strong>in</strong>g characteristics are closely<br />
l<strong>in</strong>ked with the hemodynamic parameters of the blood<br />
circulation system. Changes <strong>in</strong> pulse waveform<br />
characteristics are an important basis to evaluate the<br />
physiological and pathological state of the human<br />
cardiovascular system. When the pulse wave spreads<br />
from the heart to the arterial system, it is not only<br />
affected by the heart itself, but also by various<br />
physiological factors that flow through all artery and its<br />
branches, such as vascular resistance, vessel wall<br />
elasticity, the pulse wave conta<strong>in</strong>s very rich physiological<br />
and pathological <strong>in</strong>formation <strong>in</strong> cardiovascular system, so<br />
that whether Ch<strong>in</strong>ese pulse-tak<strong>in</strong>g or Western<br />
cardiovascular tests is tried to extract a variety of<br />
physiological and pathological <strong>in</strong>formation from the<br />
pulse waveform and pressure’s changes. Therefore, the<br />
pulse wave transmitt<strong>in</strong>g studies are comb<strong>in</strong>ed with the<br />
cl<strong>in</strong>ical test<strong>in</strong>g and the pathological diagnosis <strong>in</strong> order to<br />
use non-<strong>in</strong>vasive detection to analyze and diagnose the<br />
cardiovascular disease, will play a very important<br />
practical effect [1-12].<br />
This paper proposed a solv<strong>in</strong>g method that<br />
cardiovascular function parameters K-value will be<br />
calculated based on the averag<strong>in</strong>g method, accord<strong>in</strong>g to<br />
changes of the area and waveform of the pulse <strong>in</strong><br />
different physiological and pathological conditions,<br />
comb<strong>in</strong>ed the K value with the pathological and<br />
diagnostic analysis.<br />
II. WAVE DIAGNOSTIC PRINCIPLES BASED ON BLOOD<br />
FLOW<br />
A. The Formation of Arterial Pulse Wave<br />
The driv<strong>in</strong>g force of the blood circulatory system is the<br />
heart of the ejection, which the ventricle play a major role,<br />
it is usually called the cardiac cycle, <strong>in</strong> fact, refers to the<br />
movement cycle of the ventricle. Arterial blood pressure<br />
is the driv<strong>in</strong>g force that promotes blood to flow; it must<br />
reach a certa<strong>in</strong> height <strong>in</strong> order to ensure the blood supply<br />
for all over organ. The process formed the arterial pulse<br />
wave that the arterial pressure transmits from the aorta to<br />
the small blood vessels and capillaries, which changes<br />
periodically <strong>in</strong>to the cardiac cycle [11].<br />
Figure 1. Pulse waveform coefficient K.<br />
The typical pulse wave is shown <strong>in</strong> figure 1, it can be a<br />
good reflection of cardiovascular <strong>in</strong>formation system, if<br />
the body abnormal occurs (such as atherosclerosis, etc.),<br />
the arteries’ nature will change, so pulse waveform<br />
changes must also occur.<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1472-1479
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1473<br />
B. Cardiovascular Function Parameters K Comput<strong>in</strong>g<br />
Based on Pulse Wave<br />
Needless to say, the characteristic <strong>in</strong>formation of pulse<br />
wave is closely related with the physiological factors. To<br />
study the relationship each other, many researchers get<br />
<strong>in</strong>formation from the time doma<strong>in</strong> or frequency doma<strong>in</strong><br />
characteristics based on pulse wave <strong>in</strong> cl<strong>in</strong>ical trials or<br />
model. In the time doma<strong>in</strong>, usually the pulse extracts<br />
some po<strong>in</strong>t with a clear physical mean<strong>in</strong>g (such as the<br />
ma<strong>in</strong> wave peak, heavy pump wave height, etc.). The<br />
comb<strong>in</strong>ation with the characteristic po<strong>in</strong>ts and the<br />
correspond<strong>in</strong>g physiological factors may get much<br />
cl<strong>in</strong>ical value. Some researchers have used simulation<br />
models to measure pulse wave different model<br />
parameters, to determ<strong>in</strong>e the person's physical condition<br />
accord<strong>in</strong>g to different parameters. Facts have proved that<br />
this method is more effective, but the simulation models<br />
and the extracted characteristic parameters must be<br />
proper, can effectively dist<strong>in</strong>guish the pathological state.<br />
In many studies, because the extracted parameters are<br />
too complicated to make the dist<strong>in</strong>ction between pulse<br />
waves, it often occurs the misjudg<strong>in</strong>g phenomenon.<br />
Therefore, the extraction of the pulse wave parameter is<br />
the critical research. Professor Luo Zhichang used the<br />
exist<strong>in</strong>g two-chamber model of elastic wave pulse to<br />
extract the characteristics of K (called form factor) which<br />
represents changes of the pulse wave’s area [11].<br />
Through the model theoretical analysis, thousands of<br />
animal experiments and cl<strong>in</strong>ical test<strong>in</strong>g with different<br />
age’s healthy people and patients with cardiovascular<br />
disease, confirmed that caused the pulse wave map<br />
features and the correspond<strong>in</strong>g changes <strong>in</strong> the area by<br />
physiological and pathological cardiovascular changes,<br />
and then reflect on the changes <strong>in</strong> K value. Determ<strong>in</strong>e the<br />
body's physical condition with the K value, although it<br />
can not achieve accurate quantitative analysis, but a<br />
simple calculation, differentiation, and the advantages of<br />
high sensitivity, which is important <strong>in</strong> the cl<strong>in</strong>ical<br />
reference value, is an important physiological <strong>in</strong>dicators<br />
of the cardiovascular cl<strong>in</strong>ical exam<strong>in</strong>ation.<br />
The K value reflects the characteristic quantities which<br />
changes <strong>in</strong> the amount of area of the pulse wave [11],<br />
which is def<strong>in</strong>ed as the average of the relative position of<br />
the pulse wave, which is def<strong>in</strong>ed by type (1) and figure 1.<br />
Pm<br />
− Pd<br />
K = . (1)<br />
P − P<br />
where K is the form factor; P<br />
m<br />
is mean arterial pressure,<br />
P<br />
d<br />
is the diastolic blood pressure; P s<br />
is the systolic<br />
blood pressure.<br />
Thus, the form factor K value have noth<strong>in</strong>g to do with<br />
the absolute value of systolic and diastolic blood pressure,<br />
it only depends on wave map area of the pulse wave, is a<br />
dimensionless parameter. Pulse waveform and area will<br />
have a great change <strong>in</strong> different physiological and<br />
pathological conditions, these changes can be expressed<br />
as K value.<br />
Because the pulse wave is difficult to accurately<br />
measure and solve, this paper propose a solution based on<br />
s<br />
d<br />
the averag<strong>in</strong>g method that K value of the pulse wave can<br />
be computed, and then through the specific network<br />
simulation of the cerebral circulation, the results is<br />
co<strong>in</strong>cided with cl<strong>in</strong>ical measurement.<br />
Ⅲ. CARDIOVASCULAR NETWORK HEMODYNAMIC<br />
ANALYSIS AND AVERAGING COMPUTATION<br />
Accord<strong>in</strong>g to the aforementioned study, <strong>in</strong> order to<br />
solve the pulse wave of blood circulation network<br />
diagram, first, analyze its network model [12-18]. In<br />
order to build blood circulation network's model, at first<br />
establishes the dynamic equation of one blood vessel<br />
branch. For simplicity, we make the follow<strong>in</strong>g<br />
assumptions: Al. the blood is <strong>in</strong>compressible; A2.the<br />
temperatures <strong>in</strong> all branches are identical. Under<br />
assumptions Al and A2, one branch of the blood network<br />
is described with the follow<strong>in</strong>g equations [12-18]:<br />
dQ<br />
j<br />
T<br />
j<br />
= −R<br />
j<br />
Q<br />
j<br />
Q<br />
dt<br />
TQ<br />
2<br />
= −Q<br />
R + H<br />
D<br />
j<br />
+ H<br />
j<br />
. (2)<br />
where Q<br />
j<br />
is flow through a branch j , R<br />
j<br />
are<br />
hemodynamic resistances, H<br />
j<br />
are pressure drops of the<br />
branches, Tj = ρl j<br />
/ S are <strong>in</strong>ertia coefficients, j = 1,<br />
,<br />
n<br />
j<br />
and n is the number of network branches (exclud<strong>in</strong>g the<br />
generator branch). T = diag T } , R = col R } and<br />
{ j<br />
{ j<br />
2<br />
Q = diag{<br />
Q Q } . (3)<br />
D<br />
Let nc<br />
denote the number of nodes. Then l = n − nc<br />
+ 1<br />
is the number of l<strong>in</strong>ks (exclud<strong>in</strong>g the generator branch)<br />
and n − l is the number of tree branches.<br />
Like an electrical network, a fluid network must satisfy<br />
Kirchhoff's current law, i.e., the flow out of any node is<br />
equal to the flow <strong>in</strong>to that node. Mathematically,<br />
Kirchhoff's current law for fluid flow networks can be<br />
expressed as:<br />
n<br />
∑<br />
j=<br />
1<br />
E<br />
Qij<br />
E<br />
⎡Q<strong>in</strong><br />
⎤<br />
⎢ ⎥ = 0<br />
⎣ Q ⎦<br />
Q<strong>in</strong><br />
or<br />
Q + e<br />
j<br />
Q<strong>in</strong>i<br />
Q<br />
<strong>in</strong><br />
j<br />
j<br />
= 0,<br />
i = 1, , n − l . (4)<br />
where n − l + 1 is the number of nodes (of which one is a<br />
“reference” node), Q is a vector of flows,<br />
E = [ e E ] Q<br />
, and E = E ] is a full rank matrix of<br />
Q<strong>in</strong><br />
Q<strong>in</strong><br />
Q<br />
[<br />
Qij<br />
order ( n − l)<br />
× n where E = 1 if branch j is connected<br />
Qij<br />
to node i and the flow goes away from node i ,<br />
E = −1 if it goes <strong>in</strong>to node i , E = 0 if branch j is<br />
Qij<br />
not connected to node i ; e<br />
Q<strong>in</strong><br />
is an (n-l)×1 vector such<br />
that, if the generator is connected to node i and the flow<br />
goes away from node i then e = 1 , if the flow goes<br />
Q<strong>in</strong>i<br />
Qij<br />
© 2013 ACADEMY PUBLISHER
1474 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
<strong>in</strong>to node i then e = −1<br />
, and e = 0 if the generator<br />
Q<strong>in</strong>i<br />
is not connected to node i .<br />
Similarly, the network satisfies Kirchhoff's voltage law,<br />
i.e., the sum of the pressure drops around any loop <strong>in</strong> the<br />
network must be equal to zero, or mathematically<br />
E H<br />
H = 0 or<br />
n<br />
∑<br />
j = 1<br />
E<br />
Hij<br />
H<br />
j<br />
Q<strong>in</strong>i<br />
= 0,<br />
i = 1, , l,<br />
(5)<br />
where H<br />
j<br />
is the pressure drop of the branch j , H is a<br />
vector of pressure drops, E<br />
H<br />
= [ EHij<br />
] is an l × n mesh<br />
matrix, <strong>in</strong> which each mesh (loop) is formed by a l<strong>in</strong>k and<br />
a unique cha<strong>in</strong> <strong>in</strong> the tree connect<strong>in</strong>g the two nodes of the<br />
l<strong>in</strong>k. The elements of E Hij<br />
are def<strong>in</strong>ed as follows:<br />
E<br />
Hij<br />
= 1 if branch j is conta<strong>in</strong>ed <strong>in</strong> mesh i and has the<br />
same direction, E<br />
Hij<br />
= −1<br />
if branch j is conta<strong>in</strong>ed <strong>in</strong><br />
mesh i and has the opposite direction, E<br />
Hij<br />
= 0 if branch<br />
j is not conta<strong>in</strong>ed <strong>in</strong> mesh i .<br />
In order to establish a dynamic model of m<strong>in</strong>imal order,<br />
one has to f<strong>in</strong>d <strong>in</strong>dependent variables as states of the<br />
system. We take the flows of l<strong>in</strong>k (co-tree) branches as<br />
state variables. If regards one time heartbeat as one<br />
period T , decomposes the blood pressure wave f (t)<br />
<strong>in</strong>to each k<strong>in</strong>d of simple harmonic wave comb<strong>in</strong>ation,<br />
that is:<br />
n<br />
⎛ 2πk<br />
⎞<br />
Q<strong>in</strong>(<br />
t)<br />
= Q0<br />
+ ⎜∑ak<br />
s<strong>in</strong>( t + φk<br />
) ⎟<br />
⎝ k=<br />
1 T ⎠<br />
(6)<br />
n<br />
= Q + a s<strong>in</strong>( kωt<br />
+ φ )<br />
0<br />
∑<br />
k=<br />
1<br />
k<br />
For convenience of analysis, we label the l<strong>in</strong>k branches<br />
(except the generator branch) from 1 to l. Def<strong>in</strong>e<br />
⎡Qc<br />
⎤ ⎡H<br />
c ⎤<br />
Q = ⎢ ⎥ , H = ⎢ ⎥ (7)<br />
⎣Qa<br />
⎦ ⎣H<br />
a ⎦<br />
so that Q c<br />
and H<br />
c<br />
vectors describe flow and pressure<br />
drop, respectively, <strong>in</strong> the l<strong>in</strong>ks, exclud<strong>in</strong>g the generator<br />
branch, and Q and H vectors describe them <strong>in</strong> the tree<br />
branches.<br />
The matrices<br />
where [18-19]<br />
E<br />
a<br />
Qa<br />
a<br />
E<br />
H<br />
and EQ<br />
<strong>in</strong> can be split <strong>in</strong>to blocks<br />
H<br />
[ E E ]<br />
E = (8)<br />
Q<strong>in</strong><br />
Hc<br />
Ha<br />
[ eQ<strong>in</strong><br />
EQc<br />
EQa]<br />
E = (9)<br />
= I , E<br />
Hc<br />
= I l × l<br />
, E<br />
( n−l<br />
) × ( n−l<br />
)<br />
k<br />
= − (10)<br />
T<br />
Ha<br />
E Qc<br />
Hence, the structure of the network can be expressed <strong>in</strong><br />
the matrix form as<br />
⎡ 0<br />
E = ⎢<br />
⎢⎣<br />
e<br />
Q<strong>in</strong><br />
E<br />
I<br />
Qc<br />
− E<br />
I<br />
T<br />
Qc<br />
⎤<br />
⎥<br />
⎥⎦<br />
(11)<br />
Furthermore,<br />
⎡T<br />
c<br />
T = ⎢<br />
⎣0<br />
0 , [ ] T<br />
⎤<br />
T T<br />
T<br />
⎥ R = R c<br />
Ra<br />
(12)<br />
a⎦<br />
Fluid circulation through the network of network<br />
model<strong>in</strong>g, accord<strong>in</strong>g to the aforementioned study, us<strong>in</strong>g<br />
the average method can solve the flow waveform, and<br />
then f<strong>in</strong>d its pulse wave flow waveform[15-20], that is:<br />
n 2<br />
⎛ a ⎞<br />
k −1<br />
Q<br />
⎜<br />
⎟<br />
c<br />
( t)<br />
= Qc0<br />
− ∑ V U<br />
⎝ k=<br />
1 4 ⎠<br />
(13)<br />
n<br />
⎛<br />
⎞<br />
+ Bc<br />
⎜∑<br />
ak<br />
s<strong>in</strong>( kωt<br />
+ φk<br />
) ⎟<br />
⎝ k=<br />
1<br />
⎠<br />
where<br />
Q ( t)<br />
= ( −E<br />
a<br />
Qc<br />
⎛<br />
+ Bc<br />
⎜<br />
⎝<br />
Q<br />
c0<br />
n<br />
∑<br />
k=<br />
1<br />
− e<br />
Q<strong>in</strong><br />
⎛<br />
Q +<br />
⎜<br />
0)<br />
⎝<br />
n<br />
∑<br />
k=<br />
1<br />
⎞<br />
ak<br />
s<strong>in</strong>( kωt<br />
+ φk<br />
) ⎟<br />
⎠<br />
T ( T)<br />
= T + E T E<br />
2<br />
a ⎞<br />
k<br />
⎟E<br />
4 ⎠<br />
Qc<br />
V<br />
−1<br />
U<br />
(14)<br />
T<br />
0 c Qc a Qc<br />
(15)<br />
2<br />
T 2<br />
{ B R } E col{ B R }<br />
U ( R,<br />
T,<br />
E)<br />
= col −<br />
(16)<br />
ci<br />
ci<br />
Qc<br />
ai<br />
ai<br />
T<br />
{ Q R } − E W<br />
V ( R,<br />
E,<br />
Q0)<br />
= diag<br />
c0i<br />
ci Qc<br />
(17)<br />
= E ( −E<br />
Q − e Q R (18)<br />
{<br />
Qcij Qci c0 Q<strong>in</strong> 0)<br />
ci} n l l<br />
W<br />
i ( − ) ×<br />
0<br />
( R,<br />
E,<br />
Q0<br />
and Q c<br />
) denotes l-dimensional solution of<br />
quadratic equation, that is:<br />
2<br />
T<br />
2<br />
Q R − E diag ( E Q + e Q ) R (19)<br />
i<br />
{ } 0<br />
c0 D c Qc<br />
Qci c0<br />
Q<strong>in</strong> 0 a<br />
=<br />
−<br />
such that V is nons<strong>in</strong>gular and − T 1 V is Hurwitz. Then<br />
for a given Q<br />
0<br />
> 0 , for sufficiently small a and<br />
sufficiently large ω the solutions of the system (1) ~ (6)<br />
4<br />
locally exponentially converge to a O ( 1 ω + a )<br />
neighborhood.<br />
IV. PULSE WAVE K VALUE SIMULATION AND CLINICAL<br />
PATHOLOGICAL DIAGNOSIS<br />
A. Healthy Middle-aged Cl<strong>in</strong>ical Detection and Pulse<br />
Wave Simulation Analysis<br />
To observe the relationship between the cl<strong>in</strong>ical value<br />
of K changes and the major physiological factors (such as<br />
the harden<strong>in</strong>g degree of the blood vessel wall, peripheral<br />
resistance, etc.). First we measured the pulse waveform to<br />
a thousand patients with different age groups, <strong>in</strong>clud<strong>in</strong>g<br />
healthy people and people with vary<strong>in</strong>g degrees of high<br />
blood pressure or vascular sclerosis. The <strong>in</strong>strument is<br />
used with cardiovascular blood flow parameters TP-CBS<br />
detector. After statistical analysis, the typical waveform<br />
and the correspond<strong>in</strong>g coefficient K are shown <strong>in</strong> Figure<br />
2.<br />
After measurement and cl<strong>in</strong>ical trials, the results<br />
showed that:<br />
(1) Young and healthy people, pregnant women,<br />
athletes are low vascular resistance, arterial elasticity, the<br />
K value is about 0.33 (Figure 2 (a));<br />
0<br />
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(2) Healthy young people <strong>in</strong> the vascular resistance<br />
and arterial elastic are medium, the K value between<br />
about 0.34 to 0.39 (Figure 2 (b), (c), (d), (e));<br />
(3) Middle aged and elderly people are higher vascular<br />
resistance, poor arterial elasticity, the K value is about 0.4<br />
or so (Figure 2 (f));<br />
(4) Patients with severe hypertension and<br />
atherosclerosis are high vascular resistance, poor arterial<br />
elasticity, the K value is about 0.45 to 0.5 (Figure 2 (g),<br />
(h) ).<br />
Generally we measured radial artery pulse wave,<br />
because of its high flow, it is easy to measure, but<br />
consider<strong>in</strong>g that the circulatory system is large and<br />
complex, its model is difficult to solve, because the<br />
arterial pulse wave is constant <strong>in</strong> the transmission cycle,<br />
Therefore, we use the above method to solve cerebral<br />
circulation network.<br />
Cerebral circulation refers to the movement of blood<br />
through the network of blood vessels supply<strong>in</strong>g the bra<strong>in</strong>.<br />
The arteries deliver oxygenated blood, glucose and other<br />
nutrients to the bra<strong>in</strong> and the ve<strong>in</strong>s carry deoxygenated<br />
blood back to the heart, remov<strong>in</strong>g carbon dioxide, lactic<br />
acid, and other metabolic products. S<strong>in</strong>ce the bra<strong>in</strong> is very<br />
vulnerable to compromises <strong>in</strong> its blood supply, the<br />
cerebral circulatory system has many safeguards. Failure<br />
of these safeguards results <strong>in</strong> cerebrovascular accidents,<br />
commonly known as strokes. The amount of blood that<br />
the cerebral circulation carries is known as cerebral blood<br />
flow.<br />
Cerebral arteries describe three ma<strong>in</strong> pairs of arteries<br />
and their branches, which irrigate the cerebrum of the<br />
bra<strong>in</strong>. The three ma<strong>in</strong> arteries consist of the: Anterior<br />
cerebral artery (ACA), Middle cerebral artery (MCA),<br />
Posterior cerebral artery (PCA). Both the ACA and MCA<br />
orig<strong>in</strong>ate from the cerebral portion of <strong>in</strong>ternal carotid<br />
artery, while PCA branches from the <strong>in</strong>tersection of the<br />
posterior communicat<strong>in</strong>g artery and the anterior portion<br />
of the basilar artery. The three pairs of arteries are l<strong>in</strong>ked<br />
via the anterior communicat<strong>in</strong>g artery and the posterior<br />
communicat<strong>in</strong>g arteries. All three arteries send out<br />
arteries that perforate bra<strong>in</strong> <strong>in</strong> the medial central portions<br />
prior to branch<strong>in</strong>g and bifurcat<strong>in</strong>g further. Anatomy of<br />
the cerebral circulation is shown <strong>in</strong> figure 4, the cerebral<br />
circulation equivalent plane structure (18 branches) is<br />
shown <strong>in</strong> figure 5.<br />
Figure 2. Pulse waves and K of people <strong>in</strong> different ages and healthy<br />
conditions.<br />
Thus, <strong>in</strong>creased with age or the development of<br />
hypertension, atherosclerosis, vascular resistance, pulse<br />
wave waveform develops bread-type waveform by the<br />
steep progressive, the waveform coefficient K <strong>in</strong>creases<br />
correspond<strong>in</strong>gly (<strong>in</strong> general changes between 0.35 ~ 0.5).<br />
It is shown <strong>in</strong> figure 3, maps of K values <strong>in</strong> the different<br />
age groups<br />
Figure 4. Anatomy of the cerebral circulation.<br />
Figure 3. Maps of K values <strong>in</strong> the different age groups<br />
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1476 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Loop 7: H<br />
7<br />
− H9<br />
− H10<br />
+ H11<br />
= 0 ,<br />
Loop 8: H<br />
8<br />
− H10<br />
+ H11<br />
− H12<br />
− H13<br />
+ H14<br />
− H15<br />
= 0 .<br />
We knew l , d<br />
1<br />
, ρ of the cerebral circulation network<br />
from paper [1], it is shown <strong>in</strong> table I.<br />
TABLE I.<br />
THE ARTERIAL GEOMETRY PARAMETERS OF THE CIRCLE OF WILLIS<br />
artery number length(cm) diameter(cm)<br />
<strong>in</strong>ternal carotid a. 7,1 25 0.4<br />
basilar a. 9 3 0.4<br />
Posterior communicat<strong>in</strong>g 11,15 2 0.12<br />
a.<br />
posterior cerebral a.Ⅰ 10,8 2 0.3<br />
anterior cerebral a.Ⅰ 12,14 2 0.25<br />
anterior communicat<strong>in</strong>g a. 13 0.5 0.15<br />
middle cerebral a. 5,2 7 0.35<br />
posterior cerebral a.Ⅱ 6,16 7 0.3<br />
Figure 5. The network equivalent plane diagram of cerebral circulation<br />
(16 branches).<br />
The network of the cerebral circulation has 16<br />
branches, 8 nodes and 1 generator branch. Choose<br />
branches 9 to 16 and generator as the tree of the network.<br />
The node equations can be expressed as:<br />
Node 1: Q <strong>in</strong><br />
− Q1 − Q7<br />
− Q9<br />
= 0 ;<br />
Node 2: Q<br />
8<br />
+ Q10<br />
− Q9<br />
= 0 ;<br />
Node 3: Q<br />
6<br />
− Q10<br />
− Q11<br />
= 0 ;<br />
Node 4: Q<br />
5<br />
− Q7<br />
+ Q11<br />
+ Q12<br />
= 0 ;<br />
Node 5: Q<br />
4<br />
− Q12<br />
+ Q13<br />
= 0 ;<br />
Node 6: Q<br />
3<br />
− Q13<br />
− Q14<br />
= 0 ;<br />
Node 7: Q<br />
2<br />
+ Q14<br />
+ Q15<br />
− Q1<br />
= 0 ;<br />
Node 8: Q<br />
16<br />
− Q8<br />
− Q15<br />
= 0 ;<br />
After transformation:<br />
Q <strong>in</strong><br />
= Q1 + Q7<br />
+ Q9<br />
Q <strong>in</strong><br />
= Q1 + Q7<br />
+ Q8<br />
+ Q10<br />
Q <strong>in</strong><br />
= Q1 + Q6<br />
+ Q7<br />
+ Q8<br />
− Q11<br />
Q <strong>in</strong><br />
= Q1 + Q5<br />
+ Q6<br />
+ Q8<br />
+ Q12<br />
Q <strong>in</strong><br />
= Q1 + Q4<br />
+ Q5<br />
+ Q6<br />
+ Q8<br />
+ Q13<br />
Q <strong>in</strong><br />
= Q1 + Q3<br />
+ Q4<br />
+ Q5<br />
+ Q6<br />
+ Q8<br />
− Q14<br />
Q <strong>in</strong><br />
= Q2 + Q3<br />
+ Q4<br />
+ Q5<br />
+ Q6<br />
+ Q8<br />
+ Q15<br />
Q <strong>in</strong><br />
= Q2 + Q3<br />
+ Q4<br />
+ Q5<br />
+ Q6<br />
+ Q16<br />
The loop equations can be expressed as:<br />
Loop 1: H<br />
1<br />
− H<br />
9<br />
− H10<br />
− H11<br />
+ H12<br />
− H13<br />
− H14<br />
= 0 ;<br />
Loop 2: H<br />
2<br />
− H15<br />
− H16<br />
= 0 ;<br />
Loop 3: H<br />
3<br />
+ H14<br />
− H15<br />
− H16<br />
= 0 ;<br />
Loop 4: H<br />
4<br />
− H13<br />
+ H14<br />
− H15<br />
− H16<br />
= 0 ,<br />
Loop 5: H<br />
5<br />
− H12<br />
− H13<br />
+ H14<br />
− H15<br />
− H16<br />
= 0 ,<br />
Loop 6: H + H − H − H + H − H − H 0 ,<br />
6 11 12 13 14 15 16<br />
=<br />
anterior cerebral a.Ⅱ 4,3 5 0.25<br />
ρl<br />
1.63l<br />
We can obta<strong>in</strong> T from T = and R from R = .<br />
4<br />
S<br />
D<br />
We may obta<strong>in</strong> Q c0 equation set from type (19), this<br />
equation only has numerical solution, but does not have<br />
the exact solution, uses the genetic algorithm to get the<br />
iterative solution. We can get H from Q , H is equal to<br />
P .<br />
First, we solve the cerebral circulation blood flow Q<br />
with the normal person, and we can get H from (2), that<br />
is P <strong>in</strong> (1), its comput<strong>in</strong>g simulation result is shown <strong>in</strong><br />
figure 6.<br />
`<br />
© 2013 ACADEMY PUBLISHER
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It is shown <strong>in</strong> figure 6, the normal cerebral circulation<br />
network 10 times harmonic waveform are basically the<br />
same with healthy middle-aged <strong>in</strong> figure 2 and figure 3 ,<br />
the K value is 0.356 by calculat<strong>in</strong>g, and K is cl<strong>in</strong>ically<br />
consistent with 0.34 ~ 0.39.<br />
B. Cerebral Infarction Cl<strong>in</strong>ical Detection and Pulse<br />
Wave Pathological Analysis<br />
Cerebral <strong>in</strong>farction causes bra<strong>in</strong> tissue partial arterial<br />
blood flows poorly or completely stop due to <strong>in</strong>sufficient<br />
blood supply, and blood viscosity is an important factor<br />
<strong>in</strong> caus<strong>in</strong>g vascular resistance, and its dynamic changes<br />
are related with the cerebral lesions closely. From paper<br />
[11], <strong>in</strong> order to clarify the correlation between the<br />
waveform characteristic K value and the blood viscosity,<br />
<strong>in</strong> cl<strong>in</strong>ical test, the observed 100 cerebral <strong>in</strong>farction<br />
patients with CT or NMR diagnosis (mean age 54 years,<br />
male 63 cases, females 37 cases) are vary<strong>in</strong>g degrees of<br />
hyperviscosity and microcirculation. Before and after<br />
treatment, use blood flow parameters TP.CBS<br />
nondestructive detector to detect the patient's pulse wave<br />
pressure and K-value. At the same time, use LS30 to test<br />
blood viscosity, and compared with the K value, the<br />
results is shown <strong>in</strong> Table II.<br />
TABLE II.<br />
CLINICAL EXAMINING RESULTS<br />
Parameter<br />
Before treatment After treatment<br />
K 0.55±0.12 0.31±0.1<br />
Blood viscosity 6.27±1.9 3.6±1.2<br />
Sett<strong>in</strong>g the term<strong>in</strong>al resistance value of R 2 that is 3<br />
times higher than normal to simulate the side of the<br />
middle cerebral artery area <strong>in</strong>farction lesions, choose to<br />
simulate the case of compensatory cerebral calculation,<br />
select the compensatory situation <strong>in</strong> which the normal<br />
circle of Willis before and after the traffic artery open.<br />
Tak<strong>in</strong>g the term<strong>in</strong>al resistance value of R 2 which is 3<br />
times higher than normal to simulate the side of the<br />
middle cerebral artery area <strong>in</strong>farction lesions, choose the<br />
compensatory situation to simulate cerebral calculation,<br />
which the traffic arteries of the circle of Willis are open.<br />
Tak<strong>in</strong>g the diameter of the anterior communicat<strong>in</strong>g artery<br />
to calculate parameters, D13=0.2cm, the diameter of the<br />
posterior communicat<strong>in</strong>g artery D 11 =D 15 =0.15cm, R 13 ,<br />
R 11 , R 15 are 590, 6439 and 6439 dyn·s/cm, T 13 =119.4908,<br />
we can get Ten harmonics from (13) and (14), The circle<br />
of Willis pulse wave with the cerebral <strong>in</strong>farction is shown<br />
<strong>in</strong> figure 7.<br />
Figure 6. The circle of Willis pulse wave with the normal human.<br />
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1478 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 7. The circle of Willis pulse wave with the cerebral <strong>in</strong>farction.<br />
We can see the pulse wave of the cerebral <strong>in</strong>farction<br />
from the simulation figure 6, the K value is 0.495, and is<br />
close to the cl<strong>in</strong>ical test of cerebral <strong>in</strong>farction <strong>in</strong> Table II,<br />
K = 0.55 ± 0.12, from the chang<strong>in</strong>g trend of the K<br />
value, this result matches with the actual cl<strong>in</strong>ical<br />
detection basically.<br />
V. CONCLUSION<br />
In summary, the pulse waveforms extracted the K<br />
value by averag<strong>in</strong>g computation and the wave area,<br />
although it does not fully reflect subtle changes <strong>in</strong> the<br />
pulse curve that conta<strong>in</strong>s all the local physiological and<br />
pathological significance, but it represents some<br />
important physiological parameters <strong>in</strong> the human blood<br />
circulatory system, such as peripheral vascular resistance,<br />
blood viscosity and so on. Consider<strong>in</strong>g the characteristic<br />
<strong>in</strong>formation to reduce only one characteristic quantity K,<br />
it is easy to remember, a clear physiological significance,<br />
and changes very regular, can be easily accepted by<br />
cl<strong>in</strong>icians, so it can be used as important cardiovascular<br />
physiological parameters of the cl<strong>in</strong>ical exam<strong>in</strong>ation.<br />
In the averag<strong>in</strong>g comput<strong>in</strong>g pulse wave process, the<br />
network only needs to know the relevant basic<br />
physiological parameters of blood vessel branch, and<br />
calculat<strong>in</strong>g the pulse wave and the K value is more high<br />
precision than pulse wave detector. The stability test<strong>in</strong>g<br />
results do not affect with the emotional fluctuates <strong>in</strong> the<br />
waveform, the different K values corresponds to different<br />
pathological conditions, so that it can provide an nondestructive<br />
test<strong>in</strong>g mathematical calculation and analysis<br />
methods for the cl<strong>in</strong>ical parameters of blood circulation.<br />
ACKNOWLEDGMENT<br />
This work is supported by NSF 60970105; education<br />
department S&T plan J08LJ70 and NSF of Shandong<br />
Prov<strong>in</strong>ce ZR2010FL015 and ZR2010FL021; MOHURD<br />
and Shandong Development science and technology<br />
project 2010-K9-26 and 2011YK05.<br />
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Li Yang received the B.S. degree <strong>in</strong> the<br />
applied mathematics from yantai university,<br />
Yantai <strong>in</strong> 2002 and the M.S. degree and <strong>in</strong><br />
the operational research and cybernetics<br />
from Beij<strong>in</strong>g Jiaotong University, Ch<strong>in</strong>a, <strong>in</strong><br />
2005. Currently, she is an <strong>in</strong>structor with<br />
Shandong Institute of Bus<strong>in</strong>ess and<br />
Technology and doctoral student with<br />
Naval Aeronautical Eng<strong>in</strong>eer<strong>in</strong>g University,<br />
Ch<strong>in</strong>a. His research <strong>in</strong>terests are <strong>in</strong>telligent control, fluid<br />
network control.<br />
J<strong>in</strong>xue Sui, associate professor, he<br />
received the M.S. degree <strong>in</strong> the control<br />
theory and control eng<strong>in</strong>eer<strong>in</strong>g from<br />
Northeast Dianli University, Jil<strong>in</strong>, Ch<strong>in</strong>a<br />
<strong>in</strong> 2005 and the Ph.D.~degree <strong>in</strong> the<br />
navigation, guidance and control from<br />
Naval Aeronautical Eng<strong>in</strong>eer<strong>in</strong>g<br />
University, Yantai, Ch<strong>in</strong>a <strong>in</strong> 2009.<br />
Currently, he is a <strong>in</strong>structor with<br />
Shandong Institute of Bus<strong>in</strong>ess and<br />
Technology, Ch<strong>in</strong>a. His research <strong>in</strong>terests are <strong>in</strong>telligent sensor,<br />
fluid network control and biological control now.<br />
© 2013 ACADEMY PUBLISHER
1480 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Multi-Step Prediction Algorithm of Traffic Flow<br />
Chaotic Time Series based on Volterra Neural<br />
Network<br />
Lisheng Y<strong>in</strong><br />
School of Electrical and Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of Technology, Hefei, Ch<strong>in</strong>a<br />
E-mail: yls20000@163.com<br />
Yigang He, Xuep<strong>in</strong>g Dong, Zhaoquan Lu<br />
School of Electrical and Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of Technology, Hefei, Ch<strong>in</strong>a<br />
E-mail: hyghnu@yahoo.com.cn, hfdxp@126.com, luzhquan@126.com<br />
Abstract—The accurate traffic flow time series prediction is<br />
the prerequisite for achiev<strong>in</strong>g traffic flow <strong>in</strong>ducible system.<br />
Aim<strong>in</strong>g at the issue about multi-step prediction traffic flow<br />
chaotic time series, the traffic flow Volterra Neural Network<br />
(VNN) rapid learn<strong>in</strong>g algorithm is proposed. Comb<strong>in</strong>g with<br />
the chaos theory and the Volterra functional analysis,<br />
method of the truncation order and the truncation items is<br />
given and the VNN model of traffic flow time series is built.<br />
Then the mechanism of the chaotic learn<strong>in</strong>g algorithm is<br />
described, and the adaptive learn<strong>in</strong>g algorithm of VNN for<br />
traffic flow time series is designed. Last, a multi-step<br />
prediction of traffic flow chaotic time series is researched by<br />
traffic flow VNN network model, Volterra prediction filter<br />
and the BP neural network based on chaotic algorithm. The<br />
simulations show that the VNNTF network model predictive<br />
performance is better than the Volterra prediction filter and<br />
the BP neural network by the simulation results and rootmean-square<br />
value.<br />
Index Terms—Chaos Theory, Phase Space Reconstruction,<br />
Time Series Prediction, VNN Neural Networks, Algorithm<br />
I. INTRODUCTION<br />
The Volterra series is a model for non-l<strong>in</strong>ear behavior<br />
similar to the Taylor series. It differs from the Taylor<br />
series <strong>in</strong> its ability to capture 'memory' effects. It has the<br />
advantages of high precision and clear physical mean<strong>in</strong>g,<br />
has become one of the very effective non-parametric<br />
model of nonl<strong>in</strong>ear system [1-4]. Traffic flow chaotic<br />
time series with the nonl<strong>in</strong>ear behavior of the response<br />
and memory function, the Volterra series to become one<br />
of the primary means of traffic flow <strong>in</strong> nonl<strong>in</strong>ear system<br />
identification [5-6]. Many scholars and technology<br />
developers have proposed a lot of Volterra identification<br />
algorithm, but the establishment of nonl<strong>in</strong>ear systems on<br />
Volterra Series model is very difficult [7-9]. Volterra<br />
series has an obvious drawback is that if you want to<br />
achieve a satisfactory accuracy may require a<br />
considerable number of estimated parameters. The highlevel<br />
nuclear estimates are fac<strong>in</strong>g the greatest difficulties.<br />
Therefore, the Volterra functional model of the<br />
application is to be greatly restricted, and sometimes <strong>in</strong><br />
order to avoid solv<strong>in</strong>g the higher-order kernel function<br />
and Volterra functional model artificially simplified,<br />
result<strong>in</strong>g <strong>in</strong> the model<strong>in</strong>g <strong>in</strong>accuracy.<br />
With the rapid development of computer technology,<br />
the neural network is more deeply and widely used <strong>in</strong><br />
nonl<strong>in</strong>ear systems [11-13]. The neural network not only<br />
has the self-adaptive, parallelism and fault tolerance<br />
characteristics, but also has the ability to approximate any<br />
nonl<strong>in</strong>ear function. Based on these advantages, the neural<br />
network model of the nonl<strong>in</strong>ear system has a very wide<br />
range of applications [14-16]. Due to the consistency of<br />
the Volterra model and the three-layer ANN model,<br />
comb<strong>in</strong>ed with the traffic flow chaotic time series chaotic<br />
characteristics, how to make use the Volterra accurate<br />
model<strong>in</strong>g of the advantages to overcome the<br />
shortcom<strong>in</strong>gs of Solutions of Higher Order kernel<br />
function; and how to use the advantages of ANN neural<br />
network model for learn<strong>in</strong>g and tra<strong>in</strong><strong>in</strong>g network to<br />
overcome the bl<strong>in</strong>dness of the ANN neural network<br />
model<strong>in</strong>g is worth explor<strong>in</strong>g.<br />
Based on the above considerations, the physical<br />
significance of the truncation order of the Volterra series<br />
model and the truncated number and the mathematical<br />
properties of the m<strong>in</strong>imum embedd<strong>in</strong>g dimension and<br />
delay time <strong>in</strong> traffic flow chaotic time series<br />
reconstructed phase space, thus, traffic flow chaotic time<br />
series VNNTF network model and the correspond<strong>in</strong>g<br />
algorithm has been established [17-20]. VNNIF neural<br />
network model to learn the advantages of the Volterra<br />
series to establish an accurate traffic prediction model<br />
and the ANN network tra<strong>in</strong><strong>in</strong>g is easy to solve the<br />
Volterra model kernel function; thus, to overcome the<br />
difficulties on Volterra series model for solv<strong>in</strong>g the<br />
higher order kernel function and the bl<strong>in</strong>dness of the<br />
ANN network model, <strong>in</strong> the traffic flow chaotic time<br />
series prediction, obta<strong>in</strong>ed good results.<br />
II. TRAFFIC FLOW CHAOTIC TIME SERIES VOLTERRA<br />
MODEL<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1480-1487
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1481<br />
For nonl<strong>in</strong>ear systems, discretization of the Volterra<br />
model is as follows:<br />
Where,<br />
∞<br />
∑∑<br />
yn ( ) = h( l, , l) xn ( −l) xn ( −l)<br />
(1)<br />
nl , i<br />
i l1<br />
, , li<br />
= 0<br />
i 1 i 1<br />
i<br />
∈ R, yn ( ) is the output of the nonl<strong>in</strong>ear<br />
system; x( n− l i<br />
) is the <strong>in</strong>put of the nonl<strong>in</strong>ear system and<br />
hi( l1, l2, , li)<br />
( i = 1, 2, , n ) is Volterra kernel function<br />
of order i .<br />
A. Model of Chaotic Time Series Prediction<br />
The chaotic time series prediction is based on the<br />
Takens' delay-coord<strong>in</strong>ate phase reconstruct theory. If the<br />
time series of one of the variables is available, based on<br />
the fact that the <strong>in</strong>teraction between the variables is such<br />
that every component conta<strong>in</strong>s <strong>in</strong>formation on the<br />
complex dynamics of the system, a smooth function can<br />
be found to model the portraits of time series. If the<br />
chaotic time series are{ x()<br />
t }, then the reconstruct state<br />
vector is x( t) = ( x( t), x( t+ τ ), , x( t+ ( m−1) τ )) , Where<br />
m ( m = 2,3, ) is called the embedd<strong>in</strong>g dimension<br />
( m = 2d<br />
+ 1, d is called the freedom of dynamics of the<br />
system), and τ is the delay time. The predictive<br />
reconstruct of chaotic series is a <strong>in</strong>verse problem to the<br />
dynamics of the system essentially. There exists a smooth<br />
m<br />
function def<strong>in</strong>ed on the reconstructed manifold <strong>in</strong> R to<br />
<strong>in</strong>terpret the dynamics x( t+ T) = F( x( t))<br />
,<br />
where T ( T > 0)<br />
is forward predictive step length, and<br />
F()<br />
⋅ is the reconstructed predictive model.<br />
B. The Determ<strong>in</strong>ation of the Truncation Order on Traffic<br />
Flow Chaotic Time Series Volterra Model<br />
Assume that the measured traffic flow chaotic time<br />
series is { xt ()( t= 1,2,3, )}, the traffic flow chaotic time<br />
series phase space reconstruction based on Takens<br />
Theorem, you can get the <strong>in</strong>put of the nonl<strong>in</strong>ear system is<br />
xt ( ), xt ( + τ ), xt ( + 2 τ), , xt ( + ( m−1) τ)<br />
, where, m is the<br />
embedd<strong>in</strong>g dimension, namely the reconstruction of<br />
phase space dimension, τ is the delay time. Here, m<br />
corresponds to the number of f<strong>in</strong>ite order <strong>in</strong> the<br />
discretization of the Volterra model, and to predict the<br />
traffic flow is predicted on the basis of the m item, then<br />
the traffic flow chaotic time series phase space<br />
reconstruction model with m-order truncation Volterra<br />
series model can be characterized as follows:<br />
x( t′ + T) = F( X( t)) = h + h ( l ) x( t−lτ<br />
)<br />
∞ ∞ ∞<br />
∑∑<br />
∞<br />
l1= 0l2= 0 lp<br />
= 0<br />
∞<br />
∑∑<br />
∞<br />
∑<br />
0 1 0 0<br />
l0<br />
= 0<br />
+ h ( l , l ) x( t−lτ) x( t− lτ)<br />
+ <br />
2 1 2 1 2<br />
l1= 0l2=<br />
0<br />
∑<br />
+ h ( l, l, , l ) xt ( −lτ ) xt ( −lτ) xt ( −lτ)<br />
m 1 2 m 1 2<br />
m<br />
(2)<br />
where, hm( l1, l2, , lm)<br />
is the m order Volterra kernel<br />
function, t′ = t+ ( m− 1) τ , T ( T > 0 ) is the forward<br />
prediction step. This <strong>in</strong>f<strong>in</strong>ite series, theoretically, can be<br />
very accurately predict<strong>in</strong>g traffic flow chaotic time series,<br />
but difficult to achieve <strong>in</strong> practical applications, it must<br />
be a f<strong>in</strong>ite order truncation and the f<strong>in</strong>ite sum <strong>in</strong> the form.<br />
Your goal is to simulate the usual appearance of papers<br />
<strong>in</strong> a Journal of the <strong>Academy</strong> <strong>Publisher</strong>. We are request<strong>in</strong>g<br />
that you follow these guidel<strong>in</strong>es as closely as possible.<br />
For traffic flow chaotic time series prediction from<br />
equation (2), it is the m-order truncated <strong>in</strong>f<strong>in</strong>ite item<br />
summation form. For example, when m = 3, it is a f<strong>in</strong>ite<br />
sum of the third order <strong>in</strong>tercept Volterra series model:<br />
N1<br />
−1<br />
∑<br />
x( t′ + T) = F( X( t)) = h + h ( l ) x( t−lτ<br />
)<br />
N2−1N2−1<br />
∑∑<br />
l1= 0 l2=<br />
0<br />
0 1 0 0<br />
l0<br />
= 0<br />
+ h ( l , l ) x( t−lτ<br />
) x( t−lτ<br />
)<br />
2 1 2 1 2<br />
N3−1N3−1N3−1<br />
∑∑∑ h2( l1, l2, l3) x( t l1τ ) x( t l2τ) x( t l3τ)<br />
(3)<br />
l1= 0 l2= 0 l3=<br />
0<br />
+ − − −<br />
so, actually want to calculate the total number of<br />
2 2<br />
coefficients is 1+ N1+ N2 + N3<br />
. Be seen with the<br />
<strong>in</strong>crease of m <strong>in</strong> the Volterra series, the number of items<br />
of Volterra Series will power rapid <strong>in</strong>crease; the<br />
correspond<strong>in</strong>g required number of calculations also<br />
showed exponential growth, which makes the actual<br />
traffic flow chaotic time series predicted to achieve more<br />
and more difficult. The total number of items of Volterra<br />
series number decreases exponentially growth. In practice,<br />
the truncation order is generally the second-order<br />
truncation or third order <strong>in</strong>tercept.<br />
C. The Determ<strong>in</strong>ation of the Truncation Items on<br />
Traffic Flow Chaotic Time Series Volterra Model<br />
In the form of the flow chaotic time series Volterra<br />
series model is (2), assume that the truncated form of<br />
limited items are as follows:<br />
N1<br />
−1<br />
∑<br />
x( t′ + T) = F( X( t)) = h + h ( l ) x( t−lτ<br />
)<br />
N2−1N2−1<br />
∑∑<br />
l1= 0 l2=<br />
0<br />
Nm−1Nm−1 Nm−1<br />
∑∑<br />
l1= 0 l2= 0 lp<br />
= 0<br />
0 1 0 0<br />
l0<br />
= 0<br />
+ h ( l , l ) x( t−lτ) x( t− lτ)<br />
+ <br />
∑<br />
2 1 2 1 2<br />
+ h ( l , l , , l ) x( t−lτ ) x( t−lτ) x( t−l<br />
τ)<br />
m 1 2 m 1 2<br />
m<br />
For traffic flow chaotic time series, it is assumed that<br />
x()<br />
t and yt () are the <strong>in</strong>put and output signals of the<br />
functional system f (, txt (′), t′ ≤ t)<br />
<strong>in</strong> the traffic flow, the<br />
<strong>in</strong>put signal of the functional system <strong>in</strong> the traffic flow to<br />
meet:<br />
1 Traffic flow <strong>in</strong>put signal is a causal relationship is<br />
met when t < 0 , then xt () = 0.<br />
2 Traffic flow functional system f (, txt (′), t′ ≤ t)<br />
is<br />
the limited memory, that is, for the t time <strong>in</strong> the system,<br />
(4)<br />
© 2013 ACADEMY PUBLISHER
1482 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
t<br />
0<br />
time very far from the t time, t 0<br />
→∞, x( t− t0<br />
) has<br />
no effect on yt (); means that the predicted value of yt ()<br />
is irrelevant to x( t− t0<br />
).<br />
In the prediction of chaos traffic flow chaotic time<br />
series, t′ = t+ ( m− 1) τ , T ( T > 0 ) is forward prediction<br />
step, x( t′ + T)<br />
represents the output associated with the<br />
<strong>in</strong>put signal x()<br />
t and the delay time τ , then<br />
N l −1<br />
1<br />
l1 l<br />
<br />
2 N li 0 ∑ 1 1 1<br />
l1<br />
= 0<br />
x( t′ + T) = f( x , x , x ) = h + h ( l ) x( t−lτ<br />
)<br />
Nl<br />
−1N<br />
1<br />
2 l −<br />
2<br />
∑∑<br />
+ h ( l , l ) x( t−lτ<br />
) x( t−l<br />
τ )<br />
l1= 0 l2=<br />
0<br />
2 1 2 1 2<br />
Nl −1N 3 l −1N<br />
1<br />
3 l −<br />
3<br />
∑∑∑ h3( l1, l2, l3) xt ( l1τ) xt ( l2τ) xt ( l3τ)<br />
(5)<br />
l1= 0 l2= 0 l3=<br />
0<br />
+ − − − +<br />
note<br />
Nmax = max( N , N , N , N ) , ( i = 1, 2, 3, ),<br />
when n≥<br />
N<br />
li<br />
max<br />
l1 l2 l3<br />
l i<br />
, the same to meet the <strong>in</strong>put traffic flow<br />
signal x = xt ( − lτ ) is irrelevant to yt () , then the<br />
formula (4) can be written as:<br />
i<br />
Nmax<br />
−1<br />
l1 l<br />
<br />
2 N li 0 ∑ 1 1 1<br />
l1<br />
= 0<br />
x( t′ + T) = f( x , x , x ) = h + h ( l ) x( t−lτ<br />
)<br />
Nmax<br />
−1Nmax<br />
−1<br />
∑ ∑<br />
+ h ( l , l ) x( t−lτ<br />
) x( t−lτ<br />
)<br />
l1= 0 l2=<br />
0<br />
Nmax −1Nmax −1Nmax<br />
−1<br />
∑ ∑ ∑<br />
l1= 0 l2= 0 l3=<br />
0<br />
2 1 2 1 2<br />
+ h ( l , l , l ) x( t−lτ) x( t−lτ) x( t− lτ)<br />
+ <br />
3 1 2 3 1 2 3<br />
Know from the above analysis of the traffic flow<br />
functional systems, the power series expansion item of<br />
prediction results are <strong>in</strong> fact only related to Know from<br />
the above analysis of the traffic flow functional systems,<br />
the power series expansion item of prediction results are<br />
<strong>in</strong> fact only related to summation form all the products of<br />
the Input signal and the first power delay time signal.<br />
This means that the value of<br />
Nmax = max( Nl , N , , )<br />
1 l<br />
N<br />
2 l<br />
N<br />
3 l i<br />
, ( i = 1, 2, 3, ) is only<br />
related with the number of <strong>in</strong>put signal and the delay time<br />
signal, which is the m<strong>in</strong>imum embedd<strong>in</strong>g dimension m<br />
of phase space, so Nmax = max( Nl , N , , )<br />
1 l<br />
N<br />
2 l<br />
N<br />
3 l i<br />
= m.<br />
Such traffic flow chaotic time series Volterra series<br />
model is f<strong>in</strong>alized by the formula (5) as follows:<br />
m−1<br />
l1 l<br />
<br />
2 N li 0 ∑ 1 1 1<br />
l1<br />
= 0<br />
x( t′ + T) = f( x , x , x ) = h + h ( l ) x( t−lτ<br />
)<br />
m−1 m−1 m−1<br />
∑∑∑<br />
m−1 m−1<br />
∑∑<br />
+ h ( l , l ) x( t−lτ<br />
) x( t−lτ<br />
)<br />
2 1 2 1 2<br />
l1= 0l2=<br />
0<br />
+ h( l, l, l) xt ( −lτ) xt ( −lτ) xt ( − lτ)<br />
+ <br />
3 1 2 3 1 2 3<br />
l1= 0l2= 0l3=<br />
0<br />
m−1m−1m−1 m−1<br />
∑∑∑ ∑<br />
+ h (, l l, l, , l xt−lτ)( xt−lτ)( xt−lτ) xt ( −lτ)<br />
(7)<br />
m 1 2 3 m 1 2 3<br />
m<br />
l1= 0l2= 0l3= 0 lm=<br />
0<br />
(6)<br />
III. TRAFFIC FLOW TIME SERIES VOLTERRA NEURAL<br />
NETWORK MODEL (VNNTF)<br />
A. Representation of Nonl<strong>in</strong>ear Systems Us<strong>in</strong>g Artificial<br />
Neural Network<br />
Has proven that the BP neural network with one<br />
hidden layer can approximate any cont<strong>in</strong>uous bounded<br />
non-l<strong>in</strong>ear system, therefore, generally selected to conta<strong>in</strong><br />
a three-layer back propagation BP network with one<br />
hidden layer to approximate nonl<strong>in</strong>ear systems. A s<strong>in</strong>gle<br />
output three-layer back propagation neural network is<br />
shown <strong>in</strong> Figure 1. In the figure, the <strong>in</strong>put vector<br />
T<br />
x = [ x , x , x ] at moment n can obta<strong>in</strong> by the<br />
k k,0 k,1 k,<br />
M<br />
delay of x( k ), where x<br />
,<br />
= xk ( − m)<br />
, the <strong>in</strong>put of the l<br />
km<br />
hidden unit ( l = 1, 2, , L) is<br />
Z<br />
= S ( u ); ulk ,<br />
= ∑ wlm ,<br />
xkm<br />
,<br />
(8)<br />
lk , l lk ,<br />
M<br />
m=<br />
0<br />
A s<strong>in</strong>gle output three-layer back propagation neural<br />
network is shown <strong>in</strong> Figure 1.<br />
x k,0<br />
x km ,<br />
x kM ,<br />
w L , m<br />
w 1,0<br />
w<br />
,0<br />
w l<br />
L,0<br />
w 1,m<br />
w lm ,<br />
w 1,M<br />
w lM ,<br />
w L , M<br />
U 1,k<br />
U lk ,<br />
U L , k<br />
S()<br />
⋅<br />
S()<br />
⋅<br />
S()<br />
⋅<br />
Z 1,k<br />
Z lk ,<br />
Z L , k<br />
<strong>in</strong>put hidden layer output<br />
Figure 1. Three layer neural networks <strong>in</strong> response to M+1 <strong>in</strong>put and<br />
s<strong>in</strong>gle output system<br />
If the implicit function selected the sigmoid function,<br />
then<br />
1<br />
Sl( u<br />
,<br />
) = l k<br />
1 + exp[ − λ( u − θ )]<br />
(9)<br />
Where, θ<br />
l<br />
is the threshold of the unit n, If the output unit<br />
is l<strong>in</strong>ear summation unit, the output at moment n is<br />
y<br />
L<br />
r l<br />
lk ,<br />
r 1<br />
r L<br />
k l l,<br />
k<br />
l = 1<br />
l<br />
Z<br />
= ∑ rZ<br />
(10)<br />
The output of each hidden unit to expand <strong>in</strong>to a Taylor<br />
series at the threshold θ<br />
l<br />
:<br />
Z = ϕ ( u ) =∑ d ( θ ) u<br />
i<br />
(11)<br />
l, k l l, k i l l,<br />
k<br />
i=<br />
0<br />
where, d ( θ ) is the commencement of the coefficient,<br />
i<br />
l<br />
the value associated with<br />
M<br />
lk , lm , km ,<br />
m=<br />
0<br />
∞<br />
θ<br />
l<br />
y k<br />
, and because of<br />
u = ∑ w x , then the output of the neural network<br />
is<br />
L ∞<br />
M M<br />
∑∑ ∑ ∑<br />
y = r d ( θ ) ⋅ w w x x (12)<br />
k l i l l, m1 l, mi<br />
k, m1<br />
k,<br />
mi<br />
l= 1 i= 0 m1<br />
= 0 mi<br />
= 0<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1483<br />
B. Traffic Flow Volterra Neural Network Model<br />
Analysis and comparison of traffic flow Volterra series<br />
model <strong>in</strong> equation (6) and three-layer BP neural network<br />
<strong>in</strong> equation (12), if the <strong>in</strong>put vector <strong>in</strong> equation (12) <strong>in</strong><br />
VNNTF to take the traffic flow chaotic time series, then<br />
between them <strong>in</strong> the function, structure and method for<br />
solv<strong>in</strong>g are <strong>in</strong>herently close contact and similarity.<br />
1) From a functional po<strong>in</strong>t of view, the traffic flow<br />
chaotic time series, Volterra series model and ANN<br />
model can be measured traffic flow chaotic time series, to<br />
simulate and predict the traffic flow process. Traffic flow<br />
chaotic time series Volterra model can determ<strong>in</strong>e the<br />
model truncation order of the truncation by the<br />
characteristics analysis of the traffic flow time series.<br />
Then, it can use the system identification to strike a<br />
nuclear function of the Volterra series model, or proper<br />
orthogonal decomposition method, stepwise multiple<br />
regression method, iterative decl<strong>in</strong>e <strong>in</strong> the gradient<br />
method, Volterra filter and constra<strong>in</strong>ts orthogonal<br />
approximation method to solve the nuclear function or<br />
Volterra series, which reflect the chaotic nonl<strong>in</strong>ear law of<br />
the traffic flow.<br />
2) From a structural po<strong>in</strong>t of view, the traffic flow<br />
chaotic time series Volterra model and ANN model is<br />
also isomorphic. Length of the storage memory of past<br />
traffic flow relative to chaotic time series <strong>in</strong> the traffic<br />
flow Volterra model, that is, the m<strong>in</strong>imum embedd<strong>in</strong>g<br />
dimension <strong>in</strong> phase space reconstruction of is equivalent<br />
to the number of neurons of the ANN model <strong>in</strong>put layer.<br />
3) From a method for solv<strong>in</strong>g po<strong>in</strong>t of view, Traffic<br />
flow chaotic time series Volterra model is based on<br />
orthogonal polynomials for the numerical approximation<br />
to f<strong>in</strong>d the approximate solution.the Meixner function<br />
systems and network weights have the same effect.<br />
x()<br />
t<br />
xt ( + τ )<br />
xt ( + ( m−1) τ )<br />
w N ,1<br />
w 1,m<br />
w 1,0<br />
w2,0<br />
wN ,0<br />
w 1,1<br />
w 2,1<br />
w 2,m<br />
w N , m<br />
V () t 1<br />
V () t yt <br />
g ()<br />
2 2<br />
V () N<br />
t<br />
Input Hidden layer Output<br />
Figure 2. The chaotic time series Volterra neural network traffic flow<br />
model (VNNTF)<br />
Through consistency of traffic flow chaotic time series<br />
Volterra model and ANN model, <strong>in</strong> this paper, the traffic<br />
flow chaotic time series Volterra neural network model<br />
(VNNTF) has been proposed <strong>in</strong> Figure 2. In the figure,<br />
X() t = ( xt (), xt ( + τ ), , xt ( + ( m−1) τ ) T ( t = 1, 2, ) is the<br />
traffic flow chaotic time series reconstructed phase space<br />
vector; w<br />
i,<br />
j<br />
( i = 1, 2, ; j = 1, 2, ), r n<br />
is the traffic flow<br />
chaotic time series Volterra neural network weights<br />
parameters; g , ( s = 1, 2, , N ) is the activation function<br />
s<br />
and Vs<br />
( k ) is the traffic flow of the convolution of the<br />
<strong>in</strong>put signal:<br />
g 1<br />
g N<br />
r 2<br />
r 1<br />
r N<br />
m<br />
V () t = w x( t+ ( i−1) τ )<br />
N<br />
∑ Ni<br />
(13)<br />
i=<br />
0<br />
Thus, the traffic flow chaotic time series Volterra<br />
neural network expression is<br />
N<br />
<br />
<br />
y( t) = f( X( t)) = f( x( t)) =∑ rsgs( VN( t))<br />
N<br />
m<br />
s s si<br />
s= 1 i=<br />
0<br />
s=<br />
1<br />
∑ ∑ (14)<br />
= rg ( w xt ( + ( i−1) τ ))<br />
IV. TRAFFIC FLOW VOLTERRA NEURAL NETWORK RAPID<br />
LEARNING ALGORITHM<br />
A. Activation Function Analysis of Traffic Tlow Volterra<br />
Neural Network<br />
Activation function of hidden layer to the VNNTF<br />
model designed for the follow<strong>in</strong>g polynomial function:<br />
g = a + a x+ a x + + a x + (15)<br />
2<br />
i<br />
s 0, s 1, s 2, s i,<br />
s<br />
where ais<br />
,<br />
∈ R is the polynomial coefficients, and then<br />
So, to get:<br />
N<br />
N +∞<br />
<br />
i<br />
y( t) = r g ( V ( t)) = ra ( V ( t))<br />
∑<br />
∑∑<br />
s s N s i,<br />
s N<br />
s= 1 s= 1 i=<br />
1<br />
N<br />
+∞<br />
m<br />
∑∑ ∑<br />
i<br />
= ra ( w xt ( + ( i−1) τ ))<br />
s i,<br />
s si<br />
s= 1 i= 1 i=<br />
0<br />
N<br />
h ( l , l , l ) = ∑ ra w w w<br />
j 1 2 j s js , sl , 1 sl , 2 sl , j<br />
s=<br />
1<br />
( j = 1, 2, , m) (16)<br />
In the VNNTF model, the sigmoid function or other<br />
functions as the activation function gs( Vs( t )) tra<strong>in</strong><strong>in</strong>g<br />
VNNTF network, the weights and thresholds are obta<strong>in</strong>ed,<br />
the activation function gs( Vs( t )) is expanded <strong>in</strong>to a<br />
Taylor series, you can obta<strong>in</strong> the polynomial coefficients:<br />
a<br />
js .<br />
( j)<br />
gs<br />
( θs<br />
)<br />
= (17)<br />
j!<br />
Among them, ( j<br />
g ) ( θ ) is the j -order derivative of<br />
s<br />
s<br />
function gs( Vs( t ) <strong>in</strong> θ s<br />
; that is a different activation<br />
function, you can get a<br />
js .<br />
. VNNTF network learn<strong>in</strong>g and<br />
tra<strong>in</strong><strong>in</strong>g, accord<strong>in</strong>g to the connection weights of the<br />
network of neurons and the coefficients of a<br />
js .<br />
, you can<br />
solve any order kernel function, which would address the<br />
difficulties of solv<strong>in</strong>g high-level nuclear function <strong>in</strong> the<br />
Volterra model. In general, if directly us<strong>in</strong>g the<br />
polynomial function for the activation function, the<br />
polynomial order is taken as m , the same Taylor<br />
expansion of the Taylor series, the order is taken to the<br />
m , so VNNTF model by sett<strong>in</strong>g different order of the<br />
activation functions to reflect the effect equivalent to the<br />
Volterra model higher order kernel function.<br />
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1484 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
B. Traffic Flow Volterra Neural Network Rapid Learn<strong>in</strong>g<br />
Algorithm<br />
On the establishment of traffic flow chaotic time series<br />
WNN, Network <strong>in</strong>put the number of neurons, hidden<br />
layers and the number of neurons <strong>in</strong> the hidden layer are<br />
to be considered. The follow<strong>in</strong>g traffic flow data used are<br />
from "Chongq<strong>in</strong>g Road Traffic Management Data Sheet<br />
I" and "Chongq<strong>in</strong>g Road Traffic Management Data Sheet<br />
II" <strong>in</strong> 2006. There is the study of traffic volume time<br />
series of two-lane road 28 hours and 5 m<strong>in</strong>utes every 5<br />
m<strong>in</strong>utes, <strong>in</strong>clud<strong>in</strong>g m<strong>in</strong>i-vehicles, passenger cars, light<br />
trucks, midsize, large cars, trailer, micro van, not<br />
stereotypes, such as vehicles, and its sequence length<br />
n = 337 .First, Pretreatment of the traffic flow time series,<br />
the m<strong>in</strong>imum embedd<strong>in</strong>g dimension m = 4 and delay<br />
time τ = 3 are obta<strong>in</strong>ed by calculation. Then, the traffic<br />
flow Volterra neural network can be constructed: traffic<br />
flow Volterra neural network is designed to be three<br />
layers: <strong>in</strong>put layer, s<strong>in</strong>gle hidden layer and output layer;<br />
the number of hidden layer wavelet neural taken as 9 by<br />
Kolmogorov Theorem, the number of <strong>in</strong>put layer neurons<br />
equal to the m<strong>in</strong>imum embedd<strong>in</strong>g dimension ( m = 4 ),<br />
the number of output layer is 1, so that the 4-9-1 structure<br />
of traffic flow Volterra neural network was obta<strong>in</strong>ed,<br />
specifically shown <strong>in</strong> Figure 2. The hidden layer<br />
activation function can be used sigmoid function or other<br />
commonly used functions, and here it be used with<br />
polynomial activation functions<br />
2<br />
i<br />
gs = a0, s<br />
+ a1, sx+ a2, sx + + ai,<br />
sx<br />
+ , ais<br />
,<br />
∈ R is<br />
polynomial coefficients. Optimal network parameter w<br />
s,<br />
j<br />
and r<br />
s<br />
( s = 1, 2, N , j = 1, 2, m ) can be obta<strong>in</strong>ed by<br />
learn<strong>in</strong>g and tra<strong>in</strong><strong>in</strong>g the network for reduc<strong>in</strong>g the<br />
error E , and further hj( l1, l2, lj)<br />
( j = 1, 2, m) can be<br />
calculated by comb<strong>in</strong><strong>in</strong>g the polynomial coefficients.<br />
The steps of traffic flow chaotic time series Volterra<br />
Neural Network fast learn<strong>in</strong>g algorithm is showed and the<br />
specific steps are as follows:<br />
Algorithm VNNTF model fast learn<strong>in</strong>g algorithm<br />
Step1) The hidden neurons number is 9 by<br />
Kolmogorov Theorem, so that the 4-9-1 structure of<br />
traffic flow VNNTF neural networks was obta<strong>in</strong>ed. The<br />
traffic flow time series <strong>in</strong>put signal is<br />
( xt ( ), xt ( + τ ), , xt ( + ( m−1) τ ) T , ( t = 1, 2, ) ; the<br />
<br />
output signal is yt (); the weight coefficient matrix of the<br />
hidden layer is w = ( ws, l<br />
)<br />
N× m<br />
= ( ws,<br />
i)<br />
N×<br />
m<br />
, ( s = 1, 2, 9 ,<br />
j<br />
i , j = 1, 2, , 4 ) and the parameter is r s<br />
( s = 1, 2, 9 ).<br />
Step2) The traffic flow chaotic time series Volterra<br />
Neural Network parameters w = ( w<br />
s,<br />
i)<br />
N×<br />
m<br />
and r<br />
s<br />
( s = 1, 2, 9 , i = 1, 2, 4 ) are <strong>in</strong>itialized, where the<br />
parameters w = ( w<br />
s,<br />
i)<br />
N×<br />
m<strong>in</strong> each component take random<br />
function between 0 and 1; and r s<br />
are <strong>in</strong>itialized to take 9<br />
number between 0 and 1 by the random function.<br />
Step3) Us<strong>in</strong>g phase space reconstruction theory to<br />
preprocess the traffic flow chaotic time series, and<br />
perform normalization for the reconstructed network<br />
<strong>in</strong>put signal. Based on Takens theorem, the m<strong>in</strong>imum<br />
embedd<strong>in</strong>g dimension m = 4 , and the delay time τ = 3 .<br />
The reconstruction phase space vector number is<br />
N −1 −( m− 1) τ = 327, which the top 250 vector are used<br />
as network <strong>in</strong>put signals. the form is<br />
( xt ( ), xt ( + τ ), , xx ( + ( m−1) τ )) T , where t = 1, 2, 250 ,<br />
m = 4 and τ = 3.<br />
Then, the 250 phase space vectors to make a simple<br />
normalized, the normalized as<br />
[ x() t − mean( x())]/[max( t x()) t − m<strong>in</strong>( x())]<br />
t<br />
,<br />
t = 1, 2, 250 and, mak<strong>in</strong>g the value is owned by a range<br />
of -1 / 2 to 1/2.<br />
Step4) Us<strong>in</strong>g the <strong>in</strong>itialized network and the<br />
preprocessed traffic flow time series, the first VNNTF<br />
neural network tra<strong>in</strong><strong>in</strong>g beg<strong>in</strong> with the function<br />
N +∞ m<br />
<br />
i<br />
yt () = ra ( wxt ( + ( i−1) τ )) ,<br />
∑∑<br />
∑<br />
s i,<br />
s si<br />
s= 1 i= 1 i=<br />
0<br />
and the assumed activation function is a polynomial<br />
activation function g s<br />
, here a is ,<br />
∈ R are polynomial<br />
coefficients.<br />
Step5) Calculate error function, the function formula:<br />
250<br />
1 2<br />
E( θ ) = ( y( t) − y( t))<br />
∑<br />
2 t = 1<br />
Set the maximum error is E max<br />
= 0.035 , if E < Emax<br />
,<br />
the storage VNNTF neural network parameter use<br />
w = ( w<br />
s,<br />
i)<br />
N×<br />
m<br />
and r<br />
s<br />
( s = 1, 2, 9 , i = 1, 2, 4 ) ; and<br />
further hj<br />
( l1, l2, lj<br />
) ( j = 1, 2, m) can be calculated by<br />
comb<strong>in</strong><strong>in</strong>g the polynomial coefficients, otherwise,<br />
transferred to step6).<br />
Step6) Calculate local gradient of the traffic flow<br />
chaotic time series Volterra neural network. Specifically,<br />
accord<strong>in</strong>g to the formula δ ( t) = ( y( t) − y ( t)) g ′( V ( t))<br />
( j is the output layer) and the formula<br />
j j s j<br />
∂Et<br />
()<br />
δ<br />
j() t =− g ′<br />
s<br />
( Vj())<br />
t<br />
(18)<br />
∂ y () t<br />
j<br />
where, the local gradients are calculated <strong>in</strong> the hidden<br />
layer.<br />
Step7) By <strong>in</strong>troduc<strong>in</strong>g the momentum term, to adjust<br />
the learn<strong>in</strong>g weights of the traffic flow chaotic time series<br />
Volterra neural network. Introduce nonl<strong>in</strong>ear feedback<br />
<strong>in</strong>to the weight<strong>in</strong>g formal to adopt Chaos Mechanisms,<br />
due to the nonl<strong>in</strong>ear feedback is vector form of weight<strong>in</strong>g<br />
variables. In order to facilitate understand<strong>in</strong>g,<br />
respectively, gives the vector w and its weight<strong>in</strong>g formal,<br />
as follows. Note Δ w l ( t+ 1) = w l ( t+ 1) −w l ( t)<br />
, which<br />
ji ji ji<br />
represents the current value of weight<strong>in</strong>g variables, then<br />
1<br />
Δ w l ( t+ 1) = w l ( t+ 1) − w l () t = −ηδ l+<br />
() t x l () t .<br />
ji ji ji j i<br />
In order to speed up the learn<strong>in</strong>g process, <strong>in</strong> the right to<br />
l<br />
jo<strong>in</strong> a momentum term αΔw () t , then<br />
Δ w + = − x + Δw<br />
ji<br />
l 1<br />
( 1) l +<br />
( ) l ( ) l<br />
ji<br />
t ηδ<br />
j<br />
t<br />
i<br />
t α<br />
ji<br />
( t)<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1485<br />
where α is <strong>in</strong>ertia factor; η is learn<strong>in</strong>g step;<br />
αΔ wji<br />
,<br />
( t+ 1) is the <strong>in</strong>troduction of the momentum and<br />
δ () t is calculated with the formula (9).<br />
j<br />
Expand this equation <strong>in</strong>to scalar form as follow:<br />
l l+<br />
1 l l<br />
⎧Δ wji( t+ 1) =− ηδ<br />
j<br />
() t xi () t + g( Δwji())<br />
t<br />
⎪<br />
l l+<br />
1 l l<br />
⎪Δ wji( t+ 1 + τ) =− ηδj ( t+ τ) xi ( t+ τ) + g( Δ wji( t+<br />
τ))<br />
⎪<br />
l l+<br />
1 l l<br />
⎨Δ wji( t+ 1+ 2) τ =− ηδj ( t+ 2) xi ( t+ 2) τ + g( Δ wji<br />
( t+<br />
2)) τ<br />
⎪<br />
⎪<br />
<br />
⎪ l l+<br />
1<br />
l l<br />
Δ wji( t+ 1 + ( m− 1) τ) =− ηδj ( t+ ( m− 1) τ) xi ( t+ ( m− 1) τ) + g(<br />
Δwji( t+ ( m−1) τ))<br />
⎩<br />
(19)<br />
where, feedback can take a variety of vector functions,<br />
for example:<br />
2<br />
g( x) = tanh( px) exp( − qx ) or<br />
g( x) = pxexp( − q x)<br />
,<br />
<strong>in</strong> the study, p = 0.7 , q = 0.1.<br />
Step8) Calculat<strong>in</strong>g the modified weights <strong>in</strong> the traffic<br />
flow chaotic time series Volterra neural network <strong>in</strong> Step8)<br />
and transferred to step4), and tra<strong>in</strong> network aga<strong>in</strong>, then<br />
<br />
calculate the network output yt () and the error E ,<br />
repeated tra<strong>in</strong><strong>in</strong>g until the relative error <strong>in</strong> traffic meet<br />
E < E max<br />
= 0.035 .<br />
Step9) Output of every tra<strong>in</strong><strong>in</strong>g storage of network<br />
parameters w = ( w<br />
s,<br />
i)<br />
N×<br />
m<br />
and r<br />
s<br />
( s = 1,2, 9 ,<br />
i = 1, 2, 4 ) <strong>in</strong> the traffic flow chaotic time series<br />
Volterra neural network. The activation function<br />
g ( V ( t )) is expanded <strong>in</strong>to a Taylor series at the<br />
s<br />
s<br />
threshold θ<br />
s<br />
and the expansion coefficient di( θ<br />
s)<br />
is<br />
obta<strong>in</strong>ed. If the activation function is a polynomial, then<br />
d ( θ ) = a ( s = 1, 2, 9 , i = 1, 2, 4 ).<br />
i s i,<br />
s<br />
Step10) Accord<strong>in</strong>g to the formula<br />
N<br />
h ( l , l , l ) = ∑ rd ( θ ) w w w (20)<br />
j 1 2 j s i s sl , 1 sl , 2 sl , j<br />
s=<br />
1<br />
the kernel function ( s = 1, 2, 9 , i = 1, 2, 4 ) of the<br />
output system is calculated.<br />
N + 3 values... N + T values ( T > 0 ). That is, for the<br />
known sample set can be extrapolated to predict T step.<br />
The follow<strong>in</strong>g multi-step prediction of the traffic flow<br />
VNNTF network, and the results compare with the multistep<br />
prediction of the BP neural network and filter<br />
Voltrra, further, analyz<strong>in</strong>g the causes of the different<br />
predictions. In fact, the multi-step prediction results can<br />
also be compared with the prediction results of wavelet<br />
neural network Algorithm and Wavelet Neural Network<br />
Based on Chaotic Algorithm. Can also be an attempt of<br />
the analysis for the prediction of the different results.<br />
Where, the m<strong>in</strong>imum embedd<strong>in</strong>g dimension <strong>in</strong> phase<br />
space is m = 4 , the delay time is τ = 3 , and the vector<br />
number of phase space reconstruction which can be used<br />
to tra<strong>in</strong> and predict is N − ( m− 1) τ = 327.<br />
Figure 4. The 2-step forecast result and real result<br />
Figure 5. The 2-step forecast error curve<br />
V. EXPERIMENTAL RESULTS AND ANALYSIS<br />
Experimental objective is study how much extent does<br />
the prediction performance <strong>in</strong> VNNTF neural network<br />
improve from the aspects of model construction and<br />
algorithm application.<br />
In order to study the prediction performance of traffic<br />
flow time series <strong>in</strong> traffic flow VNNTF network,<br />
respectively the VNNTF network model, Volterra<br />
prediction filter and ANN to predict the network traffic<br />
flow chaotic time series, and analyze and compare their<br />
predictions.<br />
Multi-step prediction is a major aspect to reflect the<br />
performance of predictive model. Traffic flow time series<br />
Multi-step prediction is as follows: If the sample size is<br />
N , <strong>in</strong> the new data po<strong>in</strong>t cannot be used or only the<br />
sample po<strong>in</strong>ts N , It can be predicted beyond N + 1<br />
values, can also predict the N + 2 values,<br />
Figure 6. The 3-step forecast result and real result<br />
In the network tra<strong>in</strong><strong>in</strong>g of the multi-step prediction,<br />
such as Step 2 to Step 4, the tra<strong>in</strong><strong>in</strong>g objectives of the 250<br />
reconstructed vector among the 327 reconstructed phase<br />
space vector are the traffic flow signals from t′ to<br />
t′ + 249 ( t′ = 12,13,14 ).Network tra<strong>in</strong><strong>in</strong>g, <strong>in</strong> order to<br />
compare with the measured traffic flow signal, the<br />
TT= ( 2,3,4) step forecast traffic flow signal<br />
© 2013 ACADEMY PUBLISHER
1486 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
correspond<strong>in</strong>g 260 + T ( T = 2,3, 4 ) to 337 traffic flow<br />
signal, that is, if the forecast number of steps each one<br />
more, then its projection is reduced by one. If not to make<br />
a prediction comparison with the measured signal, it does<br />
not have this restriction.<br />
Figure 7. The 3-step forecast error curve<br />
which corresponds to 2-step, 3-step and 4-step absolute<br />
error curve. Figure 4 to Figure 9 shows the effect of 3-<br />
step prediction results is worse than the 2-step prediction,<br />
the effect of 4-step prediction results is worse than the 3-<br />
step prediction; and the general trend is to predict the<br />
longer the step, the prediction performance has become<br />
gett<strong>in</strong>g worse.<br />
Analysis of multi-step prediction results to VNNTF<br />
network, the 2-step, 3-step and 4-step predictable<br />
performance overall is better than the BP neural network<br />
prediction and the Volterra filter prediction; this is<br />
because the network VNNTF comb<strong>in</strong>es the Volterra<br />
series and ANN network advantages, to overcome the<br />
difficulties of solv<strong>in</strong>g the Volterra kernel function and the<br />
bl<strong>in</strong>dness of ANN network model<strong>in</strong>g. In fact, the<br />
prediction results to VNNTF network is better than the<br />
wavelet neural network prediction based on chaotic<br />
algorithm, and this may be the establishment of a good<br />
traffic flow time series prediction model is relatively<br />
more important than to choose a good algorithm, from<br />
this sense, the establishment of traffic flow prediction<br />
model is the most critical.<br />
TABLE I.<br />
NORMALIZATION OF RMSE COMPARISON<br />
Figure 8. The 4-step forecast result and real result<br />
prediction<br />
step<br />
BP<br />
network<br />
Volterra<br />
filter<br />
VNNTF<br />
network<br />
1 step 0.7014 0.3567 0.1368<br />
2 step 0.8074 0.3941 0.1507<br />
3 step 0.8653 0.4225 0.2322<br />
4 step 0.9799 0.4782 0.2417<br />
VI. CONCLUSIONS<br />
In the paper traffic flow chaotic time series VNNTF<br />
model was designed. A traffic flow VNNTF fast learn<strong>in</strong>g<br />
algorithm based on chaos theory was proposed. The<br />
method of model selection and algorithm design, are<br />
considered the chaotic characteristics of traffic flow time<br />
series, which is a theoretical value. Simulation results<br />
show that the method can reduce network tra<strong>in</strong><strong>in</strong>g time<br />
and improve the forecast accuracy, and show better<br />
predictive effectiveness and reliability.<br />
Figure 9. The 4-step forecast error curve<br />
Were calculated the error root mean square <strong>in</strong> Figure 5,<br />
7 and 9, and these results are compared with the error<br />
root mean square of the BP network and the wavelet<br />
neural network based on the non-chaotic algorithm, and<br />
the compare results are shown <strong>in</strong> Table 1. From Table 1,<br />
with the <strong>in</strong>creas<strong>in</strong>g number of prediction steps, <strong>in</strong> which<br />
the same prediction step, the root mean square of the<br />
wavelet neural network based on chaotic algorithm is<br />
significantly less than the root mean square of BP neural<br />
network and the wavelet neural network based on nonchaotic<br />
algorithm.<br />
Figure 4, 6 and 8, respectively, which corresponds to<br />
2-step, 3-step and 4-step predicted and actual comparison<br />
curves of VNNTF network based VNNTF network rapid<br />
learn<strong>in</strong>g algorithm; and “+” shows the true value, “o”<br />
shows the forecasted value Figure 3, 7, and 9 respectively,<br />
ACKNOWLEDGMENT<br />
This research is f<strong>in</strong>ancially supported by the National<br />
Natural Science Funds of Ch<strong>in</strong>a for Dist<strong>in</strong>guished Young<br />
Scholar under Grant (50925727), and the Fundamental<br />
Research Funds for the Central Universities, Hefei<br />
University of Technology for Professor He Yigang, the<br />
National Natural Science Foundation of Ch<strong>in</strong>a (NSFC)<br />
for Professor Xue-p<strong>in</strong>g Dong (No. 60974022) and the<br />
Universities Natural Science Foundation of Anhui<br />
Prov<strong>in</strong>ce (No.KJ2012A219) for Professor Y<strong>in</strong> Lisheng.<br />
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[13] Wei Si, Zhe-M<strong>in</strong> Duan, Hai-Tao Wang, “Novel Method<br />
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Systems with Applications, vol. 36: pp.6244-6255.2009.<br />
[16] Wu Jian-Da, Hsu Chuang-Ch<strong>in</strong>, Wu Guozhen. “Fault gear<br />
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[17] Lee Jong Jae, Kim Dookie, Chang Seong Kyu. “An<br />
improved application technique of the adaptive<br />
probabilistic neural network for predict<strong>in</strong>g concrete<br />
strength”, Computational Materials Science, vol. 44:<br />
pp.988-998, 2009.<br />
[18] Hu xiao-jian, wang wei, sheng hui. “Urban Traffic Flow<br />
Prediction with Variable Cell Transmission Model”,<br />
Journal of Transportation Systems Eng<strong>in</strong>eer<strong>in</strong>g and<br />
Information Technology, no. 4, pp.17-22, 2010.<br />
[19] A. Ya. Yakubov, “On nonl<strong>in</strong>ear Volterra equations of<br />
convolution type”, Differential Equations, 2009, 45, no. 9),<br />
pp.1326-1336.<br />
[20] Satoru Murakami, Pham Huu, Anh Ngoc, “On stability and<br />
robust stability of positive l<strong>in</strong>ear Volterra equations <strong>in</strong><br />
Banach lattices”, Central European Journal of Mathematics,<br />
vol. 8, no. 5, pp. 966-984, 2010.<br />
[21] Yu. V. Bibik, “The second Hamiltonian structure for a<br />
special case of the Lotka-Volterra equations”,<br />
Computational Mathematics and Mathematical Physics, ,<br />
vol. 47, no. 8, pp. 1285-1294, 2007.<br />
[22] Li-Sheng Y<strong>in</strong>, Xi-Yue Huang, Zu-Yuan Yang, et al,<br />
“Prediction for chaotic time series based on discrete<br />
Volterra neural networks”, Lect Notes Comput SC, vol.<br />
3972, pp. 759-764, 2006.<br />
Lisheng Y<strong>in</strong> (yls20000@163.com) received his doctor’s degree<br />
<strong>in</strong> Control Theory and Control Eng<strong>in</strong>eer<strong>in</strong>g from School of<br />
Automation, Chongq<strong>in</strong>g University, Chongq<strong>in</strong>g Ch<strong>in</strong>a. He is an<br />
associate professor <strong>in</strong> the School of Electrical and Automation<br />
Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of Technology.He conducts<br />
research <strong>in</strong> Modern <strong>in</strong>telligent algorithm, Chaos Theory, Neural<br />
network theory and Fuzzy Theory.<br />
Yigang He (hyghnu@yahoo.com.cn) received his doctor’s<br />
degree <strong>in</strong> Electrical Eng<strong>in</strong>eer<strong>in</strong>g from Electrical Eng<strong>in</strong>eer<strong>in</strong>g,<br />
Xi'an Jiaotong University, Xian Ch<strong>in</strong>a. He is a professor <strong>in</strong> the<br />
School of Electrical and Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei<br />
University of Technology. He conducts research <strong>in</strong> Electrical<br />
science and eng<strong>in</strong>eer<strong>in</strong>g, automatic test and diagnostic<br />
equipment, High-speed low-voltage low-power <strong>in</strong>tegrated<br />
circuits, systems, <strong>in</strong>telligent and real-time <strong>in</strong>formation<br />
process<strong>in</strong>g, Smart grid, electrical measurement techniques and<br />
Circuit theory of massive proportions and Mixed-signal system<br />
test<strong>in</strong>g and diagnosis<br />
Xuep<strong>in</strong>g Dong (hfdxp@126.com) received his doctor’s degree<br />
<strong>in</strong> Control Theory and Control Eng<strong>in</strong>eer<strong>in</strong>g from School of<br />
Automation, Nanj<strong>in</strong>g University Of Science and Technology,<br />
Nangj<strong>in</strong>g Ch<strong>in</strong>a. He is an associate professor <strong>in</strong> the School of<br />
Electrical and Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of<br />
Technology.He conducts research <strong>in</strong> Model<strong>in</strong>g and control of<br />
complex systems, Modern control theory and its application.<br />
Zhaoquan Lu (luzhquan@126.com) received his doctor’s<br />
degree from University of Science and Technology of Ch<strong>in</strong>a,<br />
Hefei Ch<strong>in</strong>a. He is a professor <strong>in</strong> the School of Electrical and<br />
Automation Eng<strong>in</strong>eer<strong>in</strong>g, Hefei University of Technology. He<br />
conducts research <strong>in</strong> Large time delay uncerta<strong>in</strong> process and<br />
control, complex systems and controls, <strong>in</strong>telligent control,<br />
wireless communication network and automation systems,<br />
automotive electronics technology research and development,<br />
energy-sav<strong>in</strong>g control system research and development.<br />
© 2013 ACADEMY PUBLISHER
1488 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Adaptive Track<strong>in</strong>g Control for Nonaff<strong>in</strong>e<br />
Nonl<strong>in</strong>ear Systems with Zero Dynamics<br />
Hui Hu<br />
Dept of Electrical and Information Eng<strong>in</strong>eer<strong>in</strong>g, Hunan Institute of Eng<strong>in</strong>eer<strong>in</strong>g, Hunan Xiangtan, Ch<strong>in</strong>a<br />
Email: onlymyhui@126.com<br />
Peng Guo<br />
Dept of Computer Science, Hunan Institute of Eng<strong>in</strong>eer<strong>in</strong>g, Hunan Xiangtan, Ch<strong>in</strong>a<br />
Email: da_peng219@126.com<br />
Abstract—A direct adaptive neural network track<strong>in</strong>g<br />
control scheme is presented for a class of nonaff<strong>in</strong>e<br />
nonl<strong>in</strong>ear systems with zero dynamics. The method does not<br />
assume boundedness on the time derivative of a control<br />
effectiveness term. Parameters <strong>in</strong> neural networks are<br />
updated us<strong>in</strong>g a gradient descent method which designed <strong>in</strong><br />
order to m<strong>in</strong>imize a quadratic cost function of the error<br />
between the unknown ideal implicit controller and the used<br />
neural networks controller. The f<strong>in</strong>al updated law is a<br />
nonl<strong>in</strong>ear function of output error. No robust control term<br />
is used <strong>in</strong> controller. The convergence of parameters and the<br />
uniformly ultimately bounded of track<strong>in</strong>g error and all<br />
states of the correspond<strong>in</strong>g closed-loop system are<br />
demonstrated by Lyapunov stability theorem.Simulation<br />
results illustrate the availability of this method.<br />
Index Terms—nonaff<strong>in</strong>e nonl<strong>in</strong>ear, neural network,<br />
track<strong>in</strong>g control, gradient descent method, zero dynamic<br />
I. INTRODUCTION<br />
Modern mechanical or electrical systems that are to be<br />
controlled become more and more complicated and, thus,<br />
their mathematical models are often hard to be<br />
established. In recent years, adaptive neural network [1, 2,<br />
3, 4, 7, 8, 9, 10, 12, 15] that model the functional<br />
mechanism of the human bra<strong>in</strong> and fuzzy logic control [5,<br />
6, 11, 13, 14, 16, 17, 18] that can cooperate with human<br />
expert knowledge have been successfully applied to many<br />
control problems because they need no accurate<br />
mathematical models of the system under control. These<br />
methodologies become especially more helpful if control<br />
of highly uncerta<strong>in</strong>, nonl<strong>in</strong>ear and complex systems is the<br />
design issue. The ma<strong>in</strong> philosophy that is exploited<br />
heavily <strong>in</strong> system theory applications is the universal<br />
function approximation property of neural networks or<br />
fuzzy logic. Benefits of us<strong>in</strong>g neural networks or fuzzy<br />
logic for control applications <strong>in</strong>clude its ability to<br />
effectively control nonl<strong>in</strong>ear plants while adapt<strong>in</strong>g to<br />
unmodeled dynamics.<br />
In fact, most of the works [1-4, 6, 9, 11, 12, 13, 15-18,<br />
22-25]are devoted to the control problem of the aff<strong>in</strong>e-<strong>in</strong>control<br />
nonl<strong>in</strong>ear systems, i.e., systems characterized by<br />
<strong>in</strong>puts appear<strong>in</strong>g l<strong>in</strong>early <strong>in</strong> the system state equation.<br />
Few results are available for nonaff<strong>in</strong>e nonl<strong>in</strong>ear systems<br />
where the control <strong>in</strong>put appears <strong>in</strong> a nonl<strong>in</strong>ear fashion [5,<br />
7, 8, 10, 14, 19, 21]. In general, a two-step procedure is<br />
taken <strong>in</strong> nonaff<strong>in</strong>e nonl<strong>in</strong>ear system. First, based on<br />
implicit function theorem an ideal controller is developed<br />
to stabilize the underly<strong>in</strong>g system and makes the track<strong>in</strong>g<br />
approach a neighborhood of zero. Then, a neural network<br />
or fuzzy logic to approximate this ideal controller is<br />
designed. Based on the Lyapunov stability analysis, an<br />
adaptation law is devised to update the adjustable<br />
parameters. However a bound<strong>in</strong>g controller may also be<br />
added for more performance robustness.<br />
In the above most methods the parameter adaptation<br />
laws are designed based on a Lyapunov approach, where<br />
an error signal between the desired output and the actual<br />
output is used to update the adjustable parameters and the<br />
control laws are composed of three control terms: a l<strong>in</strong>ear<br />
control term, an adaptive neural network control term and<br />
a robust control term used to compensate for disturbances<br />
and approximation errors. On the other hand, almost all<br />
of the above works don’t consider the zero dynamics,<br />
though it plays an important role <strong>in</strong> nonl<strong>in</strong>ear system<br />
control. Consider<strong>in</strong>g that zero dynamics exist <strong>in</strong> many<br />
practical systems, <strong>in</strong>clud<strong>in</strong>g isothermal cont<strong>in</strong>uous stirred<br />
tank reactors, aircraft trajectory track<strong>in</strong>g control systems<br />
and others, it is necessary to <strong>in</strong>vestigate their <strong>in</strong>fluence on<br />
nonl<strong>in</strong>ear system.<br />
In the paper, accord<strong>in</strong>g to [5], we <strong>in</strong>troduce a direct<br />
adaptive neural network control approach for a class of<br />
nonaff<strong>in</strong>e nonl<strong>in</strong>ear systems with zero dynamics. The<br />
basic idea is to use neural network to adaptively construct<br />
an unknown ideal controller and the parameter adaptive<br />
laws is designed, based on the gradient descent method,<br />
to directly m<strong>in</strong>imiz<strong>in</strong>g the error between the unknown<br />
ideal controller and the neural network controller And no<br />
robust control term is used <strong>in</strong> controller. This paper<br />
proves the availability of the method <strong>in</strong> both theory and<br />
simulation experiment.<br />
The paper is organized as follows. First, the problem is<br />
formulated <strong>in</strong> Section II. Zero dynamics is given <strong>in</strong> III.<br />
Design<strong>in</strong>g a control law with on-l<strong>in</strong>e tun<strong>in</strong>g of neural<br />
network weight<strong>in</strong>g factors is given <strong>in</strong> Section IV. In<br />
Section V, convergence and stability analysis of control<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1488-1495
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1489<br />
system is given. In Section VI, simulation results are<br />
presented to confirm the effectiveness and applicability of<br />
the proposed method. F<strong>in</strong>ally, conclusions are <strong>in</strong>cluded.<br />
A. Notations and Prelim<strong>in</strong>aries<br />
The follow<strong>in</strong>g notations and def<strong>in</strong>itions will<br />
extensively be used throughout the paper. Let be the<br />
real number, n<br />
n×<br />
m<br />
and represent the real n-vectors<br />
and the real n× m matrices, respectively. i denotes the<br />
usual Euclidean norm of a vector. In the case where y is<br />
a scalar, y denotes its absolute value and if Y is a<br />
matrix, Y means Frobenious norm def<strong>in</strong>ed as<br />
Y<br />
T<br />
{ }<br />
= tr Y Y .where tr{ i}<br />
stands for trace operator.<br />
Implicit Function Theorem: Assume that<br />
n m n<br />
h : × → is cont<strong>in</strong>uously differentiable at each<br />
n m<br />
ab of an open set S ⊂ × a , b be a<br />
po<strong>in</strong>t ( , )<br />
. Let ( 0 0)<br />
po<strong>in</strong>t <strong>in</strong> S for which ( , )<br />
h a b and for which the<br />
0 0<br />
Jacobian matrix ⎡∂h<br />
⎤( a , b )<br />
⎣<br />
∂a⎦<br />
0 0<br />
is nons<strong>in</strong>gular. Then<br />
n<br />
m<br />
there exist neighborhoods U ⊂ of a0<br />
and V ⊂ of<br />
b0<br />
such that for each b∈V<br />
the equation h( a, b ) = 0has a<br />
unique solution a∈<br />
U . Moreover, the solution can be<br />
given as a = g( b)<br />
where g is cont<strong>in</strong>uously differentiable<br />
at b= b0<br />
.<br />
II. PROBLEM FORMALATION<br />
Consider the follow<strong>in</strong>g SISO nonaff<strong>in</strong>e nonl<strong>in</strong>ear<br />
system [8]:<br />
where [ ]<br />
⎧ dξi<br />
⎪ = ξi+<br />
1<br />
i =1, , r−1<br />
dt<br />
⎪<br />
dξr<br />
⎪ = h( ξη , , u)<br />
⎨ dt<br />
⎪ dη<br />
⎪ = q(, ξη, u)<br />
⎪ dt<br />
⎪ ⎩ y = ξ1<br />
, ,<br />
T r<br />
ξ = ξ1 ξ r<br />
∈ Rξ<br />
⊂ ,<br />
(1)<br />
n−r<br />
η∈R η<br />
⊂ are<br />
system states and u ∈Ωu<br />
⊂ , y ∈ are system <strong>in</strong>put<br />
and output respectively. h(, ξη, u)<br />
is a smooth partially<br />
known function, and q(, ξη , u)<br />
is a smooth partially<br />
known vector field.<br />
The control objective is to design an adaptive neural<br />
network controller for a class of SISO nonaff<strong>in</strong>e<br />
nonl<strong>in</strong>ear systems (1) such that the system output follows<br />
a desired trajectory while all signals <strong>in</strong> the closed-loop<br />
system rema<strong>in</strong> bounded.<br />
∂h(, ξη, u)<br />
Assumption 1: The function hu<br />
(, ξη , u)<br />
=<br />
∂u<br />
is nonzero and bounded for all (, ξη, u) ∈ × ×<br />
R<br />
R<br />
.<br />
This implies that h (, ξη , u)<br />
is strictly either positive or<br />
u<br />
ξ<br />
η<br />
negative for all ( ξη , , u) ∈ × ×<br />
R<br />
R<br />
.Without loss of<br />
generality, it is assumed that it exists a constant c such<br />
that hu<br />
(, ξη , u) ≥ c > 0.<br />
Def<strong>in</strong>e the reference vector<br />
( r−1)<br />
T r<br />
y = ( y y y ) ∈R<br />
ξ<br />
d d d d<br />
The reference signal y d<br />
and its time derivative are<br />
assumed to be smooth and bounded. We also def<strong>in</strong>e the<br />
track<strong>in</strong>g error as<br />
e= yd<br />
− y<br />
and correspond<strong>in</strong>g error vector as<br />
( r−1)<br />
T r<br />
e = (,, e e e ) ∈ R .<br />
Assumption 2: When the desired output y d<br />
and its r-<br />
order derivative are of known bound, there exists a<br />
positive constant bd<br />
to satisfy<br />
(1) ( r−1)<br />
T<br />
( yd yd yd ) ≤ bd<br />
Then the error equation is as follows:<br />
η<br />
(2)<br />
( r)<br />
e = A0 e + b⎡<br />
⎣yd<br />
−h(, ξη, u)<br />
⎤<br />
⎦ (3)<br />
⎡ 0 1 0 0⎤<br />
⎡0⎤<br />
⎢<br />
0 0 1 0<br />
⎥<br />
⎢<br />
<br />
⎢<br />
⎥<br />
0<br />
⎥<br />
⎢ ⎥<br />
where A0<br />
= ⎢ ⎥<br />
, b = ⎢0⎥<br />
.<br />
⎢ ⎥<br />
⎢ ⎥<br />
⎢ 0 0 0 1⎥<br />
⎢<br />
⎥<br />
⎢<br />
⎣ 0 0 0 0 0⎥<br />
⎦<br />
⎢<br />
r × r ⎣1⎥<br />
⎦ r × 1<br />
A b is controllable, then there will exist a<br />
Obviously, ( , 0 )<br />
constant matrix [ , , ]<br />
T<br />
0 1 r 1<br />
T<br />
c<br />
K = k k k −<br />
which makes<br />
eigenvalues of matrix A = A0<br />
− bK all have negative<br />
real part. Thus, for any given positive def<strong>in</strong>ite symmetric<br />
matrix Q , there exists a unique positive def<strong>in</strong>ite<br />
symmetric solution P to the follow<strong>in</strong>g Lyapunov<br />
algebraic equation:<br />
A P+ PA = − Q<br />
(4)<br />
T<br />
c<br />
Def<strong>in</strong>e a signal<br />
T<br />
( r)<br />
T<br />
⎛b Pe ⎞<br />
ν= yd<br />
+ K e + λtanh⎜ ⎟<br />
⎝ Ξ ⎠<br />
where tanh( •) ∈− ( 1,1) is the hyperbolic tangent function,<br />
Ξ,λ<br />
are the positive design parameters, when error<br />
T<br />
⎛bPe⎞ e →+<br />
∞ , the value of tanh ⎜ ⎟ → + ∞ , and when<br />
⎝ Ξ ⎠<br />
T<br />
⎛b Pe ⎞<br />
error e →-∞ the value of tanh ⎜ ⎟ → - ∞ .<br />
⎝ Ξ ⎠<br />
T<br />
⎛b Pe ⎞<br />
When e → 0 , tanh ⎜ ⎟ → 0 .The term<br />
⎝ Ξ ⎠<br />
T<br />
⎛b Pe ⎞<br />
λ tanh ⎜ ⎟ is a smooth approximation of the<br />
⎝ Ξ ⎠<br />
T<br />
discont<strong>in</strong>uous term sign( b Pe )<br />
c<br />
λ usually used <strong>in</strong> robust<br />
© 2013 ACADEMY PUBLISHER
1490 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
control. So, λ is selected larger than the magnitude of the<br />
uncerta<strong>in</strong>ty and it will affect the convergence rate of the<br />
track<strong>in</strong>g error, and Ξ is chosen very small to best<br />
approximate the sign function and it will affect the size<br />
of the residual set to which the track<strong>in</strong>g error will<br />
converge. The sign function is not used here to avoid<br />
problems associated with it as chatter<strong>in</strong>g and solutions<br />
existence.<br />
By add<strong>in</strong>g and subtract<strong>in</strong>g ν <strong>in</strong> (3), we obta<strong>in</strong><br />
T<br />
T<br />
bPe<br />
e ⎛ ⎞<br />
= ( A0 −bK ) e −bλ<br />
tanh ⎜ ⎟−b[ h( ξη , , u)<br />
−v]<br />
(5)<br />
⎝ Ξ ⎠<br />
From the fact that the signal v does not explicitly<br />
depend upon the control <strong>in</strong>put u and Assumption 1, the<br />
partial derivative of h(, ξη , u)<br />
− v with respect to the<br />
<strong>in</strong>put u satisfies<br />
( ξη )<br />
∂ h(, , u) −v ∂h(, ξη, u)<br />
= > 0<br />
∂u<br />
∂u<br />
Thus accord<strong>in</strong>g to the implicit function theorem, there<br />
exists some ideal controller u * ( ξην , , ) satisfy<strong>in</strong>g the<br />
follow<strong>in</strong>g equality for all (, ξη,) v ∈ × ×<br />
R<br />
R<br />
:<br />
ξ<br />
η<br />
(6)<br />
*<br />
h(, ξη, u (, ξη ,)) v − v = 0<br />
(7)<br />
Therefore, if the control <strong>in</strong>put u is chosen as the ideal<br />
controller u<br />
* (, ξη ,) v , the closed-loop error dynamic (5) is<br />
reduced to<br />
T<br />
T<br />
b Pe<br />
e ⎛ ⎞<br />
= ( A0 −bK ) e −bλ<br />
tanh ⎜ ⎟ (8)<br />
⎝ Ξ ⎠<br />
Consider<strong>in</strong>g the follow<strong>in</strong>g positive function to the<br />
error dynamic:<br />
V<br />
T<br />
= e Pe<br />
(9)<br />
Us<strong>in</strong>g (4) and (8), the time derivative of (9) becomes<br />
T<br />
T T b Pe<br />
V ⎛ ⎞<br />
=−e Qe −2λb Pe tanh⎜ ⎟ (10)<br />
⎝ Ξ ⎠<br />
T<br />
⎛b Pe ⎞<br />
Because the term b T Pe and tanh ⎜ ⎟ always<br />
⎝ Ξ ⎠<br />
have same sign, we conclude that V<br />
≤ 0 , and only<br />
when e = 0 , V = 0 , which means lim | e | = 0 .<br />
t→∞<br />
III. ZERO DYNAMICS<br />
If system (1) is controlled by the <strong>in</strong>put u, the state<br />
vector η is completely unobservable from the output,<br />
then the subsystem<br />
dη<br />
q(0, , u(0, , v(0, )))<br />
dt = η η η (11)<br />
is addressed as the zero dynamic.<br />
Assumption 3: Zero dynamics (11) is exponentially<br />
stable, and the function q( ξη , , u)<br />
is Lipschitz <strong>in</strong>ξ . There<br />
exists Lipschitz constants L ξ<br />
and L<br />
q<br />
such that<br />
q(, ξη, u) − q(0, η, u ≤ L ξ + Lq<br />
(12)<br />
where u = u(0, η η<br />
, v(0, η ))) .<br />
By Lyapunov converse theorem, there is a Lyapunov<br />
function V ( ) 0<br />
η which satisfies<br />
η<br />
2 2<br />
1<br />
V0( )<br />
2<br />
ξ<br />
σ η ≤ η ≤ σ η (13)<br />
∂V0<br />
( η)<br />
q(0, η)<br />
≤−σ3<br />
η<br />
∂η<br />
∂V ( η)<br />
0<br />
∂η<br />
≤ σ<br />
Where σ , i = 1,2,3,4 are positive constant.<br />
i<br />
4<br />
η<br />
IV. DESIGN OF CONTROLLER<br />
2<br />
(14)<br />
(15)<br />
In control eng<strong>in</strong>eer<strong>in</strong>g, radial basis function (RBF)<br />
NNs are usually used as a tool for model<strong>in</strong>g nonl<strong>in</strong>ear<br />
functions because of their good capabilities <strong>in</strong> function<br />
approximation. RBFNN represents a class of l<strong>in</strong>early<br />
parameterized approximations and can be replaced by any<br />
other l<strong>in</strong>early parameterized approximations such as<br />
spl<strong>in</strong>e functions or fuzzy systems. Moreover, nonl<strong>in</strong>early<br />
parameterized approximations, such as multilayer neural<br />
network (MNN), can be l<strong>in</strong>earized as l<strong>in</strong>early<br />
parameterized approximations, with the higher order<br />
terms of Taylor series expansions be<strong>in</strong>g taken as part of<br />
the model<strong>in</strong>g error.<br />
In this paper, the follow<strong>in</strong>g RBF NN based on GGAP-<br />
RBF [20] algorithm which can avoid to select <strong>in</strong>itial<br />
neural network parameters and nodes number of hidden<br />
T<br />
layer artificially uz ( ) = φ ( z)<br />
θ is used to approximate<br />
the ideal controller<br />
1<br />
* T T<br />
u ( z ) , where z = ⎡ ⎣ ξ , η , v⎤<br />
⎦ ,<br />
φ( z) = ( φ ( z), , φ ( z)) T is the basic function vector, and<br />
M<br />
θ = ( θ1, , θ ) T<br />
M<br />
is the adjustable parameter. It has been<br />
proven that neural network can approximate any smooth<br />
q<br />
function over a compact set ΩZ<br />
⊂ R to arbitrarily any<br />
accuracy as<br />
( ) = φ ( ) θ + δ( ) (16)<br />
* T *<br />
u z z z<br />
with bounded function approximation error δ ( z)<br />
satisfy<strong>in</strong>g δ ( z)<br />
≤ δ .Where<br />
vector which m<strong>in</strong>imizes the function δ ( z)<br />
*<br />
θ is an ideal parameter<br />
T<br />
. In this paper,<br />
we assume that the used neural network does not violate<br />
the universal approximation property on the compact set<br />
Ω<br />
Z<br />
, which is assumed large enough so that the variable<br />
z rema<strong>in</strong>s <strong>in</strong>side it under closed-loop control.<br />
Let us def<strong>in</strong>e the control error between the controllers<br />
uz ( ) and u<br />
* ( z ) as<br />
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* T<br />
e = u ( z) − u( z) = φ ( z) θ + δ( z)<br />
(17)<br />
u<br />
*<br />
where θ = θ −θ<br />
is the parameter estimation error vector.<br />
Accord<strong>in</strong>g to the mean value theorem, there exist<br />
constant 0< α < 1, h(, ξη , u)<br />
can be described as<br />
( )<br />
h ξηu h ξη u h u z u z (18)<br />
* *<br />
(, , ) = (, , ) +<br />
u<br />
() − ()<br />
λ<br />
where<br />
h =∂h(, ξη , u) ∂u|<br />
uλ<br />
u=<br />
uλ<br />
uλ = αu z + − α u z<br />
*<br />
( ) (1 ) ( )<br />
By substitut<strong>in</strong>g (5) <strong>in</strong>to the equation (18) and consider<strong>in</strong>g<br />
(7), we get<br />
T<br />
bPe<br />
*<br />
e<br />
⎛ ⎞<br />
= Ac<br />
e −bλtanh ⎜ ⎟−b⎡<br />
⎣h( ξη , , u ) −ν⎤<br />
⎦−<br />
⎝ Ξ ⎠<br />
*<br />
−bhu<br />
( u( z) −u ( z)<br />
)<br />
(19)<br />
λ<br />
T<br />
⎛bPe⎞<br />
*<br />
= Ae c −bλ<br />
tanh ⎜ ⎟−bhu<br />
( u( z) −u ( z)<br />
)<br />
λ<br />
⎝ Ξ ⎠<br />
T<br />
Consider<strong>in</strong>g Ac<br />
= A0<br />
− bK , then (19) can be rewritten as<br />
T<br />
( r) T ⎛bPe⎞<br />
*<br />
e + K e + λ tanh ⎜ ⎟ = h ( u ( z) − u( z)<br />
u ) = h e (20)<br />
λ<br />
uλ<br />
u<br />
⎝ Ξ ⎠<br />
We notice here that u<br />
* ( z)<br />
is an unknown quantity, so<br />
the signal e u<br />
def<strong>in</strong>ed <strong>in</strong> (17) is not available. Eq. (20) will<br />
be used to overcome the difficulty. Indeed, from (20), we<br />
see that even if the signal e is not available for<br />
measurement, the quantity h uλ<br />
e u<br />
is measureable. This fact<br />
will be exploited <strong>in</strong> the design of the parameters adaptive<br />
law.<br />
In order to obta<strong>in</strong> the update law ofθ , we consider a<br />
quadratic cost function def<strong>in</strong>ed as<br />
u<br />
1 2 1 * T<br />
J ( ( ) ( ) ) 2<br />
θ<br />
= eu<br />
= u z − φ z θ (21)<br />
2 2<br />
By apply<strong>in</strong>g the gradient descent method, we obta<strong>in</strong> as an<br />
adaptive law for the parameters θ<br />
θ = - γ∇ θ<br />
J ( θ) = γφ( ze ) u<br />
(22)<br />
From (22), we know e u is not available, the adaptive<br />
law (22) cannot be implemented. In order to render (22)<br />
computable, from Eq. (20), we select the design<br />
parameter γ = γ θ<br />
hu<br />
λ<br />
, where γ<br />
θ<br />
is a positive constant. We<br />
have<br />
θ = γ φ( zh ) e<br />
θ<br />
γφ<br />
⎧⎪<br />
uλ<br />
u<br />
λ<br />
( r)<br />
T<br />
=<br />
θ<br />
( z) ⎨e + K e + tanh<br />
⎪⎩<br />
⎛<br />
⎜<br />
⎝<br />
T<br />
bPe<br />
Ξ<br />
⎞⎫⎪<br />
⎟⎬<br />
⎠⎪⎭<br />
(23)<br />
At the same time, <strong>in</strong> order to improve the robustness of<br />
adaptive law <strong>in</strong> the presence of the approximation error,<br />
we modify it by <strong>in</strong>troduc<strong>in</strong>g a σ -modification term as<br />
follows:<br />
T<br />
<br />
⎧⎪<br />
( r)<br />
T<br />
⎛b Pe ⎞⎫⎪<br />
θ = γθφ( z) ⎨e + K e + λ tanh⎜<br />
⎟⎬−γ θσθ<br />
(24)<br />
⎪⎩<br />
⎝ Ξ ⎠⎪⎭<br />
whereσ is a small positive constant<br />
S<strong>in</strong>ce the function of the σ -modification adaptive law<br />
is to avoid parameter drift, it does not need to be active<br />
when the estimated parameters are with<strong>in</strong> some<br />
acceptable bound. The system stability relies entirely on<br />
the neural network because the proposed adaptive<br />
controller <strong>in</strong> the paper is only composed of a neural<br />
network part without additional control terms. The term<br />
T<br />
⎛b Pe ⎞<br />
λ tanh ⎜ ⎟<strong>in</strong> the parameter adaptive law (24) plays,<br />
⎝ Ξ ⎠<br />
<strong>in</strong> some way, the role of a robustify<strong>in</strong>g control term. Thus<br />
by select<strong>in</strong>g a large positive value for the design<br />
parameter λ and a small positive value for the<br />
parameter Ξ , the robustness of the controller can be<br />
improved.<br />
V. STABILITY AND CONVERGENCE ANALYSIS OF<br />
CONTROL SYSTEM<br />
In order to analysis the convergence of neural network<br />
weights, we firstly consider the follow<strong>in</strong>g positive<br />
function:<br />
V θ<br />
1<br />
= T<br />
θ θ<br />
(25)<br />
2 γ<br />
Us<strong>in</strong>g (17), (20) and (24), the time derivative of (25)<br />
can be written as<br />
Consider<strong>in</strong>g the <strong>in</strong>equalities<br />
θ<br />
( z hu<br />
eu<br />
)<br />
T<br />
V<br />
θ<br />
= - θ φ( ) -σθ<br />
λ<br />
T<br />
T<br />
= - φ ( z)<br />
θhu<br />
e<br />
λ u<br />
+ σθ<br />
θ<br />
T<br />
=− h e + h δ ( z)<br />
e + σθ<br />
θ<br />
2<br />
uλ<br />
u uλ<br />
u<br />
T σ σ σ<br />
σθ θ =− θ − θ + θ + θ<br />
2 2 2<br />
σ 2 σ *<br />
2<br />
≤− θ + θ<br />
2 2<br />
2 2<br />
2<br />
(26)<br />
(27)<br />
2 1 2 1 2 1<br />
− e ( ) ( ) ( ( )) 2<br />
u<br />
+ δ z eu = − eu + δ z − eu<br />
−δ<br />
z<br />
2 2 2<br />
(28)<br />
1 2 1 2<br />
≤− eu<br />
+ δ ( z))<br />
2 2<br />
Consider<strong>in</strong>g (27) and (28), Eq. (26) can be bounded as<br />
1 2<br />
2 1 2 *<br />
2<br />
V σ σ<br />
θ<br />
≤− hu eu + hu<br />
δ ( z)<br />
− θ + θ (29)<br />
λ<br />
λ<br />
2 2 2 2<br />
Because the functions δ ( z)<br />
and hu<br />
λ<br />
are bounded <strong>in</strong> this<br />
paper, and the parameters θ * are constants, so we can<br />
def<strong>in</strong>e a positive constant bound ψ as<br />
⎛1<br />
2 ⎞ σ *<br />
2<br />
ψ = sup ⎜ hu<br />
δ ( z)<br />
θ<br />
λ ⎟+<br />
(30)<br />
t ⎝2 ⎠ 2<br />
Then<br />
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1492 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
V 1 1<br />
2 V 2 h e<br />
θ<br />
≤− ρ<br />
θ<br />
+ ψ −<br />
u λ u<br />
≤− ρV<br />
+ ψ<br />
θ<br />
2<br />
(31)<br />
where ρ = σγ<br />
θ<br />
Eq. (31) implies that for V<br />
ψ<br />
θ<br />
> , V<br />
0 ρ θ<br />
<<br />
and, therefore, θ is bounded. By <strong>in</strong>tegrat<strong>in</strong>g (31), we can<br />
establish that:<br />
From (32), we have<br />
ψ<br />
θ θ γ<br />
ρ<br />
2 2<br />
− t<br />
≤ (0) e ρ + 2<br />
θ<br />
(32)<br />
(33)<br />
−0.5ρt<br />
θ ≤ θ(0) e + 2γθψ ρ<br />
Us<strong>in</strong>g (33) and the fact that δ ( z)<br />
and hu<br />
λ<br />
are bounded,<br />
we can write<br />
T<br />
(<br />
+ )<br />
βξη ( , ) hu<br />
φ ( z) θ δ( z)<br />
λ<br />
T<br />
≤ βξη ( , ) hu<br />
φ ( z) θ+ βξη ( , ) hu<br />
δ( z)<br />
λ<br />
λ<br />
T<br />
≤ βξη ( , ) h φ ( z) θ + <br />
uλ<br />
+ βξη ( , ) h δ( z)<br />
uλ<br />
−0.<br />
5ρt<br />
T<br />
≤ βξη ( , ) h φ ( z) θ(0)<br />
e<br />
uλ<br />
T<br />
+ βξη ( , ) h φ ( z) 2 γψ ρ+<br />
<br />
uλ<br />
+ βξη ( , ) h δ( z)<br />
uλ<br />
≤ ψ e + ψ<br />
−0.5ρt<br />
0 1<br />
θ<br />
(34)<br />
+ <br />
Where ψ<br />
0,<br />
ψ<br />
1<br />
are some f<strong>in</strong>ite positive constants.<br />
Lemma 1: The follow<strong>in</strong>g <strong>in</strong>equality holds for all<br />
Ξ> 0 and ς ∈ R with K = 0.2785 .<br />
c<br />
⎛ς<br />
⎞<br />
0≤ ς −ς<br />
⋅tanh⎜<br />
⎟≤ KcΞ<br />
⎝Ξ<br />
⎠<br />
(35)<br />
Theorem 1: Suppose that Assumption1-3 are satisfied<br />
for the system (1), then the neural network controller and<br />
adaptation law given by (24) guarantees the convergence<br />
of the neural network parameters and to be uniformly<br />
ultimately bounded of all the signal <strong>in</strong> the closed-loop<br />
system.<br />
Proof: Consider the Lyapunov function candidate:<br />
V( e, η) = e T Pe +μV<br />
( η ) (36)<br />
Where μ > 0 is the design parameter. Consider<strong>in</strong>g (4),<br />
(19), (20), (34) and lemma 1, differentiat<strong>in</strong>g V( e, η ) with<br />
respect to time, we obta<strong>in</strong><br />
0<br />
T<br />
T T T bPe<br />
Ve <br />
⎛ ⎞<br />
(,) η = e ( Ac<br />
P+ PAc)<br />
e− 2bPeλ<br />
tanh⎜<br />
⎟+<br />
<br />
⎝ Ξ ⎠<br />
T * dV0<br />
() η<br />
+2 bPehu<br />
( u− u)<br />
+ μ<br />
λ<br />
dt<br />
T<br />
T T<br />
⎛bPe⎞<br />
dV0<br />
() η<br />
=−eQe− 2bPeλtanh<br />
⎜ ⎟+ μ + <br />
⎝ Ξ ⎠ dt<br />
T<br />
( φ θ+<br />
δ )<br />
T<br />
+2 bPeh ( z) ( z)<br />
uλ<br />
T<br />
T T<br />
⎛bPe⎞ dV0<br />
() η<br />
≤−eQe−2 bPeλ<br />
tan h⎜<br />
⎟ ++ μ + <br />
⎝ Ξ ⎠ dt<br />
T<br />
−0.5<br />
t<br />
+ 2 bPe ψ e ρ + ψ<br />
( 0 1)<br />
(37)<br />
If the design parameter λ is large enough to make<br />
λ ≥ ψ 1<br />
and consider<strong>in</strong>g assumption 4, we have<br />
<br />
T T −0.5ρt<br />
Ve ( , η) eQe 2 bPeψ<br />
e +2ψ<br />
K<br />
0 1 c<br />
≤− + Ξ+ <br />
<br />
∂V<br />
( η)<br />
[ q(0, η, u ) q( ξ, η, u) q(0, η, u )<br />
η<br />
η<br />
]<br />
0<br />
+ μ<br />
+ −<br />
∂η<br />
T<br />
2<br />
e Qe μσ<br />
3<br />
μσ<br />
4Lξ<br />
μσ<br />
4Lq<br />
≤ − − η + ξ η + η + <br />
(38)<br />
T<br />
+ 2 b Pe ψ e + 2ψ<br />
K Ξ<br />
Then<br />
−0.5ρt<br />
0 1<br />
Consider<strong>in</strong>g assumption 2 and<br />
c<br />
T −0.5ρt 2 T<br />
2<br />
2 −ρt<br />
ψ0 ≤ + ψ0<br />
2 b Pe e 0.5 e 2 b P e<br />
ξ ≤ e + y y y ≤ e + b<br />
(1) ( r−1)<br />
T<br />
(<br />
d d<br />
<br />
d<br />
)<br />
d<br />
( λ )<br />
Ve ( , η) ≤- ( Q) −0.5<br />
e − + <br />
Us<strong>in</strong>g the <strong>in</strong>equality<br />
2 2<br />
m<strong>in</strong><br />
μσ3<br />
η<br />
+ μσ L e η + μσ L b η + <br />
4 ξ<br />
4<br />
ξ d<br />
T<br />
2<br />
2 −ρt<br />
4 q<br />
η<br />
0 1 c<br />
+ μσ L + 2 b P ψ e + 2ψ<br />
K Ξ<br />
4 ξ 4 ξ 1 4 ξ<br />
2 2ε1<br />
(39)<br />
1 2 1<br />
2<br />
μσ L e η ≤ μσ L ε η + μσ L e (40)<br />
μσ<br />
( ) ( ( )) 2 2<br />
Lb<br />
ξ d<br />
Lq μσ ε Lb<br />
ξ d<br />
Lq<br />
1<br />
+ η ≤ + η + (41)<br />
4 4 2 2<br />
4ε<br />
2<br />
Then (39) satisfies<br />
V<br />
( e, η)<br />
⎛<br />
1 ⎞ 2<br />
≤- ⎜λm<strong>in</strong> ( Q) −0.5− μσ4Lξ<br />
⎟ e + <br />
⎝<br />
2 ε1<br />
⎠<br />
⎡ 1<br />
2<br />
⎤ 2<br />
−μ⎢σ3 − σ4Lξε1 − μ( σ4ε2( Lξbd<br />
+ Lq)<br />
)<br />
2<br />
⎥ η +<br />
⎣<br />
⎦<br />
T<br />
2<br />
1<br />
+ 2 bP ψ e + 2ψ<br />
KΞ+<br />
2 −ρt<br />
0 1 c 2<br />
4ε<br />
2<br />
(42)<br />
where ε1,<br />
ε<br />
2<br />
are suitable positive constants. We<br />
adjust ε1,<br />
ε<br />
2<br />
to<br />
1<br />
make σ ( ( )) 2<br />
3<br />
σ4Lξε1 μ σ4ε2<br />
Lξbd<br />
Lq<br />
− − + > 0 .<br />
2<br />
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Suppos<strong>in</strong>g<br />
select<strong>in</strong>g μ =<br />
1<br />
T<br />
2<br />
2 −ρt<br />
ε = + 2 bP ψ0e + 2ψ1K c<br />
Ξ , and<br />
4ε<br />
2<br />
2<br />
1⎛<br />
1 ⎞<br />
⎜σ 3<br />
− σ4Lξ<br />
ε1⎟<br />
2⎝<br />
2 ⎠<br />
, then<br />
( σε<br />
4 2( Lb<br />
ξ d<br />
+ Lq)<br />
)<br />
1<br />
2<br />
V<br />
⎛<br />
⎞<br />
( e, η) ≤−⎜λm<strong>in</strong> ( Q) −0.5− μσ4Lξ<br />
⎟ e + <br />
⎝<br />
2 ε1<br />
⎠<br />
Adjust<strong>in</strong>g Q to make<br />
⎛ 1 ⎞<br />
3 4 1<br />
1<br />
⎜σ − σ Lξ<br />
ε ⎟<br />
2<br />
2<br />
−<br />
⎝<br />
⎠<br />
η + ε<br />
2<br />
4<br />
( σε<br />
4 2( Lb<br />
ξ d<br />
+ Lq)<br />
)<br />
1<br />
λ ( ) −0.5− μσ > 0.<br />
m<strong>in</strong><br />
Q<br />
4L ξ<br />
2ε1<br />
2<br />
2<br />
(43)<br />
From the above equation, we can know that track<strong>in</strong>g<br />
error and <strong>in</strong>ternal states η are all uniformly ultimately<br />
bounded.<br />
Besides,<br />
s<strong>in</strong>ce ξ ≤ e + y y y ≤ e + b , then<br />
(1) ( r−1)<br />
T<br />
(<br />
d d<br />
<br />
d<br />
)<br />
d<br />
the state ξ is uniformly ultimately bounded too. This<br />
completes the proof.<br />
VI. SIMULATION RESULTS<br />
In this part, the follow<strong>in</strong>g SISO nonaff<strong>in</strong>e nonl<strong>in</strong>ear<br />
system with zero dynamics is simulated to illustrate the<br />
effectiveness of the proposed adaptive neural network<br />
track<strong>in</strong>g controller. The nonaff<strong>in</strong>e nonl<strong>in</strong>ear system is<br />
described as follows:<br />
ξ = ξ<br />
1 2<br />
2<br />
(( ) )( )<br />
ξ =−2 ξ −η −1 ξ −η −η − 0.2η<br />
+ <br />
2 1 1 2 2 1 2<br />
⎡ 1 3 ⎤<br />
+ ( 2 + s<strong>in</strong> ([ ξ1−η1][ ξ2 − η2]<br />
))<br />
⎢u+ u + s<strong>in</strong>( u)<br />
3 ⎥ (44)<br />
⎣<br />
⎦<br />
η1 = η2<br />
η =−2η − 0.2η + ξ<br />
2 1 2 1<br />
y = ξ<br />
1<br />
The control objective is to force the system output y<br />
to track the desired trajectory yd<br />
= 2s<strong>in</strong>t+ cos ( 0.5t).The<br />
simulation parameters are selected as follows:<br />
15 5<br />
Q = diag[10,10] , P = ⎡ ⎤<br />
⎢<br />
5 5 ⎥ , K = [ 1, 2]<br />
T<br />
, Ξ = 0.01 ,<br />
⎣ ⎦<br />
λ = 10 , γ = 11 , σ = 0.02 .<br />
θ<br />
T<br />
The output of RBFNN controller is uz ( ) = φ ( z)<br />
θ . The<br />
basis function vector is φ( z) = ( φ1<br />
( z) φ ( )) T<br />
M<br />
z , where<br />
T<br />
( z μ ) ( z μ )<br />
⎡− −<br />
i<br />
− ⎤<br />
i<br />
φi<br />
( z) = exp ⎢<br />
⎥, i = 1, , M . M is the<br />
2<br />
⎢⎣<br />
σ<br />
i ⎥⎦<br />
number of hidden layer nodes which is stable at the 33<br />
nodes by tra<strong>in</strong><strong>in</strong>g on-l<strong>in</strong>e us<strong>in</strong>g the GGAP-RBF<br />
algorithm.<br />
Accord<strong>in</strong>g to (23), the control law is<br />
T<br />
uz ( ) = φ ( z)<br />
θ<br />
θ =− 11 φ( z) e + e+ 2e + 10 tanh 100 × (5e+<br />
5 e<br />
)<br />
− 11×<br />
0.02θ<br />
{ ( )}<br />
The system <strong>in</strong>itial conditions are ξ = [ ]<br />
(0) 1 2 T<br />
.The<br />
simulation results us<strong>in</strong>g MATLAB are shown <strong>in</strong> Fig1, 2,<br />
3, 4.<br />
Figure 1. Plots of output track<strong>in</strong>g of system<br />
Figure 1 shows the result of output track<strong>in</strong>g, and the<br />
control <strong>in</strong>put signal is shown <strong>in</strong> Figure 2. The grow<strong>in</strong>g<br />
and prun<strong>in</strong>g automatically of hidden layer nodes are<br />
shown <strong>in</strong> Figure 3.<br />
Figure 2. Plots of Control <strong>in</strong>put<br />
Figure 3. Node Number of Hidden Layer<br />
© 2013 ACADEMY PUBLISHER
1494 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 4. Norm of the weight vector θ<br />
Figure 4 shows the weights is always bounded <strong>in</strong><br />
whole control process though the structure and<br />
parameters of neural network is adjusted on l<strong>in</strong>e. It can be<br />
seen that the actual trajectories converge rapidly to the<br />
desired ones. The computer simulation results show that<br />
the adaptive neural network controller can perform<br />
successful control and achieve desired performance.<br />
VII. CONCLUSIONS<br />
A new adaptive neural network track<strong>in</strong>g control<br />
algorithm is presented for a class of SISO nonaff<strong>in</strong>e<br />
nonl<strong>in</strong>ear systems with zero dynamics <strong>in</strong> this paper. The<br />
method does not assume boundedness on the time<br />
derivative of a control effectiveness term, and only need<br />
sign known and boundedness of the control effectiveness<br />
term. The update law of neural network adjustable<br />
parameters is obta<strong>in</strong>ed by the gradient descent algorithm.<br />
The overall adaptive scheme guarantees that all signals<br />
<strong>in</strong>volved are uniformly ultimately bounded and the output<br />
of the closed-loop system tracks the desired output<br />
trajectory. Simulation results demonstrate the feasibility<br />
of the proposed control scheme.<br />
ACKNOWLEDGMENT<br />
It is a project supported by Prov<strong>in</strong>cial Natural Science<br />
Foundation of Hunan, Ch<strong>in</strong>a (Grant No.09JJ3094), the<br />
Research Foundation of Education Bureau of Hunan<br />
Prov<strong>in</strong>ce, Ch<strong>in</strong>a (Grant No.09B022), the Great Item of<br />
United Prov<strong>in</strong>ces Natural Science Foundation of Hunan,<br />
Ch<strong>in</strong>a (Grant No.09JJ8006), the Planned Science and<br />
Technology Project of Hunan Prov<strong>in</strong>ce, Ch<strong>in</strong>a (Grant<br />
No.2011FJ3126). Supported by the Construct Program of<br />
the Key Discipl<strong>in</strong>e <strong>in</strong> Hunan Prov<strong>in</strong>ce: Control Science<br />
and Eng<strong>in</strong>eer<strong>in</strong>g Science and Technology Innovation<br />
Team of Hunan Prov<strong>in</strong>ce: Complex Network Control.<br />
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[9] Hu H, Liu G R, Liu D B, Guo P, “Output feedback<br />
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[10] Ge S S, Zhang J, “Neural-network control of nonaff<strong>in</strong>e<br />
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[11] Qiu J B, Feng G, Gao H J, “Asynchronous Outputfeedback<br />
control of network nonl<strong>in</strong>ear systems with<br />
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[12] L<strong>in</strong> C.M, Chen T.Y, “Self-organiz<strong>in</strong>g CMAC control for a<br />
class of MIMO uncerta<strong>in</strong> nonl<strong>in</strong>ear systems”,.IEEE<br />
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[13] S. Blazic, I. Skrjanc, D. Matko, “Globally stable direct<br />
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[14] Wang W Y, Chien Y S, Lee T T., “Observer-based T-S<br />
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[15] Jianm<strong>in</strong>g Lian, Yonggon Lee, Stanislaw H. Zak, “Variable<br />
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IEEE Transactions on Automatic Control, vol. 53, 11, pp.<br />
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[16] S.Labiod, M.S.Boucherit, “Direct stable fuzzy adaptive<br />
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[17] N. Golea, A. Golea, K. benmahammed, “Stable <strong>in</strong>direct<br />
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[18] J<strong>in</strong>peng Yu, B<strong>in</strong>g Chen, Haisheng Yu, “Position track<strong>in</strong>g<br />
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[19] Karimi B. Menhaj M B, Karimi G M, Saboori I,<br />
“Decentralized adaptive control of large-scale aff<strong>in</strong>e and<br />
nonaff<strong>in</strong>e nonl<strong>in</strong>ear systems”, IEEE Transactions on<br />
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[20] Huang G B, Saratchandran, Sundararajan N, “A<br />
Generalized Grow<strong>in</strong>g and Prun<strong>in</strong>g RBF (GGP-RBF)<br />
Neural Network for Function Approximation”, IEEE<br />
Transactions on Neural Networks, vol. 16, pp. 57-67, 2005<br />
[21] J.-H. Park, G.-T. Park, S.-H. Kim, C.-J. Moon, “Direct<br />
adaptive self-structur<strong>in</strong>g fuzzy controller for nonaff<strong>in</strong>e<br />
nonl<strong>in</strong>ear systems”, Fuzzy sets and systems, vol. 153, pp.<br />
429-445, 2005.<br />
[22] J.-H. Park, S.-H. Kim, C.-J. Moon, “Adaptive neural<br />
control for strict-feedback nonl<strong>in</strong>ear systems without<br />
backstepp<strong>in</strong>g”, IEEE Transactions on Neural Networks,<br />
vol. 20, 7, pp. 1204-1209, 2009.<br />
[23] H.-X, Li, S.C. Tong, “A hybrid adaptive fuzzy control for<br />
a class of nonl<strong>in</strong>ear MIMO systems”, IEEE Transactions<br />
on Fuzzy Systems, vol. 11, pp. 24-34, 2003.<br />
[24] G.Nurnberger, “Approximation by spl<strong>in</strong>e functions, “New<br />
York: Spr<strong>in</strong>ger-Verlag, 1999,<br />
[25] Pepe P, “Input-to-state stabilization of stabilizable, timedelay,<br />
control-aff<strong>in</strong>e, nonl<strong>in</strong>ear systems”, IEEE<br />
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2009.<br />
Hui HU is a lecturer of Department of electrical and<br />
<strong>in</strong>formation eng<strong>in</strong>eer<strong>in</strong>g, Hunan <strong>in</strong>stitute of eng<strong>in</strong>eer<strong>in</strong>g. Dr.Hu<br />
received the B.S. degree <strong>in</strong> electronics and <strong>in</strong>formation<br />
eng<strong>in</strong>eer<strong>in</strong>g from Hunan University of Science and Technology<br />
<strong>in</strong> 2001.And received the M.S. degree <strong>in</strong> power electronics and<br />
drives from Xiangtan University <strong>in</strong> 2004.And received the Ph.<br />
D degree <strong>in</strong> control theory and control eng<strong>in</strong>eer<strong>in</strong>g from Hunan<br />
University <strong>in</strong> 2010. Her research <strong>in</strong>terests <strong>in</strong>clude nonl<strong>in</strong>ear<br />
systems track<strong>in</strong>g control, MIMO systems control, uncerta<strong>in</strong><br />
nonl<strong>in</strong>ear system control and <strong>in</strong>telligent control.<br />
Peng GUO is a lecturer of Department of Computer and<br />
Science, Hunan <strong>in</strong>stitute of eng<strong>in</strong>eer<strong>in</strong>g. He received the B.S.<br />
degree <strong>in</strong> electronics and <strong>in</strong>formation eng<strong>in</strong>eer<strong>in</strong>g from Hunan<br />
University of Science and Technology <strong>in</strong> 2000, and received the<br />
M.S. degree <strong>in</strong> computer science from Hunan University <strong>in</strong><br />
2006. His research <strong>in</strong>terests <strong>in</strong>clude <strong>in</strong>telligent control and<br />
comput<strong>in</strong>g theory, multimedia comput<strong>in</strong>g and network<strong>in</strong>g and<br />
agent technology.<br />
© 2013 ACADEMY PUBLISHER
1496 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Improved Feasible SQP Algorithm for Nonl<strong>in</strong>ear<br />
Programs with Equality Constra<strong>in</strong>ed Sub-<br />
Problems<br />
Zhijun Luo 1 , Guohua Chen 3 and Simei Luo 4<br />
Department of Mathematics & Applied Mathematics, Hunan University of Humanities, Science and Technology, Loudi,<br />
Ch<strong>in</strong>a<br />
Email: ldlzj123@163.com<br />
Zhib<strong>in</strong> Zhu 2<br />
School of Mathematics and Comput<strong>in</strong>g Science, Guil<strong>in</strong> University of Electronic Technology, Guil<strong>in</strong>, Ch<strong>in</strong>a<br />
Email: zhu_zhib<strong>in</strong>@163.com<br />
Abstract—This paper proposed an improved feasible<br />
sequential quadratic programm<strong>in</strong>g (FSQP) method for<br />
nonl<strong>in</strong>ear programs. As compared with the exist<strong>in</strong>g SQP<br />
methods which required solv<strong>in</strong>g the QP sub-problem with<br />
<strong>in</strong>equality constra<strong>in</strong>ts <strong>in</strong> s<strong>in</strong>gle iteration, <strong>in</strong> order to obta<strong>in</strong><br />
the feasible direction, the method of this paper is only<br />
necessary to solve an equality constra<strong>in</strong>ed quadratic<br />
programm<strong>in</strong>g sub-problems. Comb<strong>in</strong>ed the generalized<br />
projection technique, a height-order correction direction is<br />
yielded by explicit formulas, which can avoids Maratos<br />
effect. Furthermore, under some mild assumptions, the<br />
algorithm is globally convergent and its rate of convergence<br />
is one-step superl<strong>in</strong>early. Numerical results reported show<br />
that the algorithm <strong>in</strong> this paper is effective.<br />
Index Terms—Nonl<strong>in</strong>ear programs, FSQP method, Equality<br />
constra<strong>in</strong>ed quadratic programm<strong>in</strong>g, Global convergence,<br />
Superl<strong>in</strong>ear convergence rate<br />
I. INTRODUCTION<br />
Consider the follow<strong>in</strong>g nonl<strong>in</strong>ear programs<br />
m<strong>in</strong> f( x)<br />
s.. t g ( x) ≤0, j∈ I = {1,2, , m},<br />
j<br />
Where f ( x), g ( ): n<br />
j<br />
x R → R( j∈I)<br />
are cont<strong>in</strong>uously<br />
differentiable functions. Denote the feasible set for (1) by<br />
n<br />
X = { x∈R | g<br />
j<br />
( x) ≤0, j∈ I}<br />
.<br />
The Lagrangian function associated with (1) is def<strong>in</strong>ed<br />
as follows:<br />
Lx ( , λ) f( x) λ g( x)<br />
m<br />
= +∑<br />
j=<br />
1<br />
A po<strong>in</strong>t x ∈ X is said to be a KKT po<strong>in</strong>t of (1), if it is<br />
satisfies the equalities<br />
This work was supported <strong>in</strong> part by the National Natural Science<br />
Foundation (11061011) of Ch<strong>in</strong>a, and the Educational Reform Research<br />
Fund of Hunan University of Humanities, Science and Technology<br />
(NO.RKJGY1030), correspond<strong>in</strong>g author, E-mail: ldlzj123@163.com .<br />
j<br />
j<br />
(1)<br />
m<br />
∇ f( x) + λ ∇ g ( x) = 0,<br />
j=<br />
1<br />
λ g ( x) = 0, j∈I,<br />
j<br />
j<br />
∑<br />
where λ = ( λ1<br />
, , λ ) T<br />
m<br />
is nonnegative, and λ is said to<br />
be the correspond<strong>in</strong>g KKT multiplier vector.<br />
Method of Sequential Quadratic Programm<strong>in</strong>g (SQP)<br />
is an important method for solv<strong>in</strong>g nonl<strong>in</strong>early<br />
constra<strong>in</strong>ed optimization [1, 2, 18]. It generates<br />
iteratively the ma<strong>in</strong> search direction d 0<br />
by solv<strong>in</strong>g the<br />
follow<strong>in</strong>g quadratic programm<strong>in</strong>g (QP) sub-problem:<br />
j<br />
T 1 T<br />
m<strong>in</strong> ∇ f( x)<br />
d + d Hd<br />
2<br />
T<br />
s.. t g ( x) + ∇g ( x) d ≤0, j∈I,<br />
j<br />
n n<br />
where H ∈ R × is a symmetric positive def<strong>in</strong>ite matrix.<br />
However, such type SQP algorithms have two serious<br />
shortcom<strong>in</strong>gs:<br />
1) SQP algorithms require that the relate QP subproblems<br />
(2) must be consistency;<br />
2) There exists Matatos effect.<br />
Many efforts have been made to overcome the<br />
shortcom<strong>in</strong>gs through modify<strong>in</strong>g the quadratic subproblem<br />
(2) and the direction d [4, 5, 7, 8]. Some<br />
algorithms solve the problem (1) by us<strong>in</strong>g the idea of<br />
filter method or trust-region [13, 16, 17].<br />
For the problem (2), it is also a hot topic to solve the<br />
QP problem like (2) <strong>in</strong> the field of optimization. By us<strong>in</strong>g<br />
the idea of active constra<strong>in</strong>ts set, some algorithms solve<br />
step by step a series of correspond<strong>in</strong>g QP problems with<br />
only equality constra<strong>in</strong>ts to obta<strong>in</strong> the optimum solution<br />
to the QP sub-problem (2). P. Spellucci [6] proposed a<br />
new method, the d 0<br />
is obta<strong>in</strong>ed by solv<strong>in</strong>g QP subproblem<br />
with only equality constra<strong>in</strong>ts:<br />
j<br />
j<br />
(2)<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1496-1503
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1497<br />
T 1 T<br />
m<strong>in</strong> ∇ f( x)<br />
d + d Hd<br />
2<br />
T<br />
s.. t g ( x) +∇ g ( x) d = 0, j∈A⊆<br />
I,<br />
j<br />
j<br />
where the so-called work<strong>in</strong>g set A ⊆ I is suitably<br />
determ<strong>in</strong>ed. If d 0<br />
= 0 and λ ≥ 0 ( λ is said to be the<br />
correspond<strong>in</strong>g KKT multiplier vector.), the algorithm<br />
stops. The most advantage of these algorithms is merely<br />
necessary to solve QP sub-problems with only equality<br />
constra<strong>in</strong>ts. However, if d<br />
0<br />
= 0 , but λ < 0 , the algorithm<br />
will not implement successfully. In [10], proposed an<br />
SQP method for general constra<strong>in</strong>ed optimization. Firstly,<br />
make use of the technique which handle the general<br />
constra<strong>in</strong>ed optimization as an <strong>in</strong>equality parametric<br />
programm<strong>in</strong>g, then, consider a new quadratic<br />
programm<strong>in</strong>g with only equality constra<strong>in</strong>ts as follow:<br />
T 1 T<br />
m<strong>in</strong> ∇ f( x)<br />
d + d Hd<br />
2<br />
T<br />
s.. t g ( x) +∇ g ( x) d =−m<strong>in</strong>{0, π ( x)}, j∈J( x).<br />
j<br />
j<br />
Where π ( x)<br />
is a suitable vector, J ( x ) is a suitable<br />
approximate active set. But the QP problems may no<br />
solution under some conditions. Recently, Zhu [14]<br />
Consider the follow<strong>in</strong>g QP sub-problem:<br />
T 1 T<br />
m<strong>in</strong> ∇ f( x)<br />
d + d Hd<br />
2<br />
T<br />
s.. t p ( x) +∇ g ( x) d = 0, j∈L.<br />
j<br />
j<br />
where p ( x ) is a suitable vector, L is a suitable<br />
j<br />
approximate active, which guarantees to hold that if<br />
d<br />
0<br />
= 0 , then x is a KKT po<strong>in</strong>t of (1), i.e., if d<br />
0<br />
= 0 , then<br />
it holds that λ ≥ 0 . Depended strictly on the strict<br />
complementarity, which is rather strong and difficult for<br />
test<strong>in</strong>g, the superl<strong>in</strong>ear convergence properties of the<br />
SQP algorithm are obta<strong>in</strong>ed. For avoid<strong>in</strong>g the superl<strong>in</strong>ear<br />
convergence depend strictly on the strict complementarity,<br />
Another some SQP algorithms (see [15]) have been<br />
proposed, however it is regretful that these algorithms are<br />
<strong>in</strong>feasible SQP type and nonmonotone. In [16], a feasible<br />
SQP algorithm is proposed. Us<strong>in</strong>g generalized projection<br />
technique, the superl<strong>in</strong>ear convergence properties are still<br />
obta<strong>in</strong>ed under weaker conditions without the strict<br />
complementarity.<br />
We will develop an improved feasible SQP method for<br />
solv<strong>in</strong>g optimization problems based on the one <strong>in</strong> [14].<br />
The traditional FSQP algorithms, <strong>in</strong> order to prevent<br />
iterates from leav<strong>in</strong>g the feasible set, and avoid Maratos<br />
effect, it needs to solve two or three QP sub-problems<br />
like (2). In our algorithm, per s<strong>in</strong>gle iteration, it is only<br />
necessary to solve an equality constra<strong>in</strong>ed quadratic<br />
programm<strong>in</strong>g, which is very similar to (4). Obviously, it<br />
is simpler to solve the equality constra<strong>in</strong>ed QP problem<br />
than to solve the QP problem with <strong>in</strong>equality constra<strong>in</strong>ts.<br />
In order to void the Maratos effect, comb<strong>in</strong>ed the<br />
generalized projection technique, a height-order<br />
correction direction is computed by an explicit formula,<br />
and it plays an important role <strong>in</strong> avoid<strong>in</strong>g the strict<br />
(3)<br />
(4)<br />
complementarity. Furthermore, its global and superl<strong>in</strong>ear<br />
convergence rate is obta<strong>in</strong>ed under some suitable<br />
conditions.<br />
This paper is organized as follows: In Section II, we<br />
state the algorithm; the well-def<strong>in</strong>ed of our approach is<br />
also discussed, the accountability of which allows us to<br />
present global convergence guarantees under common<br />
conditions <strong>in</strong> Section III, while <strong>in</strong> Section IV we deal<br />
with superl<strong>in</strong>ear convergence. F<strong>in</strong>ally, <strong>in</strong> Section V,<br />
numerical experiments are implemented.<br />
II. DESCRIPTION OF ALGORITHM<br />
The active constra<strong>in</strong>ts set of (1) is denoted as follows:<br />
I( x) = { j∈ I | g ( x) = 0, j∈ I}.<br />
(5)<br />
Now, the follow<strong>in</strong>g algorithm is proposed for solv<strong>in</strong>g<br />
the problem (1).<br />
Algorithm A:<br />
Step 0 Initialization:<br />
Given a start<strong>in</strong>g po<strong>in</strong>t<br />
0<br />
x ∈ X , and an <strong>in</strong>itial<br />
n n<br />
symmetric positive def<strong>in</strong>ite matrix H 0<br />
∈ R × . Choose<br />
1<br />
parameters ε0<br />
∈(0,1), α∈(0, ), τ ∈ (2,3) . Set k = 0 ;<br />
2<br />
Step 1. Computation of an approximate active set J<br />
k<br />
.<br />
Step 1.1. For the current po<strong>in</strong>t<br />
0<br />
j<br />
k<br />
x<br />
k<br />
ε ( x ) = ε ∈ (0,1).<br />
i<br />
∈ X , set i = 0,<br />
Step 1.2. If det( A ( x k ) T A( x k )) ≥ ε ( x<br />
k ) , let<br />
i i i<br />
k k k<br />
Jk<br />
= J( x ), Ak<br />
= A( x ), i( x ) = i , and go to Step 2.<br />
Otherwise go to Step 1.3, where<br />
k k k<br />
J ( x ) = { j∈I | −ε<br />
( x ) ≤ g ( x ) ≤0},<br />
i i j<br />
k k k<br />
A( x ) = ( ∇g ( x ), j∈J ( x )).<br />
i i i<br />
k 1 k<br />
Step 1.3. Let i = i+ 1, εi( x ) = εi<br />
− 1( x ) , and go to<br />
2<br />
Step1. 2.<br />
k<br />
Step 2. Computation of the vector d<br />
0<br />
.<br />
Step 2.1<br />
B A A A v v j J B f x<br />
T −1<br />
T k k k<br />
k<br />
= (<br />
k k) k<br />
, = (<br />
j, ∈<br />
k) = −<br />
k∇<br />
( ),<br />
k k<br />
⎧ , 0<br />
k ⎪ − vj<br />
vj<br />
<<br />
k k<br />
pj = ⎨<br />
p = ( pj, j∈Jk).<br />
k k<br />
⎪⎩ g<br />
j( x ), vj<br />
≥ 0<br />
Step 2.2 Solve the follow<strong>in</strong>g equality constra<strong>in</strong>ed QP<br />
k<br />
Sub problem at x :<br />
k T 1 T<br />
m<strong>in</strong> ∇ f( x ) d + d Hkd<br />
2<br />
k k T<br />
s. t. p +∇ g ( x ) d = 0, j∈J<br />
.<br />
j j k<br />
k<br />
Let d0<br />
be the KKT po<strong>in</strong>t of (8), and<br />
k k<br />
b = ( b , j∈J<br />
) be the correspond<strong>in</strong>g multiplier vector.<br />
j<br />
k<br />
k<br />
If d<br />
0<br />
= 0 , STOP. Otherwise, CONTINUE;<br />
(6)<br />
(7)<br />
(8)<br />
© 2013 ACADEMY PUBLISHER
1498 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Step 3<br />
Computation of the feasible direction with descent<br />
Where<br />
δ<br />
ek<br />
k<br />
d :<br />
k k T −1<br />
d = d0 − δ<br />
kAk( Ak Ak)<br />
ek<br />
(9)<br />
T | Jk<br />
|<br />
= (1, ,1) ∈R<br />
, and<br />
|| d || ( d ) H d<br />
k k T k<br />
0 0 k 0 k T −1<br />
T k<br />
k<br />
= , μ =−( Ak Ak) Ak∇f( x )<br />
kT k<br />
2 | μ ek<br />
||| d0<br />
|| + 1<br />
Step 4. Computation of the high-order revised direction<br />
k<br />
d :<br />
where<br />
d A A A d e g x d (10)<br />
k T −1<br />
k k k<br />
=− ( ) (||<br />
0<br />
|| τ<br />
k k k k<br />
+<br />
J<br />
( + )),<br />
k<br />
k k k k k k T k<br />
g<br />
( x + d ) = g ( x + d ) −g ( x ) −∇g ( x ) d .<br />
J J J<br />
k k k J k<br />
Step 5. L<strong>in</strong>e search:<br />
Compute t k<br />
, the first number t <strong>in</strong> the sequence<br />
1 1 1<br />
{1, , , ,...}<br />
satisfy<strong>in</strong>g<br />
2 4 8<br />
2<br />
f ( x k + td k + t d k ) ≤ f( x k ) + αt∇f( x k ) T d<br />
k , (11)<br />
g x td t d j I<br />
(12)<br />
k k 2 k<br />
j<br />
( + + ) ≤0, ∈ .<br />
Step 6. Update:<br />
Obta<strong>in</strong> H<br />
k +<br />
by updat<strong>in</strong>g the positive def<strong>in</strong>ite matrix<br />
1<br />
H k<br />
us<strong>in</strong>g some quasi-Newton formulas. Set<br />
k 1 k k 2 k<br />
x + = x + t d + t d , and k = k+ 1 . Go back to step 1.<br />
k<br />
Throughout this paper, follow<strong>in</strong>g basic assumptions<br />
are assumed.<br />
H2.1 The feasible set X ≠Φ, and functions f ( x ),<br />
g<br />
j<br />
( x),<br />
j∈ I are twice cont<strong>in</strong>uously differentiable.<br />
H2.2 ∀ x ∈ X , the vectors { ∇g ( x), j∈I( x)}<br />
are<br />
l<strong>in</strong>early <strong>in</strong>dependent.<br />
Lemma 2.1 Suppose that H2.1and H2.2 hold, then<br />
1) For any iteration, there is no <strong>in</strong>f<strong>in</strong>ite cycle <strong>in</strong> step 1.<br />
2) If a sequence { x k } of po<strong>in</strong>ts has an accumulation<br />
po<strong>in</strong>t, then there exists a constant _ ε > 0<br />
ε<br />
kik ,<br />
_<br />
> ε for k large enough.<br />
j<br />
such that<br />
Proof.<br />
1) Suppose that the desired conclusion is false, that is<br />
to say, there exists some k, such that there is an <strong>in</strong>f<strong>in</strong>ite<br />
cycle <strong>in</strong> Step 1, then we obta<strong>in</strong>, ∀ i = 1, 2, , that Aki<br />
,<br />
is<br />
not of full rank, i.e., it holds that<br />
det( A A ) = 0, i = 1,2, , (13)<br />
T<br />
ki , ki ,<br />
And by (6), we can know that Jki<br />
, + 1<br />
⊆ Jki<br />
,<br />
. S<strong>in</strong>ce there<br />
are only f<strong>in</strong>itely many choices for J<br />
ki ,<br />
⊆ I , it is sure that<br />
~<br />
J ≡ J L for i large enough. From (6) and (13),<br />
ki , + 1 ki , k<br />
with i →∞, we obta<strong>in</strong><br />
~<br />
L k<br />
k = I ( x ), det( A A ) = 0.<br />
T<br />
k k<br />
I( x ) I( x )<br />
This is a contradiction to H 2.2, which shows that the<br />
statement is true.<br />
2) Suppose K is an <strong>in</strong>f<strong>in</strong>ite <strong>in</strong>dex set such that<br />
*<br />
{ x } → x . We suppose that the conclusion is false,<br />
k k∈K<br />
i.e., there exists<br />
for<br />
~<br />
L<br />
k<br />
Let<br />
~<br />
'<br />
'<br />
K ⊆ K K<br />
(| | =∞ ) , such that<br />
ε<br />
ki<br />
→ k∈K k →∞<br />
'<br />
,<br />
0, , .<br />
k<br />
Lk = Jk, i k −1. From the def<strong>in</strong>ition of ε<br />
ki , k<br />
, it holds,<br />
k∈<br />
K ' ,<br />
k large enough, that<br />
~<br />
T T k<br />
~ ~ ε<br />
ki , k j k<br />
Lk<br />
Lk<br />
det( A A ) = 0, −2 ≤ g ( x ) ≤0, j∈ L . (14)<br />
S<strong>in</strong>ce there are only f<strong>in</strong>itely many choices for sets<br />
⊆ I , it is sure that there exists<br />
such that<br />
~ ~<br />
''<br />
k<br />
, ( )<br />
'' ' ''<br />
K ⊆ K (| K | =∞ ) ,<br />
L ≡ L k∈ K , for k large enough.<br />
Denote ~ *<br />
A = { ∇g ( x )| j∈ L<br />
~<br />
} , then, let<br />
from (14), it holds that<br />
j<br />
~ T ~ ~<br />
* *<br />
=<br />
j<br />
= ∈ ⊆<br />
k∈K '' , k →∞ ,<br />
det( A A) 0, g ( x ) 0, j L I( x ).<br />
This is a contradiction to H 2.2, too, which shows that<br />
the statement is true.<br />
Lemma 2.2 For the QP sub-problem (8) at x<br />
k , if<br />
k<br />
d<br />
0<br />
= 0 , then x k<br />
k<br />
is a KKT po<strong>in</strong>t of (1). If d0 ≠ 0 , then<br />
k<br />
x computed <strong>in</strong> step 4 is a feasible direction with descent<br />
k<br />
of (1) at x .<br />
Proof.<br />
By the KKT conditions of QP sub-problem (8), we<br />
have<br />
k k k<br />
∇ f( x ) + Hkd0<br />
+ Akb<br />
= 0,<br />
k k T k<br />
p +∇ g ( x ) d = 0, j∈J<br />
,<br />
j j 0<br />
k<br />
k<br />
If d<br />
0<br />
= 0 , we obta<strong>in</strong><br />
k k k<br />
∇ f ( x ) + A b = 0, p = 0, j∈<br />
J ,<br />
k j k<br />
k<br />
Thereby, from (7) and x ∈ X,<br />
∀ k implies that<br />
k<br />
k<br />
g ( x ) = 0, v ≥0, j∈<br />
J .<br />
j j k<br />
b k B k k<br />
k<br />
f x v<br />
In addition, we have =− ∇ ( ) = , <strong>in</strong> a word,<br />
we obta<strong>in</strong><br />
k k<br />
∇ f ( x ) + A b<br />
k k<br />
= 0, g ( x ) = 0, b ≥0, j∈<br />
J ,<br />
k j j k<br />
k<br />
Let bj<br />
= 0, j∈ I \ Jk<br />
, which shows that x k is a KKT<br />
po<strong>in</strong>t of (1).<br />
k<br />
If d0 ≠ 0 , we have<br />
k T k T k k<br />
g ( x ) d = A d = −p − δ e ,<br />
So,<br />
Jk<br />
k k k<br />
k T k k T k kT k<br />
∇ f ( x ) d = − ( d ) H d + b p ,<br />
0 0 k 0<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1499<br />
∇ f ( x ) d =∇f( x ) d −δ<br />
∇f( x ) A ( A A ) e<br />
k T k k T k k T T −1<br />
0 k k k k k<br />
1 k T k kT k 1 k T k<br />
≤− ( d0 ) Hkd0 + b p ≤− ( d0)<br />
Hkd0 < 0.<br />
2 2<br />
Thereby, we know that d<br />
k is a feasible descent<br />
k<br />
direction of (1) at x .<br />
III. GLOBAL CONVERGENCE OF ALGORITHM<br />
In this section, firstly, it is shown that Algorithm A<br />
given <strong>in</strong> section 2 is well-def<strong>in</strong>ed, that is to say, for every<br />
k, that the l<strong>in</strong>e search at Step 5 is always successful<br />
Lemma 3.1 The l<strong>in</strong>e search <strong>in</strong> step 5 yields a stepsize<br />
1 i<br />
t<br />
k<br />
= ( ) for some f<strong>in</strong>ite i = i( k)<br />
.<br />
2<br />
Proof.<br />
It is a well-known result accord<strong>in</strong>g to Lemma 2.2. For<br />
(11),<br />
k k 2 k k k T k<br />
s f( x + td + t d<br />
) − f( x ) −αt∇f( x ) d<br />
k T k 2 k k T k<br />
=∇ f ( x ) ( td + t d<br />
) + o( t) −αt∇f( x ) d<br />
k T k<br />
= (1 −α) t∇ f( x ) d + o( t).<br />
For (12), if<br />
k k<br />
j∉ I( x ), gj<br />
( x ) < 0;<br />
k k k T k<br />
j∈ I( x ), gj( x ) = 0, ∇ gj( x ) d < 0,<br />
so we have<br />
k k 2 k k T k 2 k<br />
g<br />
j<br />
( x + td + t d<br />
) =∇ f( x ) ( td + t d<br />
) + o( t)<br />
k T k<br />
= αt∇ g<br />
j<br />
( x ) d + O( t).<br />
In the sequel, the global convergence of Algorithm A<br />
is shown. For this reason, we make the follow<strong>in</strong>g<br />
additional assumption.<br />
H3.1 { x k } is bounded, which is the sequence<br />
generated by the algorithm, and there exist constants<br />
2 T<br />
2<br />
b≥ a > 0 , such that a|| y|| ≤ y Hk<br />
y ≤ b|| y||<br />
, for all k<br />
n<br />
and all y∈ R .<br />
S<strong>in</strong>ce there are only f<strong>in</strong>itely many choices for sets<br />
k k k k k<br />
Jk<br />
⊆ I , and the sequence { d0, d1<br />
, d , v , b } is bounded,<br />
we can assume without loss of generality that there exists<br />
a subsequence K, such that<br />
x → x , H → H , d →d , d →d , d<br />
→d<br />
,<br />
b b v v J J k K<br />
k * k * k * k *<br />
k * 0 0<br />
k * k *<br />
→ , → ,<br />
k<br />
≡ ≠ Φ, ∈ ,<br />
where J is a constant set.<br />
(15)<br />
Theorem 3.2 The algorithm either stops at the KKT<br />
k<br />
po<strong>in</strong>t x of the problem (1) <strong>in</strong> f<strong>in</strong>ite number of steps, or<br />
generates an <strong>in</strong>f<strong>in</strong>ite sequence { x k } any accumulation<br />
*<br />
po<strong>in</strong>t x of which is a KKT po<strong>in</strong>t of the problem (1).<br />
Proof.<br />
The first statement is easy to show, s<strong>in</strong>ce the only<br />
stopp<strong>in</strong>g po<strong>in</strong>t is <strong>in</strong> step 3. Thus, assume that the<br />
algorithm generates an <strong>in</strong>f<strong>in</strong>ite sequence { x k }, and (15)<br />
holds. Accord<strong>in</strong>g to Lemma 2.2, it is only necessary to<br />
*<br />
prove that d =<br />
0<br />
0<br />
. Suppose by contradiction that<br />
*<br />
d0 ≠ 0 .<br />
Then, from Lemma 2.2, it is obvious that d * is welldef<strong>in</strong>ed,<br />
and it holds that<br />
* T * * T * *<br />
∇ f ( x ) d < 0, ∇ g<br />
j<br />
( x ) d < 0, j∈I( x ) ⊆ J (16)<br />
Thus, from (16), it is easy to see that the step-size t k<br />
obta<strong>in</strong>ed <strong>in</strong> step 5 are bounded away from zero on<br />
K , i.<br />
e.<br />
t ≥ t* = <strong>in</strong>f{ t , k∈ K} > 0, k∈ K.<br />
(17)<br />
k<br />
k<br />
In addition, from (11) and Lemma 2.2, it is obvious<br />
k<br />
that { f ( x )} is monotonous decreas<strong>in</strong>g. So, accord<strong>in</strong>g to<br />
*<br />
assumption H 2.1, the fact that { x<br />
k } → x implies that<br />
k<br />
*<br />
f( x ) → f( x ), k →∞ .<br />
(18)<br />
So, from (11), (16), (17), it holds that<br />
k *<br />
k T k<br />
0= lim( f ( x ) − f( x )) ≤lim( αt ∇f( x ) d )<br />
x∈K<br />
x∈K<br />
1<br />
* T *<br />
≤ αt*<br />
∇ f( x ) d < 0,<br />
2<br />
k<br />
which is a contradiction thus lim d0<br />
= 0 . Thus, x * is a<br />
x→∞<br />
KKT po<strong>in</strong>t of (1).<br />
IV. THE RATE OF CONVERGENCE<br />
Now we discuss the convergent rate of the algorithm,<br />
and prove that the sequence { x<br />
k } generated by the<br />
algorithm is one-step super-l<strong>in</strong>early convergent under<br />
some mild conditions without the strict complementarily.<br />
For this purpose, we add some regularity hypothesis.<br />
H 4.1 The sequence { x<br />
k } generated by Algorithm A is<br />
bounded, and possess an accumulation po<strong>in</strong>t x * , such<br />
* *<br />
that the KKT pair ( x , u ) satisfies the strong secondorder<br />
sufficiency conditions, i.e.,<br />
T 2 * *<br />
d ∇<br />
xxL( x , u ) d > 0,<br />
n<br />
* T<br />
∀d∈Ω<br />
{ d∈R : d ≠ 0, ∇ gI<br />
+<br />
( x ) d = 0},<br />
+<br />
*<br />
Lxu ( , ) = f( x) + ug( x), I = { j∈ I: u > 0}.<br />
∑<br />
j∈I<br />
j j j<br />
Lemma 4.1 Suppose that assumptions H 2.1-H 3.1 hold,<br />
then,<br />
1) There exists a constant ζ > 0 , such that<br />
T −1<br />
|| ( Ak<br />
Ak) || ≤ ζ ;<br />
2) lim d k 0<br />
= 0; lim d k = 0; lim d<br />
k = 0;<br />
k→∞ k→∞ k→∞<br />
3)<br />
k k k k 2<br />
|| d || ∼|| d0<br />
||, || d<br />
|| = O(|| d || ),<br />
.<br />
k k k 3 k k 2<br />
|| d − d0||= O(|| d0<br />
|| ), || d<br />
|| = O(|| d || ).<br />
Proof.<br />
1) By contradiction, suppose that sequence<br />
T 1<br />
{|| ( Ak<br />
Ak) − ||} is unbounded, then there exists an <strong>in</strong>f<strong>in</strong>ite<br />
subset K, such that<br />
T −1<br />
|| ( A A ) || →∞, ( k∈<br />
K).<br />
k<br />
k<br />
K<br />
k<br />
© 2013 ACADEMY PUBLISHER
1500 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
In view of the boundedness of { x k } and J<br />
k<br />
be<strong>in</strong>g a<br />
subset of the f<strong>in</strong>ite set I = {1, 2, , m}<br />
as well as<br />
Lemma 2.1, we know that there exists an <strong>in</strong>f<strong>in</strong>ite <strong>in</strong>dex<br />
'<br />
set K ⊆ K such that<br />
' '<br />
T<br />
k k k k<br />
k<br />
x → x, J ≡ J , ∀k∈K , det( A A ) ≥ε, ε ≥ ε.<br />
As a result,<br />
T<br />
lim( ) ( T<br />
A A =∇g x) ∇g ( x),<br />
'<br />
k∈K<br />
k k '<br />
'<br />
J J<br />
T<br />
det( ∇g <br />
'( x) ∇g '( x)) ≥ ε > 0.<br />
J<br />
J<br />
T −1<br />
Hence, we obta<strong>in</strong> T<br />
|| ( A ) || || <br />
k<br />
Ak → ∇g '( x) ∇ g '( x) ||,<br />
J J<br />
T −1<br />
this contradict || ( Ak<br />
Ak) || →∞, ( k∈ K).<br />
So the first<br />
conclusion 1) follows.<br />
k<br />
2) We firstly show that lim d0<br />
= 0 .<br />
k →∞<br />
k<br />
We suppose by contradiction that lim d0<br />
≠ 0, then<br />
k →∞<br />
there exist an <strong>in</strong>f<strong>in</strong>ite <strong>in</strong>dex set K and a constant σ > 0<br />
k<br />
such that || d0<br />
|| > σ holds for all k∈<br />
K.<br />
Tak<strong>in</strong>g notice<br />
of the boundedness of { x<br />
k } , by tak<strong>in</strong>g a subsequence if<br />
necessary, we may suppose that<br />
k <br />
'<br />
x → x, Jk<br />
≡ J , ∀k∈<br />
K.<br />
Us<strong>in</strong>g Taylor expansion, we analyze the first search<br />
<strong>in</strong>equality of Step 5, comb<strong>in</strong><strong>in</strong>g the proof of Theorem 3.2,<br />
k<br />
the fact that x → x * ,( k →∞ ) implies that it is true.<br />
k<br />
k<br />
The proof of limd<br />
= 0; limd = 0 are elementary<br />
k→∞<br />
k→∞<br />
from the result of 1) as well as formulas (9) and (10).<br />
3) The proof of 3) is elementary from the formulas (9),<br />
(10) and assumption H2.1.<br />
Lemma 4.2. Let H2.1 to H4.1 holds,<br />
k+<br />
1 k<br />
lim || x − x || = 0 . Thereby, the entire sequence { x<br />
k }<br />
k →∞<br />
* k<br />
converges to x i.e. x → x * , k →∞ .<br />
Proof.<br />
From the Lemma 4.1, it is easy to see that<br />
k+<br />
1 k k 2 k<br />
lim || x − x || = lim(|| tkd + tkd<br />
||)<br />
k→∞<br />
k→∞<br />
k<br />
k<br />
≤ lim(|| d || + || d<br />
||) = 0<br />
k →∞<br />
Moreover, together with Theorem 1.1.5 <strong>in</strong> [4], it shows<br />
k<br />
that x → x * , k →∞<br />
Lemma 4.3 It holds, for k large enough, that<br />
* k<br />
* k *<br />
1) J<br />
k<br />
≡ I( x ) I* , b → uI = ( u ,<br />
* j<br />
j∈I* ), v →( uj, j∈I*<br />
)<br />
k k T k<br />
2) I + ⊆ Lk = { j∈ Jk : g<br />
j( x ) +∇ g<br />
j( x ) d0<br />
= 0} ⊆ Jk.<br />
Proof.<br />
1) Prove J<br />
k<br />
≡ I*<br />
.<br />
On one hand, from Lemma 2.1, we know, for k large<br />
enough, that I *<br />
⊆ J k<br />
. On the other hand, if it doesn’t<br />
hold that J<br />
k<br />
⊆ I*<br />
, then there exist constants j 0<br />
and<br />
β > 0 , such that<br />
*<br />
g<br />
j<br />
( x ) ≤− β < 0, j<br />
0<br />
0<br />
∈ Jk.<br />
k<br />
So, accord<strong>in</strong>g to d 0<br />
→ 0 and the functions g ( x ),<br />
j<br />
( j∈<br />
I ) are cont<strong>in</strong>uously differentiable, for k large<br />
k<br />
enough, if v < 0 , we have<br />
j0<br />
k * T k k * T k<br />
+∇<br />
j0 0<br />
=−<br />
j<br />
+∇<br />
0 j0<br />
0<br />
p ( x ) g ( x ) d v g ( x ) d<br />
j0<br />
1 k<br />
≥− v<br />
j<br />
> 0.<br />
0<br />
2<br />
Otherwise,<br />
k * T k<br />
p ( x ) +∇g ( )<br />
j<br />
j<br />
x d<br />
0<br />
0<br />
0<br />
k * T k 1<br />
k<br />
= g<br />
j<br />
( x ) +∇g ( )<br />
0 j<br />
x d<br />
0 0<br />
≤− β < 0, ( vj<br />
≥0)<br />
0<br />
2<br />
which is contradictory with (8) and the fact j 0<br />
∈ J k<br />
. So,<br />
J<br />
k<br />
≡ I*<br />
(for k large enough).<br />
k<br />
* k *<br />
Prove that b → uI = ( u ,<br />
* j<br />
j∈I* ), v →( uj, j∈ I*<br />
).<br />
k *<br />
For the v →( uj<br />
, j∈I*<br />
) statement, we have the<br />
k<br />
follow<strong>in</strong>g results from the def<strong>in</strong>ition of v ,<br />
k * T −1 T *<br />
v →−−B∇ f( x ) =−( A A ) A ∇ f( x )<br />
* * * *<br />
In addition, s<strong>in</strong>ce x * is a KKT po<strong>in</strong>t of (1), it is<br />
evident that<br />
* *<br />
∇ f( x ) + Au .<br />
* I<br />
= 0, u<br />
* I<br />
= −B * *<br />
∇ f( x )<br />
T −1 T *<br />
i.e. uI<br />
=−( A<br />
* *<br />
A* ) A*<br />
∇ f( x ).<br />
k<br />
Otherwise, from (8), the fact that d0 → 0 implies that<br />
k k k k<br />
*<br />
∇ f ( x ) + Hkd0 + Akb = 0, b →−B*<br />
∇ f( x ) = uI<br />
.<br />
*<br />
The claim holds.<br />
2) For<br />
Furthermore, it has<br />
*<br />
lim( k k<br />
x , d ) ( x , 0)<br />
0<br />
k →∞<br />
k *<br />
uI+ uI+<br />
x→∞<br />
= , we have<br />
Lk<br />
*<br />
⊆ I( x ) .<br />
lim = > 0 , so the proof is<br />
f<strong>in</strong>ished.<br />
In order to obta<strong>in</strong> super-l<strong>in</strong>ear convergence, a crucial<br />
requirement is that a unit step size is used <strong>in</strong> a<br />
neighborhood of the solution. This can be achieved if the<br />
follow<strong>in</strong>g assumption is satisfied.<br />
H4.2 Let<br />
2 k k k k<br />
|| (<br />
xxLx ( , uJ ) H) || (|| ||)<br />
k k<br />
d o d<br />
∇ − = , where<br />
= +∑ .<br />
k<br />
k<br />
Lxu ( , ) f( x) u g( x)<br />
Jk<br />
Jk<br />
j<br />
j∈Jk<br />
Lemma 4.4 Suppose that Assumption H 2.1 to H 4.2<br />
are all satisfied. Then, the step size <strong>in</strong> Algorithm A<br />
always one, i.e. tk<br />
≡ 1, if k is large enough.<br />
Proof.<br />
It is only necessary to prove that<br />
f ( x k + d k + d k ) ≤ f( x k ) + α∇f( x k ) T d<br />
k , (19)<br />
k k k<br />
g ( x + d + d ) ≤0, j∈I.<br />
(20)<br />
j<br />
*<br />
For (12) if j ∈ I \ I we have g ( ) 0<br />
*<br />
j<br />
x < ,<br />
k k<br />
k<br />
*<br />
( x , d , d ) →( x , 0, 0)( k →∞ ), then, it is easy to<br />
obta<strong>in</strong> g ( k k k<br />
j<br />
x + d + d ) ≤0<br />
holds.<br />
If j ∈ I*<br />
we have<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1501<br />
g ( x + d + d ) = g ( x + d ) +∇ g ( x + d ) d + O(|| d<br />
|| )<br />
k k k k k k k T k k 2<br />
j j j<br />
k k k T k k<br />
gj<br />
x + d +∇ gj<br />
x d + O d<br />
k<br />
d k<br />
+ O d<br />
2<br />
k k k T k k<br />
gj<br />
x + d +∇ gj<br />
x d<br />
+ O d<br />
k<br />
d<br />
= ( ) ( ) (|| |||| ||) (|| || )<br />
= ( ) ( ) (|| |||| ||).<br />
In addition, from (9) and (10),<br />
k T k k T k<br />
∇ g<br />
j<br />
( x ) d =∇g j( x ) d0<br />
− δ<br />
k,<br />
k T<br />
k<br />
( ) <br />
k τ<br />
k k<br />
∇ g<br />
j<br />
x d = −|| d0<br />
|| − g<br />
j( x + d )<br />
k k T k<br />
+ g<br />
j( x ) +∇g j( x ) d ,<br />
so, for τ ∈ (2,3) we have<br />
k k k<br />
gj<br />
( x + d + d<br />
)<br />
= − || d || + g ( x ) +∇g ( x ) d − δ + O(|| d |||| d<br />
||)<br />
k τ k k T k k k<br />
0 j j 0 k<br />
k τ<br />
k k<br />
0<br />
(21)<br />
≤− || d || + O(|| d |||| d ||) ≤0.<br />
Hence, the second <strong>in</strong>equalities of (20) hold for t = 1<br />
and k is sufficiently large.<br />
The next objective is to show the first <strong>in</strong>equality of (19)<br />
holds. From Taylor expansion and tak<strong>in</strong>g <strong>in</strong>to account<br />
Lemma 4.1 and Lemma 4.3, we have<br />
k k k k k T k<br />
s f( x + d + d<br />
) − f( x ) + α∇f( x ) d<br />
k T k k 1 k T 2 k T k<br />
= ∇ f ( x ) ( d + d ) + ( d ) ∇ f( x ) d (22)<br />
2<br />
k T k k 2<br />
−α∇ f( x ) d + o(|| d || ).<br />
On the other hand, from the KKT condition of (8) and<br />
the active set L<br />
k<br />
def<strong>in</strong>ed by Lemma 4.3 one has<br />
∑<br />
∇ f( x ) =−H d − u ∇g ( x )<br />
k k k k<br />
k 0<br />
j j<br />
j∈Lk<br />
k k k k 2<br />
=−Hd k<br />
−∑<br />
uj∇ g<br />
j( x) + o(|| d || ),<br />
j∈Lk<br />
So, from (23) and Lemma 4.3, we have<br />
∇f( x ) d<br />
k T k<br />
∑<br />
k T k k k T k<br />
( d ) Hkd uj g<br />
j( x ) d<br />
k 2<br />
o(|| d || )<br />
j∈Lk<br />
k<br />
d<br />
T k k k T k<br />
Hkd ∑ uj g<br />
j<br />
x d0<br />
o<br />
k<br />
d<br />
2<br />
j∈Lk<br />
=− − ∇ +<br />
= −( ) − ∇ ( ) + (|| || )<br />
k T k<br />
k<br />
∇ f( x ) ( d + d<br />
)<br />
∑<br />
k T k k k T k<br />
k<br />
k 2<br />
k j j<br />
j∈Lk<br />
=−( d ) H d − u ∇ g ( x ) ( d + d ) + o(|| d || ),<br />
Aga<strong>in</strong>, from (21) and Taylor expansion, it is clear that<br />
k 2<br />
k k k<br />
o(|| d || ) = gj( x + d + d<br />
)<br />
1<br />
g x +∇ g x d + d<br />
+ d ∇ g x d + o d<br />
2<br />
where j∈<br />
L , then, we obta<strong>in</strong><br />
(23)<br />
(24)<br />
(25)<br />
k k T k k k T 2 k T k k 2<br />
=<br />
j( )<br />
j( ) ( ) ( )<br />
j( ) (|| || )<br />
k<br />
∑<br />
k k T k<br />
k<br />
− u ∇ g ( x ) ( d + d<br />
)<br />
j j<br />
j∈Lk<br />
k k T<br />
∑ uj<br />
g<br />
j( x )<br />
j∈Lk<br />
1 ⎛ ( )<br />
2 T ⎞<br />
k T k (<br />
k )<br />
k (||<br />
k ||<br />
2<br />
+ d uj<br />
g<br />
j<br />
x d o d ),<br />
2 ⎜∑<br />
∇ ⎟<br />
+<br />
j∈Lk<br />
= ∇<br />
From (25) and (26), we have<br />
⎝<br />
k T k<br />
k<br />
∇ f( x ) ( d + d<br />
)<br />
k T k k k<br />
=−( d ) H d − u ∇g ( x )<br />
1<br />
k j j<br />
j∈Lk<br />
⎛<br />
k T k 2 k T k k 2<br />
+ ( d ) j j( ) (|| || )<br />
2 ⎜<br />
u ∇ g x ⎟<br />
d + o d<br />
j∈Lk<br />
⎝<br />
∑<br />
∑<br />
Substitut<strong>in</strong>g (27) and (24) <strong>in</strong>to (22), it holds that<br />
1 k T k k k<br />
s ( α − )( d ) Hkd + (1 −α) ∑ ujg j( x )<br />
2<br />
1 ⎛<br />
⎞<br />
2<br />
⎜ ∑<br />
⎟<br />
⎝<br />
j∈Lk<br />
⎠<br />
1 k T k k k<br />
=( α − )( d ) Hkd + (1 −α) ∑ ujg j( x )<br />
2<br />
⎠<br />
⎞<br />
⎠<br />
j∈Lk<br />
(26)<br />
(27)<br />
+<br />
k T<br />
( d )<br />
T<br />
2 k k 2 k<br />
k k 2<br />
∇ f ( x ) + u ∇ g ( x ) − H d + o(|| d || )<br />
j j k<br />
j∈Lk<br />
1 k T 2 k k k k 2<br />
+ ( d ) ( ∇ L( x , uJ<br />
) − H ) (|| || ).<br />
k k<br />
d + o d<br />
2<br />
Then, together assumption H 3.1 and H 4.2 as well as<br />
k k<br />
ug( x) ≤ 0, shows that<br />
j<br />
j<br />
1 1<br />
s ≤ α − a d + o d ≤ α∈<br />
2 2<br />
Hence, the <strong>in</strong>equality of (19) holds.<br />
k 2 k 2<br />
( ) || || (|| || ) 0. ( (0, )).<br />
Furthermore, <strong>in</strong> a way similar to the proof of Theorem<br />
5.2 <strong>in</strong> [5] and <strong>in</strong> [19, Theorem 2.3], we may obta<strong>in</strong> the<br />
follow<strong>in</strong>g theorem:<br />
Theorem 4.5 Under all above-mentioned assumptions,<br />
the algorithm is superl<strong>in</strong>early convergent, i.e., the<br />
sequence { x k } generated by the algorithm satisfies that<br />
1 * *<br />
|| k<br />
k<br />
x + − x || = o(|| x − x ||).<br />
Proof.<br />
From Lemma 4.1 and Lemma 4.4, we can know that<br />
the sequence { x<br />
k } yielded by Algorithm A has the form<br />
of<br />
k 1 k k<br />
k<br />
x + = x + d + d<br />
k k k<br />
k<br />
k<br />
= x + d0 + ( d + d −d0)<br />
k<br />
k k<br />
x + d + d<br />
.<br />
0<br />
k<br />
where k<br />
k<br />
( k<br />
d = d + d − d ) (for k large enough) and<br />
k<br />
k 3<br />
d O d0<br />
0<br />
|| || = (|| || ) . Consequently, we can obta<strong>in</strong> the<br />
result together with Ref. [5] and [19].<br />
V. NUMERICAL RESULTS<br />
© 2013 ACADEMY PUBLISHER
1502 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
In this section, we carry out numerical experiments<br />
based on the Algorithm A. The code of the proposed<br />
algorithm is written by us<strong>in</strong>g MATLAB 7.0 and utilized<br />
the optimization toolbox. The results show that the<br />
algorithm is effective. Dur<strong>in</strong>g the numerical experiments,<br />
it is chosen at random some parameters as follows:<br />
ε = 0.5, α = 0.25, τ = 2.25, H = I,<br />
0 0<br />
where I is the n× n unit matrix. H<br />
k<br />
is updated by the<br />
BFGS formula [2].<br />
k k<br />
H = k+ 1<br />
BFGS( H<br />
k, s , y ),<br />
Where,<br />
^<br />
k k+<br />
1 k k k k<br />
= − = θ + −θ<br />
k<br />
s x x , y y (1 ) H s ,<br />
^<br />
m<br />
k k+ 1 k k k+<br />
1<br />
k<br />
=∇ −∇ + ∑ j<br />
∇<br />
j<br />
−∇<br />
j<br />
j = 1<br />
y f( x ) f( x ) u ( g ( x ) g ( x )),<br />
kT<br />
⎧1, if y s k<br />
≥ 0.2( s k<br />
) T<br />
H k<br />
k<br />
s ,<br />
⎪<br />
θ =<br />
k T k<br />
⎨ 0.8( s ) Hk<br />
s<br />
⎪ , otherwise.<br />
kT<br />
k T k<br />
( ) k<br />
⎪⎩ s Hk<br />
s − y s<br />
In the implementation, the stopp<strong>in</strong>g criterion of Step 2<br />
k −8<br />
is changed to “If || d || ≤ 10 , STOP.”<br />
0<br />
TABLE I.<br />
THE DETAIL INFORMATION OF NUMERICAL EXPERIMENTS<br />
NO. n, m NT CPU<br />
HS12 2, 1 10 0<br />
HS43 4, 3 17 10<br />
HS66 3, 8 14 0<br />
HS100 7, 4 18 62<br />
HS113 10, 8 45 50<br />
NO.<br />
HS12<br />
HS43<br />
HS66<br />
HS100<br />
HS113<br />
TABLE II.<br />
THE APPROXIMATE OPTIMAL SOLUTION<br />
*<br />
x FOR TABLE I<br />
*<br />
x<br />
the approximate optimal solution<br />
(1.999999999995731, 3.000000000011285) T<br />
(0.000000000000000, 1.000000000000000,<br />
2.000000000000000, −1.000000000000000) T<br />
(0.184126482757009, 1.202167866986839,<br />
3.327322301935746) T<br />
(2.330499372903103, 1.951372372923884,<br />
-0.477541392886392, 4.365726233574537,<br />
-0.624486970384889, 1.038131018506466,<br />
1.594226711671913) T<br />
(2.171996371254668, 2.363682973701174,<br />
8.773925738481299, 5.095984487967813,<br />
0.990654764957730, 1.430573978920189,<br />
1.321644208159091, 9.828725807883636,<br />
8.280091670090108, 8.375926663907775) T<br />
This algorithm has been tested on some problems from<br />
Ref.[20], a feasible <strong>in</strong>itial po<strong>in</strong>t is either provided or<br />
obta<strong>in</strong>ed easily for each problem. The results are<br />
summarized <strong>in</strong> Table 1 to Tabe 4. The columns of this<br />
table have the follow<strong>in</strong>g mean<strong>in</strong>gs:<br />
No.: the number of the test problem <strong>in</strong> [20];<br />
n: the number of variables;<br />
m: the number of <strong>in</strong>equality constra<strong>in</strong>ts;<br />
NT: the number of iterations;<br />
CPU: the total time taken by the process (unit:<br />
millisecond) ;<br />
FV: the f<strong>in</strong>al value of the objective function.<br />
TABLE III.<br />
THE APPROXIMATE VALUE OF THE DIRECTION<br />
k<br />
d<br />
0<br />
FOR TABLE I<br />
k<br />
|| d ||<br />
NO. n, m<br />
0<br />
HS12 2, 1 7.329773437334 E-09<br />
HS43 4, 3 5.473511535838 E-09<br />
HS66 3, 8 8.327832675386 E-09<br />
HS100 7, 4 8.595133692328 E-09<br />
HS113 10, 8 6.056765632745 E-09<br />
TABLE IV.<br />
THE FINAL VALUE OF THE OBJECTIVE FUNCTION FOR TABLE I<br />
NO.<br />
FV<br />
HS12 -29.999999999999705<br />
HS43 -44.000000000000000<br />
HS66 0.518163274181542<br />
HS100<br />
6.806300573744022e+002<br />
HS113 24.306209068179822<br />
VI. CONCLUSION<br />
This paper proposed an improved feasible sequential<br />
quadratic programm<strong>in</strong>g (FSQP) method for nonl<strong>in</strong>ear<br />
programs. As compared with the exist<strong>in</strong>g SQP methods<br />
which required solv<strong>in</strong>g the QP sub-problem with<br />
<strong>in</strong>equality constra<strong>in</strong>ts <strong>in</strong> s<strong>in</strong>gle iteration, <strong>in</strong> order to obta<strong>in</strong><br />
the feasible direction, the method of this paper is only<br />
necessary to solve an equality constra<strong>in</strong>ed quadratic<br />
programm<strong>in</strong>g sub-problems. Comb<strong>in</strong>ed the generalized<br />
projection technique, a height-order correction direction<br />
is yielded by explicit formulas, which can avoids Maratos<br />
effect. Furthermore, under some mild assumptions, the<br />
algorithm is globally convergent and its rate of<br />
convergence is one-step super-l<strong>in</strong>early. Numerical results<br />
reported show that the algorithm <strong>in</strong> this paper is effective.<br />
ACKNOWLEDGMENT<br />
The author would like to thank the editors, whose<br />
constructive comments led to a considerable revision of<br />
the orig<strong>in</strong>al paper.<br />
REFERENCES<br />
[1] S. P. Han. “Superl<strong>in</strong>early Convergent Variable Metric<br />
Algorithm for General Nonl<strong>in</strong>ear Programm<strong>in</strong>g Problems”,<br />
Mathematical Programm<strong>in</strong>g, Berl<strong>in</strong>, vol.11 (1), pp. 263–<br />
282, December 1976.<br />
[2] M. J. D. Powell. “A Fast Algorithm for Nonl<strong>in</strong>early<br />
Constra<strong>in</strong>ed Optimization Calculations”, In: Waston, G.A.<br />
(ed). Numerical Analysis. Spr<strong>in</strong>ger, Berl<strong>in</strong>, pp. 144–157,<br />
1978.<br />
[3] P. T. Boggs, J. W. Tolle. “A Strategy for Global<br />
Convergence <strong>in</strong> a Sequential Quadratic Programm<strong>in</strong>g<br />
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© 2013 ACADEMY PUBLISHER
1504 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
F<strong>in</strong>ite Element Analysis Based Design of Mobile<br />
Robot for Remov<strong>in</strong>g Plug Oil Well<br />
Xiaojie Tian<br />
College of Mechanical and Electronic Eng<strong>in</strong>eer<strong>in</strong>g, Ch<strong>in</strong>a University of Petroleum, Dongy<strong>in</strong>g, Ch<strong>in</strong>a<br />
Email: tianxj20050101@163.com<br />
Yonghong Liu, Rongju L<strong>in</strong>, Baop<strong>in</strong>g Cai, Zengkai Liu, Rui Zhang<br />
College of Mechanical and Electronic Eng<strong>in</strong>eer<strong>in</strong>g, Ch<strong>in</strong>a University of Petroleum, Dongy<strong>in</strong>g, Ch<strong>in</strong>a<br />
Email: liuyh@upc.edu.cn, 1440644797@qq.com, caibaop<strong>in</strong>g987@163.com, liuzengk@163.com, flyrockgod@163.com<br />
Abstract—In order to develop the mobile robot for remov<strong>in</strong>g<br />
the plug oil well, the robot was designed based on the wheeltype<br />
and leg-type robot mechanism. A well function<strong>in</strong>g<br />
prototype has been manufactured. To demonstrate the<br />
validity and the benefit of the mobile robot, support<strong>in</strong>g<br />
mechanism and guid<strong>in</strong>g rod were chosen to design based on<br />
the FEM. The mathematical model of the support<strong>in</strong>g<br />
mechanism is established and the mechanical property is<br />
analyzed us<strong>in</strong>g the FEM. The deformation and stress of<br />
some components of the support<strong>in</strong>g mechanism and the<br />
guid<strong>in</strong>g rod is <strong>in</strong>vestigated. The results show that the<br />
support<strong>in</strong>g mechanism and the guid<strong>in</strong>g rod have excellent<br />
performance with little displacement and small stress under<br />
work<strong>in</strong>g condition. The strength and rigidity of support<strong>in</strong>g<br />
mechanism and the guid<strong>in</strong>g rod are good enough to ensure<br />
the reliability of the whole robot mechanism.<br />
Index Terms—Mobile robot; Oil well; FEM; Support<strong>in</strong>g<br />
mechanism<br />
I. INTRODUCTION<br />
Mobile robots have been widely used to carry out<br />
manifold tasks such as <strong>in</strong>dustrial applications, planetary<br />
exploration, rescue operation and medical services <strong>in</strong><br />
recent years. In the oil and gas field, there are a lot of<br />
pipes that need to be detected and rescued, which<br />
promote the development of the mobile robots.<br />
Most reservoirs <strong>in</strong> the oil field are low permeability<br />
because of oil reservoirs pollution, scale formation,<br />
paraff<strong>in</strong> deposit and so on. The low permeability usually<br />
causes the reduction of oil production [1, 2]. Accord<strong>in</strong>gly<br />
the technology of remov<strong>in</strong>g plug oil well has become a<br />
important guarantee to protect oil reservoirs, improve oil<br />
production and oil recovery ratio [3]. The technology of<br />
remov<strong>in</strong>g plug oil well manly <strong>in</strong>cludes the chemical<br />
remov<strong>in</strong>g plug oil well and physical remov<strong>in</strong>g plug oil<br />
well. The plug removal technology with electrical pulse<br />
for oil reservoir is a new method developed to solve the<br />
problem of oil well plugg<strong>in</strong>g. It uses a mobile robot<br />
Correspond<strong>in</strong>g author. Tel.: +86 546 8392303; Fax: +86 546<br />
8393620. Email addresses: liuyhupc@126.com, liuyh@upc.edu.cn<br />
(Y.H. Liu)<br />
putt<strong>in</strong>g positive and negative electrodes <strong>in</strong>to the<br />
perforation and loads discharge pulse on them generated<br />
by pulse power. Ow<strong>in</strong>g to the special work condition of<br />
the mobile robot, the design of the robot is very important.<br />
Accord<strong>in</strong>g to a locomotive mechanism to achieve the<br />
desired mobility, mobile robots may be split <strong>in</strong>to<br />
follow<strong>in</strong>g categories: leg-type, track-type and wheel-type<br />
mobile robots. While the leg-type mobile robot ensures<br />
the most superior adaptability to all k<strong>in</strong>ds of<br />
environments, its mechanism is quite complicated<br />
because active control algorithms equipped with<br />
additional actuators and sensors are required to steadily<br />
ma<strong>in</strong>ta<strong>in</strong> its balance, which <strong>in</strong>evitably leads to slow<br />
movement and poor energy efficiency [4, 5]. The tracktype<br />
mobile robot provides acceptable mobility on an offroad<br />
environment by virtue of its <strong>in</strong>herently stable<br />
mechanism. However, the excessive friction is lost dur<strong>in</strong>g<br />
chang<strong>in</strong>g a direction, which also results <strong>in</strong> poor energy<br />
efficiency [6]. Compared to other alternatives, the wheeltype<br />
mobile robot can be developed <strong>in</strong> the simplest<br />
configuration. Therefore the fast movement as well as<br />
good energy efficiency is guaranteed without any<br />
complicated control strategy. However, its adaptability to<br />
an environment does not seem to be sufficiently good and<br />
its mobility is restricted depend<strong>in</strong>g on both the type and<br />
the size of encountered obstacle [7].<br />
Therefore, it is not surpris<strong>in</strong>g that high mobility on<br />
various environments have been a primary factor among<br />
others when evaluation the performance of the mobile<br />
robot. Li Peng et al. [8] proposed an adaptive mobile<br />
robot which had the adaptability to the change of pipe<br />
diameters. When the robot encounters a step, the adaptive<br />
mobile mechanism of the robot will change its work<strong>in</strong>g<br />
mode to surmount the obstacle. Compared to classical<br />
screw-driven robots, this robot does not employ the l<strong>in</strong>ktype<br />
configuration, but only uses one actuator to solve the<br />
low capability of surmount<strong>in</strong>g obstacle. The observed<br />
rotation problem of the support<strong>in</strong>g parts is solved by the<br />
k<strong>in</strong>ematical analysis of the robot. Joshi et al. [9] designed<br />
a spherical mobile robot, roll<strong>in</strong>g on a plane with the help<br />
of two <strong>in</strong>ternal rotors and work<strong>in</strong>g on the pr<strong>in</strong>ciple of<br />
conservation of angular momentum. The robot is a classic<br />
nonholonomic system. The k<strong>in</strong>ematic model of the<br />
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JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1505<br />
system is developed us<strong>in</strong>g quaternion for the description<br />
of the orientation of the robot. The model is fully<br />
controllable and can be taken from any arbitrary<br />
configuration to any arbitrary configuration with<strong>in</strong> the<br />
unit 3-sphere <strong>in</strong> the quaternion space. Kim et al. [10]<br />
presented an optimal design of a wheel-type mobile robot<br />
hav<strong>in</strong>g high mobile stability as well as excellent<br />
adaptability while climb<strong>in</strong>g stairs. The Taguchi method<br />
is adopted as an optimization tool and the sensitivity<br />
analysis with respect to design parameters is carried out<br />
to provide an <strong>in</strong>sight to their effects on the performance<br />
criterion under k<strong>in</strong>ematic constra<strong>in</strong>s which are imposed to<br />
avoid undesired <strong>in</strong>terference between a mobile robot and<br />
stairs. Aracil et al. [11] proposed the parallel robots for<br />
autonomous climb<strong>in</strong>g along tubular structures and studied<br />
the dynamics of some different configurations. The<br />
parallel robot is based on the application of the Gough-<br />
Stewart (G-S) platform. Technical specifications of the<br />
system are presented and the control scheme is analyzed.<br />
Several experiments have been carried out and the<br />
analysis of the results has checked the high capacity of<br />
the parallel robot to climb on tubular structures with<br />
unknown trajectories.<br />
Based on the wheel-type mobile mechanism, an<br />
optimal design of the mobile robot for remov<strong>in</strong>g the plug<br />
oil well is presented. A well function<strong>in</strong>g prototype has<br />
been manufactured. Section 2 describes the structure of<br />
the mobile robot <strong>in</strong>clud<strong>in</strong>g micro-step walk<strong>in</strong>g<br />
mechanism, revolv<strong>in</strong>g measur<strong>in</strong>g mechanism, and EDM<br />
remov<strong>in</strong>g plug mechanism. Section 3 presents the<br />
mathematical and FEM models for the support<strong>in</strong>g<br />
mechanism. Section 4 gives the analysis results. And<br />
Section 5 summarized the paper.<br />
II. STRUCTURE PRINCIPLE OF THE ROBOT<br />
A. The Whole Mobile Robot System<br />
To remove the plug oil well, the technology of EDM<br />
(electrical discharge mach<strong>in</strong><strong>in</strong>g) remov<strong>in</strong>g plug well is<br />
proposed <strong>in</strong> this paper. And the mobile robot is developed<br />
for this technology. The wheel-type robot has the<br />
simplest configuration and the fast movement. The legtype<br />
mobile robot has the most superior adaptability to all<br />
k<strong>in</strong>ds of environments. Based on the merits of the wheeltype<br />
and leg-type robot, the mobile robot mechanism is<br />
designed to use <strong>in</strong> the oil pipe. Consider<strong>in</strong>g the rigors<br />
environments of the oil pipe, the configuration of the<br />
mechanism should be simple, small sizes, flexibility and<br />
reliability. Therefore the prototype of mobile robot has<br />
been manufactured <strong>in</strong> the laboratory. The whole mobile<br />
robot system for remov<strong>in</strong>g the plug oil well is shown <strong>in</strong><br />
Fig.1 (a).<br />
As shown <strong>in</strong> Fig.1 (b), the mobile mechanism is ma<strong>in</strong>ly<br />
composed of micro-step walk<strong>in</strong>g mechanism, revolv<strong>in</strong>g<br />
measur<strong>in</strong>g mechanism, and EDM remov<strong>in</strong>g plug<br />
mechanism. When the oil pipe is plugged, the mov<strong>in</strong>g<br />
robot is tripped <strong>in</strong>to the oil pipe under several kilometers<br />
by the drawworks. Once the robot arrives at the<br />
designated position, the drawwoks will stop work<strong>in</strong>g.<br />
Then the micro-step walk<strong>in</strong>g mechanism will start<br />
mov<strong>in</strong>g to search for the perforat<strong>in</strong>g position because the<br />
designed position is not the perforat<strong>in</strong>g position exactly.<br />
The robot crawls along the <strong>in</strong>ner surface of the oil pipe by<br />
the micro-step walk<strong>in</strong>g mechanism; and the revolv<strong>in</strong>g<br />
measur<strong>in</strong>g mechanism rotates to detect the perforat<strong>in</strong>g<br />
position accord<strong>in</strong>g to the sensors at the same time. Once<br />
the perforat<strong>in</strong>g position is detected, the robot will stop<br />
mov<strong>in</strong>g and halted <strong>in</strong> the oil pipe. And then the EDM<br />
remov<strong>in</strong>g plug mechanism will remove the plugged<br />
objects under the enormous discharge energy. Moreover<br />
the movement of robot is controlled by the remote control<br />
system and the whole work<strong>in</strong>g process can be monitored<br />
on the ground.<br />
Figure 1. Schematic diagram of the mobile robot.<br />
B. Micro-step Walk<strong>in</strong>g Mechanism<br />
The micro-step walk<strong>in</strong>g mechanism is one of the ma<strong>in</strong><br />
members of the mobile robot. It can enable the mobile<br />
robot walk and stop <strong>in</strong> any position of the vertical oil pipe.<br />
It also can guide and centralize the robot <strong>in</strong> the pipe.<br />
Moreover it can be adaptive to different diameters of the<br />
pipe.<br />
Figure 2. Micro-step walk<strong>in</strong>g mechanism<br />
As shown <strong>in</strong> Fig 2, the micro-step walk<strong>in</strong>g mechanism<br />
conta<strong>in</strong>s two sets of adaptive guid<strong>in</strong>g mechanism,<br />
support<strong>in</strong>g mechanism and electric telescopic rod. Based<br />
on the pr<strong>in</strong>ciple of slider-crank mechanism, the adaptive<br />
guid<strong>in</strong>g mechanism has four cranks distributed for 90°<br />
that are opened by the slider push<strong>in</strong>g at the effect of the<br />
pretighten<strong>in</strong>g force of spr<strong>in</strong>g. It can be self-adaptive to<br />
different diameters of pipe. The tension wheels are<br />
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1506 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
<strong>in</strong>stalled on the adaptive guid<strong>in</strong>g mechanism to reduce<br />
the friction force and help the robot tripped <strong>in</strong>to the oil<br />
pipe smoothly. The support<strong>in</strong>g mechanism is composed<br />
of four support<strong>in</strong>g legs distributed for 90° and controlled<br />
by the electric telescopic rod. The electric telescopic rod<br />
can push the support<strong>in</strong>g legs of the support<strong>in</strong>g<br />
mechanism on to the <strong>in</strong>ner surface of the pipe. And the<br />
friction force between support<strong>in</strong>g legs and pipe is large<br />
enough to ensure the robot hover<strong>in</strong>g steadily for a long<br />
time. The electric telescopic rod also can control the<br />
distance per step while the robot walk<strong>in</strong>g, which is<br />
changed by controll<strong>in</strong>g its telescopic direction and turnon<br />
time.<br />
C. Revolv<strong>in</strong>g Measur<strong>in</strong>g Mechanism<br />
The revolv<strong>in</strong>g measur<strong>in</strong>g mechanism is responsible for<br />
detect<strong>in</strong>g the perforat<strong>in</strong>g location <strong>in</strong> the oil well and can<br />
revolve 360° <strong>in</strong> the pipe, which makes the measur<strong>in</strong>g<br />
sensor detect the circumferential surface of the pipe. The<br />
revolv<strong>in</strong>g mechanism is manly composed of step motor,<br />
support<strong>in</strong>g bear<strong>in</strong>g, shaft coupl<strong>in</strong>g and conduct<strong>in</strong>g slip<br />
r<strong>in</strong>g, as shown <strong>in</strong> Fig 3(a). It can be revolved by the step<br />
motor and transmitted motion by the shaft coupl<strong>in</strong>g. The<br />
conduct<strong>in</strong>g slip r<strong>in</strong>g is an important part to transmit the<br />
signals among the revolv<strong>in</strong>g parts with the non-revolv<strong>in</strong>g<br />
parts. There are four connect<strong>in</strong>g rods between the step<br />
motor and the conduct<strong>in</strong>g slip r<strong>in</strong>g. This can ensure the<br />
steady and centralization of the revolv<strong>in</strong>g measur<strong>in</strong>g<br />
mechanism.<br />
current. The EDM remov<strong>in</strong>g plug mechanism feeds on<br />
the tool electrode wire used for remov<strong>in</strong>g plug<br />
cont<strong>in</strong>uously. This can compensate the removed tool<br />
electrode dur<strong>in</strong>g the plug remov<strong>in</strong>g process. In one word<br />
the revolv<strong>in</strong>g measur<strong>in</strong>g mechanism should have higher<br />
position<strong>in</strong>g accuracy to ascerta<strong>in</strong> the detection of the<br />
perforat<strong>in</strong>g location.<br />
III. MECHANICAL MODEL FOR THE SUPPORTING<br />
MECHANISM<br />
A. Mathematical Model<strong>in</strong>g<br />
It is worthwhile to consider the static analysis on the<br />
robot mechanism so as to meet the requirement of the<br />
strength and rigidity of the whole mechanism. The<br />
support<strong>in</strong>g mechanism is composed of four pairs of<br />
support<strong>in</strong>g legs distributed for 90°, the upper support<strong>in</strong>g<br />
plate, and the lower support<strong>in</strong>g plate. The upper<br />
support<strong>in</strong>g plate is fixed with the electric telescopic rod<br />
by nut, whose position could not be moved. However the<br />
lower support<strong>in</strong>g plate is mobile, which is fixed with the<br />
central pole of the electric telescopic rod by nut. Through<br />
adjust<strong>in</strong>g the nut of the lower support<strong>in</strong>g plate, the mobile<br />
robot can be adaptive to various diameters of pipe. The<br />
central pole of electric telescopic rod moves up and down<br />
by controll<strong>in</strong>g the power on and off of the electric<br />
telescopic rod. Therefore the support<strong>in</strong>g mechanism can<br />
be opened to the pipe wall and enable the whole mobile<br />
robot stop <strong>in</strong> the vertical oil pipe.<br />
Figure 3.<br />
(a) Remov<strong>in</strong>g measur<strong>in</strong>g mechanism; (b) EDM remov<strong>in</strong>g<br />
plug mechanism.<br />
Moreover the lower part of the revolv<strong>in</strong>g measur<strong>in</strong>g<br />
mechanism is attached with the measur<strong>in</strong>g sensor and the<br />
EDM remov<strong>in</strong>g plug mechanism distributed<br />
symmetrically, as shown <strong>in</strong> Fig 3(b). When the<br />
perforat<strong>in</strong>g location is detected, the revolv<strong>in</strong>g measur<strong>in</strong>g<br />
mechanism will rotate 180° and the EDM remov<strong>in</strong>g plug<br />
mechanism is <strong>in</strong> alignment with the perforat<strong>in</strong>g location<br />
exactly. The measur<strong>in</strong>g work is ma<strong>in</strong>ly depend<strong>in</strong>g on the<br />
electric eddy current sensor which is a non-contact<strong>in</strong>g<br />
sensor and produces the output signals accord<strong>in</strong>g to the<br />
eddy current. So the remov<strong>in</strong>g plug work can be carried<br />
out. The remov<strong>in</strong>g plug work is ma<strong>in</strong>ly completed by the<br />
electric discharge between the electrodes. And the power<br />
supply on the ground provides the discharge voltage and<br />
Figure 4. Mathematical model<strong>in</strong>g of the support<strong>in</strong>g mechanism (a)<br />
simplified model of the support<strong>in</strong>g mechanism; (b) mechanical analysis<br />
of connect<strong>in</strong>g p<strong>in</strong> A.<br />
The support<strong>in</strong>g mechanism is the most important<br />
component <strong>in</strong> the whole robot mechanism and ensures the<br />
stability of the whole mechanism. It endures the gravity<br />
of the whole mechanism, the support<strong>in</strong>g force of the pipe<br />
wall and the friction force. In order to analyze the<br />
<strong>in</strong>teraction forces between the support<strong>in</strong>g mechanism and<br />
the pipe wall dur<strong>in</strong>g the EDM remov<strong>in</strong>g plug mechanism<br />
work<strong>in</strong>g condition, we established the mathematical<br />
© 2013 ACADEMY PUBLISHER
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model. Consider<strong>in</strong>g the symmetry of the mechanism, the<br />
mathematical model is simplified as shown <strong>in</strong> Fig. 4(a).<br />
The support<strong>in</strong>g leg could be simplified to the two-force<br />
bar [12-14]. The force on the p<strong>in</strong> A that is contacted with<br />
the pipe wall is analyzed <strong>in</strong> Fig. 4(b). Accord<strong>in</strong>g to the<br />
pr<strong>in</strong>ciple of force balance, the force can be expressed as<br />
∑ F ( 0) = F x + Fy<br />
= 0<br />
(1)<br />
( ) − F × ( θ + θ ) L<br />
F x = F2 × L × s<strong>in</strong> θ 1 1 s<strong>in</strong> 1 2 × (2)<br />
( )<br />
F y = f × F2 × cos θ 2<br />
(3)<br />
F = F s<strong>in</strong>( )<br />
(4)<br />
1 0 2 θ2<br />
Where F is the resultant force; F 0 is the force produced<br />
by the spr<strong>in</strong>g on the lower support<strong>in</strong>g plate; F 1 is the<br />
support<strong>in</strong>g force of the support<strong>in</strong>g leg; F 2 is the force on<br />
the support<strong>in</strong>g mechanism by the pipe wall, L is the<br />
length of the upper support<strong>in</strong>g leg, f is the friction<br />
coefficient between pipe wall and support<strong>in</strong>g mechanism;<br />
θ 1 is the angle of the upper support<strong>in</strong>g leg to the<br />
horizontal l<strong>in</strong>e; θ 2 is the angle of the lower support<strong>in</strong>g leg<br />
to the horizontal l<strong>in</strong>e.<br />
The force on the support<strong>in</strong>g mechanism by the pipe<br />
wall F 2 can be achieved by Equation (1), (2), (3) and (4)<br />
and expressed as<br />
F0<br />
s<strong>in</strong>( θ1<br />
+ θ2)<br />
F2<br />
= (5)<br />
2(s<strong>in</strong>θ<br />
− f cosθ<br />
)<br />
From Equation (5), the force on the support<strong>in</strong>g<br />
mechanism by the pipe wall F 2 is related to the force<br />
produced by the spr<strong>in</strong>g on the lower support<strong>in</strong>g plate F 0<br />
and the angle of the upper support<strong>in</strong>g leg to the horizontal<br />
l<strong>in</strong>e θ 1 , the angle of the lower support<strong>in</strong>g leg to the<br />
horizontal l<strong>in</strong>e θ 2 . And it has the maximum value only<br />
when the sum of θ 1 and θ 2 is the largest and s<strong>in</strong>θ 1 is<br />
almost equal to cosθ 2 .<br />
B. FEM Modell<strong>in</strong>g<br />
FEM software is used to simulate and analyze stress<br />
and deformation of the support<strong>in</strong>g mechanism to ensure<br />
the strength and rigidity of the whole robot mechanism.<br />
When the mobile robot arrives at the perforation position,<br />
the electric telescopic rod is power on and the support<strong>in</strong>g<br />
legs are supported onto the pipe wall. The whole robot<br />
mechanism is hovered <strong>in</strong> the oil pipe steadily and the<br />
EDM plug mechanism starts to work. Therefore the<br />
support<strong>in</strong>g mechanism should have enough support<strong>in</strong>g<br />
force to support the whole mechanism. The forces on the<br />
support<strong>in</strong>g mechanism are ma<strong>in</strong>ly the electromagnetic<br />
force, the gravity and the act<strong>in</strong>g force with the pipe wall.<br />
Therefore the electromagnetic force and the gravity can<br />
be simplified to the force acted on the upper and lower<br />
support<strong>in</strong>g plates only.<br />
The f<strong>in</strong>ite element model of the support<strong>in</strong>g mechanism<br />
is established us<strong>in</strong>g the 3-D model<strong>in</strong>g element SOLID98<br />
as shown <strong>in</strong> Fig. 5. The high precision element SOLID98<br />
is adopted to analyze the stress and deformation. It is<br />
1<br />
2<br />
because that the SOLID98 element is a ten nodes<br />
Tetrahedral element and more suitable for produc<strong>in</strong>g the<br />
irregular shape grid [15, 16]. In addition, the guid<strong>in</strong>g rod<br />
is <strong>in</strong>troduced to be analyzed the stress and deformation<br />
based on FEM. The guid<strong>in</strong>g rod is throughout the<br />
support<strong>in</strong>g mechanism (shown <strong>in</strong> Fig. 1 (b)) and places<br />
an important role at the aspect of guid<strong>in</strong>g and support<strong>in</strong>g<br />
the whole robot mechanism. Its strength and rigidity can<br />
ensure the stability of the whole robot mechanism.<br />
Sta<strong>in</strong>less steel and alum<strong>in</strong>ium alloy are considered for<br />
simulation <strong>in</strong> the FEM models because the support<strong>in</strong>g<br />
mechanism is manufactured with sta<strong>in</strong>less steel and the<br />
guid<strong>in</strong>g rod is manufactured with alum<strong>in</strong>ium alloy. The<br />
sta<strong>in</strong>less steel has the merit of high strength and the<br />
alum<strong>in</strong>ium alloy has the merit of light weight [17, 18].<br />
The boundary conditions are fixed on the models and<br />
static analyses are performed <strong>in</strong> sequence <strong>in</strong> order to<br />
obta<strong>in</strong> the analysis results of the stress and deformation of<br />
the components.<br />
Figure 5. FEM model of the support<strong>in</strong>g mechanism<br />
IV. RESULTS AND DISCUSSION<br />
A. Displacement and Stress of the Upper Support<strong>in</strong>g<br />
Plate<br />
The upper support<strong>in</strong>g plate is round and has four<br />
connect<strong>in</strong>g p<strong>in</strong>s with the upper support<strong>in</strong>g legs. And it is<br />
stationary fixed with the electric telescopic rod. So it<br />
manly bears the forces of the upper support<strong>in</strong>g legs when<br />
the support<strong>in</strong>g mechanism is supported on to the pipe<br />
wall. Under the effect of the electromagnetic force and<br />
gravity, the displacement of the upper support<strong>in</strong>g plate is<br />
shown <strong>in</strong> Fig. 6 (a). The maximal deformation emerges at<br />
the connect<strong>in</strong>g po<strong>in</strong>ts with the upper support<strong>in</strong>g legs. This<br />
is ma<strong>in</strong>ly ow<strong>in</strong>g to the weight of the whole mechanism<br />
that ultimately caused the connect<strong>in</strong>g po<strong>in</strong>ts buckled.<br />
Therefore the rigidity of the connect<strong>in</strong>g po<strong>in</strong>ts should be<br />
improved. And the manufacture of the connect<strong>in</strong>g po<strong>in</strong>ts<br />
could adopt the special mach<strong>in</strong><strong>in</strong>g technology or the<br />
material used could be the high strength materials<br />
different from the round support<strong>in</strong>g plate. The stress of<br />
the upper support<strong>in</strong>g plate is shown <strong>in</strong> Fig. 6 (b). It can be<br />
seen that the stress value of the upper support<strong>in</strong>g plate is<br />
very small and the maximum value is only 8.85Mpa,<br />
which only emerges <strong>in</strong> m<strong>in</strong>or places. The stress value is<br />
© 2013 ACADEMY PUBLISHER
1508 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
much smaller than the allowable stress of material.<br />
Therefore the thickness of the upper plate can be reduced<br />
properly.<br />
places with the pipe wall. The stress between upper<br />
support<strong>in</strong>g leg and lower support<strong>in</strong>g leg is also very large.<br />
Therefore the materials with high strength and light<br />
weight will be a better chose for the upper support<strong>in</strong>g<br />
legs.<br />
Figure 6. Simulation results of the upper support<strong>in</strong>g plate (a)<br />
displacement (b) stress.<br />
B. Displacement and Stress of the Upper Support<strong>in</strong>g Leg<br />
The support and steady effect of the support<strong>in</strong>g<br />
mechanism ma<strong>in</strong>ly depends on the upper and lower<br />
support<strong>in</strong>g legs support<strong>in</strong>g on to the pipe wall. The upper<br />
support<strong>in</strong>g leg is connected to the lower support<strong>in</strong>g leg by<br />
p<strong>in</strong>s. So the upper leg moves with the movement of the<br />
lower leg. Therefore the force of upper support<strong>in</strong>g leg<br />
ma<strong>in</strong>ly comes from the lower support<strong>in</strong>g leg.<br />
In this FEM analysis it is supported that the<br />
displacement between the upper support<strong>in</strong>g leg and the<br />
<strong>in</strong>ner pipe wall is zero. And the maximal displacement of<br />
the upper support<strong>in</strong>g leg emerges at the <strong>in</strong>termediate<br />
section as shown <strong>in</strong> Fig. 7 (a). It is concluded that the<br />
upper support<strong>in</strong>g leg is liable to produce bend<strong>in</strong>g<br />
deformation and the material of the upper support<strong>in</strong>g leg<br />
can be chosen to the better material with high strength.<br />
Obviously, the upper support<strong>in</strong>g leg is a ma<strong>in</strong>ly forc<strong>in</strong>g<br />
component and bears the effect of electromagnetic force.<br />
So the support<strong>in</strong>g arm could produce larger stress as<br />
shown <strong>in</strong> Fig. 7 (b). And the greatest stress value is to<br />
56Mpa which also meets the strength requirement. The<br />
greatest stress is ma<strong>in</strong>ly distributed <strong>in</strong> the contact<strong>in</strong>g<br />
Figure 7. Simulation results of the upper support<strong>in</strong>g leg (a)<br />
displacement (b) stress.<br />
C. Displacement and Stress of the Lower Support<strong>in</strong>g Leg<br />
The lower support<strong>in</strong>g leg is another important<br />
support<strong>in</strong>g component of the support<strong>in</strong>g mechanism. It is<br />
connected with the lower support<strong>in</strong>g plate and moves by<br />
the push<strong>in</strong>g of the lower plate. Therefore the force of<br />
lower support<strong>in</strong>g leg ma<strong>in</strong>ly comes from the lower<br />
support<strong>in</strong>g plate. The shape of the lower support<strong>in</strong>g leg is<br />
different from the upper one. It is used to support the<br />
upper leg.<br />
The lower support<strong>in</strong>g leg could be regarded as a two<br />
force bar whose force is <strong>in</strong> the direction of its application.<br />
Therefore the deformation of the lower support<strong>in</strong>g leg is<br />
<strong>in</strong> the direction of its application. As shown <strong>in</strong> Fig. 8 (a),<br />
the maximal displacement of the lower support<strong>in</strong>g leg<br />
emerges at the connect<strong>in</strong>g jo<strong>in</strong>t with the lower support<strong>in</strong>g<br />
plate. The lower support<strong>in</strong>g leg is ma<strong>in</strong>ly under the effect<br />
of the compressive force com<strong>in</strong>g from the lower plate<br />
because it moves with the movement of the lower<br />
support<strong>in</strong>g plate. As shown <strong>in</strong> Fig. 8 (b), the maximum<br />
stress is produced at the p<strong>in</strong>s connect<strong>in</strong>g place. The stress<br />
is a little greater due to the effect of the electromagnetic<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1509<br />
force by the lower support<strong>in</strong>g plate. And the greatest<br />
value is 48.8Mpa which also meets the strength<br />
requirement. In general, the size of the lower support<strong>in</strong>g<br />
leg is suitable and the displacement and the stress based<br />
on FEM are <strong>in</strong> the reasonable scope.<br />
uniformly at about 0.56Mpa. But the maximal stress<br />
value of is to 56.1Mpa. This only emerges at the<br />
connect<strong>in</strong>g place. Also the stress concentration appears at<br />
the sharp angle. Therefore, the high rigidity material<br />
should be chosen to mach<strong>in</strong>e this part. And the sharp<br />
angle should be filleted to reduce the stress concentration<br />
dur<strong>in</strong>g mach<strong>in</strong><strong>in</strong>g.<br />
Figure 8. Simulation results of the lower support<strong>in</strong>g leg (a)<br />
displacement (b) stress.<br />
D. Displacement and Stress of the Lower Support<strong>in</strong>g<br />
Plate<br />
Compar<strong>in</strong>g to the upper support<strong>in</strong>g plate, the lower<br />
support<strong>in</strong>g plate has a smaller size and is moveable. It is<br />
fixed with the central pole of the electric telescopic rod<br />
and moves up and down by controll<strong>in</strong>g the power on and<br />
off of the electric telescopic rod. Under the movement of<br />
the lower support<strong>in</strong>g plate, the support<strong>in</strong>g mechanism can<br />
be adaptive to many sizes of pipe. So it manly bears the<br />
electromagnetic force from the electric telescopic rod<br />
when the support<strong>in</strong>g mechanism is supported on to the<br />
pipe wall.<br />
The maximal deformation of the lower support<strong>in</strong>g<br />
plate emerged at the centre as shown <strong>in</strong> Fig. 9 (a), which<br />
is differently from the deformation of upper support<strong>in</strong>g<br />
plate. This is because that the electromagnetic force and<br />
gravity is directly put on the centre of the lower<br />
support<strong>in</strong>g plate. Therefore the lower support<strong>in</strong>g plate<br />
should have sufficient rigidity. As shown <strong>in</strong> Fig. 9 (b) the<br />
stress of the lower support<strong>in</strong>g plate is almost distributed<br />
Figure 9. Simulation results of the lower support<strong>in</strong>g plate (a)<br />
displacement (b) stress.<br />
E. Displacement and Stress of the Guid<strong>in</strong>g Rod<br />
The guid<strong>in</strong>g rod is located at the upper part of the<br />
whole robot and throughout the support<strong>in</strong>g mechanism.<br />
It is a centre rod to hold the stability and the verticality of<br />
the whole mechanism. It also bears the weight of the<br />
whole mechanism and belongs to a bear<strong>in</strong>g bar. There are<br />
two holes on the guid<strong>in</strong>g rod as shown <strong>in</strong> Fig. 10. The<br />
upper one is used to fix the cables and the lower one is<br />
used to <strong>in</strong>stall the spr<strong>in</strong>g reta<strong>in</strong>er r<strong>in</strong>g. When the robot <strong>in</strong><br />
tripped <strong>in</strong>to the oil pipe, the guid<strong>in</strong>g rod bears the pull<strong>in</strong>g<br />
force of the cable and the gravity of the whole<br />
mechanism; when the robot is hovered <strong>in</strong> the oil pipe, it<br />
manly bears the gravity.<br />
Before develop<strong>in</strong>g the mathematical optimum model<br />
of the guid<strong>in</strong>g rod, the follow<strong>in</strong>g assumption are made<br />
that the gravity of the whole robot is changed <strong>in</strong>to the<br />
compressive force that is acted on the outside of the<br />
guid<strong>in</strong>g rod lower part. So the 10kg force was acted on<br />
© 2013 ACADEMY PUBLISHER
1510 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
the guid<strong>in</strong>g rod. Accord<strong>in</strong>g to the static analysis, the<br />
deformation and stress of the guid<strong>in</strong>g rod is shown <strong>in</strong> Fig.<br />
10 (a) and Fig. 10 (b). The guid<strong>in</strong>g rod ma<strong>in</strong>ly bears a<br />
tensile force and the deformation <strong>in</strong>creases gradually<br />
from the up to down. F<strong>in</strong>ally, the deformation is up to the<br />
maximum value of 0.0021mm at the lower part of the<br />
guid<strong>in</strong>g rod. The material of the guid<strong>in</strong>g rod should have<br />
enough tension strength. At the <strong>in</strong>termediate section of<br />
the guid<strong>in</strong>g rod, the stress value is almost the same.<br />
However, at the two ends the stress value is a little<br />
smaller. And the maximal stress of 8.96Mpa emerges at<br />
the lower part. The maximum stress value is smaller than<br />
the allowable stress of alum<strong>in</strong>um alloy. Therefore it can<br />
meet the requirements of strength and rigidity.<br />
value of deformation <strong>in</strong>creases from 0.0015mm to<br />
0.00526mm as the force <strong>in</strong>crease from 5Kg to 25Kg.<br />
However, the deformation value is very small, which has<br />
no <strong>in</strong>fluence to the whole mechanism.<br />
Deformation (mm)<br />
0.016<br />
0.014<br />
0.012<br />
0.01<br />
0.008<br />
0.006<br />
0.004<br />
0.002<br />
0<br />
ø6<br />
ø8<br />
ø10<br />
ø12<br />
5 10 15 20 25<br />
Force(Kg)<br />
Figure 11. Simulation results of the guid<strong>in</strong>g rod deformation under<br />
different forces<br />
Figure 10. Simulation results of the guid<strong>in</strong>g rod (a) displacement (b)<br />
stress.<br />
The simulation results of the guid<strong>in</strong>g rod under the<br />
force of 10Kg have been obta<strong>in</strong>ed above. Consider<strong>in</strong>g the<br />
work<strong>in</strong>g condition, different forces has been acted on the<br />
guid<strong>in</strong>g rod to study its deformation. Also the diameter of<br />
the guid<strong>in</strong>g rod is changed from 6mm to 12mm. The<br />
deformation of different sizes guid<strong>in</strong>g rod under the force<br />
of 5Kg to 25Kg is shown <strong>in</strong> Fig. 11. The deformation<br />
<strong>in</strong>creases with the <strong>in</strong>creas<strong>in</strong>g of the force l<strong>in</strong>early at the<br />
same guid<strong>in</strong>g rod diameter. With the <strong>in</strong>creas<strong>in</strong>g of the<br />
diameter, the deformation is also <strong>in</strong>creas<strong>in</strong>g. Moreover<br />
the deformation difference with different sizes is more<br />
obvious when the force is very large. The maximum<br />
V. CONCLUSIONS<br />
A mobile robot for remov<strong>in</strong>g the plug oil well is<br />
presented <strong>in</strong> this work and the prototype has been<br />
manufactured. The mechanical model and FEM model of<br />
the support<strong>in</strong>g mechanism is established. The<br />
deformation and stress of the upper support<strong>in</strong>g plate, the<br />
upper support<strong>in</strong>g leg, the lower support<strong>in</strong>g leg, the lower<br />
support<strong>in</strong>g plate and the guid<strong>in</strong>g rod are analyzed.<br />
(1) The mobile robot for mov<strong>in</strong>g the plug oil well is<br />
designed based on the wheel-type and leg-type mobile<br />
mechanism and adaptive to various pipe sizes. The robot<br />
has the merits of simple structure, easy operation, good<br />
adaptability and reliability.<br />
(2) The Mathematical model of the support<strong>in</strong>g<br />
mechanism is established accord<strong>in</strong>g to the force balance<br />
under the EDM remov<strong>in</strong>g plug mechanism work<strong>in</strong>g<br />
condition. The force of the support<strong>in</strong>g mechanism with<br />
the pipe wall can be obta<strong>in</strong>ed.<br />
(3) Based on the FEM, some components of the<br />
support<strong>in</strong>g mechanism are analyzed. The results of f<strong>in</strong>ite<br />
element analysis <strong>in</strong>dicate that the maximum deformation<br />
of upper support<strong>in</strong>g plate emerges at the p<strong>in</strong>s connect<strong>in</strong>g<br />
place, the maximum deformation of upper support<strong>in</strong>g leg<br />
emerges at the <strong>in</strong>termittent section, the maximum<br />
deformation of lower support<strong>in</strong>g leg emerges at the p<strong>in</strong>s<br />
connect<strong>in</strong>g place and the maximum deformation of lower<br />
support<strong>in</strong>g plate emerges at the centre. And the stress of<br />
the components is all at the range of the allowable stress<br />
of materials.<br />
(4) The guid<strong>in</strong>g rod of the robot is also analyzed<br />
based on the FEM. And the results prove that the guid<strong>in</strong>g<br />
rod has a small deformation and allowable stress value. It<br />
can meet the requirements of strength and rigidity. The<br />
whole robot mechanism has a good performance.<br />
ACKNOWLEDGMENT<br />
The authors wish to acknowledge the f<strong>in</strong>ancial support<br />
of National High-Technology Research and Development<br />
Program of Ch<strong>in</strong>a (No.2007AA09A101), National<br />
Natural Science Foundation of Ch<strong>in</strong>a (No.50874115),<br />
Taishan Scholar project of Shandong Prov<strong>in</strong>ce<br />
(TS20110823), Science and Technology Development<br />
Project of Shandong Prov<strong>in</strong>ce (2011GHY11520) and<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1511<br />
Fundamental Research Funds for the Central Universities<br />
(11CX04031A).<br />
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Softw. vol. 7, pp. 657–662, 2012. doi: 10.4304/jsw.7.3.657-<br />
662.<br />
Xiaojie Tian was born <strong>in</strong> Shandong, Ch<strong>in</strong>a, <strong>in</strong> 1985. She<br />
received her B. S. and M. S. degree <strong>in</strong> Mechanical Eng<strong>in</strong>eer<strong>in</strong>g<br />
from Ch<strong>in</strong>a University of Petroleum <strong>in</strong> 2008 and 2010<br />
respectively. Currently, she is a Ph.D. candidate <strong>in</strong><br />
Electromechanics Eng<strong>in</strong>eer<strong>in</strong>g <strong>in</strong> Ch<strong>in</strong>a University of Petroleum,<br />
Ch<strong>in</strong>a. Her recent research <strong>in</strong>terest is the cas<strong>in</strong>g cutt<strong>in</strong>g tool<br />
system.<br />
Yonghong Liu was born <strong>in</strong> Anhui, Ch<strong>in</strong>a, <strong>in</strong> 1965. He received<br />
his Ph.D. degree <strong>in</strong> Mechanical Manufacture from Harb<strong>in</strong><br />
Institute of Technology, Harb<strong>in</strong>, Ch<strong>in</strong>a, <strong>in</strong> 1996.<br />
He is currently a professor and doctoral supervisor <strong>in</strong> College<br />
of Mechanical and Electronic, Ch<strong>in</strong>a University of Petroleum,<br />
Ch<strong>in</strong>a. He has published over 120 papers <strong>in</strong> some <strong>in</strong>ternational<br />
or national journals and conferences. His current research<br />
<strong>in</strong>terests <strong>in</strong>clude EDM of ceramics, expansion sand screen for<br />
sand control and control system of subsea drill<strong>in</strong>g equipments.<br />
Dr. Liu is a member of Ch<strong>in</strong>a Nontraditional Mach<strong>in</strong><strong>in</strong>g<br />
Committee and Nontraditional Mach<strong>in</strong><strong>in</strong>g Association of<br />
Shandong Prov<strong>in</strong>ce. He is Prom<strong>in</strong>ent Young and Middle-aged<br />
Specialist of Shandong Prov<strong>in</strong>ce and selected <strong>in</strong> New Century<br />
National Hundred, Thousand and Ten Thousand Talent Project.<br />
Rongju L<strong>in</strong> was born <strong>in</strong> Fujian, Ch<strong>in</strong>a, <strong>in</strong> 1988. He<br />
received his B. S. degree <strong>in</strong> Mach<strong>in</strong>ery Design and<br />
Manufactur<strong>in</strong>g and its Automation from Ch<strong>in</strong>a University<br />
of Petroleum <strong>in</strong> 2010. Currently, he is a postgraduate<br />
student <strong>in</strong> Mechanical Eng<strong>in</strong>eer<strong>in</strong>g <strong>in</strong> Ch<strong>in</strong>a University of<br />
Petroleum, Ch<strong>in</strong>a. His recent research <strong>in</strong>terest is<br />
numerical control system of cas<strong>in</strong>g cutt<strong>in</strong>g tool.<br />
Baop<strong>in</strong>g Cai was born <strong>in</strong> Hebei, P. R. Ch<strong>in</strong>a, <strong>in</strong> 1982. He<br />
received his B. S. and M. S. degree <strong>in</strong> Electromechanics<br />
Eng<strong>in</strong>eer<strong>in</strong>g from Ch<strong>in</strong>a University of Petroleum <strong>in</strong> 2006 and<br />
2008 respectively. Currently, he is a Ph.D. candidate <strong>in</strong><br />
Electromechanics Eng<strong>in</strong>eer<strong>in</strong>g <strong>in</strong> Ch<strong>in</strong>a University of Petroleum,<br />
Ch<strong>in</strong>a. His recent research <strong>in</strong>terest is control system of subsea<br />
drill<strong>in</strong>g equipments.<br />
© 2013 ACADEMY PUBLISHER
1512 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Contour Error Coupled-Control Strategy based on<br />
L<strong>in</strong>e Interpolation and Curve Interpolation<br />
Guoyong Zhao<br />
Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Shandong University of Technology, Zibo, Ch<strong>in</strong>a<br />
Email: zgy709@126.com<br />
Hongj<strong>in</strong>g An and Q<strong>in</strong>gzhi Zhao<br />
Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Shandong University of Technology, Zibo, Ch<strong>in</strong>a<br />
Email: anhongj<strong>in</strong>g2006@163.com, zhaoq<strong>in</strong>gzhi@sdut.edu.cn<br />
Abstract—In practical mach<strong>in</strong><strong>in</strong>g, the multi-axis actual<br />
dynamic performances don’t match well, which reduces the<br />
profile precision greatly. The computer numerical control<br />
(CNC) mach<strong>in</strong>e tools contour error coupled-control strategy<br />
based on l<strong>in</strong>e <strong>in</strong>terpolation and curve <strong>in</strong>terpolation is<br />
developed <strong>in</strong> the paper. After analyze the conventional CNC<br />
contour error control scheme, put forward the contour<br />
error coupled-control scheme based on l<strong>in</strong>e <strong>in</strong>terpolation<br />
and curve <strong>in</strong>terpolation; Then br<strong>in</strong>g forward the contour<br />
error comput<strong>in</strong>g models based on l<strong>in</strong>e <strong>in</strong>terpolation and<br />
curve <strong>in</strong>terpolation; Furthermore, add the obta<strong>in</strong>ed contour<br />
error to the follow<strong>in</strong>g error of current sampl<strong>in</strong>g period, and<br />
send the results to CNC PID position controller to calculate<br />
position controlled quantity <strong>in</strong> order to compensate contour<br />
error. The contour error compensation control<br />
experimentation results show that the developed approach<br />
can reduce contour error effectively and enhance profile<br />
precision further.<br />
Index Terms—mach<strong>in</strong>e tools, contour error, complex parts,<br />
l<strong>in</strong>ear <strong>in</strong>terpolation, curve <strong>in</strong>terpolation<br />
I. INTRODUCTION<br />
In manufactur<strong>in</strong>g fields many parts have complex<br />
profile, and the profile <strong>in</strong>cludes analytic curve, piecewise<br />
curve, list<strong>in</strong>g curve and so on [1, 2]. In general, multiaxis<br />
CNC mach<strong>in</strong>e tools are adopted to process these<br />
complex parts, after approximat<strong>in</strong>g complex cutter<br />
position track <strong>in</strong>struction curve with straightway [3, 4].<br />
To multi-axis CNC mach<strong>in</strong>e tools, the profile precision is<br />
the important factor to determ<strong>in</strong>e its mach<strong>in</strong><strong>in</strong>g accuracy<br />
[5, 6]. But the profile precision relates with the match<strong>in</strong>g<br />
degree of all the l<strong>in</strong>ked axes dynamic performances, and<br />
is decided by both each-axis position accuracy and the<br />
multi-axis l<strong>in</strong>ked accuracy [7, 8]. Because CNC mach<strong>in</strong>e<br />
tools have complicated servo drive equipments, and the<br />
CNC system parameters may change <strong>in</strong> practical<br />
mach<strong>in</strong><strong>in</strong>g, the multi-axis actual dynamic performances<br />
This project is supported by the National Natural Science<br />
Foundation of Ch<strong>in</strong>a (No. 51105236), and the Shandong Prov<strong>in</strong>ce<br />
Promotive research fund for excellent young and middle-aged scientists<br />
of Ch<strong>in</strong>a (No. BS2011ZZ014).<br />
Correspond<strong>in</strong>g author: Guoyong Zhao, zgy709@126.com<br />
don’t match well, this reduces the profile precision [9, 10,<br />
11]. In contrast to the advanced s<strong>in</strong>gle-axis servo<br />
controller, the cross-coupled-controller is more effective<br />
to enhance profile precision [12, 13, 14], which computes<br />
the contour error and compensates each axis servo motor<br />
on each sampl<strong>in</strong>g period [15].<br />
Some research results <strong>in</strong> po<strong>in</strong>t have been achieved<br />
recently. For <strong>in</strong>stance, after <strong>in</strong>troduc<strong>in</strong>g contour error<br />
transfer function, Syh-Shiuh Yeh transforms the multiaxis<br />
cross-coupled control to a s<strong>in</strong>gle-<strong>in</strong>put-s<strong>in</strong>gle-output<br />
system, and def<strong>in</strong>es the distance of actual cutter position<br />
to the tangent on reference curve current position as<br />
contour error [16]. Myung-Hoon LEE puts forward a<br />
multi-axis contour controller based on a contour error<br />
vector us<strong>in</strong>g parametric curve <strong>in</strong>terpolation, which is a<br />
vector from the actual tool position to the nearest po<strong>in</strong>t on<br />
the desired path [17]. Peng Chao-Chung <strong>in</strong>troduces a new<br />
contour <strong>in</strong>dex (CI) aimed to arc and l<strong>in</strong>e profile, which<br />
can be looked as an equivalent contour error such that a<br />
reduction <strong>in</strong> CI implies a reduction <strong>in</strong> contour error [18].<br />
Aimed to profile curve <strong>in</strong> plane and space, Gen Lirong<br />
and Wang Baoren look the distance of actual position to<br />
the l<strong>in</strong>e which l<strong>in</strong>ks the dots of the current and the last<br />
sampl<strong>in</strong>g period as the current contour error respectively<br />
[19-20]. Zhao Ximei and Guo Q<strong>in</strong>gd<strong>in</strong>g achieve threeaxis<br />
l<strong>in</strong>ked contour error control on basis of calculat<strong>in</strong>g<br />
XY, YZ, XZ axes plane coupl<strong>in</strong>g model [21]. Liu Yi and<br />
Cong Shuang develop a Frenet coord<strong>in</strong>ate frame on a<br />
desired trajectory as the task coord<strong>in</strong>ate frame, and the<br />
contour error is computed by the normal component of<br />
track<strong>in</strong>g error <strong>in</strong> the task coord<strong>in</strong>ate frame [22]. Zhao<br />
Guoyong def<strong>in</strong>es the distance between the actual cutter<br />
position and the nearest <strong>in</strong>terpolation dot on cutter path<br />
curve as contour error on each sampl<strong>in</strong>g period [23].<br />
However, because of <strong>in</strong>ertia and frictional force, the<br />
hysteresis phenomena exist <strong>in</strong> truly CNC mach<strong>in</strong>e tool<br />
each axis movement, which is difficult to be foreseen<br />
accurately. As a result, the calculation error is uneasy to<br />
control if the hysteresis time is much longer than a<br />
sampl<strong>in</strong>g period.<br />
Consequently, <strong>in</strong> the CNC mach<strong>in</strong><strong>in</strong>g on complex parts,<br />
how to compute contour error with high precision and<br />
distribute contour error correction quantity to enhance<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1512-1519
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1513<br />
profile accuracy on each sampl<strong>in</strong>g period, has been a<br />
crucial problem for the researchers to settle. The CNC<br />
mach<strong>in</strong>e tools contour error coupled-control strategy<br />
based on l<strong>in</strong>e <strong>in</strong>terpolation and curve <strong>in</strong>terpolation is<br />
developed <strong>in</strong> the paper, which is with stable calculation<br />
error, high comput<strong>in</strong>g precision and satisfied real-time<br />
characteristic. Above all, analyze the conventional CNC<br />
contour error control scheme; Secondly, put forward the<br />
contour error coupled-control scheme based on l<strong>in</strong>e<br />
<strong>in</strong>terpolation and curve <strong>in</strong>terpolation; Thirdly, br<strong>in</strong>g<br />
forward the contour error comput<strong>in</strong>g models based on<br />
l<strong>in</strong>e <strong>in</strong>terpolation and curve <strong>in</strong>terpolation; Then add the<br />
obta<strong>in</strong>ed contour error to the follow<strong>in</strong>g error of current<br />
sampl<strong>in</strong>g period, and send the results to CNC PID<br />
position controller to calculate position controlled<br />
quantity <strong>in</strong> order to compensate contour error; F<strong>in</strong>ally, the<br />
contour error compensation control experimentations are<br />
done on the three-axis l<strong>in</strong>ked CNC test table.<br />
II. CONVENTIONAL CNC CONTOUR ERROR CONTROL<br />
SCHEME<br />
A. Def<strong>in</strong>ition of Contour Error<br />
The contour error is def<strong>in</strong>ed as the distance between<br />
the actual cutter trajectory and desired trajectory on the<br />
direction of trajectory normal. Consider<strong>in</strong>g a 2D arbitrary<br />
curve shown <strong>in</strong> Figure 1, let P* be the desired position<br />
vector, P be the actual position vector correspond<strong>in</strong>g to<br />
P* on the desired contour, P 1 be position vector on the<br />
desired contour along the direction of curve normal that is<br />
closest to P, L be the tangent through P* on the desired<br />
contour, and θ be the angle between L and X axis. Then<br />
E is the follow<strong>in</strong>g error between actual position and the<br />
<strong>in</strong>stantaneous desired position of the cutter, i.e.,<br />
*<br />
E = P − P. (1)<br />
Let E x be the part along X axis and E y along Y axis of E.<br />
And the contour error can be expressed as:<br />
ε = P − P. (2)<br />
1<br />
Let vector P plumbs tangent L on po<strong>in</strong>t P 1 *, when the<br />
follow<strong>in</strong>g error E is small on low federate. The contour<br />
error ε is approximately equal to ε * , i.e.,<br />
ε ≈ ε = − =− + . (3)<br />
* P1<br />
* P ExCx EyCy<br />
where C x and C y are computed by the follow<strong>in</strong>g equations:<br />
c<br />
c<br />
y<br />
x<br />
= s<strong>in</strong> θ − E / (2 ρ)<br />
(4)<br />
x<br />
= cos θ + E / (2 ρ)<br />
(5)<br />
where ρ is the <strong>in</strong>stantaneous radius of curvature.<br />
y<br />
Figure 1. Def<strong>in</strong>ition of contour error<br />
B. The Conventional CNC Contour Mach<strong>in</strong><strong>in</strong>g Scheme<br />
Contour error is the maximal <strong>in</strong>fluence factor <strong>in</strong> CNC<br />
mach<strong>in</strong>e system. When mach<strong>in</strong><strong>in</strong>g on complex profile<br />
parts, conventionally, CAD/CAM systems have to<br />
segment a complex curve <strong>in</strong>to a huge number of small<br />
l<strong>in</strong>ear segments and send them to CNC systems for l<strong>in</strong>ear<br />
<strong>in</strong>terpolation mach<strong>in</strong><strong>in</strong>g. But the l<strong>in</strong>ear <strong>in</strong>terpolation<br />
approach isn’t able to achieve high speed and high<br />
accuracy at the same time. Conventional CNC contour<br />
mach<strong>in</strong><strong>in</strong>g scheme usually adopts position feedback<br />
controller to m<strong>in</strong>imize follow<strong>in</strong>g error, adopts feed<br />
forward controller to m<strong>in</strong>imize track<strong>in</strong>g lag and contour<br />
deviation. In conventional cross-coupled control, the<br />
equation (3), which approximately computes contour<br />
error ε accord<strong>in</strong>g to E, is adopted to establish the<br />
contour error model. Then the cross-coupled controller<br />
computes and distributes the correction signals to<br />
<strong>in</strong>dividual axis through some PID control algorithms. The<br />
cross-coupled control system is a multivariable, nonl<strong>in</strong>ear<br />
and time-vary<strong>in</strong>g system, so it is very difficult to compute<br />
ε , θ and ρ . What is more, the approach to compute ε<br />
is only suited to condition when follow<strong>in</strong>g error E is<br />
small <strong>in</strong> the low feed rate. Especially, this approach is<br />
difficult to compute contour error on multi-axes motion.<br />
So there are some difficulties <strong>in</strong> apply<strong>in</strong>g the approach to<br />
practical NC mach<strong>in</strong><strong>in</strong>g. The conventional two-axis CNC<br />
contour control scheme is shown <strong>in</strong> Figure 2.<br />
III. CONTOUR ERROR COUPLED-CONTROL SCHEME BASED<br />
ON LINE INTERPOLATION AND CURVE INTERPOLATION<br />
After analyz<strong>in</strong>g the conventional two-axis CNC<br />
contour mach<strong>in</strong><strong>in</strong>g scheme, put forward the contour error<br />
coupled-control scheme based on l<strong>in</strong>e <strong>in</strong>terpolation and<br />
curve <strong>in</strong>terpolation. As shown <strong>in</strong> Figure 3, firstly, adopt<br />
the l<strong>in</strong>ear <strong>in</strong>terpolation or curve <strong>in</strong>terpolation on the<br />
complex parts cutter path <strong>in</strong>struction curve, and measure<br />
the real worktable position; Secondly, compute the<br />
contour error based on <strong>in</strong>terpolation dots and actual<br />
worktable position; Thirdly, compute the contour error<br />
correction quantity for x, y, z axes, and output the<br />
correction quantity to the x, y, z axes drivers and<br />
worktable.<br />
© 2013 ACADEMY PUBLISHER
1514 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
obta<strong>in</strong><strong>in</strong>g RM and RN , the contour error ε is<br />
calculated accord<strong>in</strong>g to two k<strong>in</strong>ds of conditions.<br />
Figure 2. Conventional two-axis NC contour mach<strong>in</strong><strong>in</strong>g scheme<br />
IV. CONTOUR ERROR COMPUTING MODELS BASED ON<br />
LINE INTERPOLATION AND CURVE INTERPOLATION<br />
A. Contour Error Comput<strong>in</strong>g Model Based on L<strong>in</strong>e<br />
Interpolation<br />
The key idea of the developed contour error comput<strong>in</strong>g<br />
model is as followed: After approximat<strong>in</strong>g complex parts<br />
cutter position track <strong>in</strong>struction curve with straightway<br />
accord<strong>in</strong>g to equi-error method, calculate the current<br />
actual cutter position coord<strong>in</strong>ates ow<strong>in</strong>g to the position<br />
measure feedback from each axis and worktable on each<br />
l<strong>in</strong>e <strong>in</strong>terpolation sampl<strong>in</strong>g period; Compute the<br />
m<strong>in</strong>imum distance from current actual cutter position to<br />
cutter position track <strong>in</strong>struction curve accord<strong>in</strong>g to the<br />
actual cutter position dots and the approximate nodes, <strong>in</strong><br />
other words, to calculate the contour error.<br />
As shown <strong>in</strong> Figure 4, the contour error comput<strong>in</strong>g<br />
model is expla<strong>in</strong>ed more detailedly. Suppose to<br />
approximate part cutter track <strong>in</strong>struction curve L under<br />
the precision requirement with straightway AB, BC…,<br />
and def<strong>in</strong>e the actual cutter position as dot R on certa<strong>in</strong><br />
sampl<strong>in</strong>g period. Above all, obta<strong>in</strong> the three approximate<br />
nodes A, B, C nearest to actual cutter position R on the<br />
cutter position <strong>in</strong>struction curve L, and then calculate the<br />
distance RM , RN from actual cutter position R to<br />
straightway AB, BC. It is noticed that the calculation is<br />
complicated if transform the distance from dot to l<strong>in</strong>e, to<br />
the maximum distance from dot to plane pencil through<br />
the l<strong>in</strong>e. Consequently, the vector method with the space<br />
analytic geometry and vector algebra theory is adopted to<br />
compute the distance RM , RN from dot R to<br />
straightway AB, BC:<br />
AB×<br />
AR<br />
RM = . (6)<br />
AB<br />
BC × BR<br />
RN = . (7)<br />
BC<br />
The coord<strong>in</strong>ates of both approximate nodes A, B, C<br />
and actual cutter position R are known, so the<br />
calculations of Equation (6) and (7) are simple. After<br />
(8):<br />
Figure 3. Contour error coupled-control scheme based on l<strong>in</strong>e<br />
<strong>in</strong>terpolation and curve <strong>in</strong>terpolation<br />
If RM<br />
≤<br />
RN<br />
, obta<strong>in</strong> the contour error with Equation<br />
ε ≈ RM . (8)<br />
As shown <strong>in</strong> Figure 4, the approximate error ST is<br />
constant, suppose the <strong>in</strong>tersection po<strong>in</strong>t of RM and curve<br />
L be dot P, then the calculation error of Equation (8) is<br />
MP.<br />
Because MP ≤ ST , the calculation error of contour<br />
error comput<strong>in</strong>g model is less than or equal to<br />
approximate error.<br />
If RM > RN , obta<strong>in</strong> the contour error with Equation<br />
(9):<br />
ε ≈ RN . (9)<br />
In like manner, the calculation error of contour error<br />
comput<strong>in</strong>g model is less than or equal to approximate<br />
error.<br />
x<br />
A<br />
M<br />
z S<br />
N<br />
R<br />
L<br />
o<br />
T<br />
Figure 4. The contour error comput<strong>in</strong>g model based on l<strong>in</strong>e<br />
<strong>in</strong>terpolation<br />
B. NURBS Curve Interpolation Approach<br />
NURBS can express free and analytical curve and<br />
surface unified with the advantages of smoothness and<br />
local controllability, and has been applied <strong>in</strong> the<br />
CAD/CAM fields successfully. So it’s significant to<br />
<strong>in</strong>vestigate the NURBS curve direct <strong>in</strong>terpolator <strong>in</strong> the<br />
CNC fields. At present except the FANUC and Siemens<br />
y<br />
P<br />
B<br />
C<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1515<br />
CNC system with the NURBS curve direct <strong>in</strong>terpolator,<br />
most of the CNC systems only have l<strong>in</strong>ear <strong>in</strong>terpolation<br />
and arc <strong>in</strong>terpolation function. The NURBS curve<br />
<strong>in</strong>terpolation CNC mach<strong>in</strong><strong>in</strong>g flow is shown <strong>in</strong> Figure 5.<br />
du v<br />
=<br />
dt dP( u)/<br />
du<br />
=<br />
v<br />
. . .<br />
2 2 2<br />
( x) + ( y) + ( z)<br />
. (13)<br />
2<br />
du<br />
dt<br />
dv/<br />
dt<br />
= −<br />
2 . . .<br />
2 2 2<br />
( x) + ( y) + ( z)<br />
. .. . .. . ..<br />
2<br />
v xx+ y y+<br />
zz<br />
( )<br />
. . .<br />
2 2 2 2<br />
(( x) + ( y) + ( z) )<br />
(14)<br />
Figure 5. The NURBS curve <strong>in</strong>terpolation CNC mach<strong>in</strong><strong>in</strong>g flow<br />
The NURBS curve representation is given by<br />
Pu ( ) =<br />
n<br />
∑<br />
i=<br />
0<br />
n<br />
∑<br />
i=<br />
0<br />
where V<br />
i<br />
is the control po<strong>in</strong>t,<br />
Bik ,<br />
( u)<br />
WV<br />
i i<br />
. (10)<br />
B ( u)<br />
W<br />
ik ,<br />
i<br />
W<br />
i<br />
is its weight<strong>in</strong>g factor.<br />
By manipulat<strong>in</strong>g the values of control po<strong>in</strong>ts and weights<br />
factor, a wise variety of part shapes can be designed us<strong>in</strong>g<br />
NURBS. Each po<strong>in</strong>t on the curve is correspond<strong>in</strong>g to a<br />
certa<strong>in</strong> knot parameter u .<br />
In the I th <strong>in</strong>terpolation period, NURBS curve<br />
<strong>in</strong>terpolator computes the po<strong>in</strong>t Pu (<br />
i + 1)<br />
and send<br />
Pu (<br />
i+ 1) − Pu (<br />
i)<br />
as feed <strong>in</strong>crement to servo controller.<br />
How to determ<strong>in</strong>e successive values of u<br />
i+ 1<br />
such that<br />
appropriate feed <strong>in</strong>crement length can be accurately<br />
generated is important and complicated <strong>in</strong> NURBS curve<br />
<strong>in</strong>terpolation.<br />
Taylor’s second-order expansion is <strong>in</strong>troduced <strong>in</strong> the<br />
NURBS curve <strong>in</strong>terpolation algorithm <strong>in</strong> this paper aimed<br />
at the demands of high speed, high accuracy and realtime.<br />
The procedure for determ<strong>in</strong><strong>in</strong>g successive values of<br />
u is summarized <strong>in</strong> the follow<strong>in</strong>g.<br />
Let the NURBS curve be def<strong>in</strong>ed as<br />
Pu ( ) = ( xu ( ), yu ( ), zu ( ))' , then the knot factor u<br />
i+ 1<br />
<strong>in</strong><br />
i +1 <strong>in</strong>terpolation period can be obta<strong>in</strong>ed:<br />
2 2<br />
du ΔT d u<br />
i+ 1 i u= ui<br />
2 u=<br />
ui<br />
u ≈ u +Δ T + . (11)<br />
dt 2 dt<br />
As shown <strong>in</strong> Equation (11), the key is to compute du<br />
dt<br />
and real-time. Def<strong>in</strong>e the feed rate along the NURBS<br />
curve as:<br />
Therefore,<br />
ds dP(<br />
u)<br />
dP(<br />
u)<br />
v = = = ×<br />
dt dt du<br />
du<br />
dt<br />
. (12)<br />
Substitut<strong>in</strong>g the computed du and<br />
dt<br />
Equation (11), u<br />
i+ 1<br />
will be obta<strong>in</strong>ed.<br />
2<br />
du<br />
dt<br />
2<br />
above <strong>in</strong>to<br />
C. Contour Error Comput<strong>in</strong>g Model Based on Curve<br />
Interpolation<br />
Conventionally, CAD/CAM systems have to segment a<br />
complex curve <strong>in</strong>to a huge number of small l<strong>in</strong>ear<br />
segments and send them to CNC systems for l<strong>in</strong>ear<br />
<strong>in</strong>terpolation mach<strong>in</strong><strong>in</strong>g. However, the experimental<br />
results show this approach can’t achieve high speed and<br />
high accuracy at the same time. Especially, the<br />
<strong>in</strong>terpolation dots aren’t on the track<strong>in</strong>g curve. To<br />
overcome this problem, curve direct <strong>in</strong>terpolation has to<br />
be adopted. Furthermore, accord<strong>in</strong>g to <strong>in</strong>terpolation dots<br />
<strong>in</strong> reference profile, a “three dots arc algorithm” contour<br />
error comput<strong>in</strong>g model is developed to calculate the<br />
m<strong>in</strong>imal distance between actual dot and complex profile<br />
<strong>in</strong> each sampl<strong>in</strong>g period.<br />
As shown <strong>in</strong> Figure 6, suppose the reference curve be<br />
L and cutter actual position be M (M x , M y , M z ) <strong>in</strong> some<br />
sampl<strong>in</strong>g period. Firstly, f<strong>in</strong>d the nearest <strong>in</strong>terpolation<br />
po<strong>in</strong>t C i from M on the curve, and suppose the two<br />
adjacent <strong>in</strong>terpolation dots from C i be C i-1 and C i+1 po<strong>in</strong>ts.<br />
It is noteworth<strong>in</strong>ess that all of the three dots are on curve<br />
L. Secondly, suppose the centre of the circle through C i-1 ,<br />
C i and C i+1 be po<strong>in</strong>t O (O x , O y , O z ), and the radius be r.<br />
Compute the contour error with Eq. (15):<br />
ε = r− OM = r−<br />
( M − O ) + ( M − O ) + ( M −O<br />
)<br />
2 2 2<br />
x x y y z z<br />
. (15)<br />
where, the contour error ε is along the OM<br />
direction.<br />
F<strong>in</strong>ally, decompose vector ε along x, y and z<br />
coord<strong>in</strong>ate axis<br />
ε<br />
x<br />
= ε ∗<br />
M<br />
x<br />
− O<br />
( M − O ) + ( M − O ) + ( M −O<br />
)<br />
2 2 2<br />
x x y y z z<br />
x<br />
. (16)<br />
© 2013 ACADEMY PUBLISHER
1516 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
ε<br />
y<br />
= ε ∗<br />
M<br />
y<br />
− O<br />
( M − O ) + ( M − O ) + ( M −O<br />
)<br />
2 2 2<br />
x x y y z z<br />
y<br />
. (17)<br />
ε<br />
z<br />
= ε ∗<br />
M<br />
z<br />
− O<br />
( M − O ) + ( M − O ) + ( M −O<br />
)<br />
2 2 2<br />
x x y y z z<br />
z<br />
. (18)<br />
In conclusion, the contour error comput<strong>in</strong>g model<br />
approximates curve L <strong>in</strong> locality with arc properly, so<br />
higher precision will be achieved.<br />
V. CONTOUR ERROR COMPENSATION APPROACH<br />
Except for the three PID position controller for X axis,<br />
Y axis and Z axis, Myung-Hoon LEE sets up an<br />
additional PID contour error controller [17]. The<br />
calculation approach is rather complicated. In the paper<br />
the contour error control compensation approach is<br />
developed, which adds the obta<strong>in</strong>ed contour error to the<br />
follow<strong>in</strong>g error of current sampl<strong>in</strong>g period, and sends the<br />
result to CNC PID position controller to calculate<br />
position controlled quantity. The CNC contour error<br />
calculation and compensation program flow chart is<br />
shown <strong>in</strong> Figure 7.<br />
L<br />
Ci-1<br />
M<br />
O<br />
Ci<br />
r<br />
Ci+1<br />
Figure 6. The contour error comput<strong>in</strong>g model based on curve<br />
<strong>in</strong>terpolation<br />
Firstly, after receiv<strong>in</strong>g the N th mach<strong>in</strong><strong>in</strong>g program<br />
segment cod<strong>in</strong>g and pretreatment results on the K th<br />
sampl<strong>in</strong>g period, <strong>in</strong>terpolate and obta<strong>in</strong> follow<strong>in</strong>g error E x ,<br />
E y , E z ; Secondly, adopt the contour error comput<strong>in</strong>g<br />
model, and calculate contour error ε with Equation (8),<br />
Equation (9) or Equation (15) ; Thirdly, decompose ε to<br />
ε<br />
x<br />
, ε<br />
y<br />
, ε<br />
z<br />
along X, Y, Z coord<strong>in</strong>ate axes, and compute<br />
each axis optimal displacement of current sampl<strong>in</strong>g<br />
period after contour error compensation, which is μ ,<br />
μ , μ ; F<strong>in</strong>ally, <strong>in</strong>put the μ , μ ,<br />
y<br />
z<br />
x<br />
y<br />
μ<br />
z<br />
to X, Y, Z<br />
coord<strong>in</strong>ate axes PID position controller respectively, and<br />
compute the correction quantity to control X, Y, Z<br />
coord<strong>in</strong>ate axes servo motors.<br />
x<br />
Figure 7. The CNC contour error calculation and compensation program<br />
flow chart<br />
VI. EXPERIMENTATIONS ON CONTOUR ERROR<br />
COMPENSATION CONTROL<br />
A. The Three-axis L<strong>in</strong>ked CNC Test Table<br />
The three-axis l<strong>in</strong>ked CNC test table hardware<br />
structure is shown <strong>in</strong> Figure 8. The CNC controller is<br />
made up of PC and programmable DSP movement<br />
control card. The PC and DSP movement control card<br />
communicate through USB2.0.<br />
The PC acts as the man-mach<strong>in</strong>e <strong>in</strong>terface, which<br />
implements <strong>in</strong>struction control, code compilation, states<br />
display and other functions; And the <strong>in</strong>terpolation,<br />
position control and contour error compensation control<br />
function are carried out on the programmable DSP<br />
movement control card. The Panasonic servo drivers and<br />
motors are adopted <strong>in</strong> the X, Y, Z axes. Both the<br />
<strong>in</strong>terpolation period and sampl<strong>in</strong>g period are 4 ms.<br />
Figure 8. The three-axis l<strong>in</strong>ked CNC test table hardware structure<br />
B. The Contrast Experimentations on Contour Error<br />
Compensation<br />
Interpolate and mach<strong>in</strong>e a block of three order<br />
NURBS curve. The control knots are:<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1517<br />
A (15, 0, 15)<br />
B (15, 15, 15)<br />
C (0, 15, 0)<br />
D (-15, 15, -15)<br />
E (-15, 0, -15)<br />
F (-15, -15, -15)<br />
G (0, -15, 0)<br />
H (15, -15, 15)<br />
I (15, 0, 15) ;<br />
The scale factors are:<br />
(1, 0.6, 1, 0.5, 1, 0.5, 1, 0.6, 1) ;<br />
The knot vector is:<br />
(0, 0, 0, 0, 0.25, 0.375, 0.5, 0.625, 0.75, 1, 1, 1, 1).<br />
Firstly, <strong>in</strong>terpolate and mach<strong>in</strong>e this NURBS profile<br />
when not adopt<strong>in</strong>g the <strong>in</strong>troduced contour error coupledcontrol<br />
approach. The ideal profile curve and real profile<br />
are shown <strong>in</strong> Figure 9, where the contour error is<br />
magnified 12 times to display. The contour error when<br />
mach<strong>in</strong><strong>in</strong>g the curve is shown <strong>in</strong> Figure 10. From Figure<br />
10 it can be seen, the maximal contour error is near to<br />
0.104mm.<br />
Figure 11. The profile when adopt<strong>in</strong>g the <strong>in</strong>troduced contour error<br />
coupled-control approach based on l<strong>in</strong>ear <strong>in</strong>terpolation<br />
F<strong>in</strong>ally, <strong>in</strong>terpolate and mach<strong>in</strong>e this NURBS profile<br />
when adopt<strong>in</strong>g the <strong>in</strong>troduced contour error coupledcontrol<br />
approach based on curve <strong>in</strong>terpolation. The ideal<br />
profile curve and real profile are shown <strong>in</strong> Figure 13,<br />
where the contour error is magnified 12 times to display.<br />
The contour error when mach<strong>in</strong><strong>in</strong>g the curve is shown <strong>in</strong><br />
Figure 14. From Figure 14 it can be seen, the maximal<br />
contour error is near to 0.044mm.<br />
Figure 9. The profile when not adopt<strong>in</strong>g the <strong>in</strong>troduced contour error<br />
coupled-control approach<br />
Figure 12. The contour error when adopt<strong>in</strong>g the <strong>in</strong>troduced contour<br />
error coupled-control approach based on l<strong>in</strong>ear <strong>in</strong>terpolation<br />
Figure 10. The contour error when not adopt<strong>in</strong>g the <strong>in</strong>troduced<br />
contour error coupled-control approach<br />
Secondly, <strong>in</strong>terpolate and mach<strong>in</strong>e this NURBS<br />
profile when adopt<strong>in</strong>g the <strong>in</strong>troduced contour error<br />
coupled-control approach based on l<strong>in</strong>ear <strong>in</strong>terpolation.<br />
The ideal profile curve and real profile are shown <strong>in</strong><br />
Figure 11, where the contour error is magnified 12 times<br />
to display. The contour error when mach<strong>in</strong><strong>in</strong>g the curve is<br />
shown <strong>in</strong> Figure 12. From Figure 12 it can be seen, the<br />
maximal contour error is near to 0.054mm.<br />
Figure 13. The profile when adopt<strong>in</strong>g the <strong>in</strong>troduced contour error<br />
coupled-control approach based on curve <strong>in</strong>terpolation<br />
© 2013 ACADEMY PUBLISHER
1518 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 14. The contour error when adopt<strong>in</strong>g the <strong>in</strong>troduced contour<br />
error coupled-control approach based on curve <strong>in</strong>terpolation<br />
VII. CONCLUSIONS<br />
The CNC mach<strong>in</strong>e tools contour error coupled-control<br />
strategy based on l<strong>in</strong>e <strong>in</strong>terpolation and curve<br />
<strong>in</strong>terpolation is developed <strong>in</strong> the paper, which is with<br />
stable calculation error, high comput<strong>in</strong>g precision and<br />
satisfied real-time characteristic.<br />
For one th<strong>in</strong>g, br<strong>in</strong>g forward the contour error<br />
comput<strong>in</strong>g model based on l<strong>in</strong>e <strong>in</strong>terpolation and the<br />
contour error comput<strong>in</strong>g model based on curve<br />
<strong>in</strong>terpolation; For another th<strong>in</strong>g, add the obta<strong>in</strong>ed contour<br />
error to the follow<strong>in</strong>g error of current sampl<strong>in</strong>g period,<br />
and send the results to CNC PID position controller to<br />
calculate position controlled quantity. The contour error<br />
compensation control experimentation results show that<br />
the developed approach can reduce contour error<br />
effectively and enhance profile precision further.<br />
ACKNOWLEDGMENT<br />
The authors are grateful to the Project of the National<br />
Natural Science Foundation of Ch<strong>in</strong>a (No. 51105236),<br />
and the Shandong Prov<strong>in</strong>ce Promotive research fund for<br />
excellent young and middle-aged scientists of Ch<strong>in</strong>a<br />
(No.BS2011ZZ014).<br />
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[7] Ernesto, Charlie A, Farouki, Rida T, “High-speed<br />
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cross-coupled control for XY table based on real-time<br />
contour error estimation”, Advanced Materials Research,<br />
vol. 383-390, pp. 7054-7059, July 2012.<br />
[9] Huo Feng, Poo Aun-Neow, “Free-form two-dimensional<br />
contour error estimation based on NURBS <strong>in</strong>terpolation”,<br />
Applied Mechanics and Materials, vol. 157-158, pp. 236-<br />
240, May 2012.<br />
[10] Conway Jeremy R, Ernesto Charlie A, Farouki, Rida T,<br />
“Performance analysis of cross-coupled controllers for<br />
CNC mach<strong>in</strong>es based upon precise real-time contour error<br />
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Manufacture, vol. 52, pp. 30-39, July 2012.<br />
[11] Huo Feng, Xi Xue-Cheng, Poo Aun-Neow, “Generalized<br />
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2012.<br />
[12] Möhr<strong>in</strong>g H.-C, Gümmer O, Fischer R, “Active error<br />
compensation <strong>in</strong> contour-controlled gr<strong>in</strong>d<strong>in</strong>g”, CIRP<br />
Annals - Manufactur<strong>in</strong>g Technology, vol. 60, pp. 429-432,<br />
April 2011.<br />
[13] Wang Sheng-Bao, Liu Xiao-Hong, “New cross-coupl<strong>in</strong>g<br />
control of <strong>in</strong>dependent l<strong>in</strong>ear contour errors based on<br />
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902-905, July 2011.<br />
[14] El Khalick M. A., Uchiyama Naoki, “Contour<strong>in</strong>g<br />
controller design based on iterative contour error<br />
estimation for three-dimensional mach<strong>in</strong><strong>in</strong>g”, Robotics and<br />
Computer-Integrated Manufactur<strong>in</strong>g, vol. 27, pp. 802-807,<br />
May 2011.<br />
[15] Ernesto Charlie A., Farouki Rida T, “Solution of <strong>in</strong>verse<br />
dynamics problems for contour error m<strong>in</strong>imization <strong>in</strong> CNC<br />
mach<strong>in</strong>es”, International Journal of Advanced<br />
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2010.<br />
[16] Syh-Shiuh Yeh, Pau-Lo Hsu, “Analysis and Design of<br />
Integrated Control for Multi-Axis Motion Systems”, IEEE<br />
TRANSACTIONS ON CONTROL SYSTEMS<br />
TECHNOLOGY, vol. 11, pp. 375-382, March 2003.<br />
[17] Myung-Hoon LEE, Seung-Han YANG, Young-Suk KIM,<br />
“A multi-axis contour error controller for free form<br />
Curves”, JSME International Journal, vol. 47, pp. 144-149,<br />
April 2004.<br />
[18] Peng Chao-Chung, Chen Chieh-Li, “Biaxial contour<strong>in</strong>g<br />
control with friction dynamics us<strong>in</strong>g a contour <strong>in</strong>dex<br />
approach”, International Journal of Mach<strong>in</strong>e Tools and<br />
Manufacture, vol. 47, pp. 1542-1555, May 2007.<br />
[19] Geng Lirong, Zhou Kai, “Research on Real Time<br />
Compensation Method Based on Time Series Predictive<br />
Technology for Contour Error of CNC Mach<strong>in</strong>e Tool”,<br />
Manufactur<strong>in</strong>g Technology & Mach<strong>in</strong>e Tool, vol. 6, pp.<br />
22-25, July 2004.<br />
[20] Wang Baoren, Wang Jie, Zhang Chengrui, “Contour error<br />
vector model and its application to CNC systems”,<br />
Computer Integrated Manufactur<strong>in</strong>g Systems, vol. 16, pp.<br />
1401-1407, May 2010.<br />
© 2013 ACADEMY PUBLISHER
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[21] Zhao Ximei, Guo Q<strong>in</strong>gd<strong>in</strong>g, “Zero Phase Adaptive Robust<br />
Cross Coupl<strong>in</strong>g Control for NC Mach<strong>in</strong>e Multiple L<strong>in</strong>ked<br />
Servo Motor”, Proceed<strong>in</strong>gs of the CSEE, vol. 28, pp. 129-<br />
133, April 2008.<br />
[22] Liu Yi, Cong Shuang, “Optimal Contour<strong>in</strong>g Control Based<br />
on Task Coord<strong>in</strong>ate Frame and Its Simulation”, Journal of<br />
System Simulation, vol. 21, pp. 3381- 3386, March 2009.<br />
[23] ZHAO Guo-yong, ZHAO Fu-l<strong>in</strong>g, XU Zhi-xiang, “Highprecision<br />
cross-coupled control approach based on NURBS<br />
curve <strong>in</strong>terpolator”, Journal of Dalian University of<br />
Technology, vol. 48, pp. 210-214, July 2008.<br />
Guoyong Zhao was born <strong>in</strong> Shandong, Ch<strong>in</strong>a <strong>in</strong> 1976. He has a<br />
Ph.D. <strong>in</strong> Mechanical and Electronic Eng<strong>in</strong>eer<strong>in</strong>g (2008) from<br />
Dalian University of Technology, Dalian, Ch<strong>in</strong>a. His ma<strong>in</strong><br />
<strong>in</strong>terest is mechanical manufactur<strong>in</strong>g and automation<br />
technology.<br />
Hongj<strong>in</strong>g An was born <strong>in</strong> Hebei, Ch<strong>in</strong>a <strong>in</strong> 1987. She is a master<br />
postgraduate majored <strong>in</strong> mechanical manufactur<strong>in</strong>g and<br />
automation <strong>in</strong> Shandong University of Technology, Zibo, Ch<strong>in</strong>a.<br />
Her ma<strong>in</strong> <strong>in</strong>terest is mechanical manufactur<strong>in</strong>g and automation<br />
technology.<br />
Q<strong>in</strong>gzhi Zhao was born <strong>in</strong> Shandong, Ch<strong>in</strong>a <strong>in</strong> 1962. He has a<br />
Ph.D. <strong>in</strong> mechanical manufactur<strong>in</strong>g and automation (2005) from<br />
Nanj<strong>in</strong>g University of Aeronautics and Astronautics, Nanj<strong>in</strong>g,<br />
Ch<strong>in</strong>a. His ma<strong>in</strong> <strong>in</strong>terest is mechanical manufactur<strong>in</strong>g and<br />
automation technology.<br />
© 2013 ACADEMY PUBLISHER
1520 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Research of Leaf Quality Based on Snowflake<br />
Theory<br />
Lihui Zhou<br />
College of Sciences, Hebei United University, Tangshan, Hebei, Ch<strong>in</strong>a<br />
Email: zhoulh324@163.com<br />
Jiajia Sun, Juanjuan An and Jun Long<br />
College of Sciences, Hebei United University, Tangshan, Hebei, Ch<strong>in</strong>a<br />
Email: zhoulh324@163.com<br />
Abstract—To study the leaves quality, this paper proposed<br />
two efficient models to analyze leaf quality, which classify<br />
leaves based on different shapes, leaf shapes were classified<br />
from the macro and micro perspectives respectively. In the<br />
two perspectives, <strong>in</strong>fluential factors were extracted and<br />
analyzed by factor analysis and K-means cluster<strong>in</strong>g. After<br />
compar<strong>in</strong>g cluster<strong>in</strong>g result with actual classification result,<br />
misjudgment probability is found to be very low. In the<br />
second model, snowflake model theory was proposed. The<br />
theory is high similarity between snow structure and tree<br />
structure, and the formation of the branch copies the<br />
exterior characteristics of the backbone. Then the growth<br />
process of a tree was simulated, after calculat<strong>in</strong>g the<br />
number of smallest branches through programm<strong>in</strong>g, the<br />
total number of leaves could be calculated out. To estimate<br />
the tree leaf weight, two steps were divided. First step was to<br />
estimate the number of leaves us<strong>in</strong>g the snow theory. Second<br />
step was to estimate the area of s<strong>in</strong>gle leaf. F<strong>in</strong>ally, the area<br />
measurement model to flat leaf was set up to measure the<br />
area of the curly leaf, which was divid<strong>in</strong>g the whole curly<br />
leaf <strong>in</strong>to small pieces.<br />
Index Terms—factor analysis, snowflake theory,<br />
misjudgment probability, error evaluation<br />
I. INTRODUCTION<br />
Leaves are the material basis of photosynthesis, the<br />
“green factory” produc<strong>in</strong>g nutrients, and the medium of<br />
transpiration [1, 2]. It is not only the important factors of<br />
the growth of trees, yields of leaves and species<br />
characteristics, but also the important means for<br />
reasonable cultivation and management of trees and<br />
detection of occurrence and development of plant<br />
diseases and <strong>in</strong>sect pests [3, 4]. So leaf area is the<br />
constant consideration <strong>in</strong> the physiological and<br />
biochemical research, genetic breed<strong>in</strong>g, cultivation, etc.,<br />
of trees [5]. In trees cultivation, leaf area <strong>in</strong>dex is<br />
commonly used to weigh the trees group's growth, which<br />
is used as the referential <strong>in</strong>dex for determ<strong>in</strong><strong>in</strong>g cultivation<br />
measures [6, 7]. In addition, the determ<strong>in</strong>ation of leaf<br />
area ate by pests is the important content of study<strong>in</strong>g pest<br />
damage loss. And accurate measurement of leaf area is<br />
the premise of study<strong>in</strong>g leaf area [8].<br />
There has been a variety of algorithm for determ<strong>in</strong><strong>in</strong>g<br />
surface area of a s<strong>in</strong>gle leaf. Direct measurements have<br />
been made by many scholars with <strong>in</strong>strument<br />
measurement method, paper draw<strong>in</strong>g method, digital<br />
image process<strong>in</strong>g method [11, 12], experience formula<br />
and volume method. Leaves are divided <strong>in</strong>to two types,<br />
i.e., needle-leaved tree and broad-leaved tree, for which<br />
different methods should be taken to measure surface<br />
area of their leaves. The measurement of leaf surface area<br />
with <strong>in</strong>strument method is simple and quick <strong>in</strong> operation.<br />
Structure used <strong>in</strong> the measurement could be divided <strong>in</strong>to<br />
two types: one is leaf area structure and another is<br />
planimeter [13]. In paper draw<strong>in</strong>g method, leaves are<br />
spread out on flat paper with well-distributed coord<strong>in</strong>ates<br />
and outl<strong>in</strong>e of the leaves are drawn on the paper [14, 15].<br />
After that grids occupied by each leaf are counted to<br />
calculate surface area of respective leaf. A full grid is<br />
counted as an area unit and less than a full grid is counted<br />
accord<strong>in</strong>g to the proportion occupied by the leaf <strong>in</strong> the<br />
grid, i.e., 1 2,1 4 etc.<br />
There is a variety of shapes for leaves [16]. Leaves are<br />
the largest organ of trees exposed to air, with the largest<br />
contact area to outside environment. Therefore,<br />
environmental conditions have a significant impact on<br />
shape and structure of leaves. In the evolutionary process<br />
trees adapt<strong>in</strong>g to different ecological environment, a<br />
variety of ecological types of leaves is shaped. In dry<br />
climate and drought environment with the lack of<br />
moisture <strong>in</strong> soil, <strong>in</strong> order to adapt to drought environment,<br />
the leaf structure characteristics of trees grow<strong>in</strong>g <strong>in</strong> arid<br />
regions is work<strong>in</strong>g towards two aspects of development,<br />
i.e., reduc<strong>in</strong>g transpiration and sav<strong>in</strong>g water [17, 18].<br />
Thus leaves of those trees are usually small to reduce<br />
transpiration of leaf area.<br />
Stout branches could withstand larger pressure, and<br />
farther the branches are away from the branch nodes the<br />
shorter and th<strong>in</strong>ner they are [7]. The th<strong>in</strong>ner the branches<br />
are, the lighter the weight born by the branches is and the<br />
smaller the leaves are. The longer the length to branch<br />
nodes on the same height to the ground is, the bigger the<br />
shapes of leaves are [8, 9]. Compared with leaves on<br />
branches from the same class of branch nodes, leaves on<br />
branches lower to the ground are bigger to enhance<br />
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photosynthesis for weak sunlight they receive [10, 11].<br />
Therefore, the distribution of leaves on trees and branches<br />
affects the shape of leaves.<br />
In 1999, experts have made research <strong>in</strong>to branch<strong>in</strong>g<br />
angle of trees with statistical method, found<strong>in</strong>g that<br />
branch<strong>in</strong>g phenotypes of trees is the mutual effect of<br />
genetics and environment [12, 13]. Tree species us<strong>in</strong>g 30 0<br />
as basic branch<strong>in</strong>g system <strong>in</strong>cludes: P<strong>in</strong>nata, Spend Pear,<br />
Sap<strong>in</strong>dus , Hong Kong Quebracho, Chung Yeung Wood,<br />
etc. Tree species us<strong>in</strong>g 60 0 as basic branch<strong>in</strong>g system<br />
<strong>in</strong>cludes: White Lam , Phoenix Wood , Crabapple Tree ,<br />
Large Leaves Shi Li, etc. Tree species us<strong>in</strong>g 90 0 as basic<br />
branch<strong>in</strong>g system <strong>in</strong>cludes: Ha<strong>in</strong>an Indus, Homalium<br />
Ha<strong>in</strong>anense, Gentianales [14, 19, 20]. The bigger the<br />
branch<strong>in</strong>g angles of the trees are, the larger the leaves are.<br />
Accord<strong>in</strong>g to statistical data analysis, the bigger the<br />
branch<strong>in</strong>g angles are, the larger the crown of the trees are.<br />
Because the sunlight sh<strong>in</strong><strong>in</strong>g <strong>in</strong>tensity of the lower leaves<br />
is weak, <strong>in</strong> order to <strong>in</strong>crease photosynthesis, the shape of<br />
leaves become larger. So the shape of crown of trees<br />
affects the shape of leaves. The shape of leaves (general<br />
characteristics) is correlated to the outl<strong>in</strong>e and branch<strong>in</strong>g<br />
structure of trees.<br />
In recent years, the use of mathematical model to<br />
predict leaf area has become a very common method [7,<br />
17, 20]. With l<strong>in</strong>ear model, Robert Rogers Thomas M.<br />
H<strong>in</strong>ckley has made a research <strong>in</strong>to the relationship<br />
between leaf weight and area of oak species and sapwood<br />
produced <strong>in</strong> the same year by the same tree (expressed<br />
with CSA). Accord<strong>in</strong>g to the research, the relationship is<br />
highly correlated <strong>in</strong> yellow oaks and white oaks. Through<br />
the research <strong>in</strong>to the relationship between leaf area and<br />
chest diameter of arbors and shrubs, Kittredge has<br />
successful completed the fitt<strong>in</strong>g of leaf area and chest<br />
diameter regression equation. With BP artificial neural<br />
network, related work has effectively predicted the<br />
cucamultion volume of stand<strong>in</strong>g forest <strong>in</strong> Greater<br />
Kh<strong>in</strong>gan Range <strong>in</strong> [3, 13]. BP neural network method has<br />
been used to solve the problem of leaf shape<br />
classification, result<strong>in</strong>g <strong>in</strong> an accuracy of 86.67%.<br />
However, mathematical model is seldom used to <strong>in</strong>-depth<br />
research of leaf shape classification.<br />
To study the leaves quality, this paper proposed two<br />
efficient models to analyze leaf quality, which classify<br />
leaves based on different shapes, leaf shapes were<br />
classified from the macro and micro perspectives<br />
respectively. In the two perspectives, <strong>in</strong>fluential factors<br />
were extracted and analyzed by factor analysis and K-<br />
means cluster<strong>in</strong>g. After compar<strong>in</strong>g cluster<strong>in</strong>g result with<br />
actual classification result, misjudgment probability is<br />
found to be very low. The second model is based on<br />
snowflake theory, which is high similarity between snow<br />
structure and tree structure, and the formation of the<br />
branch copies the exterior characteristics of the backbone.<br />
Then the growth process of a tree was simulated, after<br />
calculat<strong>in</strong>g the number of smallest branches through<br />
programm<strong>in</strong>g, the total number of leaves could be<br />
calculated out. To estimate the tree leaf weight, two steps<br />
were divided. First step was to estimate the number of<br />
leaves us<strong>in</strong>g the snow theory. Second step was to<br />
estimate the area of s<strong>in</strong>gle leaf. F<strong>in</strong>ally, the area<br />
measurement model to flat leaf was set up to measure the<br />
area of the curly leaf, which was divid<strong>in</strong>g the whole curly<br />
leaf <strong>in</strong>to small pieces<br />
II. PROPOSED CLASSIFICATION MODEL<br />
A. Terms Expla<strong>in</strong>ed<br />
• Ground Diameter: Diameter of the trunk about 20cm<br />
from the ground.<br />
• Breast Diameter: Diameter of the trunk about 1.3m<br />
from the ground.<br />
• Clear length: height of trunk below m<strong>in</strong>imum<br />
branches of the crown.<br />
• Crown of a Tree: The part above the trunk of an arbor<br />
tree bear<strong>in</strong>g branches and leaves, like a crown.<br />
• Class 1 branch: Class 1 branch is the framework of a<br />
tree, the length and special arrangement of which plays<br />
a dom<strong>in</strong>ant role <strong>in</strong> shap<strong>in</strong>g the tree. It has a certa<strong>in</strong><br />
grow<strong>in</strong>g position and azimuth attributes on the trunk.<br />
• Node Sections: Sections divid<strong>in</strong>g by nodes on class 1<br />
branch.<br />
• Section Spac<strong>in</strong>g: Distance between each layer of class 1<br />
branches.<br />
• Azimuth: The horizontal angle between each class 1<br />
branch and horizontal plane <strong>in</strong> verticality to the trunk.<br />
• Branch Angle: Vertical angle between each class 1<br />
branch and vertical plane parallel to the surface of the<br />
trunk.<br />
• Curvature: Curv<strong>in</strong>g degree of class 1 branches.<br />
• Physiological Age: is a concept compar<strong>in</strong>g with growth<br />
age, represent<strong>in</strong>g plant life vitality, and could be<br />
dist<strong>in</strong>guished accord<strong>in</strong>g to the change of the structure<br />
of plant shapes. When the physiological age of the<br />
lateral branch is the same to that of the trunk, it is<br />
called “repeated growth” phenomenon, which accord<br />
with our hypothesis <strong>in</strong> snowflake theory.<br />
B. The Classification Model of Leaves 1<br />
For trees, there are <strong>in</strong>ternal and external causes<br />
affect<strong>in</strong>g their leaves shape, but the <strong>in</strong>ternal and external<br />
causes all have a variety of factors, such as for <strong>in</strong>ternal<br />
causes there are genes, ways of transportation, and<br />
mutation, etc.; for external causes there are sunsh<strong>in</strong>e,<br />
moisture, temperature, change of worms, and soil etc.<br />
Therefore, classification for leaves shapes is a complex<br />
and delicate job. Our analysis is ma<strong>in</strong>ly carried out from<br />
two perspectives, i.e., macro and micro perspectives.<br />
The theoretical result shows that the shape of leaves is<br />
not only determ<strong>in</strong>ed by their growth genes but also<br />
affected by growth environment, growth shape and<br />
growth scale of the trees. From this perspective, certa<strong>in</strong><br />
<strong>in</strong>fluential factors of the shape of tree leaves could be<br />
chosen as the <strong>in</strong>dexes. Accord<strong>in</strong>g to relevant material,<br />
factors describ<strong>in</strong>g shapes of trees <strong>in</strong>clude: ground<br />
diameter, breast diameter, tree height, clear height,<br />
average crown diameter, south-north crown length, eastwest<br />
crown length, layers, <strong>in</strong>ternodes spac<strong>in</strong>g, etc.<br />
Accord<strong>in</strong>g to the n<strong>in</strong>e factors cluster analysis is made on<br />
trees to classify the similar growth shapes <strong>in</strong>to one<br />
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category. But it just makes a rough analysis on leaves<br />
shapes, so the next step is ref<strong>in</strong>ed analysis.<br />
C. Classification Model of Leaves 2<br />
Then factor analysis is made on tree leaf shapes with<strong>in</strong><br />
one category to calculate factor score, which is used for<br />
cluster<strong>in</strong>g. This k<strong>in</strong>d of cluster<strong>in</strong>g analysis method is<br />
ref<strong>in</strong>ed. We know that there are several dozens of factors<br />
describ<strong>in</strong>g leaf shapes, such as leaf shape, leaf width, leaf<br />
length, leaf ve<strong>in</strong>, etc., but we know that the length of<br />
ve<strong>in</strong>s <strong>in</strong> a certa<strong>in</strong> extent determ<strong>in</strong>es leaf length and leaf<br />
width. And some factors could be completely described<br />
by other factors, so we use the method of reduc<strong>in</strong>g<br />
dimension firstly and then cluster<strong>in</strong>g. We use factor<br />
analysis to reduce the dimension of <strong>in</strong>fluential factors to<br />
get factor score for cluster<strong>in</strong>g. This method not only can<br />
dist<strong>in</strong>guish well leaf shapes, but also can reduce the<br />
complexity of the analyzed problem.<br />
The mathematical model for factor analysis is as<br />
follows:<br />
⎧X1 = a11F1 + a12F2 + + a1 mFm<br />
+ ε1<br />
⎪X2 = a21F1+ a22F2 + + a2 mFm<br />
+ ε<br />
2<br />
⎨<br />
, (1)<br />
⎪<br />
<br />
⎪<br />
⎩XP = aP 1F1 + aP2F2<br />
+ + aPmFm + ε<br />
P<br />
represented with matrix:<br />
⎡X1 ⎤ ⎡a11 a12 a1 m ⎤ ⎡F1<br />
⎤ ⎡ε1<br />
⎤<br />
⎢<br />
X<br />
⎥ ⎢ ⎥<br />
2<br />
a21 a22 a<br />
⎢<br />
2m<br />
F<br />
⎥ ⎢<br />
2<br />
ε<br />
⎥<br />
⎢ ⎥ ⎢<br />
<br />
2<br />
= ⎥ ⎢ ⎥+<br />
⎢ ⎥ .<br />
⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢<br />
⎥<br />
⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥<br />
⎣X P⎦ ⎣aP1 aP2<br />
aPm⎦<br />
⎣Fm<br />
⎦ ⎣ε<br />
P⎦<br />
Simply recorded as:<br />
And meet:<br />
1) m≤ P;<br />
2) cov ( F, ε ) = 0 ;<br />
X = AF + ε . (2)<br />
⎡1 0 ⎤<br />
3) D( F)<br />
=<br />
⎢ ⎥<br />
⎢<br />
<br />
⎥<br />
= Im<br />
;<br />
⎢⎣0 1 ⎥⎦<br />
F , , F is unrelated and variance are 1.<br />
1 m<br />
2<br />
⎡σ<br />
1<br />
0 ⎤<br />
⎢ ⎥<br />
4) D ( ε ) = ⎢ ⎥ .<br />
⎢<br />
2<br />
0 σ ⎥<br />
⎣ <br />
P ⎦<br />
ε<br />
1,<br />
,ε P<br />
denote unrelated and different variance.<br />
Among them is the P dimensional random vector as<br />
unobservable volume, comprised by P <strong>in</strong>dexes got <strong>in</strong><br />
F = F , F ′ is called common<br />
actual observation. ( )<br />
factor of ( )<br />
1<br />
,<br />
m<br />
X = X , , 1<br />
X ′<br />
P<br />
the above-mentioned<br />
<strong>in</strong>tegrated variable. A is factor load<strong>in</strong>g matrix, on which<br />
maximum variance rotation is made with variance, so that<br />
the structure of A simplified. In other words, the square<br />
value of every column elements of load<strong>in</strong>g matrix is<br />
made to polarization 0 or 1 or the more dispersed the<br />
contribution rate of public factor is the better is the result.<br />
Variables got from factor analysis are represented as<br />
l<strong>in</strong>ear comb<strong>in</strong>ation of public factors:<br />
Xi = ai1F1+ ai2F2 + + aimFm<br />
+ εi<br />
i = 1,2, ,P<br />
(3)<br />
But usually when public factors are used to represent<br />
the orig<strong>in</strong>al variables, it is more convenient to describe<br />
the characteristics of research object. Therefore, public<br />
factors are represented as l<strong>in</strong>ear comb<strong>in</strong>ation of variables,<br />
i.e., the factor score function, namely<br />
F′= β X + β X + + β X<br />
j j1 1 j2 2 jP P<br />
j= 1,2, ,m<br />
(4)<br />
We calculated m factor score for each left samples.<br />
Use the score of these m factors as a variable value to<br />
cluster different leaves with the method of K-means<br />
Cluster.<br />
D. Cluster<strong>in</strong>g Error Estimation<br />
We have given the evaluation method for judg<strong>in</strong>g<br />
cluster<strong>in</strong>g effect. Usually we use back substitution<br />
misjudgment probability and cross misjudgment<br />
probability. If the number of misjudg<strong>in</strong>g samples belong<br />
to G 1 as belong to G2<br />
is N<br />
1<br />
, and the number of<br />
misjudg<strong>in</strong>g samples belong to G 2 as belong to G 1 is N<br />
2<br />
,<br />
the total number of samples of the two general<br />
classifications is n ,Then misjudgment probability is:<br />
N1+<br />
N2<br />
p = (5)<br />
n<br />
Back substitution misjudgment probability<br />
Set G<br />
1<br />
, G<br />
2<br />
as two general classifications,<br />
X , , 1<br />
X<br />
m<br />
and Y , , 1<br />
Yn<br />
are tra<strong>in</strong><strong>in</strong>g samples from<br />
G<br />
1<br />
, G<br />
2<br />
respectively, with all the tra<strong>in</strong><strong>in</strong>g samples used as<br />
m+ n new samples, which is substituted gradually <strong>in</strong>to<br />
established criterion for judg<strong>in</strong>g the ownership of the new<br />
samples. The process is called back substitution. If the<br />
number of misjudg<strong>in</strong>g samples belong to G 1<br />
as belong<br />
to G<br />
2<br />
is N<br />
1<br />
, and the number of misjudg<strong>in</strong>g samples<br />
belong to G 2<br />
as belong to G 1<br />
is N<br />
2<br />
, then misjudgment<br />
probability is:<br />
N1+<br />
N2<br />
pˆ<br />
=<br />
m+<br />
n<br />
Cross judgment probability<br />
Back to generation misjudgment probability is to<br />
elim<strong>in</strong>ate a sample every time, and use the rest<br />
of m+ n− 1 tra<strong>in</strong><strong>in</strong>g samples to establish a criterion for<br />
judgment, then use established criterion to make<br />
judgment on deleted samples. The above-mentioned<br />
analysis is made on each sample of those tra<strong>in</strong><strong>in</strong>g samples,<br />
and uses its misjudgment proportion as the misjudgment<br />
probability. The specific procedure is as follows:<br />
1) From tra<strong>in</strong><strong>in</strong>g samples <strong>in</strong> general classification G 1 ,<br />
elim<strong>in</strong>ate one of the samples, and use the rest of the<br />
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samples m − 1 plus all samples <strong>in</strong> G2<br />
to establish<br />
discrim<strong>in</strong>ate function;<br />
2) Use the established discrim<strong>in</strong>ate function to make<br />
judgment on elim<strong>in</strong>ated samples;<br />
3) Repeat steps 1), 2) until the samples <strong>in</strong> G 1 <strong>in</strong> turn<br />
be deleted and judged. The number of misjudged samples<br />
is recorded as m<br />
12<br />
;<br />
4) Repeat steps 1), 2), 3) for samples <strong>in</strong> G 2 , until all of<br />
the samples <strong>in</strong> G 2 <strong>in</strong> turn be deleted and discrim<strong>in</strong>ated.<br />
The number of misjudged samples is recorded as n<br />
21<br />
. So<br />
cross misjudgment probability is estimated:<br />
m12 + n21<br />
pˆ<br />
=<br />
(6)<br />
m+<br />
n<br />
If cluster<strong>in</strong>g result is bad, the follow<strong>in</strong>g several aspects<br />
of optimization could be carried out. 1) Increase sample<br />
capacity; 2) Increase new <strong>in</strong>dex variables; 3) If statistical<br />
data is wrong, rediscover data.<br />
III. PROPOSED MODEL BASED ON SNOWFLAKE THEORY<br />
A. Snowflake Theory<br />
Each snowflake on the whole is a hexagonal star, <strong>in</strong><br />
which there are six trunks, and then each trunk has small<br />
branches, and smaller branches grow<strong>in</strong>g on small<br />
branches, and so on, as shown <strong>in</strong> figure 1 below. The<br />
process of shap<strong>in</strong>g snowflake is copy<strong>in</strong>g part and the<br />
whole sections of it constantly. The process with the<br />
above mentioned of growth characteristics is called<br />
snowflake theory.<br />
Figure 1. Snowflake<br />
We already know <strong>in</strong> the above that each tree species<br />
has its own particular branch<strong>in</strong>g angle. We th<strong>in</strong>k of tree<br />
trunk as straight, and from another perspective, we could<br />
see it as a lateral branch. We all know that each lateral<br />
branch has the function of branch<strong>in</strong>g, and all of the lateral<br />
branches have the same status. Each layer of the branches<br />
will branch <strong>in</strong> accordance with certa<strong>in</strong> similar rule.<br />
Accord<strong>in</strong>g to this growth rule, we simulate the outl<strong>in</strong>e of<br />
a tree, as shown <strong>in</strong> Fig. 2.<br />
Figure 2. The Tree of Computer Simulation<br />
Accord<strong>in</strong>g to the ideas of snowflake theory, the growth<br />
process of trees is established until it reaches the state of<br />
the tree for observation. The laws of chang<strong>in</strong>g between<br />
the state of a certa<strong>in</strong> level of branch<strong>in</strong>g and the state of its<br />
sub-level of branch<strong>in</strong>g should be found out to for the<br />
recursion relationship of programm<strong>in</strong>g. Among a certa<strong>in</strong><br />
level of branch the ma<strong>in</strong> parameters are the quantity of<br />
branches, number of sections, <strong>in</strong>terval of sections,<br />
azimuth, <strong>in</strong>cluded angle of branch<strong>in</strong>g, curvature, length<br />
of branches, and stem. In [1] three ways of branch<strong>in</strong>g<br />
have been mentioned, i.e., s<strong>in</strong>gle axis branch<strong>in</strong>g, false<br />
b<strong>in</strong>ary branch<strong>in</strong>g and merg<strong>in</strong>g axis branch<strong>in</strong>g. To<br />
simulate the growth of a tree, which way of branch<strong>in</strong>g it<br />
belongs to should be found .Then after f<strong>in</strong>d<strong>in</strong>g out the<br />
law of its branch<strong>in</strong>g, computer could be used to simulate<br />
out its growth process.<br />
B. Ways for Branch<strong>in</strong>g<br />
We have known that the growth process of trees has<br />
the characteristics of self-adaptive, uncerta<strong>in</strong>ty,<br />
emergency, f<strong>in</strong>ality and open<strong>in</strong>g. Different k<strong>in</strong>ds of trees<br />
have different ways of branch<strong>in</strong>g, and the law of copy<strong>in</strong>g<br />
is different. So we will analyze ways of branch<strong>in</strong>g.<br />
Roughly there are three ways of branch<strong>in</strong>g for trees:<br />
• S<strong>in</strong>gle axis branch<strong>in</strong>g: The apical bud of the tree<br />
constantly grows up vigorously, shap<strong>in</strong>g the stout trunk.<br />
And lateral buds also grow <strong>in</strong>to the lateral branch, on<br />
which sub-branches grow aga<strong>in</strong>, as shown <strong>in</strong> figure 3<br />
below. The trunk of s<strong>in</strong>gle axis branch<strong>in</strong>g is<br />
comparatively straight, and the growth of other branches<br />
at all levels is not so vigorous as it. Poplar, metasequoia,<br />
etc., are all with<strong>in</strong> the group of s<strong>in</strong>gle axis branch<strong>in</strong>g.<br />
False b<strong>in</strong>ary branch<strong>in</strong>g: The apical bud of the tree<br />
stops grow<strong>in</strong>g after shap<strong>in</strong>g a branch. Close to the branch<br />
two opposite auxiliary buds simultaneously grow <strong>in</strong>to a<br />
pair of opposite lateral branches. Then the apical bud and<br />
auxiliary buds on the two opposite lateral branches repeat<br />
the same grow<strong>in</strong>g process, as shown <strong>in</strong> the figure below.<br />
Clove, carnation and horse chestnut, etc., are all with<strong>in</strong><br />
the group of false b<strong>in</strong>ary branch<strong>in</strong>g.<br />
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1524 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 3. S<strong>in</strong>gle Axis Branch<strong>in</strong>g<br />
• In the growth process of the trees, the branch<strong>in</strong>g<br />
angle of float from a certa<strong>in</strong> range.<br />
• In the growth process of the trees, along with the<br />
<strong>in</strong>crease of the layer of branch<strong>in</strong>g, branches become<br />
tapered, and length of branches gradually becomes short.<br />
From a macro po<strong>in</strong>t of View l, trees have one th<strong>in</strong>g <strong>in</strong><br />
common <strong>in</strong> the composition of it’s shape and structure,<br />
namely the basic construct<strong>in</strong>g element of trees are trunks,<br />
branches and leaves. The structur<strong>in</strong>g of each basic<br />
element is follow<strong>in</strong>g a same way: the trunk gives birth to<br />
the first layer of branches, which <strong>in</strong> turn gives birth to the<br />
second layer of branches, and so on. The process of<br />
giv<strong>in</strong>g birth eventually comes to leaves. In the occurrence<br />
and development process of the shape of the trees,<br />
organizations similar to the exist<strong>in</strong>g organizations are<br />
constantly copied and added to the exist<strong>in</strong>g ones.<br />
Based on the above-mentioned clon<strong>in</strong>g process, eight<br />
basic parameters are used to be def<strong>in</strong>ed the structure of<br />
branches, as shown <strong>in</strong> Table 1.<br />
TABLE I.<br />
EIGHT BASIC PARAMETERS<br />
Figure 4. False B<strong>in</strong>ary Branch<strong>in</strong>g<br />
Merg<strong>in</strong>g axis branch<strong>in</strong>g: The growth rate of apical bud<br />
of the tree slows down or the apical is dead or become<br />
flower bud. The auxiliary bud immediately under the<br />
apical bud replaces the growth of the apical bud to shape<br />
a branch. After that the apical bud of the branch stops<br />
grow<strong>in</strong>g and replaced by the auxiliary bud immediately<br />
under it. The growth process is repeated. The length of<br />
node section of merg<strong>in</strong>g axis branch<strong>in</strong>g is comparatively<br />
short, often with a tortuous shape, as shown <strong>in</strong> the figure<br />
below. Apple, pear, peach and apricot trees, etc., are all<br />
with<strong>in</strong> the group of merg<strong>in</strong>g axis branch<strong>in</strong>g.<br />
Layer Layers of tree [2, 8]<br />
H Height of branches [0.0, 1.0]<br />
R Bottom radius of branches [0.0, 1.0]<br />
Alfa Branch<strong>in</strong>g angle [0, 90 0 ]<br />
K Rattion of top and bottom radius [0.0, 1.0]<br />
P Height of branch<strong>in</strong>g po<strong>in</strong>t [0.0, 1.0]<br />
Q<br />
Attennuation of thickness of<br />
branches<br />
[0.0, 1.0]<br />
M Attennuation of lenght of branches [0.0, 1.0]<br />
Because of the <strong>in</strong>fluence from many k<strong>in</strong>ds of factors<br />
such as gravity, w<strong>in</strong>d and sunsh<strong>in</strong>e, etc., In the process of<br />
their growth, the growth shape of trees <strong>in</strong> nature has got<br />
great uncerta<strong>in</strong>ty and randomness. In order to describe<br />
shapes of trees more vividly, <strong>in</strong> the process of<br />
establish<strong>in</strong>g mathematical model stochastic function is<br />
<strong>in</strong>troduced. Follow<strong>in</strong>g is a maple tree simulated with a<br />
computer model, as shown <strong>in</strong> Fig. 6 and Fig. 7:<br />
Figure 5. Merg<strong>in</strong>g Axis Branch<strong>in</strong>g<br />
C. Establishment of Models<br />
Model assumptions are as follows:<br />
• In the growth process of the trees, abundant nutrients<br />
are supplied for the growth of each auxiliary bud.<br />
• In the growth process of the trees, no lateral branch<br />
dies.<br />
• Environmental factors shouldn’t <strong>in</strong>crease (decrease)<br />
to the highest (lowest) po<strong>in</strong>t so that to block the normal<br />
growth of the plants.<br />
Figure 6. Simulation of maple.<br />
From the simulation render<strong>in</strong>g with computer, we can<br />
f<strong>in</strong>d out that the similarity degree between the simulated<br />
image and maple tree <strong>in</strong> real life is very high. Visibly, the<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1525<br />
reliability of estimat<strong>in</strong>g leaves number with the use of<br />
snowflake theory is very high.<br />
curvature angle follow<strong>in</strong>g the ve<strong>in</strong> is very small, and we<br />
divide leaves with this k<strong>in</strong>d of features as shown <strong>in</strong> figure<br />
6(This is divided along the ve<strong>in</strong>s on the leaves), with the<br />
hypothesis that the rectangle divided out by us is <strong>in</strong> a<br />
plane.<br />
Figure 7. simulation of maple tree<br />
IV. SINGLE LEAF AREA ESTIMATION<br />
Ideas of model: we have classified leaf shapes <strong>in</strong> the<br />
above, so when we want to establish the model for leaf<br />
area estimation, we can f<strong>in</strong>d a representative leaf for<br />
analysis. In the process of analysis, ma<strong>in</strong>ly ideas of<br />
<strong>in</strong>tegration are used, <strong>in</strong> which, a reasonable division is<br />
given to leaves <strong>in</strong> different shapes <strong>in</strong> order to divided<br />
them <strong>in</strong>to graphics, of which areas can be calculated for<br />
analysis; Also considerations are gave to the bend<strong>in</strong>g<br />
problem of edges of leaves when the ve<strong>in</strong>s become closer<br />
to the central l<strong>in</strong>e at the middle of the leaves. For the<br />
calculation of this model each leave is segmented along<br />
with the ve<strong>in</strong>s of the leave.<br />
A. Flat Leaf<br />
Take a typical leaf, and draw its shape on a piece of a<br />
coord<strong>in</strong>ate paper. Take some po<strong>in</strong>ts from the draw<strong>in</strong>g and<br />
make a fitt<strong>in</strong>g to work out the leaf outl<strong>in</strong>e function with<br />
Least squares method. We can get the function images as<br />
shown <strong>in</strong> figure 8.Then we can calculate the leaf area S<br />
with curvil<strong>in</strong>ear <strong>in</strong>tegral:<br />
x2 x2<br />
∫ 1( ) ∫ 2( )<br />
(7)<br />
S = f x dx − f x dx<br />
x1 x1<br />
Figure 8. The simulation of flat leaf<br />
B. Curv<strong>in</strong>g Leaf<br />
Through observation we can f<strong>in</strong>d out that most of the<br />
curv<strong>in</strong>g of a leaf follows the ve<strong>in</strong> and towards the middle<br />
l<strong>in</strong>e, and the curv<strong>in</strong>g is gentle. The appearance of a bigger<br />
arc of curv<strong>in</strong>g is unusual, so we suppose that the<br />
Figure 9. The division of curv<strong>in</strong>g leaf<br />
This model can only make a rough estimation of the<br />
area of the curv<strong>in</strong>g leaf, and can only have an analysis on<br />
leaves with specific curv<strong>in</strong>g characteristics.<br />
C. Results of Model<br />
N is the number of the leaves on the tree;<br />
S is the area of a s<strong>in</strong>gle leaf;<br />
ρ is the surface density ;<br />
M is the weight of leaves on the maple tree.<br />
As for the maple used as an example, the number of<br />
the leaves simulated by computer belongs to<br />
[ 2187 , 2357 ].<br />
Accord<strong>in</strong>g to statistical data: the area of a s<strong>in</strong>gle leaf is<br />
about 52cm 2 , and the surface density is about 0.17g/cm 2 .<br />
Through calculation:<br />
M = ρ ⋅S⋅ N<br />
(8)<br />
The weight of the leaves on the maple tree is 19.3kg to<br />
20.8kg.<br />
We have used the method of factor analysis for<br />
cluster<strong>in</strong>g of leaf shapes to reduce the number of<br />
variables and simplify our research workload. We use a<br />
few public factors to expla<strong>in</strong> complicated relationships<br />
exist<strong>in</strong>g <strong>in</strong> more variables <strong>in</strong> observation. We use<br />
snowflake model to catch the law tree growth, well<br />
estimat<strong>in</strong>g the leaves quality of a tree. For the calculation<br />
the area of a s<strong>in</strong>gle leaf, not only the comparatively flat<br />
leaves are considered, but also the calculation of the area<br />
of leaf surface when there is the problem of surface<br />
curv<strong>in</strong>g.<br />
However because of time constra<strong>in</strong>ts, we couldn’t f<strong>in</strong>d<br />
out large amount of data for verify<strong>in</strong>g our theory.<br />
V. CONCLUSION<br />
Our ma<strong>in</strong> objective is about leaves quality research.<br />
First, we classify leaves based on different shapes, then<br />
simulate the processes of leaf growth and calculate total<br />
leaves per tree. Accord<strong>in</strong>g to the area and density of a<br />
leaf, we can easily estimate leaves weight of a tree.<br />
In the process of leaf shape classification, we firstly<br />
analyze the diversification of leaf shape. From the genetic<br />
© 2013 ACADEMY PUBLISHER
1526 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
perspective, exist<strong>in</strong>g research data shows that long term<br />
environment impact changes the gene of tree and this is<br />
the most essential factor affected the shape of leaf. On the<br />
other hand, the open branch angle, DBH, knot spac<strong>in</strong>g,<br />
crown diameter, clear length and tree height of tree will<br />
affect the shape of leaf. Dur<strong>in</strong>g the research, we found<br />
that the position of leaf also affects leaf shape. E.g., the<br />
smaller tip Angle will be the smaller leaf shape of the top<br />
branch. In the classification of leaf shape, if we directly<br />
classify leaf shapes accord<strong>in</strong>g to the parameters of the<br />
leaf structure, it will be complicated. Dur<strong>in</strong>g analysis, we<br />
found the method that is us<strong>in</strong>g some <strong>in</strong>dexes to classify<br />
leaf shape at first, and then classify<strong>in</strong>g leaf forms aga<strong>in</strong><br />
based on the structure of leaf. The method will reduce<br />
work load <strong>in</strong> the leaf shape classification, meanwhile, get<br />
a better result.<br />
In the weight estimate of tree leaf, we divide <strong>in</strong>to two<br />
steps. First step, we estimate the number of leaves.<br />
Dur<strong>in</strong>g research, we found and built the snow model<br />
theory that is high similarity between snow structure and<br />
tree structure (Therefore we get conclusion). The<br />
formation of the branch copies the exterior characteristics<br />
of the backbone. In the experimental simulation,<br />
simulated maple tree is highly similar with the actual<br />
sample at the aspects of crown diameter, breast diameter,<br />
number of branches, length and thickness of branches and<br />
so on. This suggests that the snow theory can be applied<br />
<strong>in</strong> the three growth simulation and it can be used <strong>in</strong> tree<br />
growth model <strong>in</strong> the future. Second step is estimat<strong>in</strong>g<br />
area of s<strong>in</strong>gle leaf previous methods of the leaf area<br />
estimation are direct measurement method and<br />
mathematical model analysis. However, those methods<br />
cannot measure curvature leaves. We had the<br />
correspond<strong>in</strong>g improvement. Firstly, we set up area<br />
measurement model to flat leaf. Then the area of the curly<br />
leaf was measured, which is divid<strong>in</strong>g the whole curly leaf<br />
<strong>in</strong>to small pieces. F<strong>in</strong>ally, we calculate total area of all<br />
small pieces to get result. The measurement of the curly<br />
leaf has especially mean<strong>in</strong>g because many factors <strong>in</strong><br />
nature can <strong>in</strong>fluence of leaf form.<br />
ACKNOWLEDGMENT<br />
The fund<strong>in</strong>g organizations are Hebei Higher Social<br />
Science Research 2011 Annual Fund (No. SZ2011518)<br />
and Tangshan Municipal Bureau of Science and<br />
Technology research and development guide plan (No.<br />
111302013b, No. 111102033b).<br />
REFERENCES<br />
[1] Xu Guoxiang, Statistical forecast<strong>in</strong>g and decision- mak<strong>in</strong>g,<br />
1 st ed., Shanghai: Shanghai F<strong>in</strong>ance University Press, 1998,<br />
pp.85-89.<br />
[2] Du Zifang, Sampl<strong>in</strong>g Techniques and Practices, 1 st ed.,<br />
Beij<strong>in</strong>g: Q<strong>in</strong>ghua University Press, 2004, pp.123-124.<br />
[3] Yang Guiyuan, Huang Yili, Mathematical Model<strong>in</strong>g,Hefei:<br />
Ch<strong>in</strong>a science and technology university Press, 2008,<br />
pp.75-79.<br />
[4] He Shu, “Application of SOM Neural Network on leaves’<br />
shape classification,” <strong>in</strong> Computer development and<br />
application, vol. 17, pp. 31–33, 2003.<br />
[5] Xia Shanzhi, Zhu Xujia, “Review of the measur<strong>in</strong>g method<br />
<strong>in</strong> leaf area”, <strong>in</strong> Forestry survey and design, 2009, pp.15-<br />
17.<br />
[6] Jiang Youxu, Zang Runguo, “A prelim<strong>in</strong>ary analysis on<br />
elementary architecture of tropical trees <strong>in</strong> the topical<br />
arboretum of Jian Feng l<strong>in</strong>g”, <strong>in</strong> Resource Scienc, vol. 21,<br />
1997<br />
[7] Zhang Chuny<strong>in</strong>g, Guo J<strong>in</strong>gfeng, Liu Lu, “P-Graph and Its<br />
Application,” unpublished.<br />
[8] Zhou Lihui, Wang Hong, Du Lip<strong>in</strong>g, “A Balanced<br />
Relationship Analysis Between Ch<strong>in</strong>ese Economic Growth<br />
and the Iron and Steel Production Based on Time Series,”<br />
International Conference on E-Bus<strong>in</strong>ess and E-<br />
Government, vol.2, pp. 192-196 , August 2010<br />
[9] Zhang Chuny<strong>in</strong>g, Guo J<strong>in</strong>gfeng, Chen Xiao, “Research on<br />
random walk rough match<strong>in</strong>g algorithm of attribute subgraph”,<br />
International Conference on Advanced Materials<br />
and Computer Science, pp. 297-302, October 2011.<br />
[10] Liu Fengchun, Zhang Chuny<strong>in</strong>g, “λ-Operations on Packet<br />
Sets and the Significance of Application”, unpublished.<br />
[11] Thomas G C, John J E, “Algometric equations for four<br />
valuable trop i.cal tree species”, <strong>in</strong> Forest Ecology and<br />
Management, 2006, pp.351 - 360.<br />
[12] Zhou Lihui, “Analysis about the Effectiveness Evaluation<br />
of Ch<strong>in</strong>a’s Real Estate Enterprises based on DEA model”,<br />
International Conference on Eng<strong>in</strong>eer<strong>in</strong>g and Bus<strong>in</strong>ess<br />
Management, vol.1, pp. 1384-1387, October, 2011.<br />
[13] Yibo Tan, Zhonghui Zhao, “The Ma<strong>in</strong> Methods for<br />
Determ<strong>in</strong><strong>in</strong>g Leaf Area Index”, <strong>in</strong> Forest Inventory And<br />
Plann<strong>in</strong>g, 2008, pp. 33.<br />
[14] Yan Gao, Chengjun Zhang and Liyan Zhang,<br />
“Comparative Analysis of Three GARCH Models Based<br />
on MCMC”, The 2nd International Conference on<br />
Information Comput<strong>in</strong>g and Applications, vol., pp. 284-<br />
286, September, 2011.<br />
[15] Gao Yan, Wan X<strong>in</strong>ghuo, Liu Qiume, “Study of the<br />
Spillover Effect Based on the B<strong>in</strong>ary GED-GARCH<br />
Recent Advance <strong>in</strong> Statistics Application and Related<br />
Areas”, Conference Proceed<strong>in</strong>gs of The 4th International<br />
Institute of Stastistics & Management Eng<strong>in</strong>eer<strong>in</strong>g<br />
Symposium, vol.2, pp. 134-134, July, 2011.<br />
[16] Yan Gao, Chengjun Zhang and Liyan Zhang, “Comparison<br />
of GARCH Models based on Different Distributions,”<br />
unpublished.<br />
[17] Zhou Lihui, “The Pr<strong>in</strong>cipal Component Analysis about<br />
Three-dimensional time series data Of Ch<strong>in</strong>ese <strong>in</strong>formation<br />
process”, International Conference on E-Bus<strong>in</strong>ess and E-<br />
Government, vol.2, pp. 4901-4904, July, 2010.<br />
[18] Zhang Chuny<strong>in</strong>g, Guo J<strong>in</strong>gfeng, Chen Xiao, “Research on<br />
random walk rough match<strong>in</strong>g algorithm of attribute subgraph”,<br />
International Conference on Advanced Materials<br />
and Computer Science, pp. 297-302, May, 2011.<br />
[19] Aim<strong>in</strong> Yang, Chunfeng Liu, J<strong>in</strong>cai Chang and Li Feng,<br />
“TOPSIS-Based Numerical Computation Methodology for<br />
Intuitionistic Fuzzy Multiple Attribute Decision Mak<strong>in</strong>g”,<br />
<strong>in</strong> Nformation-an International Interdiscipl<strong>in</strong>ary Journal,<br />
2010, pp. 3169-3174<br />
[20] Zhang Chuny<strong>in</strong>g, Wang J<strong>in</strong>g, “Multi-relational Bayesian<br />
classification algorithm with rough set”, 7th International<br />
Conference on Fuzzy Systems and Knowledge Discovery,<br />
pp. 1565-1568, August, 2010.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1527<br />
Lihui Zhou was born <strong>in</strong> Tangshan of Hebei prov<strong>in</strong>ce, on<br />
November 12, 1980. She got Master Degree of Econometrics <strong>in</strong><br />
Southwestern University of F<strong>in</strong>ance and Economics <strong>in</strong> July,<br />
2006, which is <strong>in</strong> Sichun prov<strong>in</strong>ce, <strong>in</strong> ch<strong>in</strong>a. Her major field of<br />
study is multivariate statistical analysis.<br />
She has been work<strong>in</strong>g <strong>in</strong> School of Science, Hebei United<br />
University s<strong>in</strong>ce September, 2006, which located <strong>in</strong> X<strong>in</strong> Hua<br />
Street 46, Tangshan, Hebei, P. R. Ch<strong>in</strong>a. Now her Current<br />
<strong>in</strong>terests are the application of the qu<strong>in</strong>tile regression model.<br />
Jiajia Sun was born <strong>in</strong> Shijiazhuang of Hebei prov<strong>in</strong>ce, on July<br />
8, 1986. She is a junior student of Hebei United University. Her<br />
major is mathematical statistics.<br />
Juanjuan An was born <strong>in</strong> X<strong>in</strong>gtai of Hebei prov<strong>in</strong>ce, on May<br />
20, 1986. She is a junior student of Hebei United University.<br />
Her major is mathematical statistics.<br />
Jun Long was born <strong>in</strong> Zhengzhou of Henan prov<strong>in</strong>ce, on<br />
August 14, 1985. He is a junior student of Hebei United<br />
University. His major is <strong>in</strong>formation science.<br />
© 2013 ACADEMY PUBLISHER
1528 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Oscillation Criteria for Second Order Nonl<strong>in</strong>ear<br />
Neutral Perturbed Dynamic Equations on Time<br />
Scales<br />
Xiup<strong>in</strong>g Yu<br />
Department of Mathematics and Physics, Hebei Institute of Architecture and Civil Eng<strong>in</strong>eer<strong>in</strong>g, Zhangjiakou, Ch<strong>in</strong>a<br />
Email: xiup<strong>in</strong>g66@163.com<br />
Hua Du<br />
Information Science and Eng<strong>in</strong>eer<strong>in</strong>g College, Hebei North University, Zhangjiakou, Ch<strong>in</strong>a<br />
Email: dhhappy88@126.com<br />
Hongyu Yang<br />
Department of Mechanic and Eng<strong>in</strong>eer<strong>in</strong>g, Zhangjiakou Vocational Technology Institute, Zhangjiakou, Ch<strong>in</strong>a<br />
Email: yanghy88@s<strong>in</strong>a.com<br />
Abstract—To <strong>in</strong>vestigate the oscillatory and asymptotic<br />
behavior for a certa<strong>in</strong> class of second order nonl<strong>in</strong>ear<br />
neutral perturbed dynamic equations on time scales. By<br />
employ<strong>in</strong>g the time scales theory and some necessary<br />
analytic techniques, and <strong>in</strong>troduc<strong>in</strong>g the class of parameter<br />
functions and generalized Riccati transformation, some new<br />
sufficient conditions for oscillation of such dynamic<br />
equations on time scales were established. The results not<br />
only improve and extend some known results <strong>in</strong> the<br />
literature, but also unify the oscillation of second order<br />
nonl<strong>in</strong>ear neutral perturbed differential equations and<br />
second order nonl<strong>in</strong>ear neutral perturbed difference<br />
equations. In particular, the results are essentially new<br />
under the relaxed conditions for the parameter function.<br />
Some examples are given to illustrate the ma<strong>in</strong> results.<br />
Dynamic equations on time scales are widely used <strong>in</strong> many<br />
fields such as computer, electrical eng<strong>in</strong>eer<strong>in</strong>g, population<br />
dynamics, and neural network, etc.<br />
Index Terms—oscillation, nonl<strong>in</strong>ear neutral perturbed<br />
dynamic equation, time scales, Riccati transformation.<br />
I. INTRODUCTION<br />
The theory of time scales, which has recently received<br />
a lot of attention, was <strong>in</strong>troduced by Stefan Higher <strong>in</strong> his<br />
Ph.D. thesis [1] <strong>in</strong> 1988 <strong>in</strong> order to unify cont<strong>in</strong>uous and<br />
discrete analysis. Not only can this theory of so-called<br />
“dynamic equations” unify the theories of differential<br />
equations and of difference equations, but also it is able<br />
to extend these classical cases “<strong>in</strong> between”, e.g., to socalled<br />
q-difference equations. Several authors have<br />
expounded on various aspects of this new theory, see the<br />
survey paper by Agarwal [2] and references cited there<strong>in</strong>.<br />
A book on the subject of time scales by Bohner and<br />
Peterson [3] summarizes and organizes much of the time<br />
scale calculus. A time scales T is an arbitrary nonempty<br />
closed subset of the real numbers . There are many<br />
<strong>in</strong>terest<strong>in</strong>g time scales and they give rise to plenty of<br />
applications, the cases when the time scale is equal to<br />
reals or the <strong>in</strong>tegers represent the classical theories of<br />
differential and of difference equ-ations. Another useful<br />
+∞<br />
time scale a time scale P<br />
, n 0[( na b), na ( b) a]<br />
ab∪<br />
=<br />
+ + + is<br />
wi-dely used to study population <strong>in</strong> biological<br />
communities, electric circuit and so on [3].<br />
In recent years, there has been much research activity<br />
concern<strong>in</strong>g the oscillation and nonoscillation of solutions<br />
of some dynamic equations on time scales, and we refer<br />
the reader to the papers [4-17] and references cited<br />
there<strong>in</strong>. Regard<strong>in</strong>g neutral dynamic equations, Argarwal<br />
et al [6] considered the second order neutral delay<br />
dynamic quation<br />
Δ<br />
{ ( t)[( xt ( ) ctxt ( ) ( )) ] γ Δ<br />
α + − τ } + ftxt ( , ( − δ)) = 0. (1)<br />
where γ > 0 is an odd positive <strong>in</strong>teger, τ andδ are position<br />
constants, α Δ () t > 0, and proved that the oscillation<br />
of (1) is equivalent to the oscillation of a first order delay<br />
dynamic <strong>in</strong>equality. Saker [7] considered (1) where γ ≥ 1 ,<br />
is an odd positive <strong>in</strong>teger, the condition α Δ () t > 0is<br />
abolished and established some new sufficient conditions<br />
for oscillation of (1). However the results established <strong>in</strong><br />
[6-7] are only valid for the time scales ,<br />
, or h<br />
, q <br />
,<br />
<br />
where q = { t: t = q k<br />
, k∈ , q > 1} .<br />
Sah<strong>in</strong>er et al [8] considered the general equation<br />
Δ γ Δ<br />
{ α( t)[( xt ( ) + ctx ( ) ( τ( t)) ] } + ftx ( , ( δ( t))) = 0 . (2)<br />
on a time scale T , where γ ≥ 1 and τ () t ≤t, δ () t ≤ t, and<br />
followed the argument <strong>in</strong> [6-7] by reduc<strong>in</strong>g the oscillation<br />
of (2) to the oscillation of a first order delay dynamic<br />
<strong>in</strong>equality and established some sufficient conditions for<br />
the oscillation. However one can easily see that the two<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1528-1535
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1529<br />
examples presented <strong>in</strong> [8] to illustrate the ma<strong>in</strong> results are<br />
valid only when T= and cannot be applied when T = .<br />
Agarwal, O′Regan and Saker [3]considered (2) where γ ≥<br />
1 is an odd positive <strong>in</strong>teger and α Δ () t > 0, and established<br />
some new oscillation criteria by employ<strong>in</strong>g the Riccati<br />
transformation technique which can be applied on any<br />
time scale T and improved the results <strong>in</strong> [6, 8].<br />
Bohner and Saker [9] considered perturbed nonl<strong>in</strong>ear<br />
dynadynamic equation<br />
Δ<br />
{ ( t)(( x( t)) ) γ Δ<br />
} F( t, x σ ) G( t, x σ Δ<br />
α<br />
+ = , x ). (3)<br />
on a time scales T . Where γ > 0 is an odd positive<br />
<strong>in</strong>teger, us<strong>in</strong>g Riccati transformation techniques, they<br />
obta<strong>in</strong>ed some sufficient conditions for the solution to be<br />
oscillatory or converge to zero.<br />
Follow<strong>in</strong>g this trend, we shall study the oscillation for<br />
the second-order neutral nonl<strong>in</strong>ear perturbed dynamic<br />
equations of the form<br />
and<br />
Δ γ<br />
{ α( t)(( x( t) + c( t) x( τ( t))) ) }<br />
Δ<br />
+ F( tx , ( δ( t))) = Gtx ( , ( δ( t)), x),<br />
Δ γ<br />
{ α( t)(( x( t) − c( t) x( τ( t))) ) }<br />
Δ<br />
+ F( tx , ( δ( t))) = Gtx ( , ( δ( t)), x).<br />
on an arbitrary time scales T , where γ is a quotient of<br />
positive odd <strong>in</strong>teger, α, c is a positive real-valued rdcont<strong>in</strong>uous<br />
function def<strong>in</strong>ed on a time scales T and the<br />
follow<strong>in</strong>g conditions are satisfied:<br />
+∞<br />
1 γ<br />
(H1) 0 ≤ct<br />
( ) ≤ c < 1,<br />
t ( α( t))<br />
0 ∫ Δ =∞, for all t ∈ T ;<br />
t<br />
0<br />
(H2) τ , δ : T → T satisfies τ () t ≤ t,<br />
for all t ∈ T , either<br />
δ () t ≥ t or δ () t ≤ t for all suffici-ently large t , and<br />
lim τ ( t)<br />
= lim δ ( t)<br />
=∞;<br />
t→∞<br />
t→∞<br />
(H3) pq , : T → are rd-cont<strong>in</strong>uous function, such that<br />
qt () − pt () > 0, for all t ∈ T ;<br />
2<br />
(H4) F : T× →<br />
and G : T× →<br />
are functions<br />
such that uF(, t u ) > 0and uG(, t u, v ) > 0, for all u ∈ −<br />
{0} , v ∈ , t ∈ T ;<br />
(H5) F(, tu) u γ<br />
≥ qt (), and Gtuv (, , ) u γ<br />
≤ pt () for all<br />
uv∈ , −{0}<br />
, t ∈ T .<br />
We note that <strong>in</strong> all the above results the conditions<br />
0 ≤ ct ( ) < 1, γ ≥ 1 and δ () t ≤ t are required. And some<br />
authors utilized the kernel function ( t−<br />
s<br />
) m<br />
Δ<br />
Δ<br />
(4)<br />
(5)<br />
or the general<br />
class of functions H (, ts)<br />
and obta<strong>in</strong>ed some oscillation<br />
Δs<br />
criteria, but the condition H ( ts , ) ≤ 0 is required. In this<br />
paper the study is free of these restrictions and conta<strong>in</strong>s<br />
the cases when 0< γ < 1, δ ( t) ≥t,<br />
and − 1 < ct ( ) ≤ 0 . In<br />
particular, by utiliz<strong>in</strong>g the general class of functions<br />
H (, ts ), we shall derive some sufficient conditions for<br />
the solutions of (4) and (5) to be oscillatory or converge<br />
Δs<br />
to zero when the condition H (, t s) ≤ 0is relaxed. Our<br />
results are different from the exist<strong>in</strong>g results for neutral<br />
equations on time scales that were established <strong>in</strong> [6-11,<br />
13-17]. Also, we give some examples to illustrate the<br />
ma<strong>in</strong> results.<br />
S<strong>in</strong>ce we are <strong>in</strong>terested <strong>in</strong> the oscillatory and asymptotic<br />
behavior of solutions near <strong>in</strong>f<strong>in</strong>ity, we assume that<br />
sup T = ∞ , and def<strong>in</strong>e the time scale <strong>in</strong>terval [ t 0<br />
, ∞)<br />
T<br />
by<br />
[ t , ∞ ) : = [ t , ∞)<br />
∩ T . By a solution of (4), we mean a<br />
0 T 0<br />
nontrivial real-valued function x (t) satisfy<strong>in</strong>g (4)<br />
for t ≥ t . A solution x (t) of (4) is said to be oscillatory if<br />
0<br />
it is neither eventually positive nor eventually negative,<br />
otherwise it is called nonoscillatory. Equation (4) is said<br />
to be oscillatory if all its solutions are oscillatory. Our<br />
attention is restricted to those solutions of (4) which exist<br />
on some half l<strong>in</strong>e[ t 0<br />
, ∞)<br />
and satisfy sup{| xt ( ) |: t≥ t x<br />
} > 0 ,<br />
for any t ≥ t .<br />
x 0<br />
The paper is organized as follows. In next section, we<br />
present some basic formula and lemma concern<strong>in</strong>g the<br />
calculus on time scales. In Section 3, we will use Riccati<br />
transformation techniques and the general class of<br />
functions H (, ts)<br />
and give some sufficient conditions for<br />
the oscillatory behavior of solutions of (4) and (5). In last<br />
section, we give some examples to illustrate our ma<strong>in</strong><br />
results.<br />
Through this paper, we let<br />
γ<br />
d () t = max[0, d()], t Q() t = ( q() t − p())(1 t −c( δ ())), t<br />
+<br />
∫ Δs<br />
α () s<br />
d () t = max[0, − d()], t ρ(, t u): =<br />
,<br />
−<br />
() s<br />
and for sufficiently largeT ∗ ,<br />
δ () t 1 γ<br />
u<br />
t 1 γ<br />
∫ Δs<br />
α<br />
u<br />
1, δ ( t) t,<br />
∗<br />
⎧<br />
≥<br />
β (, tT ) = ⎨ γ ∗<br />
⎩ρ<br />
(, tT ), δ() t ≤ t.<br />
II. SOME PRELIMINARIES ON TIME SCALES<br />
A time scales T is an arbitrary nonempty closed subset<br />
of the real numbers . In this paper, we only consider<br />
time scales <strong>in</strong>terval of form [ t 0<br />
, ∞)<br />
T<br />
, on T we def<strong>in</strong>e the<br />
forward jump operatorσ and the gra<strong>in</strong><strong>in</strong>ess μ by<br />
{ }<br />
σ (): t = <strong>in</strong>f s∈ T : s > t and μ(): t = σ () t − t.<br />
A po<strong>in</strong>t t ∈ T with σ () t = tis called right-dense, while t<br />
is referred to as be<strong>in</strong>g right-scattered if σ () t > t . A<br />
function f : T → is said to be rd-cont<strong>in</strong>uous if it is<br />
cont<strong>in</strong>u-ous at each right-dense po<strong>in</strong>t and if there exists a<br />
left limit <strong>in</strong> all left-dense po<strong>in</strong>ts. The ( Δ derivative) f Δ of<br />
f is def<strong>in</strong>ed by<br />
Δ f ( σ ( t)) − f( s)<br />
f () t = lim , where Ut () = T \{ σ ()} t .<br />
σ () t − s<br />
s→t<br />
sU ∈ () t<br />
© 2013 ACADEMY PUBLISHER
1530 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
The derivative and the forward jump operator are<br />
related by the useful formula<br />
σ<br />
f f μ f<br />
Δ<br />
σ<br />
= + , where f : = f σ.<br />
We will also make use of the follow<strong>in</strong>g product and<br />
quotient rules for the derivative of the product f g and the<br />
quotient f g( gg σ ≠ 0) of two differentiable functions f<br />
and g :<br />
Δ<br />
⎛ f ⎞ f g−<br />
f g<br />
( f g) Δ = f Δ g+ f σ<br />
g<br />
Δ<br />
, and ⎜ ⎟ =<br />
⎝ g ⎠ gg σ<br />
Δ<br />
Δ<br />
. (6)<br />
By us<strong>in</strong>g the product rule, the derivative of f () t =<br />
( t − α) m<br />
for m ∈ andα ∈ T can be calculated as<br />
m−1<br />
Δ<br />
v<br />
m−v−1<br />
() = ( σ() −α)( −α) .<br />
v=<br />
0<br />
f t ∑ t t<br />
(7)<br />
For a, b∈ T and a differentiable function f , the<br />
Cauchy <strong>in</strong>tegral of f Δ is def<strong>in</strong>ed by<br />
b Δ<br />
∫a f () t Δ t = f( b) − f( a)<br />
.<br />
The <strong>in</strong>tegration by parts formula follows from (6) and<br />
reads<br />
b Δ<br />
b b σ Δ<br />
∫ f () tgt () Δ t= ftgt () ()| −∫ f tg()<br />
tΔt.<br />
a<br />
To prove our ma<strong>in</strong> results, we will use the formula<br />
1 1<br />
( x γ Δ<br />
( t)) [ hx σ (1 h) x] γ − Δ<br />
= γ + − dhx ( t)<br />
0<br />
a<br />
a<br />
∫ . (8)<br />
which is a simple consequence of Keller′s cha<strong>in</strong> rule [2].<br />
Also, we need the follow<strong>in</strong>g lemma [5].<br />
Lemma 1 Assume A and B are nonnegtive constants, λ<br />
> 1, then<br />
λ<br />
−<br />
− ≤( − 1) .<br />
1<br />
AB λ A λ λ B<br />
λ<br />
The reader is referred to [2] for more detailed and<br />
extensive developments <strong>in</strong> calculus on time scales.<br />
III. MAIN RESULTS<br />
First, we state the oscillation criteria for (4).<br />
Set<br />
yt () = xt () + ctx () ( τ ()). t<br />
(9)<br />
Theorem 1 Assume that (H1) - (H5) hold, Furthermore,<br />
suppose that there exists a positive Δ−differentiable<br />
function g()<br />
t such that for all sufficiently large T ∗<br />
, and<br />
∗<br />
for all δ (T) > T , we have<br />
t<br />
∗<br />
limsup ∫ ( β (, sT ) gsQs () () −<br />
t→∞<br />
T<br />
α( s)(( g ( s)) )<br />
( γ + 1) g ( s)<br />
Δ γ + 1<br />
+<br />
γ+<br />
1 γ<br />
) Δ s =∞.<br />
Then every solution of (4) is oscillatory on [ t , ∞)<br />
0 T<br />
.<br />
(10)<br />
proof Suppose (4) has a nonoscillatory solution x (t).<br />
without loss of generality, there exists some t 1<br />
≥ t 0<br />
,<br />
sufficiently large such that xt () > 0, x( τ ( t)) > 0, x( δ ( t))<br />
> 0 for all t ≥ t . Hence In the view of (9), by (H1) we<br />
1<br />
get yt () > 0. from (4) and by (H2) - (H5), we have that<br />
Δ<br />
( y )) γ<br />
γ<br />
α<br />
Δ<br />
≤ −( q() t − p()) t x ( δ()) t < 0,<br />
and us<strong>in</strong>g the same proof of Theorem 1 [4], there exists<br />
t ≥ t such that for all t ≥ t , we have<br />
2 1<br />
2<br />
Δ<br />
⎧yt () > 0, y () t > 0,<br />
(11)<br />
⎨<br />
Δ<br />
( ( y ) γ Δ<br />
γ<br />
⎩ α ) ≤ −( q( t) − p( t))(1 − c( δ( t))) y ( δ( t)) < 0.<br />
By the def<strong>in</strong>ition of Qt (), we get<br />
Δ<br />
( ( y ) γ<br />
γ<br />
α )<br />
Δ<br />
≤ − Q( t) y ( δ( t)) < 0. (12)<br />
Make the generalized Riccati substitution<br />
Δ γ<br />
α()( t y ()) t<br />
wt () = gt ()<br />
. (13)<br />
γ<br />
y () t<br />
By the product and quotient rules, we have for all t ≥ t2<br />
Δ γ Δ<br />
Δ gt ()( α()( t y())) t ⎛ gt () ⎞<br />
Δ γ<br />
w () t = ( ()( t y ())) t<br />
γ<br />
+⎜ γ ⎟ α<br />
y () t ⎝ y () t ⎠<br />
Δ γ Δ<br />
gt ()( α()( t y()))<br />
t<br />
= +<br />
γ<br />
y () t<br />
Δ<br />
γ Δ<br />
g () t g()( t y ()) t<br />
Δ γ σ<br />
( −<br />
)( α( t)( y ( t)) ) .<br />
γσ γ γσ<br />
y () t y () t y () t<br />
From (12) - (14), we obta<strong>in</strong><br />
Δ<br />
Δ<br />
⎛ y( δ ( t)) ⎞ g ( t)<br />
σ<br />
w () t ≤− g() t Q() t ⎜ ⎟ + w () t<br />
σ<br />
⎝ yt () ⎠ g () t<br />
σ γ Δ<br />
gtw () ()( t y()) t<br />
−<br />
σ<br />
γ .<br />
g () t y () t<br />
γ<br />
Δ<br />
σ<br />
(14)<br />
(15)<br />
First consider the case when δ () t ≥ t . For all large t,<br />
Δ<br />
from y () t > 0, we have<br />
which implies that<br />
y( δ ( t))<br />
≥ 1 ,<br />
yt ()<br />
Δ<br />
σ γ Δ<br />
Δ<br />
g () t σ g() t w ()( t y ()) t<br />
w () t ≤− g() t Q() t + w () t − . (16)<br />
σ σ γ<br />
g () t g () t y () t<br />
Next consider the case when δ () t ≤ t, for all large t. By<br />
us<strong>in</strong>g α( y<br />
Δ )<br />
γ<br />
is strictly decreas<strong>in</strong>g on [ t 2<br />
, ∞ ) , we can<br />
choose t ≥ t such that δ () t ≥ t , for t ≥ t . Then we<br />
3 2<br />
2<br />
3<br />
obta<strong>in</strong><br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1531<br />
and hence<br />
Δ γ 1 γ<br />
t ( α( sy ) ( s)) )<br />
y() t − y( δ ()) t = ∫<br />
Δs<br />
δ () t<br />
1 γ<br />
α () s<br />
≤<br />
t y t<br />
Δs<br />
α () s<br />
Δ<br />
γ 1 γ t<br />
( αδ ( ( ))( ( δ( ))) ) ∫ ,<br />
δ () t 1 γ<br />
Δ<br />
γ 1 γ<br />
yt () ( αδ ( ())( t y ( δ())))<br />
t t Δs<br />
≤ 1+ ∫ . (17)<br />
δ () t 1 γ<br />
y( δ( t)) y( δ( t)) α ( s)<br />
Also, for t ≥ t , we can see that<br />
3<br />
≥<br />
1 γ<br />
Δ γ<br />
δ () t<br />
y( δ( t)) > y( δ( t)) − y( t ) = s<br />
2 ∫<br />
Δ<br />
t2<br />
1 γ<br />
Δs<br />
α () s<br />
1 γ<br />
Δ<br />
γ δ () t<br />
( αδ ( ( t))( y ( δ( t))) ) ∫ ,<br />
t2<br />
1 γ<br />
and therefore<br />
( αδ ( ( ))( ( δ( ))) )<br />
( α( sy ) ( s)) )<br />
α () s<br />
1 γ<br />
Δ<br />
γ<br />
t y t δ () t s<br />
≤ ⎜∫t2<br />
1 γ<br />
y( δ( t)) α ( s)<br />
From (17) and the above <strong>in</strong>equality, we have<br />
⎛<br />
⎝<br />
Δ<br />
⎞<br />
⎟<br />
⎠<br />
−1<br />
yt () t Δs δ () t Δs<br />
−1<br />
≤ ∫ ( )<br />
t2 1 γ ∫ , (18)<br />
t2<br />
1 γ<br />
y( δ( t)) α ( s) α ( s)<br />
therefore we get the desired <strong>in</strong>equality<br />
y( δ ( t))<br />
≥ ρ(, tt),<br />
for t ≥ t . (19)<br />
2<br />
3<br />
yt ()<br />
Us<strong>in</strong>g (19) <strong>in</strong> (15), when δ () t ≤ t, we get<br />
Δ<br />
Δ<br />
γ<br />
g () t σ<br />
w () t ≤− ρ (, t t ) g() t Q() t + w () t<br />
2<br />
σ<br />
g () t<br />
σ γ Δ<br />
gtw () ()( t y()) t<br />
−<br />
σ<br />
γ .<br />
g () t y () t<br />
From (16), (20) and the def<strong>in</strong>ition of β (, tt)<br />
, we have<br />
2<br />
By (8), we obta<strong>in</strong><br />
Δ<br />
Δ<br />
g () t σ<br />
w () t ≤− β (, t t ) g() t Q() t + w () t<br />
2<br />
σ<br />
g () t<br />
σ γ Δ<br />
gtw () ()( t y()) t<br />
−<br />
σ<br />
γ .<br />
g () t y () t<br />
y t γ hy h y dh y t<br />
γ Δ 1 σ γ−1<br />
Δ<br />
( ( )) = ∫ [ + (1 − ) ] ( )<br />
0<br />
σ γ−1<br />
Δ<br />
⎧γ( y ( t)) y ( t),0< γ ≤1,<br />
≥ ⎨<br />
⎩γ<br />
yt y t γ ≥<br />
γ −1<br />
Δ<br />
( ( )) ( ), 1.<br />
S<strong>in</strong>ce α( y<br />
Δ )<br />
γ<br />
is strictly decreas<strong>in</strong>g on[ t 2<br />
, ∞ ), we get<br />
γ<br />
( y ( t))<br />
Δ<br />
⎧γα<br />
t y t y t<br />
⎪ α () t<br />
≥ ⎨<br />
⎪ γα t y t y t<br />
⎪<br />
⎩ α () t<br />
(<br />
σ 1 γ<br />
( )) (<br />
σ γ−1<br />
( )) (<br />
Δ σ<br />
( ))<br />
1 γ<br />
(<br />
σ 1 γ γ−1<br />
( )) ( ( )) (<br />
Δ σ<br />
( ))<br />
1 γ<br />
.<br />
,0< γ ≤1,<br />
, γ ≥ 1.<br />
(20)<br />
(21)<br />
From the last <strong>in</strong>equality and (21), if 0< γ ≤ 1, we have<br />
Δ<br />
Δ<br />
g () t σ<br />
w () t ≤ − β (, t t ) g() t Q() t + w () t −<br />
2<br />
σ<br />
g () t<br />
σ 11 + γ σ<br />
γ gt ()( w()) t ⎛ y () t ⎞<br />
1 γ σ 1+<br />
1 γ ⎜ ⎟<br />
α ()( t g ()) t ⎝ y()<br />
t ⎠<br />
whereas if γ > 1 , we f<strong>in</strong>d that<br />
Δ<br />
Δ<br />
g () t σ<br />
w () t ≤− β (, t t ) g() t Q() t + w () t<br />
2<br />
σ<br />
g () t<br />
γ gt w t y t<br />
−<br />
α ()( t g ()) t y()<br />
t<br />
σ 11 + γ σ<br />
()( ()) ()<br />
1 γ σ 1+<br />
1 γ .<br />
Δ<br />
And by us<strong>in</strong>g y () t > 0, we obta<strong>in</strong> that<br />
Δ<br />
Δ<br />
g () t<br />
+ σ<br />
w () t ≤− β (, t t ) g() t Q() t + w () t<br />
2<br />
σ<br />
g () t<br />
γ gt ()<br />
−<br />
α ()( t g ()) t<br />
1 γ σ λ<br />
γ<br />
,<br />
σ λ<br />
( w ( t)) ,<br />
where λ : = ( γ + 1) γ . Def<strong>in</strong>e A ≥ 0 and B ≥ 0<br />
by<br />
σ λ<br />
1( γ +1) Δ<br />
λ γ gt ()( w())<br />
t<br />
λ− 1<br />
α ()( t g ()) t<br />
+<br />
A : = , B : = ,<br />
1 γ σ λ 1 λ<br />
α ( t)( g ( t)) λ( γg( t))<br />
then us<strong>in</strong>g Lemma 1, we obta<strong>in</strong><br />
(22)<br />
g<br />
Δ 1<br />
() t ()<br />
()(( ()))<br />
() ( ()) t g Δ t<br />
γ +<br />
σ gt<br />
σ λ α<br />
+<br />
γ<br />
+<br />
w t −<br />
w t ≤<br />
.<br />
σ 1γ σ λ γ+<br />
1 γ<br />
g () t α ()( t g ()) t ( γ + 1) g () t<br />
From the last <strong>in</strong>equality and (22), we have<br />
Δ γ + 1<br />
Δ<br />
α()(( t g ())) t<br />
+<br />
w () t ≤<br />
−β<br />
(, t t ) g() t Q()<br />
t .<br />
γ+<br />
1 γ<br />
2<br />
( γ + 1) g ( t)<br />
Integrat<strong>in</strong>g both sides from t 3<br />
to t, we get<br />
Δ γ + 1<br />
t<br />
α( s)(( g ( s)) )<br />
+<br />
∫ [ β ( s, t ) g( s) Q( s) −<br />
] Δs<br />
t3<br />
2 γ+<br />
1 γ<br />
( γ + 1) g ( s)<br />
≤ wt ( ) −wt ( ) ≤ wt ( ),<br />
3 3<br />
which leads to a contradiction to (10). This completes the<br />
proof.<br />
Corollary 1 Assume that (H1) - (H5) hold, Furthermore,<br />
suppose that for all sufficiently large T ∗ , and for δ ( T ) ><br />
T ∗<br />
,<br />
we have<br />
t<br />
∗ α()<br />
s<br />
limsup ∫ ( sβ<br />
( s, T ) Q( s) − ) Δ s =∞.<br />
t→∞<br />
T<br />
γ+<br />
1 γ<br />
( γ + 1) s<br />
Then every solution of (4) is oscillatory on [ t , ∞)<br />
0 T<br />
.<br />
Corollary 2 Assume that (H1) - (H5) hold, Furthermore,<br />
suppose that for all sufficiently large T ∗ , and for δ ( T ) ><br />
T ∗<br />
,<br />
we have<br />
t<br />
∗<br />
limsup ∫ β ( sT , ) Qs ( ) Δ s=∞.<br />
t→∞<br />
T<br />
© 2013 ACADEMY PUBLISHER
1532 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Then every solution of (4) is oscillatory on [ t , ∞)<br />
0 T<br />
.<br />
We next study a Philos-type oscillation criteria for (4).<br />
First, Let us <strong>in</strong>troduce the class of functions R which<br />
will be extensively used <strong>in</strong> the sequel.<br />
2<br />
Let D= {( ts , ) ∈T : t≥ s≥t}<br />
.The function H ∈ Crd<br />
( D, )<br />
is said to belong to the class R by H ∈R, if<br />
H (,) tt 0, t t<br />
0<br />
= ≥ ; H (, ts) 0, t s t<br />
0<br />
0<br />
> > ≥ , (23)<br />
Δs<br />
and H has a cont<strong>in</strong>uous Δ− partial derivative H (, ts)<br />
with respect to the second variable.<br />
Theorem 2 Assume that (H1) - (H5) hold. Let g (t) be<br />
as def<strong>in</strong>ed <strong>in</strong> Theorem 1, and Hh , ∈C rd<br />
( D, )<br />
such that<br />
H ∈R. Furthermore, suppose that there exists a positive<br />
rd-cont<strong>in</strong>uous function ϕ()<br />
t satisfies<br />
Hts (, )<br />
≤ ϕ()<br />
s , (24)<br />
Htt (, )<br />
0<br />
Δ<br />
Δ g () s h(,)<br />
t s<br />
s γ ( γ+<br />
1)<br />
−H (, t s) − H(, t s) = ( H(, t s))<br />
, (25)<br />
σ<br />
σ<br />
g () s g () s<br />
and for all sufficiently largeT ∗ , we have<br />
1 t<br />
∗<br />
limsup ∫ [ β (, s T ) g() s Q() s H(,)<br />
t s<br />
t→∞<br />
t0<br />
Htt (, )<br />
0<br />
α()( s h (,)) t s<br />
− ] Δ s =∞.<br />
γ + 1<br />
−<br />
γ+<br />
1 γ<br />
( γ + 1) g ( s)<br />
(26)<br />
Then every solution of (4) is oscillatory on [ t , ∞)<br />
0 T<br />
.<br />
Proof Suppose (4) has a nonoscillatory solution x (t),<br />
without loss of generality, say xt () > 0, x( τ ( t)) > 0,<br />
x( δ ( t)) > 0, for all t ≥ t , for some t<br />
1<br />
1<br />
≥ t 0<br />
. By (H2) - (H5),<br />
proceed as <strong>in</strong> the proof of Theorem 1, we get that (11)<br />
holds for all t ≥ t . Aga<strong>in</strong> we def<strong>in</strong>e wt () as <strong>in</strong> the proof of<br />
1<br />
Theorem 1, then there exists t 2<br />
≥ t 1<br />
, sufficiently large such<br />
that for all t<br />
∗<br />
≥ t and for t t ∗<br />
Δ<br />
≥ , (22) holds and let g () t<br />
2<br />
+<br />
Δ<br />
be replaced by g () t <strong>in</strong> (22), thus<br />
Δ<br />
Δ g () t σ<br />
β (, tt) gtQt () () ≤− w() t + w()<br />
t<br />
2<br />
σ<br />
g () t<br />
γ gt ()<br />
−<br />
α ()( t g ()) t<br />
1 γ σ λ<br />
σ λ<br />
( w ( t)) .<br />
(27)<br />
Multiply<strong>in</strong>g both the sides of (27), with t replaced by s,<br />
by H (t, s) and <strong>in</strong>tegrat<strong>in</strong>g with respect to s from t ∗ to t,<br />
we obta<strong>in</strong><br />
t<br />
∫ ∗ Hts (,) β (, st) gsQs () () Δs≤<br />
2<br />
t<br />
Δ<br />
t<br />
Δ<br />
t g () s σ<br />
−∫<br />
∗H (, tsw ) ( s) Δ s+ ∗Hts (, ) w( s)<br />
s<br />
t<br />
∫<br />
Δ<br />
t<br />
σ<br />
g () s<br />
t<br />
γ gs ()<br />
σ λ<br />
−∫<br />
∗ Hts (, ) ( w( s)) Δs.<br />
t<br />
1 γ σ λ<br />
α ()( s g ()) s<br />
Integrat<strong>in</strong>g by parts formula and us<strong>in</strong>g (23) and (25),<br />
we get<br />
t<br />
∗ ∗<br />
∫ ∗ Hts ( , ) β( st , ) gsQs ( ) ( ) Δs≤ Htt ( , ) wt ( ) +<br />
t<br />
2<br />
1 λ<br />
t hts (, )( Hts (, )) σ γ Htsgs (, ) ( )<br />
(28)<br />
−<br />
σ λ<br />
∫ ∗[ w ( s) −<br />
( w ( s)) ] Δs.<br />
t<br />
σ 1 γ σ λ<br />
g () s α ()( s g ()) s<br />
And apply<strong>in</strong>g Lemma 1, we obta<strong>in</strong><br />
1 λ<br />
(, )( (, ))<br />
−<br />
σ γ (, ) ( ) σ λ<br />
w () s −<br />
( w ()) s<br />
σ 1 γ σ λ<br />
h t s H t s Htsgs<br />
g () s α ()( s g ()) s<br />
α<br />
≤<br />
( γ + 1) g ( s)<br />
γ + 1<br />
( h ( t, s)) ( s) −<br />
γ+<br />
1 γ .<br />
From the last <strong>in</strong>equality and (24), (28), we have<br />
1<br />
( h ( t, s)) α( s)<br />
[ (, s t ) g() s Q() s H(,) t s ] Δs<br />
Htt g s<br />
γ + 1<br />
t<br />
−<br />
∫ β<br />
−<br />
t0<br />
2 γ+<br />
1 γ<br />
(, ) ( γ + 1) ( )<br />
0<br />
∗<br />
∗ ∗ t<br />
≤ ϕ( t ) w( t ) + ∫ ϕ( s) β( s, t ) g( s) Q( s) Δ s T , we have<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1533<br />
t<br />
∗<br />
limsup ∫ [ β ( s, T ) g( s)( q( s) − p( s))<br />
t→∞<br />
T<br />
Δ γ + 1<br />
α()(( s g ())) s<br />
+<br />
− ] Δ s =∞.<br />
γ+<br />
1 γ<br />
( γ + 1) g ( s)<br />
(29)<br />
Then every solution of (5) is either oscillatory on [ t , ∞)<br />
0 T<br />
or tends to zero.<br />
proof Suppose that x is an eventually positive solution<br />
of (5), say xt () > 0, x( τ ( t)) > 0, x( δ ( t)) > 0for all t ≥ t for<br />
1<br />
some t ≥ t . We consider only this case, because the<br />
1 0<br />
proof for the case that x is eventually negative is similar.<br />
In the view of (5), by (H2) - (H5), and there exists<br />
t ≥ t such that for all t ≥ t , we have<br />
2 1<br />
2<br />
Δ<br />
( ( z ) γ<br />
γ<br />
α )<br />
Δ<br />
≤−( q( t) − p( t)) x ( δ( t)) < 0 , (30)<br />
γ<br />
then α( z<br />
Δ ) is strictly decreas<strong>in</strong>g on [ t 2<br />
, ∞ ). Hence z (t)<br />
Δ<br />
and z () t are of constant sign eventually. We claim that<br />
x()<br />
t is bounded. If not, there exists { t k<br />
} ⊆ [ t 2<br />
, ∞ ), such<br />
that lim t =∞ ,lim x( t ) =∞,<br />
and<br />
k→∞<br />
k<br />
k→∞<br />
k<br />
x( t ) = max{ x( s): t ≤ s≤<br />
t }.<br />
k<br />
S<strong>in</strong>ce lim τ ( t ) =∞, we can choose a large k such that<br />
k→∞<br />
0<br />
k<br />
τ ( t ) > t , and by (H2), we obta<strong>in</strong> that<br />
k<br />
x( τ( t )) = max{ x( s) : t ≤ s≤τ( t )}<br />
Therefore, for all large k,<br />
k<br />
0<br />
0<br />
≤ max{ x( s) : t ≤ s ≤ t } = x( t ).<br />
z( τ ( t )) ≥ x( t ) −c x( τ ( t )) ≥ (1 − c ) x( t )<br />
k k 0 k<br />
0 k<br />
,<br />
and lim zt ( ) =∞. From (H1) and (30), as <strong>in</strong> the proof of<br />
k→∞<br />
k<br />
Theorem 1 [4], there exists t 3<br />
≥ t 2<br />
such that for all t ≥ t ,<br />
3<br />
we have<br />
In view of (5), (30) and (31), we get<br />
0<br />
k<br />
Δ<br />
zt () > 0, z () t > 0. (31)<br />
Δ<br />
( ( z ) γ<br />
γ<br />
α )<br />
Δ<br />
≤−( q( t) − p( t)) z ( δ( t)) < 0. (32)<br />
Now by us<strong>in</strong>g the same proof of Theorem 1, we get a<br />
contradiction with (29). Thus x (t) is bounded and hence z<br />
(t) is bounded.<br />
Also, by us<strong>in</strong>g (H1) and the same proof of Theorem 1<br />
Δ<br />
<strong>in</strong> [4], there exist t 4 ≥ t 3 such that z () t > 0on [t 4 , ∞).<br />
There are two cases.<br />
Δ<br />
Case 1 zt () > 0 and z () t > 0. As <strong>in</strong> the proof of<br />
Theorem 1, we get a contradiction with (29).<br />
Δ<br />
Case 2 zt () < 0and z ( t) > 0 . We claim lim xt ( ) = 0 .<br />
k<br />
k<br />
k<br />
t→∞<br />
Assume not, then there exists { t } ⊆[ t , ∞)<br />
such that<br />
k 5<br />
lim t =∞,<br />
lim xt ( ) = : b> 0 and x( t ) = max{ x( s):<br />
t ≤ s<br />
k<br />
k<br />
k<br />
0<br />
k→∞<br />
t k<br />
k→∞<br />
≤ }. But, by x( τ ( t )) ≤ x( t ), we get<br />
k<br />
k<br />
0 > zt ( ) ≥ xt ( )(1 −c) →b(1 − c) > 0, as k→∞.<br />
k<br />
k<br />
0 0<br />
Which is a contradiction. This completes the proof.<br />
Corollary 4 Assume that (H1) - (H5) hold, Furthermore,<br />
suppose that for all sufficiently large T ∗ , and for δ ( T ) ><br />
T ∗<br />
,<br />
we have<br />
t<br />
∗<br />
α()<br />
s<br />
limsup ∫ ( sβ<br />
( s, T )( q( s) − p( s)) − ) Δ s =∞.<br />
t→∞<br />
T<br />
γ+<br />
1 γ<br />
( γ + 1) s<br />
Then every solution of (5) is either oscillatory on [ t , ∞)<br />
0 T<br />
or tends to zero.<br />
Corollary 5 Assume that (H1) - (H5) hold, Furthermore,<br />
suppose that for all sufficiently large T ∗ , and for δ ( T ) ><br />
T ∗<br />
,<br />
we have<br />
t<br />
∗<br />
limsup ∫ β (, sT)(() qs − ps ()) Δ s=∞.<br />
t→∞<br />
T<br />
Then every solution of (5) is either oscillatory on [ t , ∞)<br />
0 T<br />
or tends to zero.<br />
We next study a Philos-type oscillation criteria for (5).<br />
Theorem 4 Assume that (H1) - (H5) hold. Let g (t) be<br />
as def<strong>in</strong>ed <strong>in</strong> Theorem 1, and H, h∈C rd<br />
( D, )<br />
such that<br />
H ∈R . Furthermore, suppose that there exists a<br />
positive rd-cont<strong>in</strong>uous function ϕ () t such that (24), (25)<br />
hold, and for all sufficiently largeT ∗ , we have<br />
1 t<br />
∗<br />
limsup ∫ { β ( s, T ) g( s)( q( s) − p( s)) H( t, s)<br />
t→∞<br />
t0<br />
Htt (, )<br />
0<br />
α()( s h (,)) t s<br />
− } Δ s =∞.<br />
γ + 1<br />
−<br />
γ+<br />
1 γ<br />
( γ + 1) g ( s)<br />
(33)<br />
Then every solution of (5) is either oscillatory on [ t , ∞)<br />
0 T<br />
or tends to zero.<br />
Proof Suppose that (5) has a nonoscillatory solution x<br />
(t), without loss of generality, say xt () > 0, x( τ ( t)) > 0,<br />
x( δ ( t)) > 0, for all t ≥ t , for some t<br />
1<br />
1<br />
≥ t 0<br />
. By (H2) - (H5),<br />
we obta<strong>in</strong> that (30) holds for all t ≥ t , and zt () and<br />
1<br />
Δ<br />
z () t are of constant sign eventually. Similar to the proof<br />
of Theorem 3, we claim that x()<br />
t is bounded. If not, there<br />
exists{ t } ⊆[ t , ∞ ), for all large k, there exists t<br />
k 1<br />
2<br />
≥ t 1<br />
, such<br />
that (31) and (32) hold for t ≥ t . Aga<strong>in</strong> we def<strong>in</strong>e wt () as<br />
2<br />
<strong>in</strong> the proof of Theorem 1, then there exists t 3<br />
≥ t 2<br />
,<br />
sufficiently large such that for t<br />
∗<br />
≥ t and for t ≥ t ∗<br />
, we<br />
3<br />
f<strong>in</strong>d<br />
β (, tt) gt ()( qt () − pt ())<br />
3<br />
Δ g () t γ g()<br />
t<br />
≤− w () t + w () t −<br />
( w ()). t<br />
g t t g t<br />
Δ<br />
σ σ λ<br />
σ 1 γ σ λ<br />
() α ()( ())<br />
And similar to the proof of the theorem 3, we obta<strong>in</strong><br />
1 t<br />
∫ [ β ( s, t ) g( s)( q( s) − p( s)) H( t, s)<br />
t<br />
Htt (, )<br />
0 3<br />
0<br />
γ + 1<br />
( h ( t, s)) α( s) −<br />
γ+<br />
1 γ ] s (<br />
∗<br />
ϕ t ) w (<br />
∗<br />
t )<br />
− Δ ≤ +<br />
( γ + 1) g ( s)<br />
(34)<br />
© 2013 ACADEMY PUBLISHER
1534 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
∗<br />
t<br />
ϕ s β s t g s q s p s s<br />
t0 3<br />
∫<br />
() (, ) ()(() − ()) Δ 0on [ t<br />
4<br />
4<br />
, ∞ ) . And then there are<br />
two cases of Theorem 3. As <strong>in</strong> the proof of Theorem 3, if<br />
the case 1 holds, we get a contradiction with (33) ; if the<br />
case 2 holds, we obta<strong>in</strong> lim xt ( ) = 0 . This completes the<br />
t→∞<br />
proof.<br />
In Theorem 4, let g (t) =1 and H ( ts , ) = ( t− s) m<br />
, we<br />
have the follow<strong>in</strong>g result.<br />
Corollary 6 Assume that (H1) - (H5) hold, and m ≥ 1 ,<br />
for all sufficiently largeT ∗ , we have<br />
1 t<br />
m<br />
∗<br />
limsup ( ) ( , )( ( ) ( ))<br />
m ∫ t−s β sT qs − ps Δ s=∞.<br />
t→∞<br />
t0<br />
t<br />
Then every solution of (5) is either oscillatory on [ t , ∞)<br />
0 T<br />
or tends to zero.<br />
IV. EXAMPLES<br />
In this section, we give some examples to illustrate our<br />
ma<strong>in</strong> results. Def<strong>in</strong>e<br />
⎧1 , δ ( t) ≥ t,<br />
ξ () t = ⎨ γ<br />
⎩ρ<br />
(, tt), δ() t ≤ t.<br />
0<br />
∗<br />
∞<br />
1 γ<br />
β (, tT )<br />
Note that ∫ Δ t ( α( t))<br />
=∞, implies lim = 1.<br />
t0<br />
t→∞<br />
ξ () t<br />
Example 1 Consider the nonl<strong>in</strong>ear neutral perturbed<br />
dynamic equation<br />
( t (( x( t) ± x( τ ( t))) ) )<br />
t + 1<br />
Δ<br />
+ F( tx , ( δ( t))) = Gtx ( , ( δ( t)), x),<br />
γ−1 1<br />
Δ γ Δ<br />
(35)<br />
for t ∈[1, ∞)<br />
T<br />
, where γ is the quotient of odd positive<br />
<strong>in</strong>tegers. Let<br />
α<br />
k(1 + δ ( t)) 1<br />
t δ () t ξ()<br />
t t<br />
γ<br />
γ−1 2 γ<br />
() t = t , F(, t u) = ( + + u ) u ,<br />
2 γ<br />
4<br />
γ<br />
γ+<br />
2<br />
1 k(1 + δ ( t))<br />
u<br />
ct () = , Gtuv (, , ) =<br />
,<br />
2 γ<br />
2 2<br />
t+ 1 2 t δ () t ξ()( t u + v + 1)<br />
where k is a positive constant. Then<br />
2<br />
Qt () = k 2 t ξ () t .<br />
t0 t0<br />
1 γ γ 1 γ<br />
S<strong>in</strong>ce ∫ ∞ Δ t ( α( t))<br />
= ∫ ∞ Δ t t<br />
−<br />
=∞, hence the conditions<br />
(H1) - (H5) are clearly satisfied. And,<br />
t<br />
∗<br />
α()<br />
s<br />
limsup ∫ ( sβ<br />
(, sT ) gsQs () () − ) Δs<br />
t→∞<br />
T<br />
γ+<br />
1 γ<br />
( γ + 1) s<br />
k 1<br />
t Δs<br />
= ( − )limsup ,<br />
γ + 1 ∫ =∞<br />
t→∞<br />
T<br />
2 ( γ + 1)<br />
s<br />
t<br />
∗<br />
α()<br />
s<br />
limsup ∫ ( sβ<br />
( sT , ) gs ( )( qs ( ) − ps ( )) − ) Δs<br />
t→∞<br />
T<br />
γ+<br />
1 γ<br />
( γ + 1) s<br />
k 1<br />
t Δs<br />
= ( − )limsup ,<br />
γ + 1 ∫ =∞<br />
t→∞<br />
T<br />
2 ( γ + 1)<br />
s<br />
γ + 1<br />
if k > 2( γ + 1) . Thus it follows from Corollary 1 that<br />
every solution of (35) + is oscillatory on [1, ∞)<br />
T<br />
if k ><br />
γ + 1<br />
2( γ 1) ,<br />
+ and it follows from Corollary 4 that every<br />
solution of (35) − is either oscillatory on [1, ∞)<br />
T<br />
or tends<br />
1<br />
to zero if k > 2( γ 1) γ +<br />
+ .<br />
Example 2 Consider the nonl<strong>in</strong>ear neutral perturbed<br />
dynamic equation<br />
1<br />
t x t − x τ t<br />
2 + s<strong>in</strong> t<br />
Δ<br />
+ F( t, x( δ( t))) = G( t, x( δ( t)), x ).<br />
23 Δ 53 Δ<br />
( (( ( ) ( ( ))) ) )<br />
2<br />
(36)<br />
23 2<br />
for t ∈[2, ∞)<br />
T<br />
, where α() t = t , γ=53, c() t = 1( 2+<br />
s<strong>in</strong> t)<br />
Let<br />
Ftu 1 4 2 5 3<br />
(, ) = ( + ) ,<br />
tξ<br />
() t<br />
t + u u<br />
and<br />
11 3<br />
1 u<br />
Gtuv (, , ) =<br />
.<br />
2 4<br />
2 tξ<br />
( t) ( u + v + 2)<br />
Then qt () − pt () = 12 tξ<br />
() t . The conditions (H1) - (H5)<br />
are clearly satisfied. For all t > s ≥ 2 , let m=2, we have<br />
1 t<br />
2<br />
∗<br />
limsup<br />
2 ∫ ( t− s) β ( sT , )( qs ( ) − ps ( )) Δs<br />
t→∞<br />
2<br />
t<br />
2<br />
1 t ( t−<br />
s)<br />
= limsup<br />
t<br />
2 ∫ Δs<br />
→∞<br />
2<br />
t 2s<br />
1 t s t 1 t−<br />
2<br />
= limsup[ s s ] .<br />
t→∞<br />
2 ∫ Δ +<br />
2 ∫ Δ − =∞<br />
2<br />
t 2 2s t<br />
Thus it follows from Corollary 6 that every solution of<br />
(36) is either oscillatory on [2, ∞)<br />
T<br />
or tends to zero.<br />
IV. CONCLUSIONS<br />
To <strong>in</strong>vestigate the oscillatory and asymptotic behavior<br />
for a certa<strong>in</strong> class of second order nonl<strong>in</strong>ear neutral<br />
perturbed dynamic equations on time scales. This paper<br />
proposed some new sufficient conditions for oscillation<br />
of such dynamic equations on time scales were<br />
established. The results not only improve and extend<br />
some known results <strong>in</strong> the literature, but also unify the<br />
oscillation of second order nonl<strong>in</strong>ear neutral perturbed<br />
differential equations and second order nonl<strong>in</strong>ear neutral<br />
perturbed difference equations. In particular, the results<br />
are essentially new under the relaxed conditions for the<br />
parameter function.<br />
ACKNOWLEDGMENT<br />
if<br />
k<br />
γ + 1<br />
> 2( γ + 1) . Also,<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1535<br />
This work was supported by a grant from the National<br />
Natural Science Foundation of Ch<strong>in</strong>a (11161049) and the<br />
Science Foundation of Zhangjiakou, Ch<strong>in</strong>a (1112027B-1).<br />
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Eqs. & Appl. vol. 16, pp. 373–388, November 2010.<br />
[13] D. Anderson, “Oscillation and nonoscillation criteria for<br />
Two-Dimensional time-scale systems of First-Order<br />
nonl<strong>in</strong>ear dynamic equations. electronic”, J. of Diff. Eqs.<br />
Vol. 24, pp. 1–13, January 2009.<br />
[14] J. S. Yang and B. Fang, “Oscillation criteria of a class of<br />
second-order dynamic equations on time scales”, Appl.<br />
Math. A J. of Ch<strong>in</strong>ese Universities. Vol. 26, pp. 149–157,<br />
June 2011.<br />
[15] J. S. Yang, “Asymptotic behavior of second-order nonl<strong>in</strong>ear<br />
dynamic equations on time scales”, J. Inner Mongolia<br />
University. Vol. 41, pp. 153–156, March 2010.<br />
[16] X. P. Yu, H. Y. Yang and Y. X. Xu, “Oscillation criteria<br />
for second-order neutral nonl<strong>in</strong>ear dynamic equations on<br />
time scales”, Proceed<strong>in</strong>gs of the 5th ICMB, Vol. 1, pp.<br />
353–356, June 2011.<br />
[17] X. P. Yu, H. Y. Yang and J. M. Zhang, “Oscillation criteria<br />
for nonl<strong>in</strong>ear neutral perturbed dynamic equations on time<br />
scales”, Ann. Diff. Eqs., <strong>in</strong> press.<br />
Xiup<strong>in</strong>g Yu was born <strong>in</strong> Yu County, Hebei Prov<strong>in</strong>ce, Ch<strong>in</strong>a<br />
<strong>in</strong> April 1966. She graduated from Hebei Normal University,<br />
Shijiazhuang City, Ch<strong>in</strong>a major<strong>in</strong>g <strong>in</strong> mathematics with a B.S.<br />
degree <strong>in</strong> 1988. And then she earned a Master’s degree <strong>in</strong><br />
applied mathematics from Hebei University, Baod<strong>in</strong>g City,<br />
Ch<strong>in</strong>a <strong>in</strong> 2003.<br />
At present, she teaches <strong>in</strong> Department of Mathematics and<br />
Physics and serves as DIRECTOR of BASIC MATHEMATICS<br />
SECTION <strong>in</strong> Hebei Institute of Architecture and Civil<br />
Eng<strong>in</strong>eer<strong>in</strong>g, Zhangjiakou City, Ch<strong>in</strong>a. In recent years she has<br />
participated <strong>in</strong> quite a few <strong>in</strong>ternational and domestic academic<br />
conferences dur<strong>in</strong>g summer vocations. She was once a major<br />
member of the 5 th International Congress on Mathematical<br />
Biology and the 2 nd International Conference on Information<br />
Comput<strong>in</strong>g and Applications. She has been ma<strong>in</strong>ly engaged <strong>in</strong><br />
functional deferential equation and dynamic system. She has<br />
completed five prov<strong>in</strong>cial-level scientific research projects as<br />
project leader and pr<strong>in</strong>cipal researcher. Her ma<strong>in</strong> achievements<br />
are <strong>in</strong>terval oscillation criteria for high order neutral deferential<br />
equations with cont<strong>in</strong>uous deviat<strong>in</strong>g arguments (Ann. Diff. Eqs.<br />
vol. 22, pp. 411–417, August 2006), and permanence of<br />
population with Holl<strong>in</strong>g II function response <strong>in</strong> air pollution<br />
(Mathematics <strong>in</strong> Practice and Theory, vol. 37, pp. 102–108,<br />
October 2007). Currently, she has a strong <strong>in</strong>terest <strong>in</strong> the<br />
properties and applications of dynamic equations on time scales.<br />
Prof. Yu is a member of the National Functional Differential<br />
Equation Society as well as of the National Biological<br />
Mathematical Society. She also works as a director of Hebei<br />
Applied Statistics Society. Her paper, <strong>in</strong>terval oscillation<br />
criteria for high order neutral deferential equations with<br />
cont<strong>in</strong>uous deviat<strong>in</strong>g arguments, won an excellence award at the<br />
9 th National Functional Differential Equation Conference.<br />
Another paper, permanence of population with Holl<strong>in</strong>g II<br />
function response <strong>in</strong> air pollution got the first prize at the 6 th<br />
Biological Mathematical Conference. The paper, oscillation<br />
criteria for second order neutral nonl<strong>in</strong>ear dynamic equations on<br />
time scales was published <strong>in</strong> Proceed<strong>in</strong>gs of the 5 th ICMB by<br />
World Academic Press.<br />
Hua Du was born <strong>in</strong> Zhangjiakou City, Hebei Prov<strong>in</strong>ce,<br />
Ch<strong>in</strong>a <strong>in</strong> December 1981. She graduated from Hebei Normal<br />
University, Shijiazhuang City, Ch<strong>in</strong>a major<strong>in</strong>g <strong>in</strong> computer<br />
<strong>in</strong>formation technology with a B.S. degree <strong>in</strong> 2006. And then<br />
she earned a Master’s degree <strong>in</strong> computer application from<br />
Capital Normal University, Beij<strong>in</strong>g City, Ch<strong>in</strong>a <strong>in</strong> 2009.<br />
At present, she teaches <strong>in</strong> the Information Science and<br />
Eng<strong>in</strong>eer<strong>in</strong>g College of Hebei North University, Zhangjiakou<br />
City, Ch<strong>in</strong>a. In recent years, she has been ma<strong>in</strong>ly engaged <strong>in</strong><br />
<strong>in</strong>formation management and computer network.<br />
Hongyu Yang was born <strong>in</strong> Kangbao Country, Hebei<br />
Prov<strong>in</strong>ce, Ch<strong>in</strong>a <strong>in</strong> August 1966. He graduated from Hebei<br />
Agricultural University, Baod<strong>in</strong>g City, Ch<strong>in</strong>a major<strong>in</strong>g <strong>in</strong><br />
agricultural machanization with a B.E. degree <strong>in</strong> 1988. And<br />
then he earned a Master’s degree <strong>in</strong> mechanical eng<strong>in</strong>eer<strong>in</strong>g<br />
from Ch<strong>in</strong>ese Agricultural University, Beij<strong>in</strong>g City, Ch<strong>in</strong>a <strong>in</strong><br />
2012.<br />
At present, he teaches <strong>in</strong> Department of Mechanical<br />
Eng<strong>in</strong>eer<strong>in</strong>g and serves as DIRECTOR OF DEPARTMENT OF<br />
MECHANICAL ENGINEERING <strong>in</strong> Zhangjiakou Vocational<br />
Technology Institute, Zhangjiakou, Ch<strong>in</strong>a. In recent years he<br />
has participated <strong>in</strong> quite a few domestic academic conferences<br />
dur<strong>in</strong>g summer vocations. He has been ma<strong>in</strong>ly engaged <strong>in</strong><br />
dynamic system.<br />
© 2013 ACADEMY PUBLISHER
1536 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Improved Quantum Ant Colony Algorithm based<br />
on Bloch Coord<strong>in</strong>ates<br />
Xiaofeng Chen<br />
Software College, Northeastern University, Shenyang, Ch<strong>in</strong>a<br />
Email: neucxf@163.com<br />
X<strong>in</strong>gyou Xia and Ruiyun Yu<br />
Software College, Northeastern University, Shenyang, Ch<strong>in</strong>a<br />
Email: {xiaxy, yury}@mail.neu.edu.cn<br />
Abstract—The Ant Colony Algorithm is an effective method<br />
for solv<strong>in</strong>g comb<strong>in</strong>atorial optimization problems. However,<br />
<strong>in</strong> practical applications, there also exist issues such as slow<br />
convergence speed and easy to fall <strong>in</strong>to local extremum. This<br />
paper proposes an improved Quantum Ant Colony Algorithm<br />
based on Bloch coord<strong>in</strong>ates by comb<strong>in</strong><strong>in</strong>g Quantum<br />
Evolutionary Algorithm with Ant Colony Algorithm. In this<br />
algorithm, the current position <strong>in</strong>formation of ants is represented<br />
by the Bloch spherical coord<strong>in</strong>ates of qubits; position<br />
update, position variation and random behavior of ants are<br />
all achieved with quantum rotation gate. Simulations of<br />
function extremum problem, TSP problem and QoS multicast<br />
rout<strong>in</strong>g problem were conducted, the results <strong>in</strong>dicated<br />
that the algorithm could overcome prematurity, with a faster<br />
convergence speed and higher solution accuracy.<br />
Index Terms—quantum comput<strong>in</strong>g, Ant Colony Algorithm,<br />
Quantum Ant Colony Algorithm<br />
I. INTRODUCTION<br />
Ant Colony Algorithm (ACA) [1] is a heuristic algorithm<br />
for solv<strong>in</strong>g comb<strong>in</strong>atorial optimization or function<br />
optimization problems. It has advantages such as positive<br />
feedback, strong robustness, excellent distributed comput<strong>in</strong>g<br />
mechanism, easy to comb<strong>in</strong>e with other algorithms,<br />
etc., which has been widely used <strong>in</strong> the NP-complete<br />
problem. In recent years, ACA has been applied to the<br />
fields such as knapsack problem [2], Assignment Problem<br />
[3], Job-shop Assignment [4], Sequential Order<strong>in</strong>g<br />
[5], Network Rout<strong>in</strong>g [6], Vehicle Rout<strong>in</strong>g [7], Power<br />
System [8] and Controls Parameter Optimization [9], etc.<br />
and obta<strong>in</strong>ed good effect. Meanwhile, like other swarm<br />
<strong>in</strong>telligence optimization algorithms, ACA also has some<br />
shortcom<strong>in</strong>gs <strong>in</strong> the application process, such as: easy to<br />
fall <strong>in</strong>to local optimization, slow convergence speed, etc.<br />
A quantum ant colony algorithm (QACO), based on<br />
the concept and pr<strong>in</strong>ciples of quantum comput<strong>in</strong>g can<br />
overcome this defect. In [17], a QACO-based edge detection<br />
algorithm was proposed. Quantum bit (qubit) and<br />
quantum rotation gate are <strong>in</strong>troduced <strong>in</strong>to QACO to represent<br />
and update the pheromone respectively. Experiments<br />
and comparisons show that QACO is an efficient<br />
and effective approach <strong>in</strong> image edge detection. In order<br />
to select the optimal parameter, quantum-<strong>in</strong>spired ant<br />
colony optimization is employed to select the parameter<br />
of relevance vector mach<strong>in</strong>e <strong>in</strong> [18]. Quantum-<strong>in</strong>spired<br />
ant colony optimization is well suited to multi-objective<br />
optimization problems with excellent results. By measur<strong>in</strong>g<br />
experimentally the vibration signals of the gear system<br />
at different rotat<strong>in</strong>g speeds for different faults, the<br />
test<strong>in</strong>g signals are obta<strong>in</strong>ed. In [19], a novel parallel ant<br />
colony optimization algorithm based on quantum dynamic<br />
mechanism for travel<strong>in</strong>g salesman problem (PQACO)<br />
was proposed. The use of the improved 3-opt operator<br />
provides this methodology with superior local search<br />
ability. A global optimization method was proposed to<br />
analyze ground state energy of quantum mechanical systems<br />
<strong>in</strong> [20], which It simulates the way that real ants<br />
f<strong>in</strong>d a shortest path from nest to food source and back. To<br />
elim<strong>in</strong>ate system disturbances and noise from the high<br />
levels of data, a novel quantum ant colony optimization<br />
(QACO) algorithm was proposed to select the fault features<br />
[21].<br />
This paper proposed an improved quantum ant colony<br />
algorithm based on the Bloch Spherical Coord<strong>in</strong>ate [11]<br />
(BIQACA), and various solution space transformational<br />
models and fitness functions are planned for different<br />
optimization problems. Algorithm <strong>in</strong> this paper is verified<br />
by function extreme value problem, Travel<strong>in</strong>g Salesman<br />
Problem and QoS multicast rout<strong>in</strong>g problem respectively.<br />
The result of simulation shows that the algorithm not<br />
only expresses high efficiency of quantum comput<strong>in</strong>g,<br />
but also ma<strong>in</strong>ta<strong>in</strong>s the preferable optimiz<strong>in</strong>g and robustness<br />
of colony algorithm.<br />
II. QUANTUM ANT COLONY ALGORITHM (QACA)<br />
Any po<strong>in</strong>t on the Bloch sphere can be identified via θ<br />
and ϕ as: ϕ = [ cosϕ<br />
s<strong>in</strong>θ,s<strong>in</strong>ϕ<br />
s<strong>in</strong>θ,<br />
cosθ<br />
] T . Suppose<br />
there are a total of n ants <strong>in</strong> the ant colony, where each<br />
ant carries a group (m units) of qubits, current position of<br />
ant is represented by Bloch spherical coord<strong>in</strong>ate, correspond<strong>in</strong>g<br />
to approximate solution of optimization problem.<br />
A. Initialize Ant Colony<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1536-1543
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1537<br />
Pi<br />
is set as the location of the ith ant, consider<strong>in</strong>g that<br />
the randomness of cod<strong>in</strong>g for ant colony and constra<strong>in</strong>t<br />
conditions for probability amplitude of the quantum state,<br />
the <strong>in</strong>itialization of BIQACA is expressed as:<br />
j<br />
⎡P<br />
⎤<br />
ix<br />
⎡cosφi1s<strong>in</strong>θi1 cosφi 2s<strong>in</strong>θi2<br />
cosφim s<strong>in</strong>θim<br />
⎤<br />
⎢ j ⎥ ⎢ ⎥<br />
⎢Piy ⎥ =<br />
⎢<br />
s<strong>in</strong>φi1s<strong>in</strong>θi1 s<strong>in</strong>φi 2s<strong>in</strong>θi2<br />
s<strong>in</strong>φim s<strong>in</strong>θim<br />
⎥<br />
(1)<br />
⎢<br />
j<br />
P ⎥ ⎢<br />
iz ⎣ cosθi1 cosθi2<br />
cosθ<br />
⎥<br />
⎣ ⎦<br />
<br />
im ⎦<br />
Where ϕij<br />
= 2πrand<br />
, θ ij = πrand<br />
, rand are random<br />
numbers between (0, 1) ; i ∈ { 1,2,<br />
,<br />
n}<br />
, j ∈ { 1,2,<br />
,<br />
m}<br />
, n<br />
for number of ant; m for number of qubit. 3 coord<strong>in</strong>ates<br />
of qubit are regarded as 3 paratactic genes, and each ant<br />
conta<strong>in</strong>s 3 gene cha<strong>in</strong>s, which are called X-cha<strong>in</strong>, Y-<br />
cha<strong>in</strong> and Z-cha<strong>in</strong> respectively, each gene cha<strong>in</strong> stands<br />
j j j<br />
for an optimal solution P ix , P iy , P iz .<br />
B. Transformation of Solution Space<br />
In the optimization of specific problems <strong>in</strong> BIQACA,<br />
transformation between the unit quantum space and solution<br />
space of optimization problem is needed, mak<strong>in</strong>g<br />
each probability amplitude of qubit on ant correspond to<br />
an optimization variable of solution space. In this paper,<br />
the function extremum problem, TSP problem and QoS<br />
multicast rout<strong>in</strong>g problem are taken as examples to expla<strong>in</strong><br />
the process.<br />
Solution space transformation approach for function<br />
extreme-value problem: propose the doma<strong>in</strong> of def<strong>in</strong>ition<br />
j<br />
of variable X is its solution space [ a j , b j ] , record the jth<br />
qubit <strong>in</strong> P i as [ cos ϕ<br />
] T<br />
ij s<strong>in</strong>θij<br />
,s<strong>in</strong> ϕij<br />
s<strong>in</strong>θij<br />
, cosθij<br />
by us<strong>in</strong>g<br />
l<strong>in</strong>ear transformation, then the correspond<strong>in</strong>g solution<br />
space variable is:<br />
j<br />
⎡X<br />
⎤ 1 cos s<strong>in</strong> 1 cos s<strong>in</strong><br />
ix<br />
⎡ + ϕij θij − ϕij θij<br />
⎤<br />
⎢ j ⎥ 1 ⎢ b<br />
1 s<strong>in</strong> s<strong>in</strong> 1 s<strong>in</strong> s<strong>in</strong><br />
j<br />
X<br />
ϕ<br />
iy<br />
ij<br />
θij ϕij θ ⎥⎡<br />
⎤<br />
⎢ ⎥ = ij<br />
2<br />
⎢<br />
+ −<br />
⎥⎢ a<br />
⎥<br />
⎢<br />
j<br />
j<br />
X<br />
⎥ ⎢ 1+cos θij<br />
1-cosθ<br />
⎥ ⎣ ⎦<br />
⎣ iz ⎦ ⎣<br />
ij ⎦<br />
Solution space transformation approach for TSP problem<br />
and QoS multicast rout<strong>in</strong>g problem: this paper has<br />
designed two-layer transformational model <strong>in</strong> the aspect<br />
of solution space aim<strong>in</strong>g at the specific characteristic of<br />
TSP problem and QoS multicast rout<strong>in</strong>g problem, the<br />
model conta<strong>in</strong>s two transformations--l<strong>in</strong>ear transformation<br />
and lead transformation.<br />
L<strong>in</strong>ear transformation: qubit is transformed from unit<br />
space to lead space. Propose the def<strong>in</strong>itional doma<strong>in</strong> of<br />
j<br />
lead message variable, r , is [0,1] , formula (2) is used to<br />
calculate correspond<strong>in</strong>g lead solution space variable<br />
j j j T<br />
[ τ , τ , τ ] .<br />
ix iy iz<br />
Lead transformation: impact strength of lead message<br />
and <strong>in</strong>spire message to solution could be regulated by<br />
adjust<strong>in</strong>g lead factor and <strong>in</strong>spire factor. Strategy is selected<br />
accord<strong>in</strong>g to lead probability and roulette to carry out<br />
optimal decode. Suppose the current node as i, select<br />
node j as the next visit<strong>in</strong>g node:<br />
(2)<br />
p<br />
k<br />
ij<br />
ω υ<br />
⎧ rij<br />
() t iλij<br />
() t<br />
j∈<br />
allowed<br />
⎪<br />
ω υ<br />
= ⎨ ∑ ris<br />
() t i λis<br />
() t<br />
(3)<br />
⎪⎪<br />
s∈allowedk<br />
⎩0 otherwise<br />
ω υ<br />
where r () t i λ () t is for message of path, r () t stands<br />
ij<br />
ij<br />
for lead message, ω is lead factor; λ () t represents <strong>in</strong>spire<br />
message λ (t)= 1<br />
ij<br />
d ij<br />
ij<br />
, d<br />
ij<br />
means the distance from<br />
node i to node j, υ is <strong>in</strong>spire factor;<br />
allowed = {1, 2, m}<br />
− tabu means the set of available<br />
k<br />
k<br />
node may selected by ant k at the time t; tabu<br />
k<br />
is used to<br />
keep the rout<strong>in</strong>g table which obta<strong>in</strong>ed by transform<strong>in</strong>g ant<br />
k.<br />
C. Def<strong>in</strong>ition of Fitness Function<br />
A variety of fitness function needs to be designed for<br />
different optimal problems, the more fitness it is, the better<br />
solution for <strong>in</strong>dividual.<br />
Fitness function of extreme-value problem: suppose<br />
f ( X i<br />
) as the ith solution, fit( X i<br />
)<br />
ij<br />
is the adaptive value<br />
for the ith solution. m<strong>in</strong> and max denote the m<strong>in</strong>imum<br />
value and maximum value of function, respectively.<br />
⎧ 1<br />
⎪<br />
f( Xi<br />
) ≥ 0<br />
m<strong>in</strong> fit( X ) 1 (<br />
i<br />
)<br />
i<br />
= ⎨ + f X<br />
⎪<br />
⎩1 + abs( f ( X<br />
i)) f ( X<br />
i) < 0<br />
⎧ 1 + f( Xi) f( Xi) ≥ 0<br />
⎪<br />
max fit( X<br />
i<br />
) = ⎨ 1<br />
⎪<br />
1 + f( Xi<br />
) < 0<br />
⎩ abs( f ( X<br />
i<br />
))<br />
TSP fitness function: fitness of <strong>in</strong>dividual<br />
X<br />
i<br />
= { x1, x2, , xm}<br />
of TSP is def<strong>in</strong>ed as the reciprocal of<br />
path length represented by <strong>in</strong>dividual.<br />
fit(<br />
Ti<br />
)<br />
(4)<br />
(5)<br />
1<br />
fit( X<br />
i<br />
) = (6)<br />
DX ( )<br />
Fitness function for multicast rout<strong>in</strong>g problem:<br />
Wc<br />
( Wd<br />
⋅ Φ(<br />
TD − Dmax<br />
) + Wdj<br />
⋅ Φ(<br />
TDJ − DJ max ) + W pl ⋅ Φ(<br />
TPL − PLmax<br />
))<br />
TC<br />
= (7)<br />
where TD, TDJ, TPL and TC represent the delay, delay<br />
jitter, packet loss rate and cost of multicast tree<br />
respectively. Wc=0.5, Wd=0.2, Wdj=0.1 and Wpl=0.2,<br />
represent the proportion of the cost, delay, delay jitter and<br />
packet loss rate <strong>in</strong> the fitness function respectively;<br />
⋅ Φ(X ) is a penalty function, when ⋅X ≤ 0 , ⋅Φ( X ) = 1 , or<br />
else, ⋅Φ( X ) = 0. 5 . It can be seen from the above equation<br />
that, the fitness value is the bigger the better.<br />
D. Ant Position Update<br />
In the solution space of optimal problem, suppose<br />
τ ( X i<br />
) is the strength of pheromone of kth ant at X<br />
i<br />
, <strong>in</strong>itial<br />
moment all set as some constant: η ( X i<br />
) stands for<br />
i<br />
© 2013 ACADEMY PUBLISHER
1538 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
the visibility at X<br />
i<br />
. The basic framework of BIQACA<br />
described as follows:<br />
1) Select<strong>in</strong>g the target position of ant movement<br />
By apply<strong>in</strong>g the pr<strong>in</strong>ciple of randomness, a number of<br />
qubits <strong>in</strong> the current position were randomly selected to<br />
constitute a position update vector S. The transition rule<br />
and transition probability of ant k from position X to<br />
position<br />
where q∈[0, 1] is even-distributed random number, q 0<br />
∈[0, 1] is probability parameter, P is the set of occupied<br />
po<strong>in</strong>ts for ant <strong>in</strong> unit space, X<br />
s<br />
tion as per formula (8) ; α is the update parameter of<br />
pheromone, β is the update parameter of visibility.<br />
2) Realiz<strong>in</strong>g the movement of ant towards target position<br />
via quantum rotation gate<br />
After the ant has selected the target position, its<br />
movement process can be realized by chang<strong>in</strong>g the phase<br />
of qubit it brought for quantum rotation gate. In unit<br />
space, suppose the current position for ant at time t is P<br />
i<br />
,<br />
selected target position is P k , update vector of P i is S,<br />
then the update of phase angle <strong>in</strong>crement at P<br />
i<br />
is<br />
where )}<br />
t+ 1 t+ 1 t t t t+ 1 t t+<br />
1<br />
⎡cosϕij s<strong>in</strong>θ ⎤ ⎡<br />
ij<br />
cosϕij s<strong>in</strong>θ ⎤ ⎡<br />
ij<br />
cos( ϕij +Δ ϕij )s<strong>in</strong>( θij +Δθ<br />
) ⎤<br />
ij<br />
⎢ t+ 1 t+ 1⎥ ⎢ t t ⎥ ⎢ t t+ 1 t t+<br />
1 ⎥<br />
⎢s<strong>in</strong>ϕij s<strong>in</strong>θij ⎥ = U ⎢s<strong>in</strong>ϕij s<strong>in</strong>θij ⎥ = ⎢s<strong>in</strong>( ϕij +Δ ϕij )s<strong>in</strong>( θij +Δθij<br />
) ⎥<br />
⎢<br />
t+ 1 t t t 1<br />
cosθ ⎥ ⎢<br />
ij<br />
cosθ ⎥ ⎢<br />
+<br />
ij<br />
cos( θij θ ) ⎥<br />
⎣ ⎦ ⎣ ⎦ ⎣ +Δ<br />
ij ⎦ (15)<br />
Apparently, U-gate can rotate the phase of qubit by<br />
t 1<br />
ϕ +<br />
t 1<br />
Δ<br />
ij<br />
and Δ θ +<br />
ij<br />
.<br />
3) Adjustment strategy of search space<br />
i<br />
In BIQACA, the search space for each qubit is designed<br />
as [ lowBd ij , upBdij<br />
] , the search space at <strong>in</strong>itializa-<br />
X<br />
s<br />
are:<br />
α<br />
β<br />
⎧arg max{ τ ( X<br />
s) iη<br />
( Xs)} q ≤ q<br />
tion is [ 0.25π<br />
,0.75π<br />
] , dur<strong>in</strong>g optimiz<strong>in</strong>g process of ants,<br />
0<br />
⎪ Xs∈P<br />
X<br />
s<br />
= ⎨ these search spaces are related with the contraction level<br />
⎪ <br />
⎩ Xs<br />
q > q0<br />
(8) of each qubit, and decrease exponentially, which can significantly<br />
improve the solution accuracy of the algorithm.<br />
α<br />
β<br />
τ ( Xs) iη<br />
( Xs)<br />
t+<br />
1<br />
t<br />
pX (<br />
s<br />
) =<br />
α<br />
β<br />
τ ( X<br />
u) η ( X<br />
u)<br />
X<br />
∑ i ,<br />
(9)<br />
⎡lowBd<br />
⎤ ⎡ 1 ⎤⎡ ij<br />
lowBd ⎤<br />
ij<br />
⎢ t+<br />
1 ⎥ = ⎢ t ⎥<br />
ij<br />
⎢ t ⎥ (16)<br />
nL<br />
⎢<br />
s,<br />
Xu∈P<br />
⎣ upBdij<br />
⎥⎦ ⎢⎣nf<br />
⎥⎦⎢⎣upBdij<br />
⎥⎦<br />
where j ∈ { S(1),<br />
S(2),<br />
,<br />
S(<br />
sm)}<br />
, S is the update vector<br />
of ants, nf = 2 is the constriction factor, nL t represents<br />
ij<br />
is the selected target loca-<br />
the contraction level of t-th iteration.<br />
4) Process<strong>in</strong>g of ant position variation<br />
Suppose the current position is P i , update vector of P i<br />
is S, the search space of P i is [ lowBd ij , upBdij<br />
] . Then the<br />
update of phase angle <strong>in</strong>crement at P<br />
i<br />
is:<br />
⎧ Δϕij<br />
= (2rand<br />
−1)(<br />
upBdij<br />
− lowBdij<br />
)<br />
⎨<br />
⎩<br />
Δϕij<br />
= sign(<br />
Δϕij<br />
)( abs(<br />
Δϕij<br />
) + lowBdij<br />
) (17)<br />
⎧ Δθij<br />
= (2rand<br />
−1)(<br />
upBdij<br />
− lowBdij<br />
)<br />
⎨<br />
⎩<br />
Δθij<br />
= sign(<br />
Δθij<br />
)( abs(<br />
Δθij<br />
) + lowBdij<br />
) (18)<br />
( φkj − φij ) × rand<br />
t<br />
⎧⎪<br />
j<br />
φkj ≠φij<br />
Δ φij<br />
= ⎨<br />
(10) 5) Random behavior of ants<br />
⎪⎩ Δ φij φkj = φij<br />
If P i is not improved after cont<strong>in</strong>uous limited-time cycles,<br />
the position should be abandoned, the ants will generate<br />
a new P '<br />
t<br />
t<br />
⎧Δ ϕij<br />
+ 2π Δ ϕij<br />
< −π<br />
t+<br />
1 ⎪<br />
i through random behavior to substtute P i .<br />
t t<br />
Δ ϕij = ⎨ Δ ϕij −π ≤ Δϕij<br />
≤ π (11)<br />
'<br />
⎪ Δ<br />
t<br />
t<br />
⎩ ϕij<br />
− 2π Δ ϕij<br />
> π<br />
ϕij = mean( ϕi<br />
) + Δϕ ij<br />
(19)<br />
'<br />
( θkj − θij ) × rand<br />
t<br />
⎧⎪<br />
j<br />
θkj ≠θ<br />
θij = mean( θi<br />
) + Δθ ij<br />
ij<br />
(20)<br />
Δ θij<br />
= ⎨<br />
(12)<br />
⎪⎩ Δ θij θkj = θij<br />
where i ∈ { 1,2, ,<br />
n}<br />
, j ∈ { S(1),<br />
S(2),<br />
,<br />
S(<br />
sm)}<br />
, S is the<br />
update vector of current position, Δ ϕij<br />
and Δ θij<br />
are updated<br />
us<strong>in</strong>g (17), (18), mean( θ<br />
t<br />
t<br />
⎧Δ θij<br />
+ π Δ θij<br />
< −π<br />
/2<br />
t+<br />
1 ⎪ t t<br />
i ) is the mean value of<br />
Δ θij = ⎨Δ θij −π /2 ≤ Δθij<br />
≤ π /2 (13)<br />
vector of phase angle θ<br />
⎪ Δ<br />
t<br />
t<br />
i at P i .<br />
⎩ θij<br />
− π Δ θij<br />
> π /2<br />
6) Update rules for pheromone <strong>in</strong>tensity and visibility<br />
When the ant completes a traverse, the current position<br />
j ∈ { S(1),<br />
S(2),<br />
,<br />
S(<br />
sm , rand<br />
j<br />
is random num-<br />
is mapped <strong>in</strong>to the solution space of optimal problem<br />
Δ ϕij<br />
, Δ θij<br />
can be obta<strong>in</strong>ed us<strong>in</strong>g from unit space, fitness function is calculated, and the<br />
<strong>in</strong>tensity and visibility of pheromone at current position<br />
should be updated.<br />
⎧τ( X<br />
i) = (1 − ρ) τ( Xi) + ρτ( Xi)<br />
t+ 1 t+ 1 t+ 1 t+ 1 t+ 1 t t+<br />
1<br />
⎨<br />
⎡cos Δϕij cos Δθij −s<strong>in</strong> Δϕij cos Δθij s<strong>in</strong> Δ θij cos( ϕij +Δϕij<br />
) ⎤<br />
⎢ t+ 1 t+ 1 t+ 1 t+ 1 t t+<br />
1 ⎥<br />
⎩ τ ( X<br />
i) = Qfit( X<br />
i)<br />
(21)<br />
U = ⎢s<strong>in</strong> Δϕij cos Δθij cos Δϕij cos Δθij s<strong>in</strong> Δ θs<strong>in</strong>( ϕij +Δϕij<br />
) ⎥<br />
⎢<br />
t+ 1 t t+ 1 t+<br />
1<br />
−s<strong>in</strong> Δθij −tan( ϕij / 2)s<strong>in</strong> Δθij cos Δθ<br />
⎥<br />
⎣ ij ⎦ (14)<br />
ber between [0, 1];<br />
(17), (18).<br />
Update of probability amplitude of qubit based on<br />
quantum rotation gate<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1539<br />
η ( X ) = fit( X )<br />
(22)<br />
i<br />
where (1 −ρ) ∈ [0,1] is the evaporation coefficient of<br />
pheromone, Q is the enhancement coefficient of pheromone.<br />
E. Description of BIQACA<br />
Tak<strong>in</strong>g the function extremum problem as an example,<br />
BIQACA implementation steps are described as follows:<br />
Step 1: Setup relevant parameters such as the number<br />
of ants, maximum number of iterations, number of limits<br />
limit, contraction level<br />
nL<br />
ij<br />
i<br />
, constriction factor nf, Maximum<br />
contraction level MaxL, reset contraction level<br />
resetL, search space [ lowBd ij , upBdij<br />
] , etc.<br />
Step 2: Randomly generate <strong>in</strong>itial position of ants accord<strong>in</strong>g<br />
to (1), transform the solution space accord<strong>in</strong>g to<br />
(2), and calculate the fitness of each ant accord<strong>in</strong>g to (5)<br />
or (6). Update the pheromone <strong>in</strong>tensity and visibility accord<strong>in</strong>g<br />
to (21) and (22).Record the current optimum solution,<br />
i.e. global optimum solution GBest. Initialize the<br />
conceptual vector trial ( i)<br />
= 0 , record the number of nonupdates<br />
at the position of ant.<br />
Step 3: Update the search space [ lowBd ij , upBdij<br />
] accord<strong>in</strong>g<br />
to (16).<br />
Step 4: Select a mov<strong>in</strong>g target for each ant <strong>in</strong> the ant<br />
colony accord<strong>in</strong>g to (8) and (9), then realize the movement<br />
of ants us<strong>in</strong>g quantum rotation gate <strong>in</strong> light of (10),<br />
(12) and (14).<br />
Step 5: For each ant, accord<strong>in</strong>g to mutation probability,<br />
realize the variation of ant’s position us<strong>in</strong>g quantum rotation<br />
gate <strong>in</strong> light of (17) and (18).<br />
Step 6: Transform the solution space accord<strong>in</strong>g to (2),<br />
calculate the fitness of each ant accord<strong>in</strong>g to (5) or (6).<br />
Update the current position if the new position is better<br />
than the current one; otherwise trial ( i)<br />
= trial(<br />
i)<br />
+ 1 , update<br />
contraction level nL ( i,<br />
j)<br />
= nL(<br />
i,<br />
j)<br />
+ 1 , if<br />
nL ( i,<br />
j)<br />
>MaxL, nL ( i,<br />
j)<br />
=resetL.<br />
Step 7: Determ<strong>in</strong>e whether trial (i)<br />
is greater than the<br />
limit, if trial (i)<br />
>limit, abandon the current position of<br />
the i-th ant, and generate a new position accord<strong>in</strong>g to (19),<br />
(20) and (15), perform space transformation <strong>in</strong> light of<br />
(2), calculate the fitness of each ant accord<strong>in</strong>g to (5) or<br />
(6), trial ( i)<br />
= 0 .<br />
Step 8: Update the pheromone <strong>in</strong>tensity and visibility<br />
accord<strong>in</strong>g to (21) and (22). Record the current local optimum<br />
position, Best, and local worst position, Worst.<br />
Step 9: Determ<strong>in</strong>e whether the local optimum position,<br />
Best is greater than the global optimum position, GBest,<br />
if Best>GBest, update the global optimal position, GBest<br />
with local optimum position, Best, otherwise, update the<br />
local worst position, Worst with global optimum position,<br />
GBest.<br />
Step 10: Update the number of iterations t=t+1. If the<br />
current number of iterations t>maxgen or accuracy of<br />
convergence is met, stop the search, output the global<br />
optimum position, or else, turn to Step 3.<br />
III. SIMULATION EXPERIMENT<br />
To verify the effectiveness and feasibility of BIQACA<br />
algorithm, function extremum problem, travel<strong>in</strong>g salesman<br />
problem and multicast rout<strong>in</strong>g problem were selected<br />
for test<strong>in</strong>g. The simulation programs were programed<br />
and implemented <strong>in</strong> MATLAB 2009a, test results were<br />
obta<strong>in</strong>ed <strong>in</strong> a PC with an Intel Core (TM) i5 CPU runn<strong>in</strong>g<br />
at 3.2GHz, and a 2.8GB RAM.<br />
A. Function Extremum Problem<br />
Three <strong>in</strong>ternationally commonly used functions f1~f3<br />
were selected to test BIQACA performance when the<br />
number of <strong>in</strong>dependent variables was 2 and 30 respectively<br />
2 2<br />
f ( x,<br />
y)<br />
= 0.3cos3π x − 0.3cos 4πy<br />
− x − y − 0.3, −1<br />
≤ x,<br />
y 1 (23)<br />
1 ≤<br />
n<br />
f ( x ) = ∑ ( −x<br />
s<strong>in</strong>( x )), − 500 ≤ x 500 (24)<br />
2 i<br />
i<br />
i<br />
i<br />
≤<br />
i=<br />
1<br />
n<br />
∑<br />
2<br />
f3( xi<br />
) = ( xi<br />
−10cos(2π xi<br />
) + 10), −5.12<br />
≤ xi<br />
≤ 5. 12 (25)<br />
i=<br />
1<br />
1) When the number of <strong>in</strong>dependent variables is 2<br />
Test function is f1, the optimization objective is to obta<strong>in</strong><br />
the maximum value.<br />
Algorithm parameters: maximum number of iterations<br />
maxgen=500, number of ants n=20, probability parameter<br />
q<br />
0<br />
=0.5, evaporation coefficient 1−<br />
ρ =0.05, pheromone<br />
update parameter α =1, visibility update parameter β =5,<br />
pheromone enhancement coefficient Q =10, mutation<br />
probability P<br />
m<br />
=0.05; the program was term<strong>in</strong>ated when<br />
the BIQACA algorithm found the optimal solution or had<br />
run for gen=500 iterations. Simulations were conducted<br />
us<strong>in</strong>g the CQACO algorithm and ACO algorithm <strong>in</strong> Ref.<br />
[12] respectively, each algorithm was run for 50 times<br />
<strong>in</strong>dependently under the same conditions, and their optimal<br />
value (Best), optimal mean value (M-best), number<br />
of success and average number of iterations were recorded,<br />
optimization results were compared <strong>in</strong> Table 1.<br />
TABLE I.<br />
COMPARISON OF EXPERIMENTAL RESULTS OF 3 ALGORITHMS WITH TEST<br />
FUNCTION F 1<br />
Func/opt<br />
f 1/<br />
0.24<br />
Status<br />
Algorithm<br />
ACO CQACO BIQACA<br />
Best 0.2400 0.2400 0.2400<br />
M-best 0.1720 0.2388 0.2400<br />
Con-times 42 48 50<br />
Ave-Steps 198.16 84.04 17.06<br />
It can be seen from Table 1 that, BIQACA algorithm’s<br />
optimization efficiency is the highest, its optimization<br />
results is also the greatest, with the success rate of 100%;<br />
followed is CQACO, with a success rate of 96%; the last<br />
is ACO, with a success rate of 84%.<br />
2) When the number of <strong>in</strong>dependent variables is 30<br />
Test functions were f2, f3, optimization goal is to obta<strong>in</strong><br />
the m<strong>in</strong>imum value.<br />
© 2013 ACADEMY PUBLISHER
1540 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
TABLE II.<br />
COMPARISON OF EXPERIMENTAL RESULTS OF 3 ALGORITHMS WITH TEST<br />
FUNCTION F2 AND F3<br />
B. Travel<strong>in</strong>g Salesman Problem<br />
Take symmetric-distance TSP as example, five problems<br />
with different data scale was selected from TSPLIB<br />
database as cases to verify the performance of the algorithm.<br />
Compare the result with Common Genetic Algorithm<br />
(CGA), Common Particle Swarm Optimization<br />
(CPSO) and Common Ant Colony Algorithm (CACA)<br />
respectively.<br />
Algorithm parameters: each algorithm prescribes a<br />
limit to algebra of 100 and population of 50. <strong>in</strong> CGA algorithm,<br />
<strong>in</strong>teger encod<strong>in</strong>g is adopted; <strong>in</strong> CPSO algorithm,<br />
<strong>in</strong>teger encod<strong>in</strong>g is also adopted, <strong>in</strong>ertia factor W =0.5,<br />
self-factor C<br />
1<br />
=0.3, global factor C<br />
2<br />
=0.7; <strong>in</strong> CABC algorithm,<br />
<strong>in</strong>teger encod<strong>in</strong>g adopted as well, other parameters<br />
with the function extreme value problem; In BIQACA<br />
algorithm, transfer factor parameter ω = 1, stimulat<strong>in</strong>g<br />
factor parameter υ = 5, other parameters with the function<br />
extreme value problem.<br />
Then <strong>in</strong> every case, 20 experimental data would be<br />
taken, and table 3 shows contrast of optimization results.<br />
Figure 1 is the Oliver30 Optimization Results and Figure<br />
2 is the EIL51 Optimization Results. Figure 3 shows the<br />
best solution of Oliver30 quantum ant colony algorithm,<br />
the total distance for 424. Figure 4 shows the best solution<br />
of EIL51 quantum ant colony algorithm, the total<br />
distance is 458.<br />
Func/<br />
Opt<br />
f 2/<br />
-12569.5<br />
f 3/<br />
0<br />
Status<br />
Algorithm<br />
OGA/Q LEA BQACA<br />
M-nfun 302116 287365 236613<br />
M-best -12569.454 -12569.454 -12569.487<br />
St.dev 6.447×10 -4 6.831×10 -4 6.5856×10 -6<br />
M-nfun 224710 223803 223230<br />
M-best 0 2.103×10 -18 0<br />
St.dev 0 3.0359×10 -18 0<br />
Algorithm parameters: maximum number of iterations<br />
maxgen=1500, number of ants n=100, other parameters<br />
were the same as test 3.1.1. Simulations were conducted<br />
us<strong>in</strong>g the BIQACA algorithm, as well as the OGA/Q algorithm<br />
<strong>in</strong> Ref. [13] and LEA algorithm <strong>in</strong> Ref. [14] respectively,<br />
each algorithm was run <strong>in</strong>dependently for 50<br />
times under the same conditions, and their average number<br />
of function evaluations (M-nfun), optimal mean value<br />
(M-best) and standard deviation (St. dev) were recorded,<br />
optimization results were compared <strong>in</strong> Table 2.<br />
It can be seen from Table 2 that, the BIQACA algorithm<br />
is obviously superior to the OGA/Q algorithm and<br />
LEA algorithm with respect to optimal mean value, average<br />
number of function evaluations and standard deviation<br />
of function f2, f3; for f3, the BIQACA algorithm and<br />
the OGA/Q algorithm could both f<strong>in</strong>d the optimal solutions.<br />
For function f2, the three algorithms all failed to f<strong>in</strong>d<br />
the optimal solutions, but the solution f<strong>in</strong>d<strong>in</strong>g quality of<br />
BIQACA algorithm is significantly better than that of the<br />
LEA algorithm and OGA/Q algorithm, the standard deviation<br />
obta<strong>in</strong>ed by the BIQACA algorithm is also less than<br />
that of the LEA algorithm and OGA/Q algorithm.<br />
Figure 1. The Oliver30 Optimization Results<br />
Figure 2. The EIL51 Optimization Results<br />
Figure 3. The Oliver30’s Best Solution by us<strong>in</strong>g BIQACA<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1541<br />
Figure 4.<br />
the EIL51’s Best Solution by us<strong>in</strong>g BIQACA<br />
Statistics analysis of data based on table 3: from time<br />
perspective, the average time of CPSO algorithm is<br />
shortest, secondly CGA algorithm, BIQACA algorithm<br />
followed, and CACA algorithm is the last one; from steps<br />
perspective, BIQACA algorithm and CACA algorithm<br />
are at the same level and the convergence rate of them is<br />
more preferable than the other two algorithms; from the<br />
perspective of calculation result, the optimal solution of<br />
BIQACA algorithm and CACA algorithm can reach an<br />
ideal resolution recommended by TSPLIB database when<br />
urban scale is small.<br />
When the urban scale is large, the BIQACA’s optimal<br />
solution can approach to that of CACA algorithm, and its<br />
average solution and standard deviation is better than that<br />
of CPSO algorithm and CGA algorithm. To sum up,<br />
BIQACA algorithm <strong>in</strong> this paper is feasible and effective.<br />
TABLE III.<br />
TSP CALCULATION RESULTS<br />
Test library<br />
Uleysses22<br />
Oliver30<br />
EIL51<br />
EIL76<br />
GR96<br />
algorithm<br />
Optimal Worst solution<br />
value deviation deviation time step<br />
Mean Standard Mean-square Mean Average<br />
solution<br />
CGA 76.9162 93.5551 85.0164 4.3255 18.7098 1.4645 100.0000<br />
CPSO 78.9062 125.7221 105.8074 9.7533 95.1269 0.2646 88.8000<br />
CACA 75.9832 77.3018 76.3748 0.3878 0.1504 1.9651 60.0000<br />
BIQACA 75.9832 76.6314 76.2579 0.2226 0.0496 1.6571 62.0000<br />
CGA 482.6800 639.5484 570.9215 37.2503 1387.5816 2.0194 100.0000<br />
CPSO 729.5129 990.8997 850.9355 84.6154 7159.7655 0.3277 84.7500<br />
CACA 423.7406 429.7853 426.7401 1.4871 2.2115 3.1717 54.1000<br />
BIQACA 423.7406 438.6092 428.8924 3.8389 14.7375 2.2512 50.0500<br />
CGA 558.7636 812.5886 694.0846 60.0962 3611.5476 3.4789 100.0000<br />
CPSO 1055.4600 1252.3856 1146.5343 60.0677 3608.1277 0.4929 93.4500<br />
CACA 440.7957 457.3709 450.5731 4.8484 23.5068 10.0465 60.8000<br />
BIQACA 458.3380 507.1071 492.5977 11.4446 130.9781 5.9311 55.4500<br />
CGA 949.3124 1200.5125 1082.3078 77.0343 5934.2825 5.3974 100.0000<br />
CPSO 1698.2136 2090.3629 1885.3653 106.6634 11377.0827 0.6863 94.6500<br />
CACA 566.8443 576.1675 572.0972 2.8604 8.1822 18.5971 50.4500<br />
BIQACA 628.7805 670.0715 653.8038 11.0728 122.6080 11.8519 59.4000<br />
CGA 1082.0048 1467.8411 1232.7158 98.6122 9724.3659 7.1479 100.0000<br />
CPSO 2274.0041 2885.1164 2567.0244 160.3023 25696.8139 0.8681 90.8500<br />
CACA 544.8082 558.9636 552.8529 4.3274 18.7262 37.43502 63.7500<br />
BIQACA 594.9407 648.2708 626.9822 11.5389 133.1465 22.903469 54.1000<br />
C. QoS Multicast Rout<strong>in</strong>g Problem<br />
In order to compare with the GA algorithm <strong>in</strong> Ref. [15]<br />
and QCMR-ACS <strong>in</strong> Ref. [16], the network architecture<br />
model the same with them was adopted <strong>in</strong> the experiment,<br />
as shown <strong>in</strong> Figure 5.<br />
Figure 5.<br />
8-node network model<br />
In this typical 8-node network model, network can be<br />
represented us<strong>in</strong>g picture G (V, E), where V (D, DJ, PL,<br />
C) represents network node set, E (D, DJ, B, C) represents<br />
l<strong>in</strong>k set, and D, DJ, PL, C and B represent delay<br />
(ms), delay jitter (ms), packet loss rate, cost and bandwidth<br />
(Mb/s) respectively.<br />
The core idea of multicast rout<strong>in</strong>g algorithm is: <strong>in</strong> each<br />
iteration, firstly, qubits pass l<strong>in</strong>ear transformation and<br />
state transition transformation, and complete the conversion<br />
of quantum <strong>in</strong>formation <strong>in</strong> the rout<strong>in</strong>g path; secondly,<br />
use the rout<strong>in</strong>g paths to generate the multicast tree of the<br />
iteration; thirdly, compute the delay, delay jitter, packet<br />
loss rate, bandwidth, and cost of the multicast tree; f<strong>in</strong>ally,<br />
calculate the fitness of the multicast tree.<br />
Multicast tree generation: the orig<strong>in</strong>al multicast tree is<br />
generated us<strong>in</strong>g the vector <strong>in</strong>formation of multiple rout<strong>in</strong>g<br />
paths, and through the conversion from vector to matrix,<br />
the orig<strong>in</strong>al multicast tree was pruned and processed<br />
to obta<strong>in</strong> the multicast tree.<br />
Algorithm parameters: source node s=1, dest<strong>in</strong>ation<br />
node M=[2, 4, 5, 7], maximum number of iterations<br />
maxgen=16, number of ants n=8, mutation probability<br />
P = 0.1.<br />
m<br />
© 2013 ACADEMY PUBLISHER
1542 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Table 4 shows the optimization results of BIQACA algorithm<br />
when D 46 , DJ 8 , B 70 and<br />
max =<br />
max =<br />
m<strong>in</strong> =<br />
PL max = 0.001 were constra<strong>in</strong>ed; Figure 6 shows the cost<br />
convergence curves of multicast tree for three algorithms<br />
(GA, QCMR-ACS, BIQACA)<br />
Route<br />
request<br />
s=1<br />
M=[2, 4,<br />
5, 7]<br />
Figure 6.<br />
TABLE IV.<br />
BIQACA ALGORITHM OPTIMIZATION RESULTS<br />
Optimal<br />
multicast tree<br />
(1, 2), (1, 3),<br />
(3, 4), (3, 5)<br />
(4, 6), (6, 7)<br />
Delay<br />
Delay<br />
jitter<br />
Packet<br />
loss rate<br />
Cost<br />
45 7 0.0001 66<br />
Cost convergence curves of multicast tree for three algorithms<br />
Table 5 shows the optimization results of BIQACA algorithm<br />
when D 50 , DJ 6 , B 70 and<br />
max =<br />
max =<br />
m<strong>in</strong> =<br />
PL max = 0.001 were constra<strong>in</strong>ed; Figure 7 shows the cost<br />
convergence curves of multicast tree for three algorithms<br />
(GA, QCMR-ACS, BIQACA)<br />
Route<br />
request<br />
s=1<br />
M=[2, 4,<br />
5, 7]<br />
Figure 7.<br />
TABLE V.<br />
BIQACA ALGORITHM OPTIMIZATION RESULTS<br />
Optimal<br />
Delay Packet<br />
Delay<br />
multicast tree<br />
jitter loss rate<br />
Cost<br />
(1, 2), (1, 3),<br />
(2, 4), (3, 5)<br />
49 5 0.0002 62<br />
(4, 6), (6, 7)<br />
Cost convergence curves of multicast tree for three algorithms<br />
It can be seen from Figure 6 and Figure 7 that, under<br />
the conditions of the two multicast rout<strong>in</strong>g constra<strong>in</strong>ts,<br />
the three algorithms can all converge to the global optimal<br />
solution, for GA algorithm <strong>in</strong> Ref. [15], evolution<br />
generations dur<strong>in</strong>g convergence were 12 and 14, respectively,<br />
QCMR-ACS algorithm <strong>in</strong> Ref. [16] requires 6 and<br />
9 generations respectively, while the BIQACA algorithm<br />
here<strong>in</strong> requires only 2 generations, its convergence speed<br />
is much faster than that of the GA and QCMR-ACS<br />
based QoS multicast rout<strong>in</strong>g algorithms, thus the feasibility<br />
and effectiveness of the BIQACA algorithm are verified.<br />
IV. CONCLUSION<br />
In this paper, by comb<strong>in</strong><strong>in</strong>g quantum computation and<br />
ant colony algorithm, an improved quantum ant colony<br />
algorithm based on Bloch coord<strong>in</strong>ates is presented, enrich<strong>in</strong>g<br />
the research field of quantum <strong>in</strong>telligence algorithm.<br />
From the perspective of quantum computation, this<br />
algorithm proposes the adjustment strategy of search<br />
space <strong>in</strong> accordance with the exponential decrease method.<br />
A number of qubits at current position of ants are<br />
selected us<strong>in</strong>g the pr<strong>in</strong>ciple of randomness to constitute<br />
the update vector, the position update, position variation<br />
and random behavior of ants are all subject to the constra<strong>in</strong>t<br />
of update vector, thus improv<strong>in</strong>g the convergence<br />
speed of the algorithm. At the same time, the random<br />
behavior of ants <strong>in</strong>troduced can obviously overcome the<br />
prematurity of the algorithm. Different solution space<br />
transformation models and fitness functions are designed<br />
for different optimization problems, where the overall<br />
idea of the algorithm rema<strong>in</strong>s the same, the algorithm has<br />
strong versatility. Research results show that the new<br />
algorithm has certa<strong>in</strong> practical value which can improve<br />
the efficiency and accuracy. Compared with conventional<br />
<strong>in</strong>telligence algorithms, BIQACA has stronger search<br />
capability and higher efficiency, and is appropriate for<br />
complex function optimization and comb<strong>in</strong>atorial optimization<br />
problems. At the same time, as a novel optimization<br />
algorithm, BIQACA is lack of necessary theoretical<br />
proof, experimental verification alone is not comprehensive<br />
enough; further study is needed <strong>in</strong> the future.<br />
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[15] Wang Z. y<strong>in</strong>g, Shi B. x<strong>in</strong>. Solv<strong>in</strong>g QoS Multicast Rout<strong>in</strong>g<br />
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Computers, vol. 24, no. 1, pp. 55-61, 2001.<br />
[16] YANG Yun, XU Jia, GAO Fei, et al. Multiple QoS Constra<strong>in</strong>ed<br />
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© 2013 ACADEMY PUBLISHER
1544 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Image Fusion Method Based on Directional<br />
Contrast-Inspired Unit-L<strong>in</strong>k<strong>in</strong>g Pulse Coupled<br />
Neural Networks <strong>in</strong> Contourlet Doma<strong>in</strong><br />
Xi Cai<br />
Northeastern University at Q<strong>in</strong>huangdao, Q<strong>in</strong>huangdao, Ch<strong>in</strong>a<br />
Email: cicy_2001@163.com<br />
Guang Han<br />
College of Information Science and Eng<strong>in</strong>eer<strong>in</strong>g, Northeastern University, Shenyang, Ch<strong>in</strong>a<br />
Email: a00152738@sohu.com<br />
J<strong>in</strong>kuan Wang*<br />
Northeastern University at Q<strong>in</strong>huangdao, Q<strong>in</strong>huangdao, Ch<strong>in</strong>a<br />
Email: wjk@mail.neuq.edu.cn<br />
Abstract—To take full advantage of global features of source<br />
images, we propose an image fusion method based on<br />
adaptive unit-l<strong>in</strong>k<strong>in</strong>g pulse coupled neural networks<br />
(ULPCNNs) <strong>in</strong> the contourlet doma<strong>in</strong>. Consider<strong>in</strong>g that<br />
each high-frequency subband after the contourlet<br />
decomposition has rich directional <strong>in</strong>formation, we employ<br />
directional contrast of each coefficient as the external<br />
stimulus to <strong>in</strong>spire each neuron. L<strong>in</strong>k<strong>in</strong>g range is also<br />
related to the contrast <strong>in</strong> order to adaptively improve the<br />
global coupl<strong>in</strong>g characteristics of ULPCNNs. In this way,<br />
biological activity of human visual systems to detailed<br />
<strong>in</strong>formation of images can be simulated by the output pulses<br />
of the ULPCNNs. The first fir<strong>in</strong>g time of each neuron is<br />
utilized to determ<strong>in</strong>e the fusion rule for correspond<strong>in</strong>g<br />
detailed coefficients. Experimental results <strong>in</strong>dicate the<br />
superiority of our proposed algorithm, for multifocus<br />
images, remote sens<strong>in</strong>g images, and <strong>in</strong>frared and visible<br />
images, <strong>in</strong> terms of visual effects and objective evaluations.<br />
Index Terms—Image fusion, contourlet transform, unitl<strong>in</strong>k<strong>in</strong>g<br />
pulse coupled neural network<br />
I. INTRODUCTION<br />
Ow<strong>in</strong>g to widespread use of multisensor systems,<br />
much research has been <strong>in</strong>vested to develop the<br />
technology of image fusion. Ord<strong>in</strong>arily, 2-D image fusion<br />
is to merge complementary <strong>in</strong>formation from multiple<br />
images of the same scene, and obta<strong>in</strong> one s<strong>in</strong>gle image of<br />
better quality [1]-[4]. This promotes its <strong>in</strong>creas<strong>in</strong>gly<br />
extensive application <strong>in</strong> digital camera imag<strong>in</strong>g,<br />
battlefield surveillance and remote sens<strong>in</strong>g. As a major<br />
class of image fusion methods, the ones based on<br />
multiscale decomposition (MSD) take <strong>in</strong>to account the<br />
sensitivity of human visual system (HVS) to detailed<br />
* Correspond<strong>in</strong>g author.<br />
<strong>in</strong>formation, and hence receive better fusion results than<br />
other methods [5][6]. To improve the performance, MSD<br />
transforms and fusion rules have become the ma<strong>in</strong> focus<br />
<strong>in</strong> the fusion methods based on MSD [7]-[9].<br />
Typically, MSD transforms <strong>in</strong>clude: pyramid<br />
transform, wavelet transform, curvelet transform, etc.<br />
With further development of MSD theory, a superior twodimensional<br />
representation, contourlet transform was<br />
exploited to overcome limitations of traditional MSD<br />
transforms [10]. Its characteristics of multidirection and<br />
anisotropy make it sensitive to directions and sparse<br />
while represent<strong>in</strong>g objects with edges. Especially,<br />
contourlet transform allows for different and flexible<br />
number of directions at each scale, and hence can capture<br />
detailed <strong>in</strong>formation <strong>in</strong> any arbitrary direction. These<br />
advantages make the contourlet transform quite attractive<br />
to image fusion [11]-[14]. In most contourlet-based<br />
fusion methods, researchers adopt fusion rules to choose<br />
more salient high-frequency <strong>in</strong>formation, for example,<br />
[12] and [13] respectively chose the coefficient with the<br />
maximum region energy and the maximum edge<br />
<strong>in</strong>formation.<br />
However, the traditional fusion rules could not make<br />
good use of global features of images, for they were most<br />
based on features of a s<strong>in</strong>gle pixel or local regions. In our<br />
study, we present a bio-<strong>in</strong>spired salience measure based<br />
on unit-l<strong>in</strong>k<strong>in</strong>g pulse coupled neural networks<br />
(ULPCNNs), and capture the global features of source<br />
images by us<strong>in</strong>g the global coupl<strong>in</strong>g properties of the<br />
ULPCNNs. PCNN orig<strong>in</strong>ated from the experimental<br />
observations of synchronous pulse bursts <strong>in</strong> cat visual<br />
cortex [15], and is capable to simulate biological activity<br />
of HVS; ULPCNN is a simplified version of the basic<br />
PCNN with fewer parameters [16]. When motivated by<br />
external stimuli from images, ULPCNNs can generate<br />
series of b<strong>in</strong>ary pulses conta<strong>in</strong><strong>in</strong>g much <strong>in</strong>formation of<br />
features such as edges, textures, etc.<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1544-1551
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1545<br />
In this paper, we propose an image fusion method<br />
based on directional contrast-stimulated ULPCNNs with<br />
adaptive l<strong>in</strong>k<strong>in</strong>g range <strong>in</strong> the contourlet doma<strong>in</strong> (CT-<br />
ULPCNN). ULPCNN neurons are <strong>in</strong>spired by directional<br />
contrast reveal<strong>in</strong>g the prom<strong>in</strong>ence of each directional<br />
subband, and such a ULPCNN is expected to possess<br />
good sensitivity to directional <strong>in</strong>formation of objects <strong>in</strong><br />
images. The l<strong>in</strong>k<strong>in</strong>g range is also determ<strong>in</strong>ed by<br />
correspond<strong>in</strong>g directional contrast. In this way, the global<br />
coupl<strong>in</strong>g character of the ULPCNN is better represented<br />
than that with constant l<strong>in</strong>k<strong>in</strong>g range, especially for the<br />
strong stimulus. In our fusion rules, the first fir<strong>in</strong>g time of<br />
each neuron is chosen as the salience measure.<br />
Experimental results suggested that CT-ULPCNN has<br />
better fusion results for multifocus images, remote<br />
sens<strong>in</strong>g images, and <strong>in</strong>frared and visible images, which<br />
actually proves the advantages of the proposed method<br />
captur<strong>in</strong>g the prom<strong>in</strong>ent directional features of each<br />
subband <strong>in</strong> the contourlet doma<strong>in</strong>.<br />
The outl<strong>in</strong>e of the rest of the paper is as follows.<br />
Contourlet transform is briefly <strong>in</strong>troduced <strong>in</strong> Section II.<br />
In Section Ⅲ, we describe the theories of basic PCNN<br />
and ULPCNN, respectively. Detailed procedure of CT-<br />
ULPCNN algorithm is proposed <strong>in</strong> Section Ⅳ, and its<br />
effectiveness is certified and analyzed <strong>in</strong> Section Ⅴ .<br />
F<strong>in</strong>ally, conclusion is drawn <strong>in</strong> Section Ⅵ.<br />
II. CONTOURLET TRANSFORM<br />
Contourlet transform is a multi-scale and multidirectional<br />
transform. It was <strong>in</strong>itially developed <strong>in</strong><br />
discrete doma<strong>in</strong>, and hence easy for digital<br />
implementation. Contourlet transform comb<strong>in</strong>es<br />
Laplacian Pyramid (LP) and Directional Filter Bank<br />
(DFB) <strong>in</strong>to a double filter bank structure, so it is also<br />
called Pyramidal Direction Filter Bank (<strong>PDF</strong>B). In<br />
essence, LP is first executed to capture the po<strong>in</strong>t<br />
discont<strong>in</strong>uities, and then followed by DFB to l<strong>in</strong>k po<strong>in</strong>t<br />
discont<strong>in</strong>uities <strong>in</strong>to l<strong>in</strong>ear structures. Fig. 1 shows the<br />
contourlet decomposition <strong>in</strong> the frequency doma<strong>in</strong>, where<br />
shaded parts denote the support regions of correspond<strong>in</strong>g<br />
filters. Dur<strong>in</strong>g the contourlet decomposition, an image is<br />
first decomposed by LP <strong>in</strong>to a low-frequency subband<br />
and mutiple high-frequency subbands, and then each<br />
high-frequency subband is fed <strong>in</strong>to DFB to generate<br />
multiple directional subbands.<br />
In the contourlet transform, the number of directional<br />
n<br />
subbands <strong>in</strong> each scale is usually 2 ( n∈ N)<br />
and quite<br />
flexible when n is set differently. Therefore, the<br />
contourlet transform is able to provide detailed<br />
<strong>in</strong>formation <strong>in</strong> any arbitrary direction, which is its major<br />
advantage over the other MSD transforms. Meanwhile,<br />
after the contourlet decomposition, majority of the<br />
contourlet coefficients of an image are close to zero,<br />
concentrat<strong>in</strong>g the most <strong>in</strong>formation and energy, which<br />
<strong>in</strong>dicates the sparsity of the contourlet transform.<br />
Ⅲ. PCNN AND ULPCNN<br />
A. Basic PCNN<br />
PCNN is a feedback network <strong>in</strong> a s<strong>in</strong>gle layer with<br />
neurons laterally <strong>in</strong>terconnected, which can imitate the<br />
biological characteristics of HVS. Basically, each neuron<br />
consists of a receptive field, a modulation product and a<br />
pulse generator. For the neuron located at ( i, j ) <strong>in</strong> a<br />
PCNN, the receptive field <strong>in</strong>volves a l<strong>in</strong>k<strong>in</strong>g <strong>in</strong>put L ij<br />
and a feed<strong>in</strong>g <strong>in</strong>put F ; The modulation product<br />
ij<br />
comb<strong>in</strong>es F with the biased L to form a total <strong>in</strong>ternal<br />
ij<br />
ij<br />
activity<br />
U ; The generator Y<br />
ij<br />
ij<br />
will produce a pulse (i.e.<br />
fir<strong>in</strong>g) if U ij<br />
exceeds the dynamic threshold θ ij<br />
. When<br />
<strong>in</strong>spired by external stimulus S ij<br />
and <strong>in</strong>fluenced by<br />
signals from neighbor<strong>in</strong>g neurons { Y kl<br />
}<br />
mathematical equations for F ij<br />
,<br />
L ,<br />
ij<br />
, the discrete<br />
U , Y and θ can<br />
ij ij<br />
ij<br />
be described as follows.<br />
−α<br />
F ( n) = e F ( n− 1) + V M Y ( n 1) S<br />
F<br />
ij ij F ∑ − + , (1)<br />
ijkl kl ij<br />
kl<br />
−αL<br />
L ( n) = e L ( n− 1) + V W Y ( n 1)<br />
ij ij L∑ − , (2)<br />
ijkl kl<br />
kl<br />
U ( n) = F ( n) ⋅ (1 +β L ( n))<br />
, (3)<br />
Y ( n)<br />
ij<br />
ij ij ij<br />
1, U ( n) >θ ( n−1),<br />
ij<br />
ij<br />
0 , otherwise ,<br />
= ⎧ ⎨ ⎩<br />
(4)<br />
θ ( n) = e −α θ<br />
θ ( n− 1) + VY ( n)<br />
. (5)<br />
ij ij θ ij<br />
Figure 1. Frame of contourlet decomposition <strong>in</strong> the frequency doma<strong>in</strong>.<br />
Fig. 2 illustrates the basic model for a s<strong>in</strong>gle neuron<br />
located at ( i, j ) <strong>in</strong> a PCNN. Output pulses of neurons <strong>in</strong><br />
the k× l neighborhood centered at ( i, j ) enter <strong>in</strong>to the<br />
neuron at ( i, j ) and then <strong>in</strong>fluence its next output, where<br />
k× l is called l<strong>in</strong>k<strong>in</strong>g range. L ij<br />
receives pulses from<br />
surround<strong>in</strong>g neurons ((2)), and F ij<br />
receives not only the<br />
neighbor<strong>in</strong>g signals but also the external stimulus S ij<br />
© 2013 ACADEMY PUBLISHER
1546 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 2. Basic model for a s<strong>in</strong>gle PCNN neuron.<br />
((1)). U is obta<strong>in</strong>ed by multiply<strong>in</strong>g F with the biased<br />
ij<br />
ij<br />
L ((3)). If U is above the neuromime threshold θ , Y<br />
ij<br />
ij<br />
ij ij<br />
will generate a pulse ((4)), and simultaneously θ ij<br />
will<br />
<strong>in</strong>crease enormously ((5)) to block another pulse <strong>in</strong> the<br />
next iteration. Without an output pulse, θ ij<br />
would decay<br />
exponentially ((5)), until it drops below the <strong>in</strong>ternal<br />
activity and at that time a pulse will be outputted aga<strong>in</strong>.<br />
In this way, these processes run over and over aga<strong>in</strong>. In<br />
(1)-(5), n denotes the iteration times; α F<br />
, α , α and<br />
L θ<br />
V , V , V θ<br />
are attenuation time constants and <strong>in</strong>herent<br />
F<br />
L<br />
voltage potential of F ij<br />
, L and θ , respectively;<br />
ij<br />
ij<br />
W signify synaptic weight strength for F<br />
ijkl<br />
ij<br />
and<br />
M and<br />
ijkl<br />
L ;<br />
ij<br />
β <strong>in</strong>dicates l<strong>in</strong>k<strong>in</strong>g strength determ<strong>in</strong><strong>in</strong>g contribution of<br />
the l<strong>in</strong>k<strong>in</strong>g <strong>in</strong>put to the <strong>in</strong>ternal activity.<br />
B. ULPCNN<br />
PCNN is qualified to imitate the biological features of<br />
HSV and hence apply to image process<strong>in</strong>g [17]-[19];<br />
however, so many parameters <strong>in</strong> the model should be set<br />
dur<strong>in</strong>g use. So far, the relation between model parameters<br />
and network outputs is still ambiguous, and it is really<br />
difficult to determ<strong>in</strong>e the proper PCNN parameters.<br />
Therefore, ULPCNN is presented to simplify the PCNN<br />
by means of decreas<strong>in</strong>g parameters and mak<strong>in</strong>g the<br />
l<strong>in</strong>k<strong>in</strong>g <strong>in</strong>puts of ULPCNN neurons uniform [16]. Fig. 3<br />
displays the simplified model for a s<strong>in</strong>gle ULPCNN<br />
neuron. The processes of a s<strong>in</strong>gle ULPCNN neuron are<br />
displayed as<br />
F ( n)<br />
= S , (6)<br />
ij<br />
∑<br />
1, Y ( n− 1) > 0,<br />
⎧⎪<br />
kl<br />
L ( n)<br />
=<br />
kl<br />
ij ⎨<br />
⎪⎩ 0 , otherwise ,<br />
ij<br />
(7)<br />
U ( n) = F ( n) ⋅ (1 +β L ( n))<br />
, (8)<br />
ij ij ij<br />
Figure 3. Simplified model for a s<strong>in</strong>gle ULPCNN neuron.<br />
Y ( n)<br />
ij<br />
1, U ( n) >θ ( n−1),<br />
ij<br />
ij<br />
= ⎧ ⎨ (9)<br />
⎩<br />
0 , otherwise ,<br />
θ ( n) = e −α θ<br />
θ ( n− 1) + VY ( n)<br />
. (10)<br />
ij ij θ ij<br />
Accord<strong>in</strong>g to (7), if any neuron <strong>in</strong> the k×<br />
l<br />
neighborhood fires, L ij<br />
will have a unity <strong>in</strong>put, and then<br />
the centered neuron will be encouraged to fire. Obviously,<br />
impulse expand<strong>in</strong>g behavior is much clearer and more<br />
controllable with much fewer parameters than the basic<br />
PCNN.<br />
IV. THE PROPOSED IMAGE FUSION METHOD<br />
Consider<strong>in</strong>g that HVS is very sensitive to detailed<br />
<strong>in</strong>formation, researchers commonly employ fusion rules<br />
to choose more significant <strong>in</strong>formation <strong>in</strong> high-frequency<br />
subbands. In our study, we provide a new image fusion<br />
method based on directional contrast-<strong>in</strong>spired ULPCNN<br />
<strong>in</strong> the contourlet doma<strong>in</strong>. Directional features are fed <strong>in</strong>to<br />
ULPCNN to imitate the biological activity of HSV, and<br />
then transmitted <strong>in</strong> the form of pulses. The l<strong>in</strong>k<strong>in</strong>g range<br />
for each neuron is adaptive to correspond<strong>in</strong>g directional<br />
contrast. The first fir<strong>in</strong>g time of each neuron is used to<br />
determ<strong>in</strong>e the decision <strong>in</strong> fusion rules. Because of the<br />
global coupl<strong>in</strong>g characters of the ULPCNNs, global<br />
features of images can be made good use of dur<strong>in</strong>g fusion<br />
<strong>in</strong> our proposed method.<br />
Fig. 4 shows the flowsheet of our proposed method.<br />
Detailed procedure of the CT-ULPCNN method is given<br />
as follows.<br />
• Source images A and B are decomposed by the<br />
A A<br />
contourlet transform to coefficients { a , d } and<br />
,<br />
B<br />
{ a , d }, respectively. Denote the coefficients of<br />
R<br />
B<br />
r,<br />
p<br />
F F<br />
the fused image F by { a , d }. Here, R is the<br />
R r,<br />
p<br />
decomposition level, a X (X=A,B,F) denotes the<br />
R<br />
coefficients <strong>in</strong> the low-frequency subband of<br />
X<br />
image X, and d (X=A,B,F) denotes the<br />
r,<br />
p<br />
R<br />
r p<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1547<br />
Figure 4. Flowsheet of our proposed method.<br />
coefficients <strong>in</strong> the pth directional subband at the<br />
rth (1 ≤ r ≤ R)<br />
scale of image X.<br />
• In each directional subband, directional contrast at<br />
location (, ) i j can be calculated as<br />
Ctr (, i j) = d (, i j) a ( u, v)<br />
. (11)<br />
X X X<br />
r, p r,<br />
p r<br />
X<br />
where a <strong>in</strong>dicates the low-frequency subband at<br />
r<br />
the rth scale of image X, and the coarse<br />
coefficient at location ( uv , ) corresponds to the<br />
X<br />
X<br />
same region as d ,<br />
(, i j ) does. Then Ctr (, i j )<br />
,<br />
r p<br />
is imported as the external stimulus S ij<br />
<strong>in</strong>to the<br />
ULPCNN neuron located at ( i, j ). Its l<strong>in</strong>k<strong>in</strong>g<br />
range is fixed accord<strong>in</strong>g to<br />
k<br />
ij<br />
or l<br />
ij<br />
r p<br />
5,<br />
X<br />
X<br />
Ctr ( i, j) ≥ max( Ctr ) 2 ,<br />
r, p<br />
r,<br />
p<br />
3, otherwise.<br />
= ⎧ ⎨<br />
⎩<br />
(12)<br />
The ULPCNN operates iteratively as (6)-(10),<br />
until all neurons are fired at least once. The first<br />
fir<strong>in</strong>g time of the neuron at location (, i j)<br />
<strong>in</strong> the<br />
pth directional subband at the rth scale of image X<br />
X<br />
should be recorded as T (, i j ) (X=A,B).<br />
,<br />
F F<br />
•<br />
R r,<br />
p<br />
{ a , d } are obta<strong>in</strong>ed by the follow<strong>in</strong>g rules.<br />
For the low-frequency,<br />
r p<br />
( )<br />
F A B<br />
a (, i j) = a (, i j) + a (, i j) 2 , (13)<br />
R R R<br />
For the high-frequency,<br />
d<br />
F<br />
r,<br />
p<br />
(, i j)<br />
A A B<br />
d (, i j), T (, i j) < T (, i j),<br />
⎧ r, p r, p r,<br />
p<br />
= ⎨ (14)<br />
B<br />
⎩<br />
d<br />
r,<br />
p<br />
( i, j), otherwise.<br />
• The fused image F is f<strong>in</strong>ally achieved via<br />
F F<br />
contourlet reconstruction from { a , d }.<br />
R r,<br />
p<br />
V. EXPERIMENTAL RESULTS<br />
To certify the effectiveness of our proposed method,<br />
we have performed the CT-ULPCNN method on many<br />
pairs of images. Consider<strong>in</strong>g limitation of space, we take<br />
three pairs of images (shown <strong>in</strong> Fig. 5) as examples to<br />
provide the experimental results. Fig. 5(a) is a pair of<br />
multifocus images focus<strong>in</strong>g on different objects of the<br />
same scene, Fig. 5(b) displays a pair of remote sens<strong>in</strong>g<br />
images taken from different wavebands, and Fig. 5(c) is<br />
a pair of <strong>in</strong>frared and visible images.<br />
In this section, follow<strong>in</strong>g two sets of tests are designed<br />
to prove the validity of our proposed method. In Test 1,<br />
we highlight the advantage of the adaptive ULPCNNs<br />
model <strong>in</strong> our proposed method by compar<strong>in</strong>g its behavior<br />
to three exist<strong>in</strong>g contourlet-based image fusion<br />
algorithms, <strong>in</strong>clud<strong>in</strong>g CT-Miao [12], CT-Zheng [13], and<br />
CT-Yang [14]. Test 2 demonstrates the prom<strong>in</strong>ence of<br />
the CT-ULPCNN method by its comparison with some<br />
typical MSD-based image fusion methods, namely, the<br />
gradient pyramid-based method (Gradient) [20], the<br />
conventional discrete wavelet transform-based method<br />
(DWT) [21], the curvelet transform-based method<br />
(Curvelet) [22], and the nonsubsampled contourlet<br />
transform-based method (NSCT) [23].<br />
In our experiments, images were all decomposed <strong>in</strong>to<br />
four levels <strong>in</strong> use of the above MSD-based fusion<br />
methods. Especially, for the contourlet-based image<br />
fusion methods, the decomposed four scales were<br />
divided <strong>in</strong>to 4, 4, 8, and 16 directional subbands from<br />
coarse to f<strong>in</strong>e scales, respectively. Furthermore, <strong>in</strong> our<br />
proposed method, parameters were set as α = 0.5 ,<br />
θ<br />
V θ<br />
= 20 and β = 3 .<br />
A. Test 1<br />
Fig. 6-Fig. 8, respectively, provide the fusion results<br />
of pepsi, remote and camp us<strong>in</strong>g the CT-ULPCNN, CT-<br />
Miao, CT-Zheng, and CT-Yang methods. To show more<br />
clearly, we select a section of each result to enlarge.<br />
As can be seen from Fig. 6, for multifocus images, the<br />
CT-Miao, CT-Zheng, and CT-Yang methods all have the<br />
problem of r<strong>in</strong>g artifacts <strong>in</strong> their fusion results, and the<br />
partial result of the CT-Zheng has the severest ghost<br />
image even with a post-process<strong>in</strong>g of consistency<br />
verification (CV) to <strong>in</strong>tentionally reduce the r<strong>in</strong>g<strong>in</strong>g<br />
artifacts; whereas our proposed method possesses a result<br />
with the fewest r<strong>in</strong>g<strong>in</strong>g artifacts, highest contrast and<br />
f<strong>in</strong>est details without the CV.<br />
As seen from Fig. 7, the CT-ULPCNN method still<br />
has the best performance with the smoothest surface <strong>in</strong><br />
the flat regions. However, the result of the CT-Yang<br />
© 2013 ACADEMY PUBLISHER
1548 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
(a) (b) (c)<br />
Figure 5. Three pairs of test images: (a) pepsi, (b) remote and (c) camp.<br />
(a) (b) (c) (d)<br />
(e) (f) (g) (h)<br />
Figure 6. Fusion results of pepsi: (a) our method, (b) CT-Miao, (c) CT-Zheng, (d) CT-Yang,<br />
and (e)-(h) are partial enlargements of (a)-(d), respectively.<br />
method is visually unsatisfactory. This is because the<br />
fusion rule of the CT-Yang method for the lowfrequency<br />
subband is to choose the low-frequency<br />
coefficient with the maximum region variance, and such<br />
a rule makes the fused approximated image unsmooth<br />
when apply<strong>in</strong>g to source images with dist<strong>in</strong>ct basic<br />
illum<strong>in</strong>ations, such as remote sens<strong>in</strong>g images <strong>in</strong> different<br />
wavebands.<br />
Likewise, for the pair of <strong>in</strong>frared and visible images,<br />
the CT-Yang method generates the worst fusion result;<br />
whereas the hot target (i.e. the man) is the most<br />
dist<strong>in</strong>guishable <strong>in</strong> the result of our proposed method (Fig.<br />
8(a)).<br />
Obviously, the CT-ULPCNN achieves superior visual<br />
quality over the other three contourlet-based fusion<br />
methods.<br />
© 2013 ACADEMY PUBLISHER
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(a) (b) (c) (d)<br />
(e) (f) (g) (h)<br />
Figure 7. Fusion results of remote: (a) our method, (b) CT-Miao, (c) CT-Zheng, (d) CT-Yang,<br />
and (e)-(h) are partial enlargements of (a)-(d), respectively.<br />
(a) (b) (c) (d)<br />
(e) (f) (g) (h)<br />
Figure 8. Fusion results of camp: (a) our method, (b) CT-Miao, (c) CT-Zheng, (d) CT-Yang,<br />
and (e)-(h) are partial enlargements of (a)-(d), respectively.<br />
To evaluate the fusion effects more objectively, we<br />
<strong>in</strong>troduce average gradient (AG), spatial frequency (SF),<br />
mutual <strong>in</strong>formation (MI), Q AB/F [24] and a universal<br />
image quality <strong>in</strong>dex (UIQI) [25] as fusion <strong>in</strong>dices.<br />
Generally, the larger the above five objective <strong>in</strong>dices, the<br />
better the fusion result is.<br />
Table Ⅰ-Ⅲ show the <strong>in</strong>dices for fusion results of the<br />
three pairs of images <strong>in</strong> Fig. 5, respectively. Accord<strong>in</strong>g<br />
to these tables, the results of our method always have the<br />
largest values <strong>in</strong> the average gradient, spatial frequency,<br />
mutual <strong>in</strong>formation, Q AB/F and the universal image<br />
quality <strong>in</strong>dex, no matter for the pair of multifocus images,<br />
or the pair of remote sens<strong>in</strong>g images, or the pair of<br />
<strong>in</strong>frared and visible images. This clearly proves the<br />
superiority of our proposed method on the objective<br />
evaluations.<br />
B. Test 2<br />
We also make a comprehensive comparison of our<br />
proposed method with other four classical MSD-based<br />
fusion methods, <strong>in</strong>clud<strong>in</strong>g the Gradient [20], DWT [21],<br />
Curvelet [22] and NSCT [23].<br />
Because of the limitations of space, we only exhibit<br />
the fusion results of pepsi <strong>in</strong> Fig. 9. Apparently, the<br />
result of the Gradient method has the lowest contrast,<br />
and the Curvelet and the NSCT methods also generate<br />
© 2013 ACADEMY PUBLISHER
1550 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
(a) (b) (c) (d) (e)<br />
(f) (g) (h) (i) (j)<br />
Figure 9. Fusion results of pepsi: (a) our method, (b) Gradient, (c) DWT, (d) Curvelet, (e) NSCT<br />
and (f)-(j) are partial enlargements of (a)-(e), respectively.<br />
results with relatively lower contrast, and the results of<br />
the NSCT and especially the DWT methods have heavy<br />
r<strong>in</strong>g<strong>in</strong>g artifacts; whereas our proposed method produces<br />
a result with the highest contrast and the fewest r<strong>in</strong>g<strong>in</strong>g<br />
artifacts. Visually, the advantage of our proposed method<br />
is prom<strong>in</strong>ent.<br />
Table Ⅳ shows the fusion <strong>in</strong>dices of results by us<strong>in</strong>g<br />
the above five image fusion methods for pepsi. The<br />
result of our proposed method has the largest mutual<br />
<strong>in</strong>formation, Q AB/F , and the universal image quality <strong>in</strong>dex,<br />
except that, it has lower average gradient and spatial<br />
frequency than those of the DWT and the NSCT methods.<br />
This is because that, for pepsi, severe r<strong>in</strong>g<strong>in</strong>g artifacts <strong>in</strong><br />
the results of the DWT (Fig. 9(h)) and the NSCT (Fig.<br />
9(j)) may cause larger values <strong>in</strong> the average gradient and<br />
the spatial frequency.<br />
Experimental results demonstrate that, the superiority<br />
of the proposed method, <strong>in</strong> the field of visual quality and<br />
objective evaluations, is prom<strong>in</strong>ent. This ma<strong>in</strong>ly benefits<br />
from the global coupl<strong>in</strong>g characteristics of the<br />
ULPCNNs model. By us<strong>in</strong>g the features extracted from<br />
the output pulses of the ULPCNNs, the biological<br />
activity of the HVS to detailed <strong>in</strong>formation of images can<br />
be reflected very well.<br />
VI. CONCLUSION<br />
In this paper, we provide a new image fusion<br />
algorithm based on the ULPCNNs <strong>in</strong> the contourlet<br />
doma<strong>in</strong>. Directional contrast is fed <strong>in</strong>to the ULPCNNs to<br />
imitate the biological activity of HVS to directional<br />
<strong>in</strong>formation. L<strong>in</strong>k<strong>in</strong>g range is also determ<strong>in</strong>ed by the<br />
contrast, flexibly mak<strong>in</strong>g good use of global features of<br />
images. Experimental results illum<strong>in</strong>ate that, the CT-<br />
ULPCNN method outperforms the other methods <strong>in</strong> both<br />
the visual and the objective fields.<br />
ACKNOWLEDGMENT<br />
This work was supported by the Fundamental<br />
Research Funds for the Central Universities<br />
(N110323004) and the Natural Science Foundation of<br />
Hebei Prov<strong>in</strong>ce under Grant No.F2012501001.<br />
Method<br />
TABLE I.<br />
FUSION INDICES FOR PEPSI<br />
Metrics<br />
AG SF MI Q AB/F UIQI<br />
CT-ULPCNN 5.6722 13.986 6.7704 0.74015 0.89467<br />
CT-Miao 5.5759 13.923 6.4653 0.73644 0.85769<br />
CT-Zheng 5.4912 13.833 6.2256 0.71153 0.84454<br />
CT-Yang 5.5684 13.933 6.4987 0.73185 0.85492<br />
Method<br />
TABLE II.<br />
FUSION INDICES FOR REMOTE<br />
Metrics<br />
AG SF MI Q AB/F UIQI<br />
CT-ULPCNN 7.0993 15.362 1.6673 0.56055 0.69729<br />
CT-Miao 6.6244 14.646 1.4599 0.53364 0.64608<br />
CT-Zheng 6.6965 14.526 1.4182 0.49636 0.63166<br />
CT-Yang 7.0883 15.037 1.1027 0.46923 0.50629<br />
Method<br />
TABLE III.<br />
FUSION INDICES FOR CAMP<br />
Metrics<br />
AG SF MI Q AB/F UIQI<br />
CT-ULPCNN 7.2227 13.506 1.5600 0.46466 0.63175<br />
CT-Miao 6.8137 12.747 1.3814 0.4067 0.56411<br />
CT-Zheng 6.7682 12.529 1.3594 0.38244 0.55494<br />
CT-Yang 7.0183 13.064 1.5026 0.38959 0.51602<br />
TABLE IV.<br />
FUSION INDICES FOR PEPSI<br />
© 2013 ACADEMY PUBLISHER
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Method<br />
Metrics<br />
AG SF MI Q AB/F UIQI<br />
CT-ULPCNN 5.6722 13.986 6.7704 0.74015 0.89467<br />
Gradient 4.7795 11.987 6.135 0.73947 0.88898<br />
DWT 5.8093 14.173 6.3616 0.72958 0.86539<br />
Curvelet 5.6215 13.977 6.5344 0.73633 0.88186<br />
NSCT 7.7004 18.99 6.7607 0.68791 0.78435<br />
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Xi Cai received her B.S. and Ph.D. degrees from the School of<br />
Electronic and Information Eng<strong>in</strong>eer<strong>in</strong>g, Beihang University,<br />
Ch<strong>in</strong>a, <strong>in</strong> 2005 and 2011, respectively. Now she is a teacher at<br />
Eng<strong>in</strong>eer<strong>in</strong>g Optimization and Smart Antenna Institute,<br />
Northeastern University at Q<strong>in</strong>huangdao, Ch<strong>in</strong>a. Her research<br />
<strong>in</strong>terests <strong>in</strong>clude image fusion, image registration and object<br />
detection.<br />
Guang Han received his B. Eng. and M. Eng. degrees from the<br />
School of Electronic and Information Eng<strong>in</strong>eer<strong>in</strong>g, Beihang<br />
University, Ch<strong>in</strong>a, <strong>in</strong> 2005 and 2008, respectively. Now he is a<br />
Ph.D. candidate at College of Information Science and<br />
Eng<strong>in</strong>eer<strong>in</strong>g, Northeastern University. His research <strong>in</strong>terests<br />
<strong>in</strong>clude object detection and object track<strong>in</strong>g based on video<br />
sequences.<br />
J<strong>in</strong>kuan Wang received the M.Eng. degree from Northeastern<br />
University, Shenyang, Ch<strong>in</strong>a, <strong>in</strong> 1985, and the Ph.D. degree<br />
from the University of Electro-Communications, Chofu, Japan,<br />
<strong>in</strong> 1993.<br />
In 1990, he jo<strong>in</strong>ed the Institute of Space and Astronautical<br />
Science, Sagamihara, Japan, as a special member. He was an<br />
Eng<strong>in</strong>eer with the Research Department, COSEL Company, <strong>in</strong><br />
1994. He is currently the President of the Northeastern<br />
University at Q<strong>in</strong>huangdao, Hebei, Ch<strong>in</strong>a, where he has been a<br />
Professor s<strong>in</strong>ce 1998. He has been a ma<strong>in</strong> researcher <strong>in</strong> several<br />
National Natural Science Foundation research projects of Ch<strong>in</strong>a.<br />
His ma<strong>in</strong> <strong>in</strong>terests are <strong>in</strong> the areas of <strong>in</strong>telligent control,<br />
adaptive array, wireless sensor networks and image process<strong>in</strong>g.<br />
© 2013 ACADEMY PUBLISHER
1552 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
The Critical Legal Contention under the<br />
Challenge of Information Age and the<br />
Predom<strong>in</strong>ant Social Interests Concern for<br />
Develop<strong>in</strong>g Intelligent Vehicle Telematics <strong>in</strong> the<br />
United States<br />
Fa-Chang Cheng<br />
National Kaohsiung First University of Science and Technology/Graduate Institute of Science and Technology Law,<br />
Kaohsiung City, Taiwan<br />
Email: fachang1@hotmail.com<br />
Wen-Hs<strong>in</strong>g Lai *<br />
National Kaohsiung First University of Science and Technology/Dept. of Computer and Communication Eng<strong>in</strong>eer<strong>in</strong>g,<br />
Kaohsiung City, Taiwan<br />
Email: lwh@nkfust.edu.tw<br />
Abstract—Intelligent Vehicle Telematics has been a<br />
promis<strong>in</strong>g <strong>in</strong>dustry <strong>in</strong> the world. This new development of<br />
telecommunication technology has emerged with some legal<br />
concerns, especially <strong>in</strong> the liability for failure of safety<br />
devises and the protection of <strong>in</strong>formation privacy with<strong>in</strong><br />
Intelligent Vehicle Telematics. The purpose of this article is<br />
to ga<strong>in</strong> experiences from the discussion for these concerns <strong>in</strong><br />
academic papers and related cases with<strong>in</strong> the United States,<br />
<strong>in</strong> order to depict the possible solution for safety related<br />
legal concerns and the protection of <strong>in</strong>formation privacy<br />
which is based upon not only the concern of <strong>in</strong>formation age<br />
but also the concern of national security with regard to<br />
develop<strong>in</strong>g Intelligent Vehicle Telematics. The purpose of<br />
this article is <strong>in</strong>tended to offer some valuable reference to<br />
other countries which are also <strong>in</strong>volv<strong>in</strong>g <strong>in</strong> the development<br />
of <strong>in</strong>telligent Vehicle Telematics.<br />
Index Terms—Intelligent Vehicle Telematics, product<br />
liability, strict liability, <strong>in</strong>formation privacy<br />
I. INTRODUCTION<br />
The Intelligent Vehicle Telematics is highly valued by<br />
the government <strong>in</strong> the world as hav<strong>in</strong>g a lot of beneficial<br />
potential to the transportation <strong>in</strong>frastructure <strong>in</strong> such<br />
sovereignty. The features of safety design are critical to<br />
the Intelligent Vehicle Telematics and have some<br />
significant mean<strong>in</strong>g to the legal <strong>in</strong>frastructure. Those<br />
safety devises may <strong>in</strong>crease the safety of transportation<br />
which benefits to the society as a whole. Conversely; the<br />
failure of such safety devises may cause a lot of trouble.<br />
Manuscript received September 20, 2012; revised September 20,<br />
2012; accepted September 20, 2012.<br />
* Correspond<strong>in</strong>g author<br />
Therefore, the liability for system provider and devise<br />
manufacture (distributor) is one significant safety legal<br />
issue with regard to Intelligent Vehicle Telematics. Apart<br />
from the safety related legal concerns, the protection of<br />
privacy <strong>in</strong> the operation of Intelligent Vehicle Telematics<br />
is also another critical legal issue for Intelligent Vehicle<br />
Telematics. The <strong>in</strong>tention of this article is to <strong>in</strong>troduce<br />
the concept of <strong>in</strong>formation privacy <strong>in</strong> the United States<br />
and br<strong>in</strong>g up the suggestion of how to comprise the<br />
conflictions between protect<strong>in</strong>g <strong>in</strong>formation privacy and<br />
other legal <strong>in</strong>terests. S<strong>in</strong>ce this paper is ma<strong>in</strong>ly talk<strong>in</strong>g<br />
about the concerns from the prospective of the United<br />
States because due to the United states advanc<strong>in</strong>g <strong>in</strong><br />
Intelligent Vehicle Telematics research field, except the<br />
general technology description of Intelligent Vehicle<br />
Telematics, <strong>in</strong>clud<strong>in</strong>g the safety features, <strong>in</strong> the beg<strong>in</strong>n<strong>in</strong>g,<br />
this article will center the discussion on these concerns to<br />
academic papers and related cases with<strong>in</strong> the United<br />
States, <strong>in</strong> order to depict the possible solution for safety<br />
related legal concerns and the protect<strong>in</strong>g privacy concerns<br />
with regard to develop<strong>in</strong>g Intelligent Vehicle Telematics<br />
to other follow<strong>in</strong>g countries.<br />
II. THE TECHNOLOGY OF INTELLIGENT VEHICLE<br />
TELEMATICS AND ITS SAFETY FEATURES<br />
Vehicle Telematics is the <strong>in</strong>tegrated use of<br />
telecommunications and <strong>in</strong>formatics with<strong>in</strong> road vehicles.<br />
The objectives of Intelligent Vehicle Telematics are to<br />
improve safety, reduce traffic congestion, fuel<br />
consumption and carbon dioxide emissions, and <strong>in</strong>crease<br />
comfort and convenience or even enterta<strong>in</strong>ment, and the<br />
future trends focus on mak<strong>in</strong>g automobiles greener,<br />
smarter, and merg<strong>in</strong>g transportation and <strong>in</strong>formation<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1552-1559
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1553<br />
networks [1]. Most vehicle telematics projects were<br />
developed isolate. However, <strong>in</strong> some regions, like<br />
European Commission, have decided to act forwards<br />
harmoniz<strong>in</strong>g the deployment and use of ITS <strong>in</strong> road<br />
transport across Europe by means of the ITS Action Plan<br />
and the European ITS Directive [2].<br />
Wireless communications and network<strong>in</strong>g is a core<br />
enabl<strong>in</strong>g technology for ITSs (<strong>in</strong>telligent transport<br />
systems). A vehicle may communicate with other<br />
vehicles (vehicle-to-vehicle, V2V) or the <strong>in</strong>frastructure<br />
(vehicle-to-<strong>in</strong>frastructure, V2I) by us<strong>in</strong>g Dedicated Short<br />
Range Communication (DSRC), cellular communication,<br />
satellite communication, WiFi, Bluetooth or RFID.<br />
Among them, DSRC is short to medium range wireless<br />
communication promoted by US Department of<br />
Transport and specifically designed for vehicle use. US<br />
Federal Communications Commission (FCC) has<br />
allocated 75MHz <strong>in</strong> the 5.9GHz band for DSRC. Longer<br />
range communications can be accomplished by GSM, 3G,<br />
or WiMAX. It is noted that to prevent accidents, very low<br />
latency and short response times are needed for vehicleto-vehicle<br />
communications [3]. IEEE 802.11p, which is<br />
the groundwork for DSRC, is an IEEE standard to add<br />
wireless access <strong>in</strong> vehicular environments (WAVE). It<br />
def<strong>in</strong>es enhancements to 802.11 to support ITS. That is, it<br />
is specially designed for data exchange among mov<strong>in</strong>g<br />
vehicles and road <strong>in</strong>frastructure.<br />
Generally speak<strong>in</strong>g, <strong>in</strong> vehicle transportation, safety<br />
normally gets top priority, though enterta<strong>in</strong>ment and<br />
convenience have rapidly caught up to safety as the<br />
impetus for new <strong>in</strong>-car electronics development [4].<br />
Examples of many applications of vehicle safety systems<br />
are: Cooperative forward collision warn<strong>in</strong>g, Emergency<br />
brak<strong>in</strong>g notification, Lane or road departure warn<strong>in</strong>g, Precrash<br />
sens<strong>in</strong>g, Curve speed warn<strong>in</strong>g, Right turn assistance,<br />
Give way junction assistance, Traffic signal violation<br />
warn<strong>in</strong>g, Intersection collision warn<strong>in</strong>g, Road / rail<br />
collision warn<strong>in</strong>g, Road condition warn<strong>in</strong>g, Approach<strong>in</strong>g<br />
emergency vehicle warn<strong>in</strong>g, Emergency vehicle signal<br />
pre-emption, Road works warn<strong>in</strong>g, and Motorway merge<br />
assistance [5].<br />
The above safety related application systems or<br />
functions of <strong>in</strong>telligent vehicle system generally focuse<br />
on assist<strong>in</strong>g drivers and prevent<strong>in</strong>g driver errors while<br />
full autonomous, unmanned vehicles are still rema<strong>in</strong>ed as<br />
a research topic. However, these systems which designed<br />
to improve safety may, <strong>in</strong>stead, compete for driver<br />
attention and provide confus<strong>in</strong>g message [6]. That causes<br />
the telematics use becom<strong>in</strong>g a contribut<strong>in</strong>g factor for<br />
crashes, mostly due to multitask<strong>in</strong>g, distraction and<br />
longer duration usage time than conventional <strong>in</strong>-vehicle<br />
tasks [7]. Besides, more and more car <strong>in</strong>novations are<br />
from computer systems and software, and such<br />
complexity br<strong>in</strong>gs with it reliability concerns [8]. Ivan<br />
Berger [9] questioned three grow<strong>in</strong>g challenge for<br />
carmakers. First, the more complex a car electronic<br />
system, the more failure po<strong>in</strong>ts it offers. Second, the<br />
grow<strong>in</strong>g reliance on software raises more risk of fail.<br />
Third, the hardware environment becomes more<br />
demand<strong>in</strong>g because of heat and electromagnetic<br />
<strong>in</strong>terference (EMI).<br />
Some methods have been proposed to solve the safety<br />
concerns. For example, a workload manager is set to help<br />
determ<strong>in</strong>e if a driver is overloaded or distracted [7], and a<br />
structured procedural safety assessment of <strong>in</strong>terven<strong>in</strong>g<br />
systems is proposed [10]. Nevertheless, unless we can<br />
totally understand the driv<strong>in</strong>g behavior [11] - [13],<br />
<strong>in</strong>clud<strong>in</strong>g driver <strong>in</strong>tentions, how people make decisions,<br />
and how people <strong>in</strong>teract with vehicle, and model the<br />
behavior, there are still risks.<br />
In addition, there is privacy concern to aware.<br />
Know<strong>in</strong>g the accurate position and status of vehicles is<br />
the first th<strong>in</strong>g to do to make the transport <strong>in</strong>telligent.<br />
Global Position<strong>in</strong>g System (GPS) is a convenient way to<br />
calculate the <strong>in</strong>formation. However, the accuracy of<br />
standard GPS, which is generally 5 to 10 meters, is not<br />
always enough, and the accuracy and reliability of GPS<br />
are degraded <strong>in</strong> urban environments due to satellite<br />
visibility and multipath effects. Other technologies like<br />
Triangulation Method us<strong>in</strong>g mobile phones or <strong>in</strong>ertial<br />
navigation by the sensors via dead reckon<strong>in</strong>g could be<br />
<strong>in</strong>tegrated to improve the accuracy. Video cameras can<br />
also be fused [14] to help measure traffic flow or the<br />
distance between lane l<strong>in</strong>es. The computer vision<br />
technology can not only be used to look out of the vehicle<br />
to detect and track roads, but simultaneously look <strong>in</strong>side<br />
the vehicle to monitor the attentiveness or <strong>in</strong>tentions of<br />
the driver [15]. Besides camera, multiple Sensors<br />
<strong>in</strong>clud<strong>in</strong>g radar and lidar can be used to help detect<br />
various statistic or mov<strong>in</strong>g on-road obstacles [16]. Us<strong>in</strong>g<br />
standard statistics of telecom switches without extra<br />
effort <strong>in</strong> telecom network is also used to compute the<br />
speeds of vehicles [17]. By us<strong>in</strong>g the above techniques,<br />
accurate position or status <strong>in</strong>formation is obta<strong>in</strong>ed and<br />
then, these <strong>in</strong>formation is generally shared with other<br />
vehicles and <strong>in</strong>frastructure by communication. If privacy<br />
filter<strong>in</strong>g is not applied, serious privacy risk happens.<br />
Some applications like Pay-As-You-Drive Insurance<br />
model [18] have noticed it. The system performs the<br />
premium calculations locally <strong>in</strong> the vehicle, and send<br />
only aggregated data to the <strong>in</strong>surance company without<br />
leak<strong>in</strong>g location <strong>in</strong>formation.<br />
Another trend to aware is that cloud comput<strong>in</strong>g is<br />
expected to play a pivotal role <strong>in</strong> future automotive<br />
telematics services. It particularly makes the security and<br />
privacy <strong>in</strong> clouds an important issue <strong>in</strong> ITS.<br />
III. THE LIABILITY OF SYSTEM PROVIDER AND DEVISE<br />
MANUFACTURE (DISTRIBUTOR) FOR SAFETY LEGAL<br />
CONCERNS<br />
The safety concern for the Intelligent Vehicle<br />
Telematics is by far the most concerned topic both from<br />
the technical and the legal perspective. Discuss<strong>in</strong>g from<br />
the legal perspective for safety concern to Intelligent<br />
Vehicle Telematics, at first sight, there could be three<br />
potential possible k<strong>in</strong>ds of liability, negligence, warranty<br />
<strong>in</strong> contract or strict liability, for the system provider and<br />
four potential possible k<strong>in</strong>ds of liability for devise<br />
manufacture (distributor) with regard to the safety legal<br />
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concerns, add<strong>in</strong>g product liability to the three just<br />
mentioned before. The difference between the system<br />
provider and the devise manufacture (distributor) for<br />
potential liability to the safety legal concerns the product<br />
liability because the product liability is only eligible for<br />
the harm done by the tangible product, but not the<br />
services. For the purpose of elucidat<strong>in</strong>g the discussion<br />
here, briefly <strong>in</strong>troduc<strong>in</strong>g the concepts of negligence,<br />
warranty, strict liability and product liability is necessary.<br />
And the assertion of this article will <strong>in</strong>sist that strict<br />
liability theory is most appropriate to those situations<br />
based on the understand<strong>in</strong>g and characteristics of those<br />
legal <strong>in</strong>frastructures s<strong>in</strong>ce there is no real case handed<br />
down related to the safety legal concerns for Intelligent<br />
Vehicle Telematics <strong>in</strong> the United States judicial system.<br />
Regard<strong>in</strong>g this section here, the discussion will be<br />
divided <strong>in</strong>to three parts discussion: the first part of<br />
theories among negligence, warranty, product liability<br />
and strict liability; the second part of compar<strong>in</strong>g among<br />
negligence, warranty, product liability and strict liability<br />
for the culpability; and the third part of the reason to<br />
choose strict liability for the system provider and devise<br />
manufacture (distributor) as the liability solution for the<br />
related safety legal concerns to Intelligent Vehicle<br />
Telematics.<br />
A. The Theories among Negligence, Warranty, Product<br />
Liability and Strict Liability<br />
The first safety liability theory for system provider and<br />
devise manufacture (distributor) to Intelligent Vehicle<br />
Telematics is negligence. Generally speak<strong>in</strong>g, the theory<br />
of negligence is really based upon the idea of fault. To<br />
<strong>in</strong>dicate a defendant is negligent means that the defendant<br />
<strong>in</strong> the case violates the duty of care imputed by the<br />
society. And, except for some specific circumstances, the<br />
standard of care is either based upon the reasonable<br />
person [19] or professional reaction [20] under the<br />
ord<strong>in</strong>ary cases. Another specific feature for the theory of<br />
negligence is the requirement for proximate cause of<br />
which the legal mean<strong>in</strong>g is to def<strong>in</strong>e the amount of<br />
damages. The cause <strong>in</strong> fact between the wrongdoer and<br />
the consequences <strong>in</strong>voked by such wrongdoer is required<br />
<strong>in</strong> every tortious cause of action, the proximate cause is<br />
not a prerequisite for the cause of action <strong>in</strong> torts, for<br />
example the <strong>in</strong>tentional torts or product liability etc. and<br />
the proximate cause is really a means to the policy<br />
concern’s ends [21]. So, <strong>in</strong> order to substantiate <strong>in</strong> a<br />
negligence case, there are four elements need to be<br />
proved: duty of care, breach duty of care, causation<br />
(<strong>in</strong>clud<strong>in</strong>g the cause <strong>in</strong> fact and proximate cause) and<br />
damages.<br />
The second possible legal theory of the liability for<br />
system provider and devise manufacture (distributor)<br />
related to the safety devise for Intelligent Vehicle<br />
Telematics is warranty. Warranty cause of action is<br />
really someth<strong>in</strong>g between the contract theory and the torts<br />
theory. Two k<strong>in</strong>ds of warrant theory fall under this<br />
category; one is called the express warrant, the other is<br />
named the implied warranty. In the express warranty, it<br />
could be the contract liability which needs to prove the<br />
contract privity between the parties <strong>in</strong>volved <strong>in</strong> the<br />
warranty dispute. The express warrant could also be the<br />
torts liability which needs to prove the reliance of the<br />
<strong>in</strong>jured party, even though there is no requirement for<br />
prov<strong>in</strong>g the privity between the parties [22]. And the<br />
adoption of implied warrant theory is, to some extent,<br />
depend<strong>in</strong>g on the will<strong>in</strong>gness of the court and mostly<br />
used <strong>in</strong> the dispute of fitness of the object to its common<br />
application [23].<br />
The third possible legal theory to the mentioned<br />
liability is strict liability. In the strict liability theory,<br />
there is no need to prove the defendant’s fault, the<br />
contract privity, the reliance of the <strong>in</strong>jured or even<br />
pend<strong>in</strong>g on the court’s <strong>in</strong>terference. To prove some basic<br />
facts and establish that these facts results <strong>in</strong> the<br />
consequences is the only requirement to assert the strict<br />
liability. Traditionally, two types of strict liability are<br />
accepted <strong>in</strong> cases: the wild or vicious animal strict<br />
liability and the extremely dangerous activity strict<br />
liability. However, even under this str<strong>in</strong>gent liability,<br />
some exceptions exist to the general rule, like the<br />
comparative negligence of pla<strong>in</strong>tiff [24] or the Act of<br />
God [25].<br />
The last possible legal theory of the liability mentioned<br />
<strong>in</strong> this paragraph for system provider and devise<br />
manufacture (distributor) related to the safety devise for<br />
Intelligent Vehicle Telematics is product liability. The<br />
ma<strong>in</strong> purpose of product liability is to protect the user or<br />
consumer from <strong>in</strong>jured by the product threw <strong>in</strong> the stream<br />
of commerce. Theoretically, this legal theory conta<strong>in</strong>s<br />
three different types of product liability claims:<br />
manufactur<strong>in</strong>g defect, design defect and lack of warn<strong>in</strong>g<br />
[26]. Several possible legal <strong>in</strong>terpretations can del<strong>in</strong>eate<br />
the mean<strong>in</strong>g of product liability. To make the statement<br />
more clear, under the title of product liability, a product<br />
liability case can really be a negligence case [27], a<br />
warrant case [28] or a strict liability case [29]. When a<br />
product liability case is based upon the strict liability<br />
theory, the distributor or the manufacture for the product<br />
would easily be <strong>in</strong>volved <strong>in</strong> such case. The provision <strong>in</strong><br />
the Restatement (Second) of Torts embodies the strict<br />
liability approach. Accord<strong>in</strong>g to Restatement (Second) of<br />
Torts § 402A which is accepted by some of the states <strong>in</strong><br />
the United States, one who sells any product <strong>in</strong> a<br />
defective condition unreasonably dangerous to the user or<br />
consumer or to his property is subject to liability for<br />
physical harm thereby caused to the ultimate user or<br />
consumer, or to his property, even the seller has exercised<br />
all possible care <strong>in</strong> the preparation and sale of his product<br />
or the user (or consumer) has not brought the product<br />
from or entered <strong>in</strong>to any contractual relation with the<br />
seller. Even the Restatement (Second) and follow<strong>in</strong>g<br />
courts take the position that both the manufacture and the<br />
distributor shall bear the strict liability [30], there are still<br />
some jurisdictions which partially follow the Restatement<br />
(Second) would like to prove the breach of duty to the<br />
manufacture which is based upon design defect and lack<br />
of warn<strong>in</strong>g claims <strong>in</strong> a product liability litigation [31].<br />
And just similar to the strict liability, there are also a<br />
couple possible defenses, comparative negligence of<br />
pla<strong>in</strong>tiff [32] and statutory immunity (preemption) [33] or<br />
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unforeseeable misuse of the product [34], could be used<br />
as the defense aga<strong>in</strong>st the product liability. To sum up<br />
the description regard<strong>in</strong>g the product liability, the product<br />
liability is the liability to harm caused by the product<br />
which liability can present either one of the three possible<br />
choices: negligence, breach of warranty or strict liability.<br />
B. The Comparison among Negligence, Warranty,<br />
Product Liability and Strict Liability for the Culpability<br />
of Wrongdoer<br />
From the explanation <strong>in</strong> this previous paragraph, the<br />
conclusion for compar<strong>in</strong>g different legal theories for the<br />
safety related legal dispute can be summarized as the<br />
follow<strong>in</strong>g. First of all, the negligence cause of action is<br />
the most difficult liability to prove because, unlike<br />
warranty or strict liability, the duty of care needs to be<br />
substantiated. And the strict liability might be the easist<br />
legal theory to satisfy <strong>in</strong> the burden of provid<strong>in</strong>g evidence.<br />
As to the warranty cause of action, the liability would<br />
either rely on the contract privity or reliance <strong>in</strong> express<br />
warranty or count on the court <strong>in</strong>tervention <strong>in</strong> implied<br />
contract. To estimate the strength of liability or<br />
culpability, the warranty cause of action seems to stand <strong>in</strong><br />
between of the negligence and the strict liability. The last<br />
possible liability mentioned <strong>in</strong> this article-product<br />
liability, is really a mixture type of theory of liability<br />
among the negligence liability, warranty liability and the<br />
strict liability. Observ<strong>in</strong>g the history of the policy<br />
attitude toward the product liability, the substance to<br />
contend product liability is really sw<strong>in</strong>g<strong>in</strong>g between the<br />
negligence and the strict liability and some commentator<br />
believes the current court attitude <strong>in</strong> apply<strong>in</strong>g the product<br />
liability is more lenient toward the manufacture [35].<br />
C. The Reason for Choos<strong>in</strong>g Strict Liability for the<br />
System Provider and Devise Manufacture (Distributor)<br />
as the Liability Solution for the Related Safety Legal<br />
Concerns to Intelligent Vehicle Telematics<br />
This article would like to <strong>in</strong>dicate that those safety<br />
devises to Intelligent Vehicle Telematics are present<strong>in</strong>g<br />
really high social responsible concerns. Therefore, the<br />
primary policy th<strong>in</strong>k<strong>in</strong>g should be that the manufacture of<br />
these safety devise to Intelligent Vehicle Telematics is<br />
go<strong>in</strong>g to hold the highest legal responsibility under the<br />
current legal theory to the <strong>in</strong>jured person or property<br />
based upon the strict product liability. And the system<br />
provider for the operation of these safety devises to<br />
Intelligent Vehicle Telematics is the same important as<br />
the manufacture. If anyth<strong>in</strong>g goes wrong with the system,<br />
it could cause a catastrophe to the transportation.<br />
Therefore, the system provider for the operation of these<br />
safety devises to Intelligent Vehicle Telematics should<br />
also take the strict liability. The liability for both the<br />
manufacture and the system provider here is noth<strong>in</strong>g like<br />
the liability to the cell phone manufacture or the<br />
communication services provider for the user talk<strong>in</strong>g over<br />
the cell phone while he or she was driv<strong>in</strong>g because the<br />
cell phone is not designed to the protection of<br />
transportation safety and the user who <strong>in</strong>itiates<br />
communication and cause the distraction which results <strong>in</strong><br />
the traffic <strong>in</strong>cident should be responsible for his or her<br />
behavior [36]. As to the distributor between the<br />
manufacture and the user or consumer, because the<br />
distributor doesn’t directly contribute to the safety legal<br />
issue regard<strong>in</strong>g the safety devises with<strong>in</strong> Intelligent<br />
Vehicle Telematics, it is suggested the distributor doesn’t<br />
need to be strictly liable to the <strong>in</strong>jury based upon product<br />
liability by the failure of these safety devises. The<br />
current situation as to different options for liability to the<br />
distributor should rema<strong>in</strong> the same for further<br />
consideration through the case decision <strong>in</strong> the future.<br />
IV. THE PROTECTION OF INFORMATION PRIVACY IN<br />
INTELLIGENT VEHICLE TELEMATICS<br />
As mentioned <strong>in</strong> the beg<strong>in</strong>n<strong>in</strong>g of this article, <strong>in</strong><br />
apply<strong>in</strong>g Intelligent Vehicle Telematics to the real world,<br />
often times, it will acquire, collect or use personal<br />
<strong>in</strong>formation <strong>in</strong> the process of operat<strong>in</strong>g these devises or<br />
systems. This could arouse a lot of concerns to the legal<br />
issue of <strong>in</strong>formation of privacy. In this section, it <strong>in</strong>tends<br />
to <strong>in</strong>troduce the idea of <strong>in</strong>formation privacy <strong>in</strong> the United<br />
States, the protection of this legal <strong>in</strong>terest <strong>in</strong> the United<br />
States. Not only will several <strong>in</strong>cl<strong>in</strong>ed tendencies to the<br />
protection based on the concern of <strong>in</strong>formation age be<br />
<strong>in</strong>dicated here but also is the suggested hierarchy of<br />
methods to build up such protection <strong>in</strong> the legal arena for<br />
Intelligent Vehicle Telematic go<strong>in</strong>g to be discussed. One<br />
additional future possible concern to the protection of<br />
critical <strong>in</strong>frastructure based upon the reason of national<br />
security will also be briefly discussed for the purpose of<br />
this article. The purpose of all these discussions is to<br />
make projection of what would have happened if the<br />
issue of <strong>in</strong>formation privacy emerged once the <strong>in</strong>dustry of<br />
<strong>in</strong>telligent vehicle telematics becomes mature.<br />
A. The Concept of Information Privacy and the<br />
Protection <strong>in</strong> the United States<br />
The protection of “privacy” is not articulated <strong>in</strong> the<br />
Constitution <strong>in</strong> the United States, <strong>in</strong>stead it is <strong>in</strong>terpreted<br />
by the Supreme Court to say “The forgo<strong>in</strong>g cases suggest<br />
that special guarantees <strong>in</strong> the Bill of Rights have<br />
penumbras, formed by emanations from those guarantees<br />
that help give them life and substance. Various<br />
guarantees create zones of privacy.” <strong>in</strong> order to “create”<br />
the protection of privacy [37]. Through the years, the<br />
Supreme Court has recognized several k<strong>in</strong>ds of privacy as<br />
the fundamental human rights [38], for example the right<br />
to marriage, breed<strong>in</strong>g the child etc., but not the<br />
<strong>in</strong>formation privacy. The significant legal mean<strong>in</strong>g of<br />
<strong>in</strong>formation privacy as a non-fundamental human rights<br />
on the Constitutional level is that the right of privacy will<br />
probably be restricted when it directly conflicts with the<br />
protection of other fundamental human rights or<br />
important social rights, for example the freedom of<br />
speech [39]. And it is fairly to say, other than conflict<strong>in</strong>g<br />
with the protection of other fundamental human rights or<br />
important social rights, the protection of <strong>in</strong>formation<br />
privacy is really the balance of <strong>in</strong>terests between the<br />
protection of privacy and other affected legal <strong>in</strong>terests,<br />
except it wouldn’t affect any legal <strong>in</strong>terests, for example,<br />
to the protection aga<strong>in</strong>st unauthorized <strong>in</strong>vasion of<br />
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<strong>in</strong>formation privacy. From the experience of the United<br />
States <strong>in</strong> protection of <strong>in</strong>formation privacy, there are three<br />
auspicious preventive and one remedial trends worth to<br />
draw attention. The first preventive trend is to use<br />
<strong>in</strong>formed consent mechanism for reduc<strong>in</strong>g or eradicat<strong>in</strong>g<br />
the controversy of reasonable expectation of privacy.<br />
The second preventive trend is to emphasize the<br />
importance of technology prevention of <strong>in</strong>formation<br />
privacy <strong>in</strong>fr<strong>in</strong>gement. And the last one preventive trend<br />
is to enhance the liability of data collector for notification<br />
of the security breach to the <strong>in</strong>formation provider <strong>in</strong> case<br />
of some special k<strong>in</strong>d of personal <strong>in</strong>formation been<br />
unauthorized disclosed by the third party. As to the<br />
remedial trend related to the protection of <strong>in</strong>formation<br />
privacy for <strong>in</strong>telligent vehicle telematics, the focus will<br />
be the secondary liability to the <strong>in</strong>ternet service provider.<br />
Especially a secondary liability case of <strong>in</strong>ternet service<br />
provider about trademark <strong>in</strong>fr<strong>in</strong>gement <strong>in</strong> recent years is<br />
go<strong>in</strong>g to be discussed here s<strong>in</strong>ce there seems no direct<br />
judicial verdict to address the secondary liability of<br />
<strong>in</strong>formation privacy <strong>in</strong>fr<strong>in</strong>gement to the <strong>in</strong>ternet service<br />
provider.<br />
B. The Three Observations to the Preventive Measure <strong>in</strong><br />
the Protection of Information Privacy<br />
First of all, the best way to elim<strong>in</strong>ate the issue of<br />
whether or how the <strong>in</strong>formation privacy shall be<br />
protected is to receive the consent of personal<br />
<strong>in</strong>formation provider <strong>in</strong> gather<strong>in</strong>g the personal<br />
<strong>in</strong>formation. The legal th<strong>in</strong>k<strong>in</strong>g beh<strong>in</strong>d this is that the<br />
<strong>in</strong>formation privacy is a personal right and can be<br />
reduced or elim<strong>in</strong>ated by way of the consent of the<br />
<strong>in</strong>formation provider. It can be seen from a flood of<br />
statements related to privacy policy with<strong>in</strong> a variety of<br />
contract <strong>in</strong> the United States. Also, this idea of execut<strong>in</strong>g<br />
<strong>in</strong>formed consent appears <strong>in</strong> some federal legislation and<br />
adm<strong>in</strong>istrative regulation. For example, <strong>in</strong> HIPAA<br />
(Health Insurance Portability and Accountability Act)<br />
[40], the Congress require <strong>in</strong> this act that the entities for<br />
health care will basically get the <strong>in</strong>formed consent for any<br />
disclosure of personal medical <strong>in</strong>formation. The new<br />
drug application for biological product and the human<br />
body test for genetic therapy will need the <strong>in</strong>formed<br />
consent from the test or research subject before the<br />
approval of such application or test [41]. And, the<br />
<strong>in</strong>formed consent requirement also happens <strong>in</strong> The<br />
Gramm-Leach-Bliley Act and Privacy of Consumer<br />
F<strong>in</strong>ancial Information, Regulation P for electronic<br />
commerce.<br />
Secondly, beside the <strong>in</strong>formed consent methodology,<br />
to put a high value of technology prevention <strong>in</strong> protect<strong>in</strong>g<br />
<strong>in</strong>formation privacy is the other current trend of<br />
preventive measure for the <strong>in</strong>formation privacy<br />
<strong>in</strong>fr<strong>in</strong>gement. The best example for the emphasis of<br />
technology security is the <strong>in</strong>frastructure for establish<strong>in</strong>g<br />
technology standard <strong>in</strong> American Recovery and<br />
Re<strong>in</strong>vestment Act of 2009 [42]. Generally speak<strong>in</strong>g,<br />
from Subtitle C SEC 3001-3003 <strong>in</strong> American Recovery<br />
and Re<strong>in</strong>vestment Act of 2009, Congress design to<br />
establish the Office of the National Coord<strong>in</strong>ator for<br />
Health Information Technology for the purpose of sett<strong>in</strong>g<br />
up the technology standard, <strong>in</strong>clud<strong>in</strong>g the purpose of<br />
protection <strong>in</strong> <strong>in</strong>formation privacy, <strong>in</strong> order to promote the<br />
electronic medical records system.<br />
The last observed tendency for the issue of protect<strong>in</strong>g<br />
<strong>in</strong>formation privacy is to add the obligation of<br />
notification to who preserves the <strong>in</strong>dividual <strong>in</strong>formation<br />
when such <strong>in</strong>formation has been unauthorized accessed<br />
by the third party. This measurement is a fairly new legal<br />
remedy for the harm to the <strong>in</strong>formation privacy. For<br />
example, the detailed mechanism for how to work the<br />
requirement of notification <strong>in</strong> electronic medical records<br />
security breach is regulated <strong>in</strong> Subtitle D Part I SEC<br />
13400 and 13402 of American Recovery and<br />
Re<strong>in</strong>vestment Act of 2009. There are also other<br />
legislations <strong>in</strong> the United States embrac<strong>in</strong>g the similar<br />
regulation [43].<br />
C. One Potential Prediction to the Secondary Liability to<br />
the Internet Service Provider <strong>in</strong> the Protection of<br />
Information Privacy<br />
Beside the above-mentioned three preventive measures<br />
<strong>in</strong> the protection of <strong>in</strong>formation privacy, the secondary<br />
liability to the <strong>in</strong>ternet service provider for <strong>in</strong>formation<br />
privacy <strong>in</strong>vasion is potentially viable <strong>in</strong> the <strong>in</strong>formation<br />
age, especially <strong>in</strong> case of <strong>in</strong>telligent vehicle telematics.<br />
Until now, there is no general federal or state law to<br />
regulate the secondary liability of the <strong>in</strong>ternet service<br />
provider for <strong>in</strong>formation privacy <strong>in</strong>vasion, At the same<br />
time, even there seems no direct judicial verdict to the<br />
secondary liability of the <strong>in</strong>ternet service provider for<br />
<strong>in</strong>formation privacy <strong>in</strong>vasion <strong>in</strong> the United States; the<br />
article would th<strong>in</strong>k probably one important reason is<br />
because the court of the United States is still struggl<strong>in</strong>g to<br />
del<strong>in</strong>eate the scope of <strong>in</strong>formation privacy with<strong>in</strong> Internet.<br />
But this status quo is by no means to say the protection of<br />
<strong>in</strong>formation privacy with<strong>in</strong> Internet is <strong>in</strong>significant. On<br />
the other hand, ensu<strong>in</strong>g the highly developed technology<br />
of telecommunication and the more dependency of our<br />
society to such technology, the protection of <strong>in</strong>formation<br />
privacy with<strong>in</strong> Internet is deemed to be an important issue<br />
<strong>in</strong> the <strong>in</strong>formation age. Although there is no judicial<br />
decision to the secondary liability of the <strong>in</strong>ternet service<br />
provider for <strong>in</strong>formation privacy <strong>in</strong>vasion at this moment,<br />
the court <strong>in</strong> the United States did make some decision<br />
with regard to the secondary liability to the <strong>in</strong>ternet<br />
service provider <strong>in</strong> recent years and revealed the court’s<br />
leniency to the <strong>in</strong>ternet service provider through the<br />
follow<strong>in</strong>g case related to the trademark <strong>in</strong>fr<strong>in</strong>gement<br />
with<strong>in</strong> Internet. In Tiffany v. Ebay [44], Tiffany file the<br />
suit for multiple causes of action aga<strong>in</strong>st eBay. For the<br />
purpose of this discussion <strong>in</strong> this article, the focus of this<br />
case is centered on the issue of contributory <strong>in</strong>fr<strong>in</strong>gement<br />
of trademark. The facts for this case are relatively simple.<br />
eBay offers the platform for onl<strong>in</strong>e purchases to be<br />
concluded. Tiffany, the high-quality jewelry producer,<br />
was unhappy there are counterfeit<strong>in</strong>g Tiffany jewelry<br />
circulat<strong>in</strong>g on eBay’s onl<strong>in</strong>e purchas<strong>in</strong>g platform and<br />
filed the secondary liability litigation for trademark<br />
<strong>in</strong>fr<strong>in</strong>gement to eBay, even eBay did have taken some<br />
k<strong>in</strong>d of anti-fraud measurement for prevent<strong>in</strong>g the<br />
counterfeited product <strong>in</strong> its operation system. To the<br />
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issue of secondary liability to the trademark <strong>in</strong>fr<strong>in</strong>gement,<br />
based upon the <strong>in</strong>terpretation of the Supreme Court <strong>in</strong><br />
Inwood case [45], the liability lies when “a manufacturer<br />
or distributor <strong>in</strong>tentionally <strong>in</strong>duces another to <strong>in</strong>fr<strong>in</strong>ge a<br />
trademark, or if it cont<strong>in</strong>ues to supply its product to one<br />
whom it knows or has reason to know is engag<strong>in</strong>g <strong>in</strong><br />
trademark <strong>in</strong>fr<strong>in</strong>gement.” eBay def<strong>in</strong>itely did not <strong>in</strong>duce<br />
the trademark <strong>in</strong>fr<strong>in</strong>gement <strong>in</strong> this case, that left the<br />
question to whether eBay was contributory liable to the<br />
trademark <strong>in</strong>fr<strong>in</strong>gement. The court <strong>in</strong> this case discarded<br />
the “reasonable anticipation standard” as the mean<strong>in</strong>g of<br />
“knows or has reason to know”, <strong>in</strong>stead the knowledge<br />
requirement is “a contextual and fact-specific test” judged<br />
by all the surround<strong>in</strong>g circumstances, for example the<br />
specific <strong>in</strong>cident of trademark <strong>in</strong>fr<strong>in</strong>gement, which is a<br />
higher standard than “reasonable anticipation standard”.<br />
In this case, the court concluded that Tiffany could not<br />
satisfy with the high criteria for “knows or has reason to<br />
know” requirement, especially eBay has abovementioned<br />
anti-fraud measurement <strong>in</strong> force, and eBay<br />
was not liable for contributory trademark <strong>in</strong>fr<strong>in</strong>gement.<br />
The Tiffany case demonstrates two k<strong>in</strong>ds of policy<br />
attitude. One observation is that the court <strong>in</strong> the United<br />
States is reluctant to impute the liability to the <strong>in</strong>ternet<br />
service provider probably due to the concern of free flow<br />
of <strong>in</strong>formation. And the other observation is the court<br />
would enhance the mental requirement for the secondary<br />
liability <strong>in</strong>fr<strong>in</strong>ger to some extent, at least near to the<br />
requirement of “willful bl<strong>in</strong>dness” <strong>in</strong>stead of reasonable<br />
anticipation. From the description of shift<strong>in</strong>g attitude to<br />
the secondary liability of the <strong>in</strong>ternet service provider,<br />
this judicial attitude also put the preventive measure to<br />
the protection of <strong>in</strong>formation privacy with<strong>in</strong> Internet <strong>in</strong><br />
the even more important position for such <strong>in</strong>frastructure.<br />
D. The Def<strong>in</strong>ition of Information Privacy and the<br />
Suggested Model Build<strong>in</strong>g Up the Information Privacy<br />
Protection for Intelligent Vehicle Telematics<br />
After understand<strong>in</strong>g the general idea of <strong>in</strong>formation<br />
privacy and the tendency of protect<strong>in</strong>g such legal <strong>in</strong>terest<br />
<strong>in</strong> the United States, how to build the protection<br />
<strong>in</strong>frastructure of <strong>in</strong>formation privacy and strike the<br />
balance with other k<strong>in</strong>ds of conflict<strong>in</strong>g legal <strong>in</strong>terest for<br />
Intelligent Vehicle Telematics operation br<strong>in</strong>gs the<br />
discussion to the next level. With regard to the issue of<br />
protection of <strong>in</strong>formation privacy <strong>in</strong> Intelligent Vehicle<br />
Telematics operation, this article would attempt to divide<br />
it <strong>in</strong>to two different aspects: non-legal –b<strong>in</strong>d<strong>in</strong>g self<br />
regulation and legal measurements for preventive or<br />
remedial purpose to the system operator. First, to the part<br />
of self regulation with<strong>in</strong> the system operator, the<br />
proposed estimation <strong>in</strong> this article is that the self<br />
regulation wouldn’t be able to play any significant role <strong>in</strong><br />
striv<strong>in</strong>g to preserve the legal <strong>in</strong>terest of <strong>in</strong>formation<br />
privacy before the competition <strong>in</strong> market has reached<br />
sufficient status. That is not to say the idea of selfmanagement<br />
for the <strong>in</strong>formation privacy protection is not<br />
important. The statement is just to express the th<strong>in</strong>k<strong>in</strong>g<br />
that to establish the management system for the<br />
protection of <strong>in</strong>formation privacy is not easy compared<br />
with the <strong>in</strong>tellectual property management system<br />
because the concept of <strong>in</strong>formation privacy is further<br />
develop<strong>in</strong>g. So, it is argued <strong>in</strong> this article, <strong>in</strong> this stage,<br />
there is no substantial mean<strong>in</strong>g to emphasize the<br />
mechanism of self regulation. As to the preventive or<br />
remedial legal measurements for the protection of<br />
<strong>in</strong>formation privacy related to the system provider for<br />
Intelligent Vehicle Telematics, the bottom l<strong>in</strong>e is<br />
described as the old say<strong>in</strong>g: “One stitch <strong>in</strong> time safes<br />
n<strong>in</strong>e.”. That leads to the <strong>in</strong>dication that the preventive<br />
measurements of <strong>in</strong>formed consent and technology<br />
prevention are much better than the remedial<br />
measurements (the obligation of notification, civil<br />
liability or even crim<strong>in</strong>al punishment). To sum up the<br />
<strong>in</strong>frastructure for the protection of <strong>in</strong>formation privacy <strong>in</strong><br />
Intelligent Vehicle Telematics, it is fairly to say <strong>in</strong><br />
protect<strong>in</strong>g <strong>in</strong>formation privacy <strong>in</strong> operat<strong>in</strong>g Intelligent<br />
Vehicle Telematics, there is a hierarchy to construct the<br />
protection, from the legal to the non-legal <strong>in</strong> general<br />
concept, from the preventive to the remedial<br />
measurement <strong>in</strong> real practice.<br />
As to the def<strong>in</strong>ition of <strong>in</strong>formation privacy, this really<br />
means the balance of <strong>in</strong>terest. In compar<strong>in</strong>g the different<br />
<strong>in</strong>terests to confirm the legitimacy of <strong>in</strong>formation privacy<br />
<strong>in</strong> the situation of Intelligent Vehicle Teleatics, the safety<br />
concern will def<strong>in</strong>itely get its priority to the <strong>in</strong>formation<br />
privacy concern. To other comparisons between the<br />
protection of <strong>in</strong>formation privacy and proprietary<br />
<strong>in</strong>terests of the system operator, the odds are that the<br />
<strong>in</strong>formation privacy will have a good chance to fight <strong>in</strong><br />
the battlefield of balanc<strong>in</strong>g <strong>in</strong>terests. One problematic<br />
situation of protect<strong>in</strong>g <strong>in</strong>formation privacy with<strong>in</strong> the<br />
environment of <strong>in</strong>telligent vehicle telematics is its<br />
possible <strong>in</strong>teraction with the concept of protect<strong>in</strong>g critical<br />
<strong>in</strong>frastructure. General speak<strong>in</strong>g, under the idea of<br />
protect<strong>in</strong>g critical <strong>in</strong>frastructure, the Bureau of Homeland<br />
Security can acquire and reasonably use the <strong>in</strong>formation<br />
related to the critical <strong>in</strong>frastructure processed by the<br />
private sector or government agencies for the purpose of<br />
anti-terrorism, which <strong>in</strong>formation might be under the<br />
protection of <strong>in</strong>formation privacy [46]. Even under the<br />
balance of <strong>in</strong>terest approach, the legal <strong>in</strong>terest of<br />
<strong>in</strong>formation privacy will be no doubt succumbed to the<br />
<strong>in</strong>terest of national security if these two k<strong>in</strong>ds of <strong>in</strong>terest<br />
directly conflict with each other, the question is whether<br />
the environment of <strong>in</strong>telligent vehicle telematics would<br />
be treated as the critical <strong>in</strong>frastructure and to what extent<br />
of us<strong>in</strong>g the <strong>in</strong>formation conta<strong>in</strong>ed with<strong>in</strong> is reasonable<br />
[47]. The potential impact of critical <strong>in</strong>frastructure<br />
protection to <strong>in</strong>formation privacy protection is unknown<br />
and needs to wait and see. As the protection of<br />
<strong>in</strong>formation privacy is gett<strong>in</strong>g more and more importance<br />
<strong>in</strong> the hierarchy of different k<strong>in</strong>ds of legal <strong>in</strong>terest, the<br />
national security rema<strong>in</strong>s the strongest opposition. What<br />
is the l<strong>in</strong>e need to be drawn between the protection of<br />
national security and <strong>in</strong>formation privacy, especially <strong>in</strong><br />
talk<strong>in</strong>g about the <strong>in</strong>telligent vehicle telematics<br />
environment, cannot be answered until the day comes.<br />
V. CONCLUSION<br />
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1558 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
It often times comes with the legal concern when the<br />
advanced technology seems to promise the society a<br />
better life. And this is exactly what happens to the<br />
Intelligent Vehicle Telematics. These two ma<strong>in</strong>ly legal<br />
concerns which are the liability both for the safety devise<br />
manufacture and the system provider, and also the<br />
protection of <strong>in</strong>formation privacy, under the discussion <strong>in</strong><br />
this article, shall move toward the <strong>in</strong>tensive way to go.<br />
There should be noth<strong>in</strong>g wrong to be cautious about the<br />
new technology after balanc<strong>in</strong>g the benefits and the<br />
potential harm of such technology to reveal that it could<br />
do more harm than good to the society as a whole,<br />
especially such harm is imm<strong>in</strong>ent. And it is suggested <strong>in</strong><br />
this article that the potential harm to the safety devise <strong>in</strong><br />
Intelligent Vehicle Telematics could be a disaster for the<br />
reason of estimat<strong>in</strong>g human life as high-value. And also<br />
the same seriousness to the <strong>in</strong>vasion of <strong>in</strong>formation<br />
privacy would happen especially the unauthorized use or<br />
security breach of the extensive gather<strong>in</strong>g of personal<br />
<strong>in</strong>formation <strong>in</strong> operat<strong>in</strong>g Intelligent Vehicle Telematics<br />
could be fatal to the trend of enhanced protection of<br />
<strong>in</strong>formation privacy. For all the reasons mentioned here,<br />
this article will hold the position that the most restrictive<br />
legal responsibility under the current legal theory shall<br />
apply to these two concerns respectively. But, even the<br />
legal <strong>in</strong>terest of <strong>in</strong>formation privacy is mov<strong>in</strong>g its way<br />
toward the ultimate position which is one k<strong>in</strong>d of the<br />
fundamental human rights, its legal hierarchy still hasn’t<br />
reached that stage yet. And the difficulties and dilemma<br />
to protect the <strong>in</strong>formation privacy <strong>in</strong> the <strong>in</strong>formation age,<br />
especially <strong>in</strong> the <strong>in</strong>telligent vehicle telematics<br />
environment, make the preventive measure to protect the<br />
<strong>in</strong>formation privacy get its priority and alleviate the<br />
secondary liability of the <strong>in</strong>ternet service provider to<br />
some extent. The <strong>in</strong>fluence of national security to the<br />
protection of <strong>in</strong>formation privacy <strong>in</strong> the environment of<br />
<strong>in</strong>telligent vehicle telematics will be the potential<br />
problem need to be resolved s<strong>in</strong>ce there is no direct or<br />
similar judicial decision can be refered. The development<br />
of Intelligent Vehicle Telematics technology is still <strong>in</strong> its<br />
primitive stage. And it is the purpose (<strong>in</strong>tention) of this<br />
article to p<strong>in</strong>po<strong>in</strong>t the legal concerns for Intelligence<br />
Vehicle Telematics <strong>in</strong> front and try to come up the<br />
positive solutions <strong>in</strong> the hope of that the discussion could,<br />
at least, have some referential value for the possible<br />
future policy mak<strong>in</strong>g decision.<br />
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Fa-Chang Cheng received LL.M. degree from Golden Gate<br />
University and J.D. (Juris Doctor) degree from Ohio Northern<br />
University, U.S.A., <strong>in</strong> 1997 and 2001, respectively.<br />
He is a full-time associate professor <strong>in</strong> Graduate Institute of<br />
Science and Technology Law of National Kaohsiung First<br />
University of Science and Technology. His major research area<br />
is focus<strong>in</strong>g on the legal issues for both Telecommunication and<br />
Biotechnology.<br />
Wen-Hs<strong>in</strong>g Lai received the Ph.D. degrees <strong>in</strong> communication<br />
eng<strong>in</strong>eer<strong>in</strong>g from National Chiao Tung University, Hs<strong>in</strong>chu,<br />
Taiwan, <strong>in</strong> 2003.<br />
In 2006, she became an Assistant Professor of the<br />
Department of Computer and Communication Eng<strong>in</strong>eer<strong>in</strong>g,<br />
National Kaohsiung First University of Science and Technology,<br />
Taiwan. Her major research area is focus<strong>in</strong>g on digital signal<br />
process<strong>in</strong>g.<br />
© 2013 ACADEMY PUBLISHER
1560 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
MPC Controller Performance Evaluation and<br />
Tun<strong>in</strong>g of S<strong>in</strong>gle Inverted Pendulum Device<br />
Chao Cheng<br />
Department of Automation, Beij<strong>in</strong>g University of Chemical Technology, Beij<strong>in</strong>g, Ch<strong>in</strong>a<br />
Email: beryle117@163.com<br />
Zhong Zhao 1 , Haixia Li<br />
Department of Automation, Beij<strong>in</strong>g University of Chemical Technology, Beij<strong>in</strong>g, Ch<strong>in</strong>a<br />
Email: zhaozhong@mail.buct.edu.cn<br />
Abstract—Inverted pendulum is a non-l<strong>in</strong>ear, multivariable<br />
and unstable device, a model predictive control (MPC)<br />
performance evaluation and tun<strong>in</strong>g method for <strong>in</strong>verted<br />
pendulum device is proposed. MPC was designed to control<br />
the <strong>in</strong>verted pendulum device, and the m<strong>in</strong>imum variance<br />
covariance constra<strong>in</strong>ed control (MVC 3 ) was applied to<br />
evaluate the performance of the MPC controller and tune its<br />
parameters. The application results to a s<strong>in</strong>gle <strong>in</strong>verted<br />
pendulum device have verified the feasibility and<br />
effectiveness of the proposed method.<br />
Index Terms—Inverted pendulum, Model Predict Control,<br />
M<strong>in</strong>imum Variance Covariance Constra<strong>in</strong>ed Control,<br />
Performance evaluation, Controller-tun<strong>in</strong>g<br />
I. INTRODUCTION<br />
Inverted pendulum is a non-l<strong>in</strong>ear, strongly coupled,<br />
multivariable and unstable system. Because it can<br />
effectively reflect a lot of key control problems, such as<br />
the stabilization, robustness, track<strong>in</strong>g performance, many<br />
control theories and control methods can be verified with<br />
the <strong>in</strong>verted pendulum experiment. Google Technology<br />
LTD [1] designed its LQR controller. D. Chatterjee et al.<br />
[2] described the sw<strong>in</strong>g-up and stabilization with a<br />
restricted cart track length and restricted control force<br />
us<strong>in</strong>g generalized energy control methods. M. Bugeja [3]<br />
presented a sw<strong>in</strong>g-up and stabiliz<strong>in</strong>g controller on<br />
<strong>in</strong>verted pendulum non-l<strong>in</strong>ear model. S.Y. Zhang [4] and<br />
Y. Fan et al. [5] designed the fuzzy controllers for<br />
<strong>in</strong>verted pendulum. L.X. Deng [6] designed a controller<br />
based on back stepp<strong>in</strong>g for <strong>in</strong>verted pendulum.<br />
Model Predictive Controllers (MPC) was proposed by<br />
J. Richalet et al. <strong>in</strong> 1978[7]. It is a model-based optimal<br />
control strategy [8]. Its ability to <strong>in</strong>corporate mean<strong>in</strong>gful<br />
limits on manipulative as well as control variables has<br />
allowed the <strong>in</strong>dustry to move away from traditional<br />
regulation-type control and focus on the economics of<br />
operat<strong>in</strong>g po<strong>in</strong>t selection [9]. Model predictive control<br />
has been widely applied to process control [10]. On the<br />
1, Correspond<strong>in</strong>g author, zhaozhong@mail.buct.edu.cn;<br />
other hand, it is noted that less effort has been made on<br />
the performance monitor<strong>in</strong>g of MPC applications, while<br />
the performance monitor<strong>in</strong>g of conventional controllers<br />
has been well studied such as <strong>in</strong> Harris (1989) [11],<br />
Harris, Boudreau, and Macgregor (1996) [12], Huang,<br />
Shah, and Kwok (1997) [13], Huang and Shah (1999)<br />
[14], Jelali (2005) [15], Sr<strong>in</strong>ivasan, Rengaswamy, and<br />
Miller (2005) [16] [17], Xu, Lee, and Huang (2006) [18],<br />
Salsbury (2007) [19] and Bauer and Craig (2008) [20].<br />
The M<strong>in</strong>imum Variance Covariance Constra<strong>in</strong>ed<br />
Control (MVC 3 ) pr<strong>in</strong>ciple was proposed by R.E. Skelton<br />
et al. [21] as the solution of l<strong>in</strong>ear feedback control<br />
problem. For multivariable systems, D.J. Chmielewski*<br />
et al. [22] solved it with LQR method. In this work, the<br />
model predictive control (MPC) performance evaluation<br />
and tun<strong>in</strong>g system has been developed by extended<br />
MVC 3 and applied to a s<strong>in</strong>gle <strong>in</strong>verted pendulum device.<br />
The application results have verified the feasibility and<br />
effectiveness of the developed system.<br />
II. THE MATHEMATIC MODEL OF LINEAR SINGLE<br />
INVERTED PENDULUM<br />
The l<strong>in</strong>ear s<strong>in</strong>gle <strong>in</strong>verted pendulum can be described<br />
as a system composed of a cart and a homogeneous rod<br />
without air resistance and all k<strong>in</strong>ds of frictions, as is<br />
illustrated <strong>in</strong> Fig. 1.<br />
Figure 1. L<strong>in</strong>ear s<strong>in</strong>gle <strong>in</strong>verted pendulum model<br />
Where, M , m , x , F , l ,θ ,denote cart weight, rod weight,<br />
cart level displacement, force on cart, the length from the<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1560-1570
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1561<br />
axis of the rod angle to the center of rod mass, the angle<br />
of the rod from the vertical upward direction respectively.<br />
A. State Space Model of L<strong>in</strong>ear S<strong>in</strong>gle Inverted<br />
Pendulum<br />
The method of this work is based on l<strong>in</strong>ear constant<br />
state space model as:<br />
x<br />
= Ax + Bu<br />
. (1)<br />
y = Cx + Du<br />
The mathematical model of s<strong>in</strong>gle <strong>in</strong>verted pendulum can<br />
be obta<strong>in</strong>ed by mechanism analysis [1], shown <strong>in</strong> (2),<br />
where, u , is cart angular velocity. x andθ , are the same<br />
as shown <strong>in</strong> Fig 1.<br />
⎛x<br />
⎞ ⎛0 1 0 0⎞⎛x<br />
⎞ ⎛0⎞<br />
⎜<br />
x<br />
⎟ ⎜<br />
0 0 0 0<br />
⎟⎜ x<br />
⎟ ⎜<br />
1<br />
⎟<br />
⎜ ⎟<br />
<br />
= ⎜ ⎟⎜ ⎟+<br />
⎜ ⎟u<br />
⎜ θ ⎟ ⎜0 0 0 1⎟⎜θ<br />
⎟ ⎜0⎟<br />
⎜<br />
θ ⎟ ⎜ ⎟<br />
0 0 29.4 0 ⎜θ<br />
⎟ ⎜ ⎟<br />
⎝ ⎠<br />
<br />
⎝ ⎠<br />
⎝ ⎠ ⎝3⎠<br />
⎛x<br />
⎞<br />
⎜<br />
x 1 0 0 0 x<br />
⎟<br />
⎛ ⎞ ⎛ ⎞ ⎛0⎞<br />
y = ⎜ ⎟<br />
⎜ = + u<br />
θ<br />
⎟ ⎜<br />
0 0 1 0<br />
⎟⎜θ<br />
⎟ ⎜<br />
0<br />
⎟<br />
⎝ ⎠ ⎝ ⎠ ⎝ ⎠<br />
⎜ <br />
θ ⎟<br />
⎝ ⎠<br />
B. Controllability & Observability Analysis of S<strong>in</strong>gle<br />
Inverted Pendulum<br />
The controllability and observability of a system is<br />
prerequisite for analysis and controller design. Here,<br />
n−<br />
Uc = B AB A 1 B and<br />
Controllability matrix ( )<br />
n<br />
observability matrix Uo ( C CA CA −1<br />
)<br />
T<br />
(2)<br />
= were<br />
obta<strong>in</strong>ed and then rank criterion was employed to<br />
analysis its controllability and observability. It has been<br />
proved that the system as (2) has both controllability and<br />
observability.<br />
C. Stability Analysis of S<strong>in</strong>gle Inverted Pendulum<br />
The extended MVC 3 performance evolution and MPC<br />
tun<strong>in</strong>g system is based on the stabilization system. Hence,<br />
Stability analysis is necessary. The poles of the <strong>in</strong>verted<br />
pendulum as (2) are ( 5.4222 − 5.4222 0 0)<br />
, where<br />
positive real root appears. It shows that the system as (2)<br />
is <strong>in</strong>stable and this requires a stabilizer before design<strong>in</strong>g a<br />
MPC controller for the generalized controlled system [23].<br />
III. MPC PERFORMANCE EVOLUTION AND TUNING<br />
METHODE BASED ON EXTENDED MVC 3<br />
A. Introductions of LMI and Lemmas<br />
• About LMI:<br />
Assume a l<strong>in</strong>ear matrix <strong>in</strong>equality (LMI) can be stated<br />
as: F( x) = F0 + x1F1+⋅⋅⋅+ xmFm<br />
< 0 .Where, variable<br />
x constitutes a convex set, LMI can be solved us<strong>in</strong>g the<br />
method of convex optimization problem [24].<br />
1) Feasible solution of LMI:<br />
If there exists x makes, F( x ) < 0 , established, then the<br />
LMI is feasible [24].This can be expressed us<strong>in</strong>g the<br />
follow<strong>in</strong>g formulation:<br />
m<strong>in</strong>. t<br />
.<br />
s.. tF( x)<br />
< tI<br />
2) M<strong>in</strong>imization problem of LMI:<br />
The problem can be stated as a optimality problem that<br />
m<strong>in</strong>imize the largest eigenvalue, λ , of the matrix<br />
Gx ( ) under <strong>in</strong>equality constra<strong>in</strong>t H( x ) < 0 [24]:<br />
st ..<br />
Another expression is as:<br />
T<br />
m<strong>in</strong> λ<br />
G < λI<br />
.<br />
< 0<br />
( x)<br />
H ( x)<br />
T<br />
m<strong>in</strong> c x<br />
,<br />
st .. F < 0<br />
( x)<br />
where, c x is object function.<br />
• Lemmas:<br />
Consider a l<strong>in</strong>ear time-<strong>in</strong>variant state-space system:<br />
x( k + 1) = Ax( k) + Bu( k) + Ew( k)<br />
, (3)<br />
y( k) = Cx( k)<br />
where, x (k)<br />
, u ( k ) , y( k ) are state variable, manipulative<br />
variable and control output variable respectively,<br />
A , B , C and E are process model matrix, w ( k)<br />
denotes<br />
stationary, Gaussian noise with zero mean and covariance<br />
as ∑ w .<br />
State feedback controller can be expressed as:<br />
u( k) = Kx ( k)<br />
. (4)<br />
Then, the closed-loop system can be written as:<br />
x( k + 1) = ( A+ BK) x( k) + Ew ( k)<br />
. (5)<br />
Lemma1: LMI of MVC 3 [22]:<br />
For system (5), ∃ stabiliz<strong>in</strong>g K and ∑x ≥ 0 s.t.<br />
∑ , = 1... p<br />
yi i<br />
T<br />
T<br />
x w x<br />
T<br />
∑ y = ϕ<br />
i iC∑<br />
xC<br />
ϕi<br />
2<br />
∑ y < y , 1<br />
i i i = … p<br />
( A+ BK) ∑ ( A+ BK)<br />
+ E∑ E = ∑<br />
If and only if ∃ W, X > 0and Yi , = 1... ps.t.<br />
⎡<br />
T<br />
X − E∑<br />
E AX BW⎤<br />
w +<br />
⎢<br />
⎥><br />
0<br />
T<br />
⎢⎣( AX + BW ) X ⎥⎦<br />
⎡ Yi<br />
ϕiCX⎤ ⎢<br />
( ) T 0<br />
T<br />
⎥ ><br />
⎢⎣<br />
CX ϕi<br />
X ⎥⎦<br />
© 2013 ACADEMY PUBLISHER
1562 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Y i2 i < y , i = 1… p,<br />
where, K is the l<strong>in</strong>ear state feedback ga<strong>in</strong>; ∑ x is the state<br />
variables covariance; ∑ is the i th variable of output<br />
covariance ∑ y ;<br />
y i<br />
2<br />
y i is constra<strong>in</strong>t of<br />
Lemma2: Schur complements [25]:<br />
For symmetric matrix:<br />
⎡S<br />
S = ⎢<br />
⎣S<br />
11<br />
21<br />
∑ yi .<br />
The follow<strong>in</strong>g three conditions are equivalent:<br />
1) S < 0<br />
T −1<br />
22 12 11 12 0<br />
2) S 11 < 0 , S − S S S <<br />
−1<br />
T<br />
11 12 22 12 0<br />
3) S 22 < 0 , S − S S S < .<br />
B. Extended MVC 3 Problem and Its LMI Solution<br />
In this work, constra<strong>in</strong>ts on manipulative variables<br />
were <strong>in</strong>cluded <strong>in</strong> the MVC 3 scheme. The extended MVC 3<br />
can be described as:<br />
S<br />
S<br />
12<br />
22<br />
⎤<br />
⎥<br />
⎦<br />
p<br />
m<br />
m<strong>in</strong> qi ∑ yi + rj ∑u j<br />
∑ x, KY , i, Uj<br />
i= 1 j=<br />
1<br />
∑ ∑ (6)<br />
s.t. ( A+ BK) ∑ ( A+ BK) T + E∑ E<br />
T = ∑ (7)<br />
x w x<br />
T<br />
yi ϕiC<br />
C ϕi<br />
∑ = ∑ x (8)<br />
T<br />
uj ϕ jK<br />
K ϕ j<br />
∑ = ∑ x (9)<br />
2<br />
i<br />
∑ < y , i = 1... p<br />
(10)<br />
yi<br />
2<br />
j<br />
∑ < u , j = 1... m. (11)<br />
uj<br />
The ma<strong>in</strong> design target of the extended MVC 3 is<br />
obta<strong>in</strong><strong>in</strong>g l<strong>in</strong>ear feedback ga<strong>in</strong> K to make object function<br />
(6) m<strong>in</strong>imum, additionally, to make the steady-state<br />
control outputs and the covariance of manipulative<br />
variables satisfy a set of bounds respectively. The above<br />
problem can be converted to a convex form of LMI as<br />
follows.<br />
Theorem 1: If and only if ∃W, X ≥ 0 and Y i ,<br />
U , i = 1... p, j = 1... m s.t.<br />
j<br />
p m<br />
m<strong>in</strong> qY i i+<br />
rU j j<br />
XWYU , , j j i= 1 j=<br />
1<br />
∑ ∑ (12)<br />
⎡<br />
T<br />
X −E∑ E AX BW⎤<br />
w +<br />
s.t. ⎢<br />
⎥><br />
0<br />
T<br />
⎢⎣( AX + BW ) X ⎥⎦<br />
(13)<br />
⎡ Yi<br />
ϕiCX⎤ ⎢<br />
0<br />
T T ⎥ ><br />
⎣( CX ) ϕi<br />
X ⎦<br />
⎡ U j ϕ jW⎤ ⎢ T T ⎥ > 0<br />
⎢⎣<br />
W ϕ j X ⎥⎦<br />
(14)<br />
(15)<br />
Y i2 i < y , i = 1... p<br />
(16)<br />
U j2 j < u , j = 1... m<br />
(17)<br />
−1<br />
Then, u= Kx( k) = WX x( k)<br />
is the extended MVC 3 l<strong>in</strong>ear<br />
feedback controller of system (2), satisfy<strong>in</strong>g covariance<br />
constra<strong>in</strong>ts.<br />
Proof: If the closed-loop system (2) is stable, the steady<br />
state covariance matrix can be expressed<br />
T<br />
as ∑ x = lim{E[ x( k) x ( k)]}<br />
, and ∑<br />
x<br />
satisfies (7). From<br />
k→∞<br />
the def<strong>in</strong>ition of covariance, it is easily to get the<br />
T<br />
T<br />
expression ∑ = ϕC∑ x C ϕ , ∑ = ϕ K∑ x K ϕ ,<br />
where,<br />
yi i i<br />
2<br />
u j<br />
∑<br />
yi<br />
< y i<br />
,<br />
uj j j<br />
2<br />
j<br />
∑ < u .From Lemma 1,<br />
∃∑ x < X , Makes the state covariance constra<strong>in</strong>t (7) is<br />
T<br />
equivalent to LMI (13). Let ϕiCXC ϕ i < Yi, i = 1, … p ,<br />
T<br />
ϕjKXK ϕ j < U j, j = 1, … m , and Y i2 i < y , i = 1... p ,<br />
U j2 j < u , j = 1... m.Then:<br />
p<br />
m<br />
p m<br />
qi ∑ yi + rj ∑u j ≤ qY i i + rU j j<br />
i= 1 j= 1 i= 1 j=<br />
1<br />
∑ ∑ ∑ ∑ .<br />
Then, m<strong>in</strong>imiz<strong>in</strong>g the function<br />
ensure the object function<br />
p m<br />
qY i i + rU j j<br />
i= 1 j=<br />
1<br />
p<br />
m<br />
qi yi + rj uj<br />
i= 1 j=<br />
1<br />
∑ ∑ will<br />
∑ ∑ ∑ ∑ be<br />
m<strong>in</strong>imized too. Still use Lemma 1, (14)-(17) can be<br />
derived.<br />
From the def<strong>in</strong>ition of extended MVC 3 problem,<br />
controller feedback solution K ∗ can be solved by<br />
∗ ∗ ∗−1<br />
K = W X with LMI. Where, W ∗ and X ∗ denote the<br />
optimal solution matrices of the extended MVC 3 problem.<br />
Conditions (14)-(17) are exactly that required to<br />
determ<strong>in</strong>e the feasibility of the extended MVC 3 problem.<br />
If the problem turns out to be <strong>in</strong>feasible, then the<br />
2 2<br />
bound<strong>in</strong>g region def<strong>in</strong>ed by yi<br />
and u j terms should be<br />
enlarged.<br />
C. Performance Evolution Based on Extended MVC 3<br />
For closed-loop system (5) the multi-variable form of<br />
LQG performance benchmarks can be def<strong>in</strong>ed as<br />
T<br />
T<br />
J<br />
LQG<br />
= E(<br />
y Qy)<br />
+ λ E( u Ru)<br />
. In order to evaluate<br />
controllers under constra<strong>in</strong>s, the covariance constra<strong>in</strong>s are<br />
<strong>in</strong>cluded <strong>in</strong> the LQG performance evaluation benchmarks.<br />
New performance evolution is exactly an advanced<br />
© 2013 ACADEMY PUBLISHER
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MVC 3 problem. After deformation, the problem can be<br />
solved by technology of LMI:<br />
If and only if ∃W, X ≥ 0 , λ > 0 and Y i , U j , i = 1... p ,<br />
j = 1... m and the follow<strong>in</strong>g optimization as (18) can be<br />
solved,<br />
p<br />
m<br />
m<strong>in</strong> qY i i+<br />
λ rU j j<br />
XYUWi , , , = 1 j=<br />
1<br />
∑ ∑ (18)<br />
s.t. (13)-(17).<br />
Then, accord<strong>in</strong>g to the change of λ , optimized curve of<br />
control outputs variance Var( y)<br />
and manipulative variable<br />
variance Var( u ) can be obta<strong>in</strong>ed. This optimized curve<br />
can be used as the benchmark to evaluate controller<br />
performance.<br />
Accord<strong>in</strong>g to optimization objective function:<br />
T<br />
T<br />
J = E( y Qy) + λ E( u Ru)<br />
= Trace( Q ∑ y + λR<br />
∑u)<br />
.<br />
T<br />
T<br />
= QTrace( C ∑ xC ) + λRTrace( K ∑x<br />
K )<br />
T<br />
T<br />
≤ QTrace( CXC ) + λRTrace( KXK )<br />
T<br />
T<br />
Let CXC < Y , KXK < U , thus, m<strong>in</strong>imiz<strong>in</strong>g<br />
QTrace( Y ) + λRTrace( U ) can ensure J be m<strong>in</strong>imized<br />
too. Object function can be rewritten as<br />
3<br />
MVC<br />
p<br />
m<br />
i i λ j j<br />
i= 1 j=<br />
1<br />
J = ∑qY + ∑ rU . (13)-(17) can be obta<strong>in</strong>ed as<br />
the same as LMI of advanced MVC 3 .<br />
The MVC 3 benchmark curve is the lower limit of the<br />
controller performance. That is, all l<strong>in</strong>ear controllers can<br />
only be located <strong>in</strong> operat<strong>in</strong>g area above the curve.<br />
Compar<strong>in</strong>g actual run-time steady state outputs and<br />
manipulated variables covariance with the MVC 3<br />
benchmark cure, closer distance means better<br />
performance. In practice, a benchmark<br />
3<br />
MVC<br />
p m<br />
i= 1<br />
i i<br />
j=<br />
1<br />
j j<br />
J = ∑qY + ∑ rU can be calculated as λ = 1, then,<br />
judge controller performance by the ratioη which is the<br />
value of benchmark J 3 divided by actual operation<br />
MVC<br />
steady state covariance J arh .η closes to 1 means better<br />
performance.<br />
D. Extended MVC 3 and Inf<strong>in</strong>ite Horizon MPC<br />
• Solution of <strong>in</strong>f<strong>in</strong>ite horizon MPC<br />
For l<strong>in</strong>ear system, solv<strong>in</strong>g <strong>in</strong>f<strong>in</strong>ite horizon MPC is<br />
equivalent to solv<strong>in</strong>g the LQR control problem as follows,<br />
∞<br />
m<strong>in</strong> ∑ x( k) Qx( k) + u ( k) Ru( k)<br />
(19)<br />
u( k ) k = 0<br />
T<br />
x( k + 1) = Ax( k) + Bu( k)<br />
s.t.<br />
.<br />
y( k) = Cx( k)<br />
T<br />
Let<br />
T<br />
p<br />
Q= C DC,( D= ∑ qϕ ϕ ) , and let feedback<br />
i=<br />
1<br />
T<br />
i i i<br />
controller be u( k) = Kx ( k)<br />
, then,<br />
T −1<br />
T<br />
K =− ( B PB + R)<br />
B PA , where,<br />
T T T −1<br />
T<br />
P = A PA − A PB( B PB + R)<br />
B PA + Q .<br />
• LQG control problem<br />
LQG control problem can be described as:<br />
1 T<br />
T<br />
T<br />
m<strong>in</strong> lim ∑ E[ y( k) Qy( k) + u( k) Ru ( k)]<br />
(20)<br />
u T<br />
( k) T→∞ k = 0<br />
x( k + 1) = Ax( k) + Bu( k) + Ew( k)<br />
s.t.<br />
,<br />
y( k) = Cx( k)<br />
where feedback controller can be solved by<br />
T −1<br />
T<br />
K =− ( B PB + R)<br />
B PA , here, PQis , the same as the<br />
solution of <strong>in</strong>f<strong>in</strong>ite horizon MPC. Rewrite the object<br />
function <strong>in</strong> (21) as,<br />
1 T<br />
T<br />
T<br />
J = lim ∑ E[ y( k) Qy( k) + u( k) Ru( k)<br />
T →∞ T k = 0<br />
T<br />
T<br />
= lim E[ y( k) Qy( k) + u( k) Ru( k)]<br />
k→∞<br />
.<br />
= Trace ∑ + ∑<br />
{ Q y R u}<br />
p<br />
m<br />
T<br />
T<br />
∑qiϕi yϕi ∑ rjϕ j uϕ<br />
j<br />
i= 1 j=<br />
1<br />
= ∑ + ∑<br />
• Extended MVC 3 control problem without<br />
constra<strong>in</strong>ts<br />
Extended MVC 3 control problem can be described as:<br />
p m<br />
qY i i+<br />
rU j j<br />
∑ x i= 1 j=<br />
1<br />
m<strong>in</strong> ∑ ∑ (21)<br />
s.t. ( A+ BK) ∑ ( A+ BK) + E∑ w E = ∑<br />
x<br />
T T<br />
i ∑ x ϕi = i, = 1<br />
ϕ C C Y i p<br />
T<br />
T<br />
ϕ jK ∑ x K ϕ j = U j, j = 1… m .<br />
The goal is to get a feedback ga<strong>in</strong> matrix K by m<strong>in</strong>imize<br />
p m<br />
the objective function ∑qY<br />
+ ∑ rU .<br />
T<br />
i i j j<br />
i= 1 j=<br />
1<br />
Assumption 1. R > 0 , Q ≥ 0 .<br />
Assumption 2.The pairs ( A, B ) and ( A, Q)<br />
is stabilizable<br />
and detectable, respectively.<br />
T<br />
Assumption 3.The pair ( A, G∑ w G ) is controllable.<br />
Let hypotheses 1-3 hold; then the solution to of MVC 3<br />
problem as (21) is co<strong>in</strong>cident with the solution of <strong>in</strong>f<strong>in</strong>ite<br />
horizon MPC as (19). Hypotheses 1-2 <strong>in</strong>dicate that the<br />
solutions of problems (19) and (20) are unique and<br />
stabiliz<strong>in</strong>g. Hypotheses 1-3 ensure that the solution of<br />
problem (21) is unique and stabiliz<strong>in</strong>g. From the<br />
construction of problem (20), it is equivalent to problem<br />
(21), <strong>in</strong> the sense that the l<strong>in</strong>ear feedback generated by<br />
T<br />
x<br />
© 2013 ACADEMY PUBLISHER
1564 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
(21) is the solution to problem (20). F<strong>in</strong>ally, certa<strong>in</strong>ty<br />
equivalence between problems (20) and (19) completes<br />
the proof.<br />
Theorem 2: Let hypotheses 1-3 hold; then the solution<br />
of K ∗ , to problem (12)-(17) is co<strong>in</strong>cident with the<br />
solution of appropriate weighted <strong>in</strong>f<strong>in</strong>ite horizon MPC<br />
problem (19).<br />
Proof. Problem (6)-(11) can be exactly restated as the<br />
existence of Lagrange multiplier, , s.t.<br />
1 1<br />
s.t. ⎢ 0<br />
T ⎥<br />
⎣S1 I1⎦<br />
⎡ T2 S2⎤ ⎢ 0<br />
T ⎥ ><br />
⎣S2 I2⎦<br />
T<br />
λ<br />
i<br />
, γ<br />
A PA 1 P1 Q 0<br />
j<br />
⎧<br />
p m ⎫<br />
T1 ρ1I1<br />
⎪<br />
m<strong>in</strong> { ∑qY<br />
i i+ ∑ rU j j +<br />
K, ∑x≥ 0, Yi, U<br />
⎪<br />
j i= 1 j=<br />
1<br />
⎪<br />
⎪<br />
⎪<br />
p<br />
m<br />
2 2 ⎪<br />
T2 ρ2I2<br />
⎪∑λi( Y i− yi ) + ∑γ<br />
j( U j −uj<br />
)} ⎪<br />
i= 1 j=<br />
1<br />
T<br />
⎪<br />
⎪ where, 1 ( ) ( )<br />
max ⎨<br />
T<br />
s. t. ( A+ BK) ∑ ( A+<br />
BK)<br />
⎬. (22)<br />
λi≥0, γ j≥0<br />
x<br />
T<br />
T<br />
⎪<br />
⎪ S2<br />
RK B PBK B PA<br />
T<br />
⎪ + E∑ w E =∑x<br />
⎪ LQR <strong>in</strong>verse-optimal Control, ,<br />
⎪<br />
T T<br />
⎪<br />
⎪ ϕiC∑ x C ϕi = Yi<br />
⎪<br />
⎪<br />
T T<br />
⎪<br />
∃P<br />
≥ 0 , Q ≥ 0 , R > 0 , P 1 > 0 , s.t.<br />
⎪⎩<br />
ϕ jK∑ x K ϕ j = U j ⎪⎭<br />
If rewrite the m<strong>in</strong>imization objective function as:<br />
p<br />
m<br />
T<br />
T<br />
m<strong>in</strong> { ∑( qi + λi) Y i+ ∑ ( rj + γ j) U j}<br />
RK B PBK B PA<br />
K, ∑x≥ 0, Yi, U j i= 1 j=<br />
1<br />
,<br />
p<br />
m<br />
T<br />
2 2<br />
A PA<br />
− ∑λiyi − ∑γ<br />
ju<br />
1 P1<br />
Q<br />
j<br />
i= 1 j=<br />
1<br />
λ i≥ γ j ≥ .This <strong>in</strong>dicates<br />
∗<br />
λ i γ j dependent solutions, K ( λi, γ j)<br />
,co<strong>in</strong>cide<br />
⎡ T1 S1⎤ ⎢ 0<br />
T ⎥ ><br />
⎣S1 I1⎦<br />
i = qi + i i = rj + j).<br />
T T T T<br />
1<br />
Because of the variance constra<strong>in</strong>ts (16) and (17),<br />
T<br />
problem cannot be equivalent to the <strong>in</strong>f<strong>in</strong>ite<br />
1 ≤ ρ1I1<br />
⎡ T1 S1⎤ and Lemma 2, ⎢ 0<br />
Theorem 2 guarantees that the MVC 3 T ⎥ ><br />
problem would<br />
⎣S1 I1⎦<br />
∗<br />
T<br />
T<br />
K λi<br />
γ j such that there to T 1 − S 1 S 1 > 0 , that is 1 I 1 SS 1 1<br />
⎡ T2 S2⎤ λ , γ j . But, weighted matrix Q , R of <strong>in</strong>f<strong>in</strong>ite<br />
⎢ 0<br />
T ⎥ ><br />
⎣S2 I2⎦<br />
T<br />
T<br />
2 = + +<br />
T2 ≤ ρ2I2<br />
LQR <strong>in</strong>verse-optimal control can be described as:<br />
If ∃P<br />
≥ 0 , Q ≥ 0 , R > 0 , P 1 > 0 and symmetric<br />
m<strong>in</strong> ρ 1 + ρ 2<br />
(23) PPT , , , T, QR ,<br />
then, it is clear that the above three assumptions are<br />
satisfied for all values of 0, 0<br />
that all ,<br />
with the solution to some <strong>in</strong>f<strong>in</strong>ite horizon MPC problem<br />
( λ λ , γ γ<br />
MVC 3<br />
horizon MPC problem (19). Theorem 2 shows that<br />
<strong>in</strong>troduc<strong>in</strong>g variance constra<strong>in</strong>ts to MVC 3 problem (21),<br />
is exactly the reason to adjust the MPC controller weight<br />
matrix, Q , R .<br />
generate a l<strong>in</strong>ear feedback ( , )<br />
exists a feasible solution for <strong>in</strong>f<strong>in</strong>ite horizon MPC<br />
problem. Unfortunately, the exact form of this <strong>in</strong>f<strong>in</strong>ite<br />
horizon MPC problem is unclear, unless the MVC 3<br />
solution procedure provides us with the optimal<br />
Lagrangians i<br />
horizon MPC can be solved by given feedback ga<strong>in</strong>, K .<br />
Then, it can be updated with the Riccati equation.<br />
E. LQR Inverse-Optimal Control and Its LMI Method<br />
matrices, T 1 , T 2 that<br />
1 1 2<br />
⎡ T S ⎤ ><br />
(24)<br />
(25)<br />
− − < (26)<br />
< (27)<br />
< , (28)<br />
S = A+ BK P A+ BK − P+ Q+ K RK ,<br />
= + + .Then, through the solution of<br />
QR,can be obta<strong>in</strong>ed.<br />
LQR <strong>in</strong>verse-Optimal Control [27] is described as:<br />
T T T T<br />
A PA − P −K RK − K B PBK + Q = 0 (29)<br />
+ + = 0 (30)<br />
− < , (31)<br />
where, (31) ensures that ( A, Q ) is detectable. As (29)<br />
cannot be converted to the LMI form, it can be<br />
constructed as,<br />
S = A PA −P −K RK − K B PBK + Q ,<br />
where, T 1 is symmetric matrix; ρ 1 is a scalar; I 1 is a<br />
unit matrix of appropriate dimension. From LMI theory<br />
is<br />
T<br />
equivalent<br />
ρ > .Then, approximate<br />
solution of equation (29), R , P , can be gotten through<br />
choos<strong>in</strong>g a small enough ρ 1 . Similarly,<br />
S RK B PBK B PA<br />
Equation (26) is the rewrit<strong>in</strong>g of (31). Then, the LMI<br />
form of LQR <strong>in</strong>verse-Optimal Control can be gotten.<br />
Equations (29)-(31) are constructed to LMI form to get<br />
parameters QR. , However, Matrix Q here is nondiagonal<br />
matrix, practical application is <strong>in</strong>convenience.<br />
© 2013 ACADEMY PUBLISHER
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From LMI and ARE equivalence relation [28], S1<br />
is equal<br />
to:<br />
T T T T<br />
S1 = A PA + A PBK + ( BK) PA + BK P( BK)<br />
T<br />
T<br />
− P+ Q+<br />
K RK<br />
= ( A+ BK) P( A+ BK)<br />
− P+ Q+<br />
K RK<br />
Therefore, LMI form of (23)-(28) can be gotten and the<br />
solution of Q is diagonal matrix.<br />
F. MPC Tun<strong>in</strong>g Based on Extended MVC 3<br />
Consider system (3), outputs and manipulative variable<br />
constra<strong>in</strong>ts are as y ( k)<br />
< y and u ( k)<br />
< u , respectively,<br />
i<br />
i<br />
where, yi ( k)<br />
is i th element of y( k ) and u j ( k)<br />
is j th<br />
element of u ( k ) . When the MPC controller is put <strong>in</strong>to<br />
operation, extended MVC 3 performance evaluation<br />
criteria is used to monitor controller performance. If the<br />
performance evolution <strong>in</strong>dexη is below the thresholdψ ,<br />
weighted parameter R can be updated with extended<br />
MVC 3 to improve the robustness of the controlled system.<br />
The block diagram of MPC tun<strong>in</strong>g is shown <strong>in</strong> Fig. 2.<br />
Figure 2. Block diagram of MPC controller-tun<strong>in</strong>g<br />
IV. MPC CONTROLLER PERFORMANCE EVALUATION<br />
AND TUNING SYSTEM IN SINGLE INVERTED PENDULUM<br />
CONTROL<br />
A. Model Preprocess<strong>in</strong>g<br />
• Stabilizer design<br />
The s<strong>in</strong>gle <strong>in</strong>verted pendulum is unstable system,<br />
while, tun<strong>in</strong>g system of <strong>in</strong>f<strong>in</strong>ite MPC require a stable<br />
controlled object. Hence a stabilizer u =− Kx+ v is<br />
needed. For the <strong>in</strong>verted pendulum system (2), Use<br />
command K=acker(A,B,P) <strong>in</strong> Matlab, to configure<br />
closed-loop pole to:<br />
( 8 8 2 2 2 2 )<br />
j<br />
P = − − − + i − − i . (32)<br />
j<br />
T<br />
.<br />
The feedback ga<strong>in</strong> is obta<strong>in</strong>ed as:<br />
K = ( −17.4150 − 13.0612 60.9383 11.0204)<br />
. (33)<br />
The generalized system matrix after stabilization is as<br />
follows:<br />
⎛x<br />
⎞ ⎛ 0 1 0 0 ⎞⎛x<br />
⎞ ⎛0⎞<br />
⎜<br />
x<br />
⎟ ⎜<br />
0 0 1 0<br />
⎟⎜ x<br />
⎟ ⎜<br />
1<br />
⎟<br />
⎜ ⎟<br />
<br />
= ⎜ ⎟⎜ ⎟+<br />
⎜ ⎟u<br />
⎜ θ ⎟ ⎜ 0 0 0 1 ⎟⎜θ<br />
⎟ ⎜0⎟<br />
⎜ θ ⎟ ⎜ ⎟<br />
512 384 136 20 ⎜θ<br />
⎟ ⎜ ⎟<br />
⎝− − − − ⎠<br />
<br />
⎝ ⎠<br />
⎝ ⎠ ⎝3⎠<br />
. (34)<br />
⎛x<br />
⎞<br />
⎜<br />
x 1 0 0 0 x<br />
⎟<br />
⎛ ⎞ ⎛ ⎞ ⎛0⎞<br />
y = = ⎜ ⎟<br />
⎜ + u<br />
θ<br />
⎟ ⎜<br />
0 0 1 0<br />
⎟⎜θ<br />
⎟ ⎜<br />
0<br />
⎟<br />
⎝ ⎠ ⎝ ⎠ ⎝ ⎠<br />
⎜ <br />
θ ⎟<br />
⎝ ⎠<br />
The follow<strong>in</strong>g MPC controller performance evaluation,<br />
tun<strong>in</strong>g system based on extended MVC 3 was built on the<br />
stabilized generalized system (34).<br />
• Discretization<br />
S<strong>in</strong>ce the derivation of the above extended MVC 3<br />
algorithm is based on discrete state space model (3),<br />
discretization of system (34) and construct<strong>in</strong>g a suitable<br />
noise are needed. Use command sys=c2d(A,B,Ts) <strong>in</strong><br />
Matlab, here Ts = 1s<br />
, and consider the noise to be<br />
stationary, Gaussian White-noise processes, the follow<strong>in</strong>g<br />
system can be obta<strong>in</strong>ed as:<br />
⎛ xk ( + 1) ⎞ ⎛ 0.2584 0.1707 0.0306 0.0017 ⎞<br />
⎜<br />
xk ( 2)<br />
⎟ ⎜<br />
0.8519 0.3805 0.0556 0.0027<br />
⎟<br />
⎜<br />
+<br />
⎟<br />
− − − −<br />
= ⎜ ⎟<br />
⎜θ<br />
( k + 1) ⎟ ⎜ 1.3646 0.1716 −0.0181 −0.0023⎟<br />
⎜ ⎟ ⎜ ⎟<br />
⎝θ<br />
( k + 2) ⎠ ⎝ 1.1850 2.2534 0.4863 0.0282 ⎠<br />
⎛ xk ( ) ⎞ ⎛ 0.2319 ⎞ ⎛0⎞<br />
⎜<br />
xk ( + 1)<br />
⎟ ⎜<br />
0.1757<br />
⎟ ⎜<br />
⎜ ⎟<br />
1<br />
⎟<br />
× + ⎜ ⎟uk<br />
( ) + ⎜ ⎟wk<br />
( )<br />
⎜ θ ( k) ⎟ ⎜−1.<br />
3885⎟ ⎜0⎟<br />
⎜ ⎟ ⎜ ⎟ ⎜ ⎟<br />
⎝θ<br />
( k + 1) ⎠ ⎝ 0.1646 ⎠ ⎝1⎠<br />
where, ∑ w = 0.01 .<br />
⎛ xk ( ) ⎞<br />
xk ( ) 1 0 0 0<br />
⎜<br />
xk ( 1)<br />
⎟<br />
⎛ ⎞ ⎛ ⎞ +<br />
yk ( ) = ⎜ ⎟<br />
⎜<br />
θ( k) ⎟=<br />
⎜<br />
0 0 1 0<br />
⎟ , (35)<br />
⎝ ⎠ ⎝ ⎠ ⎜ θ( k)<br />
⎟<br />
⎜ ⎟<br />
⎝θ<br />
( k + 1) ⎠<br />
B. MPC Tun<strong>in</strong>g Design<br />
• MPC controller<br />
For system (35), choose the <strong>in</strong>itial objective function<br />
of extended MVC 3 as<br />
J = Y + Y + U ,where R = 1, Q = diag(1,1)<br />
,output<br />
1 2<br />
variance bounds as yi<br />
= 0.3, i = 1,2 , manipulative<br />
variable variance bounds to be u = 0.8 .Us<strong>in</strong>g the<br />
command of LMI toolbox <strong>in</strong> Matlab ,the MPC controller<br />
weight matrix of the nom<strong>in</strong>al model (35), R = 0.0167 ,<br />
Q = diag(0.0204,0.1234,0.0007,0.0160) can be gotten.<br />
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1566 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
• Mismatch model<br />
In order to create performance degradation condition,<br />
A disturbance, Δ A was added to the nom<strong>in</strong>al model (2),<br />
to construct a man-made mismatch model as,<br />
⎛ 0 1 0 0 ⎞<br />
⎜<br />
0 0 1 0<br />
⎟<br />
A'<br />
= A+Δ A= ⎜<br />
⎟. (36)<br />
⎜ 0 0 0 1 ⎟<br />
⎜<br />
⎟<br />
⎝−600 −300 −100 −30⎠<br />
• MPC tun<strong>in</strong>g parameters<br />
Based on the extended MVC 3 algorithm comb<strong>in</strong>ed<br />
with LQR <strong>in</strong>verse optimal, the MPC controller matrixes<br />
of above mismatch model can be gotten.<br />
R = 0.0388 , Q = diag(0.0706 0.0002 0.0357 0.000)<br />
Through MVC 3 performance evaluation, controller<br />
performance decl<strong>in</strong><strong>in</strong>g was detected. If it dropped below<br />
threshold, ψ , (here, ψ is set to 0.8), then, weight<br />
parameter of manipulated variable <strong>in</strong> MVC 3 , R ,is<br />
updated by R'<br />
= R+ ξ I ,(here,ψ is set to 0.5). Repeat the<br />
MPC weight matrix calculation process to update Q,<br />
R,<br />
the new MPC controller parameters<br />
as R = 0.0952<br />
,<br />
Q = diag(0.1703 0.0006 0.0552 0.0000) can be<br />
gotten. Apply the new controller parameters to operation<br />
to restore the desired operational performance.<br />
V. SIMULATION AND ANALYSIS OF MPC CONTROLLER<br />
A. Simulation and Comparison of MPC Controller and<br />
the LQR Controller<br />
• Simulation of LQR controller<br />
LQR controlled system <strong>in</strong> the Simul<strong>in</strong>k of Matlab was<br />
shown <strong>in</strong> Fig. 3. Parameter of LQR block was set to<br />
K = ( −31.623 − 20.151 72.718 13.155)<br />
, which was<br />
provided by Googol Technology LTD.<br />
Figure 3. Simulation block of LQR control loop<br />
• Simulation of MPC controller<br />
MPC controlled system <strong>in</strong> the Simul<strong>in</strong>k was shown <strong>in</strong><br />
Fig. 4, where, parameter of Acker block was set to<br />
stabilizer feedback ga<strong>in</strong>. Weighted matrixes of MPC<br />
block were set the parameters calculated by the nom<strong>in</strong>al<br />
model.<br />
Figure 4. Simulation block of MPC control loop<br />
• Analysis of simulations results<br />
Simulation curve charts of MPC controller and LQR<br />
controller are shown <strong>in</strong> Fig. 5, where, u denotes<br />
manipulative variable, which is cart angular velocity.<br />
angle, pos denote outputs, they are pendulum angle and<br />
cart position.<br />
The maximum deviation of MPC controller and LQR<br />
controller are shown <strong>in</strong> Table I and comparison bar chart<br />
is shown <strong>in</strong> Fig. 6.<br />
TABLE I.<br />
MAXIMUM DEVIATION COMPARISON<br />
u angle pos<br />
MPC 0.8240 0.0096 0.0093<br />
LQR 34.4589 0.3101 0.3533<br />
Obviously, due to the <strong>in</strong>troduction of steady state<br />
manipulative variable and outputs covariance constra<strong>in</strong>t,<br />
MPC controller can make the maximum deviation<br />
significantly reduced than LQR controller, which greatly<br />
improved the system dynamic performance.<br />
B. Simulation of MPC Controller Tun<strong>in</strong>g<br />
• Simulation of MPC controller tun<strong>in</strong>g<br />
MPC controller tun<strong>in</strong>g dynamic curves was obta<strong>in</strong>ed<br />
by replace orig<strong>in</strong>al weight matrix Q , R of MPC controller<br />
with mismatched and Controller-tuned parameters, shown<br />
<strong>in</strong> Fig. 7, where, the legend (good, bad and tuned) means<br />
controller runn<strong>in</strong>g under, nom<strong>in</strong>al model, mismatch<br />
model and MPC controller tuned.<br />
Through curves, if us<strong>in</strong>g orig<strong>in</strong>al controller parameters<br />
to control mismatch model, it would lead an <strong>in</strong>crease on<br />
manipulative variable and outputs deviation. After<br />
adjust<strong>in</strong>g controller parameters by controller tun<strong>in</strong>g<br />
system, the deviation reduced to some extent. This proves<br />
the feasible of MPC controller tun<strong>in</strong>g algorithm.<br />
• Extended MVC 3 performance evaluation method<br />
The extended MVC 3 performance evaluation curve is<br />
shown <strong>in</strong> Fig. 8.<br />
Set λ = 1 <strong>in</strong> the MVC 3 performance evolution object<br />
function (18) and get<br />
p m<br />
i= 1<br />
i i<br />
j=<br />
1<br />
j j<br />
−7<br />
benchmark J 3 = ∑qY + ∑ rU by LMI method,<br />
MVC<br />
here, J 3 = 1.3217 × 10 .Then actual run-time<br />
MVC<br />
variance was compared with this benchmark, get η<br />
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40<br />
30<br />
MPC<br />
LQR<br />
0.35<br />
0.3<br />
MPC<br />
LQR<br />
0.3<br />
0.2<br />
MPC<br />
LQR<br />
0.25<br />
20<br />
0.2<br />
0.1<br />
u<br />
10<br />
0<br />
angle<br />
0.15<br />
0.1<br />
pos<br />
0<br />
-0.1<br />
-10<br />
0.05<br />
0<br />
-0.2<br />
-20<br />
-0.05<br />
-0.3<br />
-30<br />
0 20 40 60<br />
T<br />
-0.1<br />
0 20 40 60<br />
T<br />
-0.4<br />
0 20 40 60<br />
T<br />
Figure 5. Simulations curves charts of MPC and LQR control loop<br />
35<br />
0.35<br />
0.4<br />
30<br />
0.3<br />
0.35<br />
25<br />
0.25<br />
0.3<br />
20<br />
0.2<br />
0.25<br />
u<br />
15<br />
angle<br />
0.15<br />
pos<br />
0.2<br />
0.15<br />
10<br />
0.1<br />
0.1<br />
5<br />
0.05<br />
0.05<br />
0<br />
MPC<br />
1<br />
LQR<br />
0<br />
MPC<br />
2<br />
LQR<br />
0<br />
MPC<br />
3<br />
LQR<br />
Figure 6. Bar charts of MPC and LQR simulations curves maximum deviation<br />
1.5<br />
1<br />
good<br />
bad<br />
tuned<br />
12<br />
10<br />
good<br />
bad<br />
tuned<br />
0.01<br />
0.005<br />
good<br />
bad<br />
tuned<br />
8<br />
u<br />
0.5<br />
0<br />
angle<br />
14 x 10-3 T<br />
6<br />
4<br />
pos<br />
0<br />
-0.005<br />
2<br />
-0.5<br />
0<br />
-0.01<br />
-2<br />
-1<br />
0 20 40 60<br />
T<br />
-4<br />
0 20 40 60<br />
-0.015<br />
0 20 40 60<br />
T<br />
Figure 7. Dynamic curves of nom<strong>in</strong>al model, mismatch model and MPC controller-tuned<br />
as:<br />
J 3<br />
MVC<br />
η 1 = = 0.9803 ;<br />
J<br />
arh<br />
1<br />
J 3<br />
MVC<br />
η 2 = = 0.7551 ;<br />
J<br />
arh<br />
2<br />
J 3<br />
MVC<br />
η 3 = = 0.9143 , where,<br />
J<br />
arh<br />
3<br />
J , J , J denote<br />
arh1 arh2 arh3<br />
© 2013 ACADEMY PUBLISHER
1568 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
11.5 x 10-8 Var(U)<br />
11<br />
MVC3 curve<br />
good<br />
bad<br />
tuned<br />
10.5<br />
Var(Y)<br />
10<br />
9.5<br />
9<br />
8.5<br />
8<br />
1 2 3 4 5 6 7 8 9<br />
x 10 -8<br />
Figure 10. S<strong>in</strong>gle <strong>in</strong>verted pendulum device<br />
Figure 8. MVC 3 performance evolution curve<br />
steady state error of good, bad, tuned. η 1 , η 2 , η 3 denote<br />
their correspond<strong>in</strong>g ratio. The bar chart is shown <strong>in</strong> Fig. 9.<br />
It confirms the correctness and feasibility of MPC tun<strong>in</strong>g<br />
method.<br />
1<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
Figure 11. MPC control loop<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
good bad tuned<br />
Figure 9. Bar chart of performance evolution<br />
VI. ACTUAL CONTROL ON THE DEVICE<br />
A. Construct MPC Controller<br />
The photo of s<strong>in</strong>gle <strong>in</strong>verted pendulum device<br />
provided by Googol Technology LTD is shown <strong>in</strong> Fig.10.<br />
MPC controlled system was constructed on Matlab<br />
real-time control platform provided by Googol<br />
Technology LTD shown <strong>in</strong> Fig. 11.<br />
Parameters of k_acker block was set to stabilizer<br />
feedback ga<strong>in</strong> and weight matrixes QR , of MPC<br />
controller was set to which calculated from nom<strong>in</strong>al<br />
model. Run-time curves were shown <strong>in</strong> Fig.12.<br />
Obviously, under the permission of variance<br />
constra<strong>in</strong>ts, MPC controller can reach steady state <strong>in</strong> a<br />
short period of time.<br />
B. Tun<strong>in</strong>g Process<br />
Run the MPC controller tun<strong>in</strong>g system, and preprocess<br />
manipulated variable u by limit<strong>in</strong>g filter, the effect<br />
curves can be shown <strong>in</strong> Fig. 13.<br />
Figure 12. MPC run-time operat<strong>in</strong>g curves<br />
Steady state variance of manipulative variable and<br />
outputs were calculated and shown <strong>in</strong> Fig. 14.<br />
Bar charts shows MPC controller performance has<br />
been restored and the tun<strong>in</strong>g system is feasible.<br />
VII. CONCLUSION<br />
In this work, an extended MVC 3 method and its LMI<br />
solution were applied to <strong>in</strong>f<strong>in</strong>ite MPC controller<br />
performance evaluation and parameters tun<strong>in</strong>g system.<br />
Us<strong>in</strong>g extended MVC 3 pr<strong>in</strong>ciple to monitor controlled<br />
system, if controller performance decl<strong>in</strong>ed is detected, it<br />
can be improved by resett<strong>in</strong>g MPC weighted matrixes<br />
with controller tun<strong>in</strong>g algorithm. Simulation and device<br />
operation on s<strong>in</strong>gle <strong>in</strong>verted pendulum device provided<br />
by Googol Technology LTD reaffirm the correctness of<br />
this system. Also, the <strong>in</strong>troduction of LMI solution makes<br />
© 2013 ACADEMY PUBLISHER
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1<br />
-3.12<br />
0.05<br />
0.8<br />
-3.125<br />
0.04<br />
0.6<br />
0.4<br />
-3.13<br />
0.03<br />
0.02<br />
0.2<br />
-3.135<br />
0.01<br />
u<br />
0<br />
angle<br />
-3.14<br />
pos<br />
0<br />
-0.2<br />
-3.145<br />
-0.01<br />
-0.4<br />
-0.6<br />
-3.15<br />
-0.02<br />
-0.03<br />
-0.8<br />
-3.155<br />
-0.04<br />
-1<br />
0 200 400 600 800<br />
T<br />
-3.16<br />
0 200 400 600 800<br />
T<br />
-0.05<br />
0 200 400 600 800<br />
T<br />
Figure 13. Real-time operat<strong>in</strong>g curves of MPC controller-tun<strong>in</strong>g system<br />
Figure 14. Steady state variance comparison bar charts<br />
the system easy to extend and analysis, this will provide a<br />
new way for later controller performance evaluation and<br />
tun<strong>in</strong>g research.<br />
ACKNOWLEDGMENT<br />
This work is supported by National Science<br />
Foundation of Ch<strong>in</strong>a under Grant 60974065.<br />
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Chao Cheng was born <strong>in</strong> Shanxi, Ch<strong>in</strong>a,<br />
1983. She received the bachelor degree<br />
<strong>in</strong> Beij<strong>in</strong>g Institute of Fashion<br />
Technology <strong>in</strong> 2004. From August 2004<br />
to January 2007, she worked as control<br />
eng<strong>in</strong>eer <strong>in</strong> Jiangsu Yangnong Chemical<br />
Group Co.,Ltd. She is currently a second<br />
grade postgraduate student <strong>in</strong><br />
Department of Automation <strong>in</strong> Beij<strong>in</strong>g<br />
University of Chemical Technology. Her research <strong>in</strong>terests<br />
<strong>in</strong>clude MPC and other advanced control.<br />
Zhong Zhao was born <strong>in</strong> Henan, Ch<strong>in</strong>a,<br />
1970. He received bachelor degree <strong>in</strong><br />
Zhejiang University <strong>in</strong> 1992 and master<br />
degree and Ph.D. from East Ch<strong>in</strong>a<br />
University of Science and Technology <strong>in</strong><br />
1995 and 1998 respectively.<br />
From 1998 to 2000, he worked as a<br />
postdoctol <strong>in</strong> Ts<strong>in</strong>ghua University, from<br />
2000 to 2002 as Senior Eng<strong>in</strong>eer <strong>in</strong><br />
Honeywell Hi-Spec Solutions and<br />
Visit<strong>in</strong>g fellow <strong>in</strong> Max-Planck-Institute. From 2002 to 2004 he<br />
employed as a lecturer by University of Saga, Japan.<br />
He is currently a professor <strong>in</strong> the Department of Automation,<br />
and deputy director of Institute of Automation <strong>in</strong> Beij<strong>in</strong>g<br />
University of Chemical Technology, also, member of U.S. IEEE<br />
and Japan, SICE. His research <strong>in</strong>terests are the advanced control<br />
of complex <strong>in</strong>dustrial processes, process monitor<strong>in</strong>g, and multiscale<br />
process signal analysis.<br />
Haixia Li was born <strong>in</strong> Gansu, Ch<strong>in</strong>a,<br />
1984. She received her bachelor degree<br />
and master degree <strong>in</strong> Information<br />
Science and Technology Institute of<br />
Beij<strong>in</strong>g University of Chemical<br />
Technology <strong>in</strong> 2007 and 2010<br />
respectively. Her research direction is<br />
advanced control of <strong>in</strong>dustrial process.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1571<br />
A Metadata-driven Cloud Comput<strong>in</strong>g Application<br />
Virtualization Model<br />
Yunpeng Xiao 1,2,*<br />
1. Chongq<strong>in</strong>g Eng<strong>in</strong>eer<strong>in</strong>g Laboratory of Internet and Information Security, Chongq<strong>in</strong>g University of Posts and<br />
Telecommunications (CQUPT), Chongq<strong>in</strong>g, Ch<strong>in</strong>a<br />
2. Beij<strong>in</strong>g Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beij<strong>in</strong>g University of Posts and<br />
Telecommunications (BUPT), Beij<strong>in</strong>g, Ch<strong>in</strong>a<br />
Email: sh<strong>in</strong>eagle2005@hotmail.com<br />
Guangxia Xu 1 , Yanb<strong>in</strong>g Liu 1 and Bai Wang 2<br />
1. Chongq<strong>in</strong>g Eng<strong>in</strong>eer<strong>in</strong>g Laboratory of Internet and Information Security, Chongq<strong>in</strong>g University of Posts and<br />
Telecommunications (CQUPT), Chongq<strong>in</strong>g, Ch<strong>in</strong>a<br />
2. Beij<strong>in</strong>g Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beij<strong>in</strong>g University of Posts and<br />
Telecommunications (BUPT), Beij<strong>in</strong>g, Ch<strong>in</strong>a<br />
Email: {xugx, liuyb}@cqupt.edu.cn, wangbai@bupt..edu.cn<br />
Abstract—In order to meet the requirements of<br />
standardization of virtualization <strong>in</strong> cloud comput<strong>in</strong>g<br />
platform, improve the flexibility and expansibility of the<br />
system and enhance the capability of management-control<br />
of the platform, by means of <strong>in</strong>troduc<strong>in</strong>g the features of<br />
decoupl<strong>in</strong>g and semantic of metadata, a Metadata-driven<br />
Cloud Comput<strong>in</strong>g Application Virtualization<br />
Model(MCCAVM) <strong>in</strong> software level is proposed <strong>in</strong> the<br />
paper based on Tur<strong>in</strong>g mach<strong>in</strong>e model and Von Neumann<br />
computer architecture. The model achieves the complete life<br />
cycle management of the capabilities and services. Based on<br />
the formal def<strong>in</strong>ition, analyz<strong>in</strong>g the hierarchical structure<br />
with multi-role and multi-dimensional view, the paper<br />
proposes a Metadata-driven Cloud Comput<strong>in</strong>g Application<br />
Virtualization System(MCCAVS). Tak<strong>in</strong>g the production of<br />
virtual cloud storage service as example, this paper gives<br />
formal analysis of system runn<strong>in</strong>g and compares with other<br />
relat<strong>in</strong>g work. The results show that the model presents<br />
good reference on the construction of cloud comput<strong>in</strong>g<br />
application virtualization platform.<br />
Index Terms—MCCAVM, metadata, cloud comput<strong>in</strong>g,<br />
application virtualization, software architecture<br />
I. INTRODUCTION<br />
The <strong>in</strong>ternet is gradually becom<strong>in</strong>g a k<strong>in</strong>d of<br />
comput<strong>in</strong>g platform <strong>in</strong> peace with the rapid expansion<br />
and popularization of computer communication<br />
technology. As a new comput<strong>in</strong>g mode, cloud comput<strong>in</strong>g<br />
describes a mode of <strong>in</strong>crement, use and deliver<strong>in</strong>g for a<br />
new type of IT services based on <strong>in</strong>ternet. It usually<br />
means to apply dynamic scalable and virtual resources<br />
through <strong>in</strong>ternet[1, 2]. Wikipedia def<strong>in</strong>ed cloud<br />
comput<strong>in</strong>g scenario as follow: Users or clients can submit<br />
Manuscript received August 20, 2012; revised October 8, 2012;<br />
accepted October 14, 2012.<br />
Correspond<strong>in</strong>g author: Yunpeng Xiao (xiaoyp@cqupt.edu.cn).<br />
a task, such as word process<strong>in</strong>g, to the service provider,<br />
without actually possess<strong>in</strong>g the software or hardware[3].<br />
This description shows that a core issue of cloud<br />
comput<strong>in</strong>g research is how to achieve virtualization and<br />
large-scale application scalability and availability <strong>in</strong> the<br />
virtual environment.<br />
A broadly understood of virtualization is that<br />
comput<strong>in</strong>g elements run on the virtual basis. That is a<br />
k<strong>in</strong>d of solution to simplify management and optimize<br />
resources. The key question highlights platform<br />
standardization, improvement of the platform flexibility<br />
and dynamic scalability, reduction of the degree of<br />
coupl<strong>in</strong>g of platform components and other aspects.<br />
There are many virtualization technology researches and<br />
explorations: Research [4] and [5] put forward<br />
virtualization platform architecture through researches<br />
based on service-oriented architecture (SOA), [6] and [7]<br />
focus on platform flexibility and dynamic capacity<br />
expansion, [8, 9, 10] study on virtualization from storage<br />
virtualization, virtual device, network virtualization, and<br />
other aspects.<br />
Application virtualization uncouples the applications<br />
from operat<strong>in</strong>g systems, provides a virtual operat<strong>in</strong>g<br />
environment for the applications. In this environment, not<br />
only <strong>in</strong>cludes the application executable file, but also<br />
<strong>in</strong>cludes the runtime environment it requires. In essence,<br />
application virtualization is abstracted dependent between<br />
low-level application systems and hardware. It can solve<br />
the problem of version <strong>in</strong>compatibility, the limitation of<br />
term<strong>in</strong>al capacity, application system host<strong>in</strong>g mass, realtime<br />
deployment of application, disaster recovery and so<br />
on.<br />
Metadata is descriptive <strong>in</strong>formation about the data. It is<br />
semantics on the basic concepts, basic relationships and<br />
basic constra<strong>in</strong>ts of data model. The metadata can solve<br />
problems that model layer can not resolve, such as fuzzy<br />
semantic of data model, model <strong>in</strong>tegration and shar<strong>in</strong>g of<br />
<strong>in</strong>formation. By us<strong>in</strong>g metadata we can translate<br />
© 2013 ACADEMY PUBLISHER<br />
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1572 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
functional strong coupl<strong>in</strong>g relationships <strong>in</strong>to data type<br />
weak coupl<strong>in</strong>g relationships. Metadata research is widely<br />
used <strong>in</strong> data-driv<strong>in</strong>g system such as file system,<br />
<strong>in</strong>formation system and so on [11, 12]. On the other hand,<br />
the abstract computational model: Tur<strong>in</strong>g mach<strong>in</strong>e, which<br />
can simulate any human comput<strong>in</strong>g process, is equivalent<br />
to any f<strong>in</strong>ite mathematics of logic process. The Tur<strong>in</strong>g<br />
mach<strong>in</strong>e is also a general-purpose computer and an ideal<br />
model of universal def<strong>in</strong>ition. Its abstract def<strong>in</strong>ition is a<br />
k<strong>in</strong>d of mathematical logic mach<strong>in</strong>e [13]. Von Neumann<br />
implemented the ideal model, designed store-based<br />
computer architecture [14]. The Von’s th<strong>in</strong>k<strong>in</strong>g is<br />
<strong>in</strong>herited by modern computer architectures, s<strong>in</strong>ce its<br />
clear structure and feasibility [15].<br />
Tak<strong>in</strong>g <strong>in</strong>to account the needs of application<br />
virtualization mentioned above, and by means of<br />
metadata, Tur<strong>in</strong>g mach<strong>in</strong>e and Von Neumann architecture,<br />
a Metadata-driven Cloud Comput<strong>in</strong>g Application<br />
Virtualization Model(MCCAVM) <strong>in</strong> software level is<br />
proposed <strong>in</strong> this paper. A Metadata-driven Cloud<br />
Comput<strong>in</strong>g Application Virtualization System<br />
(MCCAVS) is implemented based on MCCAVM by<br />
then. We make the follow<strong>in</strong>g three major contributions: 1)<br />
Metadata is used to drive the whole system, so that the<br />
description of the system is standard and uniform. The<br />
decoupl<strong>in</strong>g purpose is well done besides. 2) We propose<br />
an application virtualization model <strong>in</strong> software level by<br />
refer<strong>in</strong>g Von Neumann architecture. All k<strong>in</strong>d of<br />
applications and services can be managed by software<br />
bus. 3) Not only implemented eng<strong>in</strong>eer<strong>in</strong>g, the entire<br />
model and system are def<strong>in</strong>ed and verified formally by<br />
us<strong>in</strong>g Tur<strong>in</strong>g mach<strong>in</strong>e.<br />
The rest of this paper is organized as follows: after the<br />
<strong>in</strong>troduction <strong>in</strong> Section 1, Section 2 describes the formal<br />
def<strong>in</strong>ition and gives the system model; Section 3 designs<br />
system and expla<strong>in</strong>s each module <strong>in</strong> detail; Section 4<br />
presents our MCCAVS and verifies it eng<strong>in</strong>eer<strong>in</strong>g and<br />
formally respectively; Section 5 concludes this paper.<br />
II. MODEL<br />
A. Formal Def<strong>in</strong>ition<br />
Before giv<strong>in</strong>g model description formally, the<br />
def<strong>in</strong>ition of capability and Service <strong>in</strong> the model is<br />
described firstly.<br />
Def<strong>in</strong>ition 1. Capability. Any underly<strong>in</strong>g hardware<br />
and software resource <strong>in</strong> the cloud server side.<br />
Def<strong>in</strong>ition 2. Service. Product generated by a variety<br />
of capabilities, through assembl<strong>in</strong>g and reprocess<strong>in</strong>g<br />
pattern.<br />
In fact, a virtual application <strong>in</strong> the cloud server side is<br />
comb<strong>in</strong>ed of Capability and Service. Accord<strong>in</strong>g to Von<br />
Neumann architecture, computers must have five basic<br />
components: <strong>in</strong>put data and devices, memory program<br />
and data memory, data process<strong>in</strong>g comput<strong>in</strong>g device,<br />
control program execution controller, output device.<br />
Draw<strong>in</strong>g on the th<strong>in</strong>k<strong>in</strong>g of the Von Neumann computer<br />
architecture, model regards Capability and Service as an<br />
external device. Various external devices mounted to the<br />
model via a software bus and driven by model controlled<br />
components. The work of the model is based on<br />
predef<strong>in</strong>ed tasks, makes multiple types of Capability and<br />
Service work together, and provides virtualization<br />
technology by us<strong>in</strong>g the basis of hardware, software<br />
resources and the upper applications supplied by these<br />
devices. Regard<strong>in</strong>g Capability and Service as an external<br />
device, the collaborative process can be considered as the<br />
calculation of the f<strong>in</strong>ite number of steps. Based on formal<br />
def<strong>in</strong>ition, the paper proposed a Metadata-driven Cloud<br />
Comput<strong>in</strong>g Application Virtualization Model(MCCAVM)<br />
consider<strong>in</strong>g Tur<strong>in</strong>g mach<strong>in</strong>e computation model and the<br />
von Neumann computer system structure of these devices.<br />
Def<strong>in</strong>ition 3. Formal def<strong>in</strong>ition of the model. A<br />
Metadata-driven cloud comput<strong>in</strong>g application<br />
virtualization model can be formalized as a ten-tuple: T =<br />
(Q,Σ,Γ 1 ,Γ 2 ,Γ 3 ,Γ 4 ,δ,q 0 ,q a ,q r )<br />
Q is the set of states;<br />
Σ is the <strong>in</strong>put alphabet, which does not conta<strong>in</strong> a<br />
special blank symbol B;<br />
Γ 1 is the capability to take the alphabet, where B∈Γ 1<br />
and Σ∈Γ 1 ;<br />
Γ 2 is the service with the alphabet, where B∈Γ 2 and<br />
Σ∈Γ 2 ;<br />
Γ 3 is the result with the alphabet, where B∈Γ 3 and Σ<br />
∈Γ 3 ;<br />
Γ 4 is a task with an alphabet, where B∈Γ 4 andΣ∈Γ 4 ;<br />
δ : Q×Γ 4 →Q×Γ 4 ×{L,R} 4 is the transfer function,<br />
where L, R <strong>in</strong>dicates that the read-write head to the left or<br />
to the right;<br />
q 0 ∈Q is the <strong>in</strong>itial state;<br />
q a ∈Q is an accept<strong>in</strong>g state;<br />
q r ∈Q is the denial of state and q r ≠q a ;<br />
Capability alphabet and service alphabet need to be<br />
processed were recorded on work tapeΓ 1 and Γ 2 ; Γ 3<br />
records the results; Γ 4 records work processes alphabet of<br />
different virtualization tasks.<br />
Theorem 1. MCCAVM is a general comput<strong>in</strong>g model<br />
which is equivalent to the universal Tur<strong>in</strong>g mach<strong>in</strong>e.<br />
Proof: Firstly, <strong>in</strong> Def<strong>in</strong>ition 3, depend<strong>in</strong>g on the<br />
differences of storage function, def<strong>in</strong><strong>in</strong>g a number of<br />
work<strong>in</strong>g tapes. Obviously, MCCAVM is multi-tape<br />
Tur<strong>in</strong>g mach<strong>in</strong>e, and multi-tape Tur<strong>in</strong>g mach<strong>in</strong>e is<br />
equivalent with Tur<strong>in</strong>g mach<strong>in</strong>e, so MCCAVM is<br />
equivalent with Tur<strong>in</strong>g mach<strong>in</strong>e.<br />
Secondly, we set the capability alphabet, service<br />
alphabet, results alphabet and tasks alphabet as<br />
T1,T2,T3,T4 <strong>in</strong> T's each comput<strong>in</strong>g step. Tur<strong>in</strong>g mach<strong>in</strong>e<br />
M is a seven-tuple. The current state, the current tape<br />
content and the location of the read-write head constitute<br />
the pattern of M. The specific calculation process of M is<br />
conversion from one pattern to another, based on the<br />
conversion rules described <strong>in</strong> the transition function δ.<br />
The essence of the Tur<strong>in</strong>g mach<strong>in</strong>e is an algorithm or<br />
function, given data x, a mapp<strong>in</strong>g rule accord<strong>in</strong>g to the<br />
function f, calculat<strong>in</strong>g the correspond<strong>in</strong>g f(x), that is, M is<br />
equivalent to a dedicated mach<strong>in</strong>e for a particular<br />
calculation. For a specific task, it completes a specific<br />
calculation or mapp<strong>in</strong>g process by MCCAVM accord<strong>in</strong>g<br />
to task process.<br />
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For a particular task, we can fix an algorithm Mi from<br />
process of tasks alphabet T4. The implementation process:<br />
Given T1, T2, transferr<strong>in</strong>g function δ is first fixed<br />
accord<strong>in</strong>g to algorithm Mi, mak<strong>in</strong>g T from one pattern to<br />
another. Each task corresponds to a process and each<br />
process corresponds to a Tur<strong>in</strong>g mach<strong>in</strong>e. Therefore, the<br />
algorithm is equivalent to a Tur<strong>in</strong>g mach<strong>in</strong>e. The<br />
calculation of (T1, T2) <strong>in</strong>putted on Tur<strong>in</strong>g mach<strong>in</strong>e Mi<br />
and array (T1, T2, T4) on MCCAVM are equivalent.<br />
That is, to any <strong>in</strong>put of Tur<strong>in</strong>g mach<strong>in</strong>e Mi, MCCAVM<br />
can emulate the calculations of Mi, MCCAVM<br />
equivalent to <strong>in</strong>terpreter for Mi. Therefore, MCCAVM is<br />
equivalent to a universal Tur<strong>in</strong>g mach<strong>in</strong>e.<br />
B. Role View of Model<br />
From the perspective of model development and<br />
management control, the model role is divided <strong>in</strong>to<br />
developers and system operators. Among them, the<br />
developers are divided <strong>in</strong>to capability developers and<br />
service developers. Developers produce capabilities or<br />
services by us<strong>in</strong>g <strong>in</strong>terface language. The system<br />
operators use the system language to complete the control<br />
of model. Interface <strong>in</strong>struction set is related to <strong>in</strong>terface<br />
language, system <strong>in</strong>struction set is related to system<br />
language. We will expla<strong>in</strong> separately bellowed.<br />
Def<strong>in</strong>ition 4. Interface language. It is a set of grammar<br />
rules fac<strong>in</strong>g capability and service developers. Follow<strong>in</strong>g<br />
this rule, developers can operate MCCAVM directly and<br />
complete the operat<strong>in</strong>g tasks accurately. Interface<br />
language enabled developers to manage full life-cycle of<br />
capability and service. In order to facilitate developer,<br />
<strong>in</strong>terface language uses simple <strong>in</strong>struction.<br />
Def<strong>in</strong>ition 5. Interface command set. This is a set of<br />
commands which make MCCAVM to complete all k<strong>in</strong>ds<br />
of basic operat<strong>in</strong>g actions accord<strong>in</strong>g to <strong>in</strong>terface language<br />
syntax framework. To complete a certa<strong>in</strong> capability or<br />
service development tasks, a number of <strong>in</strong>terface<br />
commands are comb<strong>in</strong>ed together accord<strong>in</strong>g to the<br />
workflow. And each command can also be used to carry<br />
out specified action. The commands are made up of<br />
parameters and <strong>in</strong>terface functions. Interface functions<br />
<strong>in</strong>structs MCCAVM to complete the basic operat<strong>in</strong>g<br />
actions. Parameter stands for the execut<strong>in</strong>g target of<br />
operat<strong>in</strong>g <strong>in</strong>structions and the association attributes of<br />
operational objectives.<br />
Def<strong>in</strong>ition 6. System language. A set of grammar rules<br />
which can be discerned and read directly by the central<br />
process<strong>in</strong>g unit of MCCAVM. Under the rules of<br />
grammar <strong>in</strong> the system language, each <strong>in</strong>terface<br />
command corresponds to a number of system commands.<br />
Def<strong>in</strong>ition 7. System commands. Basic system<br />
commands set which meet the system language syntax<br />
rules. System commands directly relate to a variety of<br />
metadata operat<strong>in</strong>g, and they are significant m<strong>in</strong>imum<br />
driv<strong>in</strong>g force of model. Model task <strong>in</strong>put will be turned<br />
<strong>in</strong>to system <strong>in</strong>structions sequence f<strong>in</strong>ally.<br />
In the MCCAVM, the <strong>in</strong>terface language is source<br />
language and the system language is target language. The<br />
<strong>in</strong>terface language is developer-oriented, which presents a<br />
simple way and shields complex logic operat<strong>in</strong>g <strong>in</strong>volved<br />
with metadata <strong>in</strong> the model. The system language is the<br />
model executable language, which can complete <strong>in</strong>ternal<br />
behaviors with the core of metadata-driven.<br />
Figure 1. MCCAVM architecture<br />
C. Model Architecture<br />
Accord<strong>in</strong>g to the formal def<strong>in</strong>ition of the model, model<br />
architecture is shown <strong>in</strong> Fig.1. There are five parts:<br />
metadata entities, metadata management eng<strong>in</strong>e, bus<br />
architecture, the <strong>in</strong>put-output system and the client<br />
<strong>in</strong>terface. Referenc<strong>in</strong>g to the Von Neumann computer<br />
architecture, capability and service <strong>in</strong> MCCAVM are<br />
equivalent to the "peripheral" <strong>in</strong> computer hardware; the<br />
metadata entity is memory and driver of peripheral;<br />
Metadata management eng<strong>in</strong>es are belonged to the central<br />
controller unit. Capability and service are mounted to the<br />
correspond<strong>in</strong>g bus through the metadata entity drive and<br />
<strong>in</strong> form of peripheral, complet<strong>in</strong>g <strong>in</strong>teraction with<br />
metadata management eng<strong>in</strong>e. Capability and service are<br />
managed and controlled by metadata management eng<strong>in</strong>e.<br />
The central controller will eventually register service and<br />
capability to the user <strong>in</strong>terface and release <strong>in</strong> a<br />
standardized form of web service. The form will be<br />
transferred by client, implements transparent access to<br />
cloud resources through clients.<br />
1) Metadata entity<br />
The metadata entity is the core part of the model basis.<br />
It is generated by metadata generator when Capability or<br />
Service enters the MCCAVM. The metadata entity is<br />
divided <strong>in</strong>to two categories: descriptive metadata and<br />
adm<strong>in</strong>istrative metadata. Descriptive metadata <strong>in</strong>cludes<br />
resource description metadata, capability description<br />
metadata and service description metadata. Resource<br />
description metadata is a summary list of capability and<br />
service of the model, describ<strong>in</strong>g available resources of the<br />
entire model. Adm<strong>in</strong>istrative metadata <strong>in</strong>cludes the<br />
capability management metadata, the service<br />
management metadata and the control metadata.<br />
Metadata management eng<strong>in</strong>e controls the capability and<br />
service through the adm<strong>in</strong>istrative metadata.<br />
2) Metadata management eng<strong>in</strong>e<br />
Metadata management eng<strong>in</strong>e is <strong>in</strong>stitution of control<br />
and schedul<strong>in</strong>g of model, completes unified monitor<strong>in</strong>g,<br />
management and coord<strong>in</strong>ation work of capability and<br />
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service and other resources. Firstly, after capability (or<br />
service) enters the model metadata generator. Metadata<br />
generator requests metadata management eng<strong>in</strong>e to<br />
process by us<strong>in</strong>g <strong>in</strong>terruption. Then eng<strong>in</strong>e mounts the<br />
correspond<strong>in</strong>g resource on model bus by us<strong>in</strong>g metadata<br />
entity, completes the registration task of service and<br />
capability, <strong>in</strong>forms MCCAVM that the capability (or<br />
service) has been <strong>in</strong> a state of read<strong>in</strong>ess, then<br />
accomplishes work of further assembly and<br />
configuration of resource by deploy<strong>in</strong>g the capability (or<br />
service), coord<strong>in</strong>ates with other related equipments and<br />
components <strong>in</strong> order to make the resource executable;<br />
realizes the management and control of model resource<br />
through capability (or service) monitor<strong>in</strong>g. For any<br />
update of the capability(or service), metadata generator<br />
requests eng<strong>in</strong>e to process by us<strong>in</strong>g the <strong>in</strong>terrupt<br />
mechanism similarly. The simple mechanism makes the<br />
MCCAVM model have favorable agile characteristic and<br />
dynamic extension property.<br />
3) Bus architecture<br />
Important ligament and prom<strong>in</strong>ent feature of<br />
MCCAVM is bus architecture. In the structure of<br />
computer hardware, rational task division of data bus,<br />
address bus and control bus promotes module production<br />
which is suitable for computer components, boosts the<br />
popularity of computers. The bus architecture of<br />
MCCAVM is constituted by capability metadata bus,<br />
service metadata bus and control metadata bus.<br />
Capability metadata bus and service metadata bus f<strong>in</strong>ish<br />
the carry of service and capability. Control metadata bus<br />
transmits control signals, communicate capability<br />
management metadata and service management metadata<br />
at the same time, makes MCCAVM unified.<br />
4) Input and output <strong>in</strong>terface system of server side<br />
Server-side provides the capability and service for the<br />
system by us<strong>in</strong>g metadata, through the capability<br />
metadata generator and the metadata generator.<br />
Capability and service are provided to MCCAVM model<br />
<strong>in</strong> the form of peripheral through description and<br />
expansion of metadata. On the output side, further<br />
assembly and deployment of the model are provided to<br />
the client system <strong>in</strong> the unified form of web service.<br />
5) Client <strong>in</strong>terface<br />
Client gets k<strong>in</strong>ds of cloud applications from server side<br />
by us<strong>in</strong>g virtual desktop. Firstly, client virtual desktop<br />
gets service list from cloud side. User orders the apps<br />
which he/she likes subsequently. The load eng<strong>in</strong>e<br />
completes the transparent access to capability and service<br />
of cloud side at last.<br />
Ⅲ. SYSTEM DESIGN<br />
An open, dynamic scalable and data loosely coupled<br />
MCCAVS is designed based on MCCAVM <strong>in</strong> this<br />
section.<br />
A. System Architecture<br />
Based on the model design, MCCAVS architecture is<br />
shown <strong>in</strong> Fig.2. Correspond<strong>in</strong>g to the model, the whole<br />
system <strong>in</strong>cludes metadata entities, metadata management<br />
eng<strong>in</strong>e, and bus structure, the <strong>in</strong>put and output <strong>in</strong>terface<br />
system of server side and client <strong>in</strong>terface. Moreover,<br />
capability pool and service stores are implemented, used<br />
for stor<strong>in</strong>g capability and service.<br />
Figure 2. MCCAVS architecture<br />
B. Metadata Entity<br />
In MCCAVS, metadata entity components are series<br />
files of system capability and service for describ<strong>in</strong>g,<br />
controll<strong>in</strong>g and manag<strong>in</strong>g (.meta). As the extensible<br />
markup language (eXtensible Markup Language, XML)<br />
provides standard methods of metadata <strong>in</strong>formation<br />
exchange methods, we use XML-based metadata file<br />
format. Resource metadata files (resource.meta) record<br />
all available capability and service <strong>in</strong> system; Capability<br />
description metadata file(capability_description.meta)<br />
and capability manager meta data files<br />
(capability_manager.meta) record detail <strong>in</strong>formation of<br />
specific capability; Similarly, service description<br />
metadata file (service_description.meta) and service<br />
manag<strong>in</strong>g data files (service_manager.meta) record detail<br />
<strong>in</strong>formation of specific service; Control metadata files<br />
record permissions related to capability and service,<br />
<strong>in</strong>formation of roles and life-cycle state control and so on.<br />
The resource metadata file (resource.meta) is given as<br />
followed for example:<br />
<br />
<br />
<br />
***<br />
***<br />
***<br />
<br />
......<br />
<br />
<br />
<br />
***<br />
***<br />
***<br />
<br />
......<br />
<br />
<br />
From above we can conclude that resource metadata<br />
file <strong>in</strong>cludes all the current capability and service list.<br />
Each capability or service has a system unique id<br />
identifier, which is assigned by the system when this<br />
capability or service enters the system and registers to the<br />
metadata eng<strong>in</strong>e. Based on Von Neumann architecture,<br />
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we regard capability and service as “peripheral”, thus<br />
capability or service id is these “peripherals” address.<br />
Metadata management eng<strong>in</strong>e, which is the CPU of<br />
MCCAVS, can locate any capability or service accord<strong>in</strong>g<br />
to the "peripheral” id through meta-data bus. Individual<br />
capability or service metadata description file and path to<br />
the file metadata management are stored <strong>in</strong> the tag<br />
meta_location. We take capability described metadata file<br />
as an example to expound the entity format of <strong>in</strong>dividual<br />
capability metadata <strong>in</strong> the follow<strong>in</strong>g<br />
<br />
<br />
***<br />
***<br />
***<br />
***<br />
***<br />
***<br />
***<br />
**<br />
......<br />
<br />
<br />
Besides conta<strong>in</strong><strong>in</strong>g the capability id and other basic<br />
<strong>in</strong>formation, capability description metadata file also<br />
conta<strong>in</strong>s version tag used for controll<strong>in</strong>g capability<br />
version <strong>in</strong>formation, location tag <strong>in</strong>dicates the real<br />
location of the capability products <strong>in</strong> the capability pool,<br />
loadclass tag <strong>in</strong>dicates the entrance classes of the<br />
capability part; dependentCapability tag <strong>in</strong>dicates<br />
dependency relationship with other capability<br />
components.<br />
Figure 3. Interface language UML static structure<br />
C. Metadata Management Eng<strong>in</strong>e<br />
Metadata management eng<strong>in</strong>e, which takes responsible<br />
for pars<strong>in</strong>g the <strong>in</strong>terface command and translates it <strong>in</strong>to<br />
system commands, is the "central processor" and the core<br />
component of the system. We def<strong>in</strong>e a set of <strong>in</strong>terface<br />
commands based on object-oriented language JAVA to<br />
facilitate developers. As shown <strong>in</strong> fig.3, <strong>in</strong>terface<br />
language is divided <strong>in</strong>to three categories: the system <strong>in</strong>put<br />
and output (IOSystem), the schedul<strong>in</strong>g <strong>in</strong>terface<br />
(Schedule), and the web service <strong>in</strong>terface(WS). Interface<br />
command is the abstraction method provided by these<br />
<strong>in</strong>terfaces and the command parameter is the method<br />
parameter. Table 1 shows a typical <strong>in</strong>terface and the<br />
<strong>in</strong>terface commands.<br />
D. Bus Structure<br />
Accord<strong>in</strong>g to the design of the bus structure <strong>in</strong> the<br />
model, three types of buses <strong>in</strong> the MCCVAS system are<br />
def<strong>in</strong>ed: capability bus, service bus and control bus. For<br />
the purpose of quick address<strong>in</strong>g and ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g<br />
resources of storage efficiently, HashMap, which can<br />
complete key-value mapp<strong>in</strong>g and time complexity is O(1),<br />
is used to organize system capability and service.<br />
Capability or service id is the key and capability or<br />
service object <strong>in</strong>stance is the value. Three bus<br />
declarations are followed:<br />
protected class ControlBus extends HashMap<br />
implements Bus<br />
protected class CapabilityBus extends HashMap <br />
implements Bus<br />
protected class ServiceBus extends HashMap implements<br />
Bus<br />
Interface<br />
IOSystem<br />
Schedule<br />
WS<br />
TABLE I.<br />
TYPICAL INTERFACE AND INTERFACE COMMAND<br />
Interface<br />
commands<br />
jo<strong>in</strong>()<br />
exit()<br />
log<strong>in</strong>()<br />
load()<br />
start()<br />
update()<br />
Parameter<br />
Component: the<br />
Parent <strong>in</strong>terface<br />
of Capability and<br />
Service<br />
ditto<br />
ditto<br />
ditto<br />
ditto<br />
ditto<br />
Function Declaration<br />
To Generate metadata entity<br />
when Capability or Service<br />
enters.<br />
To make Capability or<br />
Service exits the system.<br />
To allocate component ID<br />
when register to the system<br />
Capability or Service.<br />
To load Capability or Service<br />
on the system, which requests<br />
metadata management eng<strong>in</strong>e<br />
mounted components to the<br />
correspond<strong>in</strong>g meta- data bus<br />
through <strong>in</strong>terrupt mode.<br />
To start-up Capability or<br />
Service.<br />
To update Capability or<br />
Service.<br />
stop() ditto To stop Capability or Service.<br />
logout() ditto<br />
To log out Capability or<br />
Service, log out components,<br />
exit the bus system.<br />
To generate service.xml and<br />
convert() ditto wsdl.xml for Capability or<br />
Service.<br />
publish() ditto<br />
To publish Capability or<br />
Service as a web service.<br />
E. Input and Output Interface <strong>in</strong> Server Side<br />
Server-side <strong>in</strong>put <strong>in</strong>terface <strong>in</strong>cludes capability<br />
metadata generator and service metadata generator. It<br />
shields metadata manipulation for outside of the system<br />
and generates metadata entity as described <strong>in</strong> Section 3.2.<br />
Output <strong>in</strong>terface releases system capability and service to<br />
meet the <strong>in</strong>vok<strong>in</strong>g of term<strong>in</strong>als by us<strong>in</strong>g standardization<br />
web service <strong>in</strong>terface. As shown <strong>in</strong> fig.2, we use AXIS2<br />
as release eng<strong>in</strong>e.<br />
F. Client Access<br />
As the server-side uses web service technology to<br />
provide resources, the system supports transparent access<br />
heterogeneous multi-platform capability and service of<br />
cloud side. Client <strong>in</strong>terface work steps are as follows:<br />
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a. Regard<strong>in</strong>g all cloud resources (Capability and<br />
service) <strong>in</strong> cloud side as the services, and gett<strong>in</strong>g the list<br />
of services through pars<strong>in</strong>g eng<strong>in</strong>e.<br />
b. Users order correspond<strong>in</strong>g services when enter the<br />
list of services.<br />
c. User order<strong>in</strong>g events will trigger service pars<strong>in</strong>g<br />
eng<strong>in</strong>e and get metadata file of their subscription services.<br />
d. Service load eng<strong>in</strong>e loads the service of client<br />
components accord<strong>in</strong>g to service metadata file, achiev<strong>in</strong>g<br />
transparent access<strong>in</strong>g to virtual resources of the cloud.<br />
G. Capability Pool and Service Store<br />
Capability pool and service stores are components<br />
which storage system peripherals (Capability and service).<br />
System bus manages peripheral by us<strong>in</strong>g HashMap.<br />
Capability or service id is the key and capability or<br />
service object <strong>in</strong>stance is the value. Correspond<strong>in</strong>gly, the<br />
capability pool and service store are stockpiles of the<br />
value. So, here we use two <strong>in</strong>stances of simple data<br />
structures (class Set) to implement the two components<br />
separately.<br />
network and us<strong>in</strong>g Google nexus s, Samsung and HTC<br />
etc. as test term<strong>in</strong>ation.<br />
The MCCAVS <strong>in</strong>cludes three subsystems,<br />
correspond<strong>in</strong>g three user roles: 1) Virtual desktop<br />
subsystem, which is client software, correspond<strong>in</strong>g to end<br />
user. As shown <strong>in</strong> fig.5, end user can enjoy cloud storage,<br />
browse cloud app list and virtual <strong>in</strong>stall apps which<br />
he/she likes. 2) Developer subsystem, which is a platform<br />
<strong>in</strong> the cloud side for the developers. As shown <strong>in</strong> fig.6,<br />
developers can upload, submit for review, and release<br />
apps. 3) Adm<strong>in</strong>istrator subsystem, which is a platform <strong>in</strong><br />
the cloud side for adm<strong>in</strong>istrator. As shown <strong>in</strong> fig.7,<br />
adm<strong>in</strong>istrator can use it for check<strong>in</strong>g, configur<strong>in</strong>g,<br />
monitor<strong>in</strong>g and deploy<strong>in</strong>g everyth<strong>in</strong>g <strong>in</strong> the cloud system.<br />
a) home page b) cloud storage view c) cloud apps view<br />
Figure 4. Snapshot of experimental environment<br />
d) home page after <strong>in</strong>stall<strong>in</strong>g cloud apps e) configure cloud server<br />
Figure 5. Virtual desktop subsystem<br />
IV. SYSTEM IMPLEMENTATION AND VERIFICATION<br />
A. System Implementation<br />
The experimental environment of the system is as<br />
follows: The cloud cluster is made up of 14 PCs <strong>in</strong> which<br />
master node uses memory bank of 4G, Intel(r) core(tm)2<br />
duo 2.93GHz, hard disk of 500G and 13 slave nodes are<br />
of the same configuration of Pentium(r) dual-core<br />
3.20GHz,use memory bank of 2G,hard disk of 250G.<br />
MCCVS prototype system hosted by the master node, as<br />
shown <strong>in</strong> fig.4. The IaaS layer resources and the<br />
environment are made up of 13 slave nodes, which have<br />
<strong>in</strong>stalled Hadoop0.20, choose one as NameNode from the<br />
13 slave nodes. In MCCAVS, as IaaA basic resources<br />
made up of 13 slave nodes are regarded as a common<br />
"capability" enter system and MCCAVS manages IaaS<br />
resources through NameNode, IaaS layer can expand<br />
arbitrary amount of nodes at any time accord<strong>in</strong>g to<br />
demand while there is not effect on MCCAVS. The <strong>in</strong>ner<br />
bandwidth of the cluster is 100Mbit/s, outlet bandwidth<br />
of the server is 10Mbit/s; The operat<strong>in</strong>g system is<br />
ubuntu11.04, the version of Java virtual mach<strong>in</strong>e is Java<br />
SE6; The Web conta<strong>in</strong>er is Tomcat 5.5.17; Client test<br />
platform is Android2.2, work<strong>in</strong>g <strong>in</strong> Ch<strong>in</strong>a Mobile EDGE<br />
a) home page for developer b) app upload view<br />
c) app check<strong>in</strong>g result view d) cloud app list view<br />
Figure 6. Developer subsystem<br />
a) log<strong>in</strong> page for adm<strong>in</strong>istrator b) home page<br />
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c) app monitor view d) app check view<br />
Figure 7. Adm<strong>in</strong>istrator subsystem<br />
B. System Verification<br />
Due to lack of space, we elaborate formal description<br />
and experimental analysis based on Tur<strong>in</strong>g mach<strong>in</strong>e by<br />
us<strong>in</strong>g an example of virtual cloud storage services <strong>in</strong> this<br />
section.<br />
1) Service Description<br />
Virtual cloud storage is a dest<strong>in</strong>ation service system,<br />
which makes numerous different k<strong>in</strong>ds of storage<br />
equipments <strong>in</strong> network co-operate and provides data<br />
storage and service access function jo<strong>in</strong>tly. To the<br />
movable term<strong>in</strong>ation which is resource-constra<strong>in</strong>ed<br />
system, virtual cloud storage can extend the storage<br />
capability of mobile term<strong>in</strong>als. In MCCAVS, virtual<br />
cloud storage implementation <strong>in</strong>volves four steps: First,<br />
the system IaaS layer underly<strong>in</strong>g storage resource<br />
(Hadoop HDFS) enters the system as a capability, as<br />
shown <strong>in</strong> fig.2; Then development storage services log-<strong>in</strong><br />
the system; Moreover, system transfers store service to<br />
standard web service and releases it; F<strong>in</strong>ally, the term<strong>in</strong>al<br />
device f<strong>in</strong>ds and loads the service, to provide users with a<br />
virtual storage service. Us<strong>in</strong>g the system <strong>in</strong>terface<br />
<strong>in</strong>struction def<strong>in</strong>ed <strong>in</strong> the 3.3 section, the service specific<br />
implementation steps are as follows:<br />
a. In IaaS layer, HDFS file system as a capability to<br />
enter the system and <strong>in</strong>vokes <strong>in</strong>terface IOSystem jo<strong>in</strong>()<br />
method.<br />
b. Based on HDFS, we develop cloud storage control<br />
components as service, <strong>in</strong>vok<strong>in</strong>g jo<strong>in</strong>() method of<br />
IOSystem.<br />
c. Storage capability registers to the system, <strong>in</strong>vokes<br />
log<strong>in</strong>() method of Schedule <strong>in</strong>terface.<br />
d. Storage service registers to the system, <strong>in</strong>vokes<br />
log<strong>in</strong>() method of Schedule <strong>in</strong>terface<br />
e. Invoke load() method of <strong>in</strong>terface Schedule, load the<br />
storage capability.<br />
f. Invoke load() method of <strong>in</strong>terface Schedule, load the<br />
storage service.<br />
g. Invoke start() method of <strong>in</strong>terface Schedule to start<br />
the storage capability.<br />
h. Invoke start() method of <strong>in</strong>terface Schedule to start<br />
the storage service.<br />
i. Invoke convert() method of <strong>in</strong>terface Schedule; make<br />
Storage service as standard web service.<br />
j. Invoke publish() method of <strong>in</strong>terface Schedule,<br />
release storage web service.<br />
In this section, the order of step a, b is fixed. Step c, e<br />
and d, f is the registration and load<strong>in</strong>g of the capability<br />
and service, order cannot be changed. The order of<br />
process g, h, i, j is also fixed.<br />
2) Formal Verification<br />
Accord<strong>in</strong>g to the description of the services, virtual<br />
cloud storage model of the Tur<strong>in</strong>g mach<strong>in</strong>e can decode<br />
the symbol str<strong>in</strong>g S=(a b N g h i j), <strong>in</strong> which N stands for<br />
symbol str<strong>in</strong>g sequence comb<strong>in</strong>ation of the fixed<br />
alphabetical order c, e and d, f. S is the symbol sequence<br />
after the comb<strong>in</strong>ation of these symbols. Symbols come<br />
from a f<strong>in</strong>ite alphabet Σ and all the sequences of symbols<br />
constitute a language L. Therefore, the problem is<br />
transformed to a Tur<strong>in</strong>g mach<strong>in</strong>e T which can identify the<br />
language L. The Tur<strong>in</strong>g mach<strong>in</strong>e formal description is<br />
given <strong>in</strong> the follow<strong>in</strong>g:<br />
T = (Q,Σ,Γ,δ,q 0 ,q a ,q r )<br />
Q = {q 1 ,q 2 ,…,q 8 ,q a ,q r }<br />
Σ= {a, b, c, d, e, f, g, h, i, j}<br />
Γ= {a, b, c, d, e, f, g, h, i, j, B}<br />
δ:Q×Γ→Q×Γ×{L,R} is the transfer function.<br />
q 0 ∈ Q is the <strong>in</strong>itial state;<br />
q a ∈ Q is the accept<strong>in</strong>g state;<br />
q r ∈ Q is the reject state and q r ≠q a ;<br />
The <strong>in</strong>itial state of Tur<strong>in</strong>g mach<strong>in</strong>e is q 0 , write symbol<br />
sequence S= (a b N g h i j), which needed to be read, on<br />
the work tape. Read-write head is scanned from left to<br />
right, Each read<strong>in</strong>g of a symbol will trigger a process of<br />
metadata management eng<strong>in</strong>e, transferr<strong>in</strong>g to a new state.<br />
That is, transferr<strong>in</strong>g from q 0 to q 1 is a→b, R, its state<br />
transition function is δ(q 0 , a ) = (q 1 , b, R). The service<br />
production of the state transition is shown <strong>in</strong> fig.8.<br />
Figure 8. State diagram of virtual storage<br />
3) Experimental Analysis<br />
For virtual storage, cloud capability is much larger<br />
than the term<strong>in</strong>al capability, so, time performance <strong>in</strong>dex<br />
of the system is more important than the storage capacity<br />
<strong>in</strong>dex. Fig.9 describes the relationships between capacity<br />
and response time when term<strong>in</strong>al equipment access cloud<br />
storage service. Three experimental data <strong>in</strong> the same test<br />
are showed. In every test, besides test<strong>in</strong>g mach<strong>in</strong>e, 15<br />
clients are simulated to test system concurrent effect. We<br />
can see, response time is ma<strong>in</strong>ly determ<strong>in</strong>ed by the<br />
term<strong>in</strong>al connection bandwidth, system process<strong>in</strong>g time<br />
can meet user requirement. On the other hand,<br />
virtualization technology will be the ma<strong>in</strong> comput<strong>in</strong>g<br />
tasks hosted by the cloud.<br />
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time(ms)<br />
300000<br />
250000<br />
200000<br />
150000<br />
100000<br />
50000<br />
upload to cloud<br />
download from cloud<br />
0<br />
0 500 1000 1500 2000 2500 3000 3500<br />
file size(KB)<br />
Figure 9. Relationship between cloud storage capacity and response<br />
time<br />
amount of code(l<strong>in</strong>e)<br />
24000<br />
22000<br />
20000<br />
18000<br />
16000<br />
14000<br />
12000<br />
10000<br />
8000<br />
6000<br />
4000<br />
2000<br />
0<br />
amount of code <strong>in</strong> client<br />
amount of code <strong>in</strong> cloud side<br />
1 2 3 4 5<br />
service ID<br />
Figure 10. Compare amount of code between cloud and client<br />
Fig.10 compares code quantity of 5 services released <strong>in</strong><br />
Section 4.1 (by serial number, they are <strong>in</strong>stant<br />
messag<strong>in</strong>g[16], cloud storage, campus assistant, onl<strong>in</strong>e<br />
words, mobile TV) <strong>in</strong> the clouds and the term<strong>in</strong>al to<br />
compare the amount of computations roughly. As the<br />
figure shows, numerous comput<strong>in</strong>g tasks focus on the<br />
cloud by virtualization, even respective code quantity of<br />
service term<strong>in</strong>al is relatively more; it is also be<br />
concentrated <strong>in</strong> user <strong>in</strong>terface to be processed with. In<br />
addition, fig.10 shows that when service scale is small,<br />
for improv<strong>in</strong>g user experience, the calculation of client<br />
may closer to the cloud. However, more large-scale<br />
applications are more suitable for deployment <strong>in</strong> cloud<br />
comput<strong>in</strong>g virtualization platform.<br />
C. Compare with Related Work<br />
In virtualization architecture, typical system is<br />
designed by Ch<strong>in</strong>ese <strong>Academy</strong> of Sciences, named<br />
Virtual Management Architecture (VMA)[4]. The model<br />
aims to establish a unified resource management<br />
<strong>in</strong>frastructure for enterprises to realize the unified<br />
management of resources, resource systems and ondemand<br />
service of resource. The VMA focuses on<br />
management and use of underly<strong>in</strong>g hardware facilities.<br />
This is completely different <strong>in</strong> form and nature with<br />
MCCAVM <strong>in</strong> this paper.<br />
VMA is a resource management framework model,<br />
based on virtualization technology and equipped with the<br />
technique of <strong>in</strong>dependent schedul<strong>in</strong>g, which unified the<br />
management and use of <strong>in</strong>terface. VMA is made up of a<br />
number of resource management systems; each <strong>in</strong>dividual<br />
resource management system provides a k<strong>in</strong>d of virtual<br />
resource services. VMA provides reasonable and uniform<br />
resource management <strong>in</strong>frastructure of the system by<br />
unify<strong>in</strong>g these virtual resources management functions to<br />
a unified and consistent management platform.<br />
MCCAVM is a Cloud comput<strong>in</strong>g, virtualization model<br />
based on Metadata-driven. Accord<strong>in</strong>g to the formal<br />
def<strong>in</strong>ition of the model, it <strong>in</strong>cludes metadata entities,<br />
metadata management eng<strong>in</strong>e, the bus architecture, <strong>in</strong>putoutput<br />
system and customer term<strong>in</strong>ation. From the<br />
perspective of model development and control, besides<br />
end users, the model role is divided <strong>in</strong>to two major<br />
categories of developers and system operators. Among<br />
them, the development is divided <strong>in</strong>to capability<br />
developers and service developers. Developers use the<br />
<strong>in</strong>terface language to develop capability or service, the<br />
system operator uses the system language to complete the<br />
model management control task, Table 2 shows the<br />
comparison between the two roles.<br />
TABLE II.<br />
COMPARE MCCAVM WITH VMA<br />
MCCAVM<br />
VMA<br />
Model role<br />
Developers, system<br />
operators<br />
Resource users<br />
realization mode Metadata-Driven SOA<br />
Virtual level<br />
Hardware resources ,<br />
software services<br />
Hardware source<br />
objective<br />
Dynamic scalability for<br />
Unified management<br />
capability and service,<br />
of basic resources ,<br />
platform versatility and<br />
on-demand use<br />
capability to control<br />
Hierarchy<br />
Five parts: Metadata<br />
entities ,metadata<br />
management eng<strong>in</strong>e, bus<br />
architecture, <strong>in</strong>put, output<br />
systems and customer-side<br />
<strong>in</strong>terface<br />
Consists of one or<br />
more virtual resources<br />
management services<br />
(VMS) and a system<br />
of registration and<br />
<strong>in</strong>quiry services<br />
( SRCS )<br />
From the table above we can conclude that VMA<br />
focuses on the basic <strong>in</strong>tegration of resources and rational<br />
management. It is equivalent to an <strong>in</strong>tegration of<br />
resources and schedul<strong>in</strong>g platform, which can achieve the<br />
efficient use and reasonable allocation of resources.<br />
MCCAVM achieves a reasonable distribution of<br />
resources, and forms a broader perspective to understand<br />
the connotation and extension of the capability and<br />
service. Through fig.2, we can f<strong>in</strong>d that the capability<br />
<strong>in</strong>cludes not only just basic resources <strong>in</strong> IaaS layer of<br />
cloud comput<strong>in</strong>g, but all the basic hardware and software<br />
<strong>in</strong> MCCAVS. At the same time, all the production based<br />
on the capability or reproduced through the comb<strong>in</strong>ation<br />
of capability are all service, which reflects the idea<br />
EaaS(Everyth<strong>in</strong>g as a Service). And the model realizes<br />
the dynamic expansion of service and capability and hotswappable,<br />
which further enhances the versatility and<br />
scalability of the model.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1579<br />
V. CONCLUSION<br />
This paper proposes a metadata-driven cloud<br />
comput<strong>in</strong>g virtualization model MCCAVM, based on the<br />
discussion and analysis of real needs which exists <strong>in</strong><br />
cloud comput<strong>in</strong>g virtualization technology currently. The<br />
correspond<strong>in</strong>g system MCCAVS is implemented also.<br />
We formally def<strong>in</strong>e and verify the model based on data<br />
experiments. Compared with previous work, this model<br />
has good reference value which ma<strong>in</strong>ly reflected <strong>in</strong>: 1)<br />
Architecture which proposed by the model based on the<br />
Tur<strong>in</strong>g mach<strong>in</strong>e model and the Von Neumann computer<br />
is clear and simple. Simultaneously, it implements<br />
orig<strong>in</strong>al <strong>in</strong>tention of design efficiently. 2) The concept of<br />
cloud comput<strong>in</strong>g platform capability and service with a<br />
broader perspective is proposed. The full life cycle<br />
management of capability and service is implemented.<br />
The model regards capability and service as "peripheral",<br />
mak<strong>in</strong>g the model has a good dynamic scalability. 3) The<br />
form of a metadata-driven not only make the model has<br />
management-control ability, a simple mechanism and<br />
versatility, but also transform the traditional strong<br />
function coupl<strong>in</strong>g relationship to loosely data coupled<br />
relationship of the various components <strong>in</strong> the model,<br />
which plays an important role <strong>in</strong> the decoupl<strong>in</strong>g.<br />
ACKNOWLEDGMENT<br />
This research is supported by import National Science<br />
and Technology Specific Project under grants of<br />
2011ZX03002-004-03, Science & Technology Research<br />
Program of the Chongq<strong>in</strong>g Municipal Education<br />
Committee under grants of KJ110529, Special<br />
Foundation of Cloud Comput<strong>in</strong>g of Chongq<strong>in</strong>g<br />
University of Posts and Telecommunications A2010-13,<br />
Educational Reform Projects of Chongq<strong>in</strong>g University of<br />
Posts and Telecommunications XJG1216.<br />
REFERENCES<br />
[1] Gartner.com. Gartner Say's Cloud Comput<strong>in</strong>g Will Be As<br />
Influential As E-bus<strong>in</strong>ess. http://www.gartner.com/it/page.jspid=707508.<br />
Aug 2010.<br />
[2] Eric K, Galen G. What cloud comput<strong>in</strong>g really means.<br />
http://www.<strong>in</strong>foworld.com/d/cloud-comput<strong>in</strong>g/what-cloudcomput<strong>in</strong>g-really-means-031.<br />
InfoWorld. June 2008.<br />
[3] WikiMedia. Cloud Comput<strong>in</strong>g. http://en.wikipedia.org/<br />
wiki/Cloud_comput<strong>in</strong>g. last modified, June 2011.<br />
[4] WANG M<strong>in</strong>, LI J<strong>in</strong>g, FAN Zhong-Lei, XU Lu. A Service<br />
Model for Virtual Resource Management and Its<br />
Implementation. Ch<strong>in</strong>ese Journal of Computers, 2005,<br />
28(5): 856-863.<br />
[5] Kessler M, Reifert A, Lamp D, Voith T. A Service-<br />
Oriented Infrastructure for Provid<strong>in</strong>g Virtualized Networks.<br />
Bell Labs Technical Journal, 2008, 13(3): 111-127.<br />
[6] Bhattacharya K, K<strong>in</strong>g DJ. Interview with Douglas J. K<strong>in</strong>g<br />
on "The Impact of Virtualization and Cloud Comput<strong>in</strong>g on<br />
IT Service Management". Bus<strong>in</strong>ess & Information Systems<br />
Eng<strong>in</strong>eer<strong>in</strong>g, 2011, 3(1): 49-51.<br />
[7] TIAN Guan-Hua, MENG Dan, ZHAN Jian-Feng. Reliable<br />
Resource Provision Policy for Cloud Comput<strong>in</strong>g. Ch<strong>in</strong>ese<br />
Journal of Computers, 2010, 33(10): 1859-1872.<br />
[8] Flouris MD, Lachaize R, Chasapis K, Bilas A. Extensible<br />
block-level storage virtualization <strong>in</strong> cluster-based systems.<br />
Journal of Parallel and Distributed Comput<strong>in</strong>g, 2010, 70(8):<br />
800-824.<br />
[9] HUAI J<strong>in</strong>-Peng, LI Q<strong>in</strong>, HU Chun-M<strong>in</strong>g. Research and<br />
design on hypervisor based virtual comput<strong>in</strong>g environment.<br />
Journal of Software, 2007, 18(8): 2016-2026.<br />
[10] Baroncelli F, Mart<strong>in</strong>i B, Castoldi P. Network virtualization<br />
for cloud comput<strong>in</strong>g. Annals of Telecommunicationsannals<br />
Des Telecommunications, 2010, 65(11-12): 713-<br />
721.<br />
[11] Xiong J, Hu YM, Li GJ, Tang RF, Fan ZH. Metadata<br />
Distribution and Consistency Techniques for Large-Scale<br />
Cluster File Systems. IEEE Transactions on Parallel and<br />
Distributed Systems, 2011, 22(5): 803-816.<br />
[12] Govedarica M, Boskovic D, Petrovacki D, N<strong>in</strong>kov T,<br />
Ristic A. Metadata Catalogues <strong>in</strong> Spatial Information<br />
Systems. Geodetski List, 2010, 64(4): 313-334.<br />
[13] Tur<strong>in</strong>g A M. On computable numbers, with an application<br />
to the Entscheidungsproblem. Proceed<strong>in</strong>gs of the London<br />
Mathematical Society, 1936, 42(2): 230-265.<br />
[14] Neumann J. First Draft of a Report on the EDVAC.<br />
repr<strong>in</strong>ted <strong>in</strong> full <strong>in</strong> Stern, N. From ENIAC to UNIVAC: An<br />
Appraisal of the Eckert-Mauchly Computers Bedford,<br />
Mass.: Digital Press , 1981: 181-246.<br />
[15] ZHANG Tian-N<strong>in</strong>g, YUN Xiao-Chun, ZHANG Yong-<br />
Zheng, MEN Chao-Guang, SUN Jian-Liang. A Model of<br />
Network Device Coord<strong>in</strong>ative Run. Journal of Software,<br />
2011, 34(2): 216-228.<br />
[16] Yunpeng Xiao, Yanb<strong>in</strong> Liu, Shasha Yang, Guangxia Xu.<br />
Design and implement of OMS IM system based on cloud<br />
comput<strong>in</strong>g. Journal of Chongq<strong>in</strong>g University of Posts and<br />
Telecommunications(Natural Science Edition), 2010, (4):<br />
468-472.<br />
Yunpeng Xiao, born <strong>in</strong> 1979, Ph.D. candidate. His research<br />
<strong>in</strong>terests <strong>in</strong>clude cloud comput<strong>in</strong>g, data m<strong>in</strong><strong>in</strong>g and complex<br />
network.<br />
Guangxia Xu, born <strong>in</strong> 1974, Ph.D., Associate professor. Her<br />
research <strong>in</strong>terests <strong>in</strong>clude cloud comput<strong>in</strong>g and data m<strong>in</strong><strong>in</strong>g.<br />
Yanb<strong>in</strong>g Liu, born <strong>in</strong> 1971, Ph.D., professor, Ph.D. supervisor.<br />
His research <strong>in</strong>terests <strong>in</strong>clude network management and control,<br />
strategy and security.<br />
Bai Wang, born <strong>in</strong> 1962, Ph.D., professor, Ph.D. supervisor.<br />
Her research <strong>in</strong>terests <strong>in</strong>clude distributed comput<strong>in</strong>g and data<br />
m<strong>in</strong><strong>in</strong>g.<br />
© 2013 ACADEMY PUBLISHER
1580 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Robust Portfolio Optimization with Options<br />
under VE Constra<strong>in</strong>t us<strong>in</strong>g Monte Carlo<br />
X<strong>in</strong>g Yu<br />
Department of Mathematics & Applied Mathematics Humanities & Science and Technology Institute<br />
of Hunan Loudi, 417000, P.R. Ch<strong>in</strong>a<br />
Email:hnyux<strong>in</strong>g@163.com<br />
Abstract—this paper proposes a robust portfolio<br />
optimization programm<strong>in</strong>g model with options. Under<br />
constra<strong>in</strong>s of variance efficiency and shortfall preference<br />
structure, we derive optioned portfolios with the maximum<br />
expected return of robust counterpart. A numerical example<br />
us<strong>in</strong>g Monte Carlo illustrates some of the features and<br />
applications of this model.<br />
Index Terms—Robust portfolio optimization; VE constra<strong>in</strong>t;<br />
Monte Carlo<br />
I. INTRODUCTION<br />
The ma<strong>in</strong> problem an <strong>in</strong>vestor faces is to make an<br />
optimal portfolio. The classical portfolio model is<br />
generally only associated with stocks. The derivative<br />
<strong>in</strong>struments are no more considered as the hedg<strong>in</strong>g<br />
<strong>in</strong>struments, but now they are considered as the<br />
<strong>in</strong>vestment <strong>in</strong>strument. For example, options are the<br />
derivative <strong>in</strong>struments which can <strong>in</strong>crease the liquidity<br />
and flexibility of return from the <strong>in</strong>vestment. And at the<br />
same time, they also can be regarded as an asset to be<br />
<strong>in</strong>vested.<br />
Numerous studies have <strong>in</strong>vestigated the <strong>in</strong>tegration of<br />
options <strong>in</strong> portfolio optimization models. Alexander,<br />
Coleman and Li (2006) [1] analyzed the derivative<br />
portfolio hedg<strong>in</strong>g problems based on value at risk (VaR)<br />
and conditional value at risk (CVaR). Papahristodoulou[2]<br />
proposed optioned portfolio model, and based on Black-<br />
Scholes(B-S)formula, they derived the values of all<br />
the Greek letters of the portfolio ΔΓΘto , , hedge risk.<br />
Their objective was to maximize the difference between<br />
the theoretical value and the market value of a portfolio<br />
with options. And they transformed the problem to a<br />
l<strong>in</strong>ear programm<strong>in</strong>g model. Their model is simpler, but it<br />
is tractable. Horasanli[3] extended the model proposed by<br />
Papahristodoulou to a multi-asset sett<strong>in</strong>g to deal with a<br />
portfolio of options and underly<strong>in</strong>g assets. Gao[4] also<br />
extended the exist<strong>in</strong>g literature on options strategies.<br />
With the model and the method they mentioned, the<br />
<strong>in</strong>vestors can take the options strategies <strong>in</strong> terms of one’s<br />
subjective personality, and meanwhile, adjust the risks to<br />
suit the needs of the market change. Gerhard<br />
Scheuenstuhl, Rudi Zagst[5] exam<strong>in</strong>ed the problem of<br />
manag<strong>in</strong>g portfolios consist<strong>in</strong>g of both, stocks and<br />
options, However , the target function of their models<br />
associated with the stochastic properties of the portfolio<br />
return,which is <strong>in</strong>tractable. Because we have to deal<br />
with the stochastic dynamics price model of the expected<br />
f<strong>in</strong>al portfolio value.<br />
The mentioned above are related to the problem of<br />
parameter estimation. However, the framework requires<br />
the knowledge of some <strong>in</strong>puts, such both mean and<br />
covariance matrix of the asset returns, which practically<br />
are unknown and need to be estimated. The standard<br />
approach, ignor<strong>in</strong>g estimation error, simply treats the<br />
estimates as the true parameters and plugs them <strong>in</strong>to the<br />
optimal portfolio optimization model. But most<br />
frequently the uncerta<strong>in</strong> parameters play a central role <strong>in</strong><br />
the analysis of the decision mak<strong>in</strong>g process. So the<br />
peculiarity of these parameters cannot be ignored without<br />
the risk of <strong>in</strong>validat<strong>in</strong>g the possible implications of the<br />
analysis Wets [6].<br />
Dur<strong>in</strong>g the last two decades, the idea of robust<br />
optimization has become an <strong>in</strong>terest<strong>in</strong>g area of research.<br />
Soyster [7] is the first who <strong>in</strong>troduced the idea of robust<br />
optimization, but his idea turns to be very pessimistic<br />
which makes it unfavorable among practitioners. Ben-Tal<br />
and Nemirovski [8] developed new robust methodology<br />
where the optimal solution is more optimistic. Their idea<br />
uses <strong>in</strong>terior po<strong>in</strong>t based algorithm to f<strong>in</strong>d the robust<br />
solution on a counterpart of the <strong>in</strong>itial model. They also<br />
apply their robust method on some portfolio optimization<br />
problems and show that the f<strong>in</strong>al optimal solution<br />
rema<strong>in</strong>s feasible aga<strong>in</strong>st the uncerta<strong>in</strong>ty on different <strong>in</strong>put<br />
parameters. Steve Zymler proposed a novel robust<br />
optimization model for design<strong>in</strong>g portfolios that <strong>in</strong>clude<br />
European-style options. This model trades off weak and<br />
strong guarantees on the worst-case portfolio return. The<br />
weak guarantee applies as long as the asset returns are<br />
realized with<strong>in</strong> the prescribed uncerta<strong>in</strong>ty set, while the<br />
strong guarantee applies for all possible asset returns.<br />
Nemirovski[9] proposed robust portfolio selection under<br />
ellipsoidal uncerta<strong>in</strong>ty. There is rare literature about<br />
robust portfolio optimization with options as far as we<br />
know. Steve Zymler[10] proposed a novel robust<br />
optimization model for design<strong>in</strong>g portfolios that <strong>in</strong>clude<br />
European-style options, extend<strong>in</strong>g robust portfolio<br />
optimization to accommodate options. But they only paid<br />
attention to portfolio return and ignored risk. Ai-fan<br />
L<strong>in</strong>g.etc [11] proposed robust portfolio selection models<br />
under so-called ‘‘marg<strong>in</strong>al + jo<strong>in</strong>t’’ ellipsoidal<br />
uncerta<strong>in</strong>ty set and to test the performance of the<br />
© 2013 ACADEMY PUBLISHER<br />
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JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1581<br />
proposed models. In their paper one more robust portfolio<br />
selection model with option protection is proposed by<br />
comb<strong>in</strong><strong>in</strong>g options <strong>in</strong>to the robust portfolio selection<br />
model. This paper considers the optioned robust portfolio<br />
return.<br />
The rest of the paper is organized as follows. In<br />
section 2 we review robust portfolio optimization. In<br />
Section 3 we show how a portfolio that conta<strong>in</strong>s options<br />
can be modeled <strong>in</strong> a robust optimization framework.<br />
Section 4 gives an example based on Monte Carlo<br />
simulation to illustrate the application of the model and<br />
the method. Conclusions are also drawn.<br />
II. ROBUST PORTFOLIO OPTIMIZATION<br />
We consider the portfolio <strong>in</strong>cludes several European<br />
call options and put options on different stocks. This<br />
portfolio makes extensive use of options to achieve the<br />
desired payoff profile. As we all know, the return of<br />
options depends on the return of the correspond<strong>in</strong>g<br />
underly<strong>in</strong>g stocks. And the <strong>in</strong>puts such as mean or<br />
variance are uncerta<strong>in</strong>, which is lead to the returns of<br />
option are uncerta<strong>in</strong>. However, if the uncerta<strong>in</strong> sets of<br />
underly<strong>in</strong>g <strong>in</strong>puts are determ<strong>in</strong>ed, the ones of options are<br />
correspond<strong>in</strong>g to. Mostly portfolio model <strong>in</strong>tegrated <strong>in</strong>to<br />
options are only emphasized on portfolio return at the end<br />
of the <strong>in</strong>vestment horizon. Due to the result<strong>in</strong>g<br />
asymmetric portfolio return distribution mean–variance<br />
analysis will be not sufficient to identify optimal optioned<br />
portfolios. From the second half of the last century,<br />
options have been praised for their ability to give stock<br />
holders protection aga<strong>in</strong>st adverse market fluctuations. A<br />
standard option contract is determ<strong>in</strong>ed by the follow<strong>in</strong>g<br />
parameters: the premium or price of the option, the<br />
underly<strong>in</strong>g security price, the expiration date, and the<br />
strike price. A put (call) option gives the option holder<br />
the right, but not the obligation, to sell to (buy) from the<br />
option writer the underly<strong>in</strong>g security by the expiration<br />
date and at the prescribed strike price. American options<br />
can be exercised at any time up to the expiration date,<br />
whereas European options can be exercised only on the<br />
expiration date itself. We will only aim at European<br />
options, whose expiration is at the end of <strong>in</strong>vestment<br />
horizon, that is, at time T. We will pay attention to these<br />
<strong>in</strong>struments because of their simplicity and s<strong>in</strong>ce they<br />
naturally <strong>in</strong> the s<strong>in</strong>gle period portfolio optimization<br />
framework of the previous section.<br />
A. An Introduction to Option Pric<strong>in</strong>g<br />
It is necessary to <strong>in</strong>troduce call option first. Suppose an<br />
<strong>in</strong>vestor is presented with an opportunity to enter <strong>in</strong>to a<br />
position <strong>in</strong> a European call option written on a stock, with<br />
strike price K and expiration date T. The stock price<br />
process is assumed to follow a geometric Brownian<br />
motion with mean rate of return μ> 0 and volatility<br />
σ> 0 :<br />
dSt =μ Stdt +σ StdWt<br />
where { W,t<br />
t<br />
≥ 0}<br />
is a standard Brownian motion with<br />
W0<br />
= 0. The basic model for call option of the B–S is:<br />
−rT<br />
( ) ( )<br />
C= SN d − Ke N d<br />
1 2<br />
2<br />
( ) ( )<br />
d1<br />
= ⎡ln S/K r /2 T ⎤<br />
⎣<br />
+ +σ<br />
⎦<br />
/ σ T<br />
d2 = d1−σ<br />
T<br />
where<br />
C call option price;<br />
S current stock price;<br />
K strik<strong>in</strong>g price;<br />
r riskless <strong>in</strong>terest rate;<br />
T time until option expiration;<br />
σ standard deviation of return on the underly<strong>in</strong>g<br />
security;<br />
N( d<br />
i ) cumulative normal distribution function evaluated<br />
at d<br />
i<br />
.<br />
The same as put option:<br />
−rT<br />
P = Ke N( d2) − SN( d1)<br />
where P is put option price;<br />
The mean<strong>in</strong>gs of the rest letters are similar to the<br />
formers.<br />
Next, we will improve B-S formula us<strong>in</strong>g analytical<br />
method. It is well known that the basic assumption of B-S<br />
model is to assume the underl<strong>in</strong>g price follows Geometric<br />
Brown motion:<br />
dSt = μ Stdt +σ StdWt<br />
Call option is an option is a security that gives its<br />
owner the right to trade <strong>in</strong> a fixed number of shares of a<br />
specified common stock at a fixed price at any time on or<br />
before a given date. The act of mak<strong>in</strong>g this transaction is<br />
referred to as exercis<strong>in</strong>g the option. The fixed price is<br />
termed the strike price, and the given date, the expiration<br />
date. A call option gives the right to buy the shares; a put<br />
option gives the right to sell the shares.<br />
For an European call option its value at the expired<br />
time T is<br />
CT<br />
= ( ST<br />
− K )<br />
+<br />
Because the future is uncerta<strong>in</strong>, it is stochastic. And<br />
we need to know the current value of option. So it should<br />
to deduce from its expectation ES ( T<br />
− K )<br />
+<br />
The f<strong>in</strong>ancial market is perfect, that is the current value<br />
is equal to the discount of future value.<br />
−rT<br />
C0 = e E( ST<br />
− K )<br />
+<br />
Now, to calculate the expectation based on the hypothesis<br />
of lognormal distribution.<br />
2<br />
+<br />
⎛ σ ⎞<br />
⎛ σ TZ+ r−<br />
T ⎞<br />
+<br />
⎜ 2 ⎟<br />
⎝ ⎠<br />
E ( ST<br />
− K)<br />
= E⎜S0e −K⎟<br />
⎜<br />
⎟<br />
⎝<br />
⎠<br />
where Z∼<br />
N( 0,1)<br />
whose density function is<br />
Let Se<br />
1<br />
f ( x)<br />
= e<br />
2π<br />
2<br />
Ta ⎛<br />
r σ ⎞<br />
σ + ⎜<br />
−<br />
2 ⎟<br />
T<br />
0<br />
K 0<br />
2<br />
x<br />
−<br />
2<br />
⎝ ⎠<br />
− = then<br />
© 2013 ACADEMY PUBLISHER
1582 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
2<br />
⎛ ⎞ ⎛ ⎞<br />
K σ<br />
ln ⎜ ⎟−⎜r − ⎟T<br />
S0<br />
⎝ 2 ⎠<br />
a =<br />
⎝ ⎠<br />
σ T<br />
And the <strong>in</strong>tegral <strong>in</strong>terval is divided to two parts<br />
( −∞,a] ∪ [a, +∞ )<br />
⎛<br />
⎞<br />
e E S K S e K e dx<br />
⎛ 2 ⎞<br />
2<br />
+∞ σ<br />
σ Tx+ ⎜<br />
r−<br />
2 ⎟<br />
T<br />
x<br />
+<br />
1 −<br />
−rT<br />
⎝ ⎠<br />
2<br />
( − ) = ⎜<br />
⎟<br />
T ∫ 0<br />
−<br />
⎜<br />
⎟<br />
a<br />
2π<br />
where<br />
⎝<br />
= I + I<br />
1 2<br />
2 2<br />
x ⎛ ⎞<br />
+∞ − +σ Tx+ r− T<br />
rT S<br />
σ<br />
− 0 2 ⎜ 2 ⎟<br />
⎝ ⎠<br />
∫<br />
I1<br />
= e e dx<br />
2π<br />
a<br />
2<br />
+∞<br />
x<br />
rT K −<br />
−<br />
2<br />
∫<br />
I2<br />
=−e e dx<br />
2π<br />
For I 1<br />
,<br />
a<br />
2 2<br />
x ⎛ ⎞<br />
+∞ − +σ Tx+ r− T<br />
rT S<br />
σ<br />
− 0 2 ⎜ 2 ⎟<br />
⎝ ⎠<br />
∫<br />
I1<br />
= e e dx<br />
2π<br />
=<br />
a<br />
2 2<br />
σ +∞ x<br />
− T σ Tx−<br />
0 2 2<br />
S e ∫ e dx<br />
2π a<br />
( x−σ<br />
T)<br />
⎛<br />
⎞<br />
e exp dx<br />
2 2<br />
⎛ ⎞<br />
r− T<br />
2<br />
S<br />
σ +∞<br />
⎜<br />
0 2 ⎟<br />
⎝ ⎠<br />
σ T<br />
=<br />
⎜<br />
⎟<br />
∫ − +<br />
2π a<br />
2 2<br />
⎜ ⎟<br />
Let y= x−σ T then<br />
⎝<br />
2 2<br />
σ T +∞ y<br />
−<br />
0 2 2<br />
S<br />
I1<br />
= e ∫ e dy<br />
2π a−σ<br />
T<br />
( ( ))<br />
( ( ))<br />
= −Φ −σ<br />
rT<br />
Se<br />
0<br />
1 a T<br />
= − −σ<br />
For I<br />
2<br />
,<br />
rT<br />
Se<br />
0<br />
N a T<br />
2<br />
+∞ x<br />
rT K −<br />
−<br />
2<br />
I2<br />
=−e ∫ e dx<br />
2π ( ( ))( )<br />
−rT<br />
( a)<br />
= −Φ −<br />
−rT<br />
e 1 a K<br />
=−Ke<br />
Φ −<br />
a<br />
B. Basic Model<br />
The basic notion follows [12]. Consider a portfolio<br />
X = x x x ′ of stocks1, 2<br />
n<br />
consist<strong>in</strong>g of quantities ( )<br />
1, 2 n<br />
with the return vector R= ( r1, r2 r<br />
n )<br />
′ . We assume that for<br />
each stock there are m put and m call options that mature<br />
<strong>in</strong> one year. The m strike prices of the put and call<br />
options for one particular stock are located at equidistant<br />
po<strong>in</strong>ts between 70% and 130% of the stock's current<br />
price. C<br />
R , R are denoted the correspond<strong>in</strong>g calls and<br />
ik<br />
Pik<br />
puts returns <strong>in</strong> the portfolio with stock price<br />
S , k = 1, 2m<br />
means the k -th strike price based on the<br />
i<br />
th<br />
i stock,call price C ik<br />
, and put price P ik<br />
, whose exercise<br />
⎠<br />
⎠<br />
prices are K ik<br />
, β and<br />
ik<br />
γ denote the (decision) variables on<br />
ik<br />
the numbers of the correspond<strong>in</strong>g calls and puts option.<br />
0<br />
S denotes the <strong>in</strong>itial price of stock ,which then can be<br />
i<br />
expressed as S 0 ir at the end of the period. Us<strong>in</strong>g the<br />
i<br />
payoff functions of call and put options, we can explicitly<br />
express the returns of options as:<br />
C 1 0<br />
R<br />
ik<br />
= max { 0, Si ri − Kik} = max { 0, aik + bikri<br />
}<br />
Cik<br />
with<br />
K S<br />
ik<br />
0<br />
aik<br />
=− , bik<br />
=<br />
P C<br />
ik<br />
ik<br />
Similarly, the return of a put option is<br />
P 1 0<br />
R<br />
ik<br />
= max { 0,<br />
i<br />
Kik − Si ri<br />
}<br />
Pik<br />
= max{ 0, aik<br />
+ bikri<br />
}<br />
S K<br />
with<br />
0<br />
ik<br />
aik<br />
=− , bik<br />
=<br />
Pik<br />
Pik<br />
where P<br />
ik<br />
, C will be calculated from Black–Scholes<br />
ik<br />
formula.<br />
With<strong>in</strong> this <strong>in</strong>vestment framework, the value a<br />
portfolio at the expired time the <strong>in</strong>vestor wishes to<br />
maximize can thus be formulated as:<br />
n<br />
m<br />
⎧<br />
C P⎫<br />
maxV = ∑⎨xr i i<br />
+ ∑ βik Rik + γik Rik<br />
⎬<br />
i= 1 ⎩ k=<br />
1<br />
⎭<br />
Constra<strong>in</strong>s concluded <strong>in</strong> this paper will be developed<br />
based on [13], whose model also conta<strong>in</strong>ed <strong>in</strong> optioned<br />
portfolio. The risk-return preferences of the <strong>in</strong>vestor are<br />
specified as mean–variance efficiency with additional<br />
shortfall constra<strong>in</strong>ts express<strong>in</strong>g the downside risk<br />
preferences.<br />
−1<br />
( I − L) wxβγ<br />
= C r and<br />
a<br />
QV ( ≥ Bα ( )) ≥1−<br />
α<br />
where the mean<strong>in</strong>gs of the parameters are expla<strong>in</strong>ed<br />
as: w βγ<br />
is the share vector of stocks, call options and put<br />
x<br />
− 1<br />
options. Set L = C rr′<br />
and I be<strong>in</strong>g the matrix with 1 <strong>in</strong> the<br />
c<br />
diagonal and 0 else. Let C be the covariance matrix of<br />
the (discrete) returns, r ( r1, r2<br />
rp<br />
)<br />
= the vector of<br />
expected returns and e the p -dimensional vector filled<br />
with 1 <strong>in</strong> each component of the <strong>in</strong>struments.<br />
The steps of calculat<strong>in</strong>g the parameters are follows:<br />
(1) Covariance matrix of the (discrete) returns C is<br />
estimated from history data.<br />
r = r r r is also<br />
(2) Expected returns vector ( 1, 2 p )<br />
estimated from history data.<br />
(3) a = eC ′ − r, b= rC ′ − r, c= eC ′<br />
− e,<br />
d = bc−<br />
a<br />
⎛b−<br />
ari<br />
⎞ ⎛crj<br />
− a ⎞<br />
ra<br />
= ⎜ ⎟ , rc<br />
= ⎜ ⎟<br />
⎝ d ⎠i=<br />
1,2<br />
p ⎝ d ⎠j=<br />
1,2<br />
p<br />
−1<br />
(4) ( )<br />
1 1 1 2<br />
I − L w = C r<br />
xβγ<br />
a<br />
The follow<strong>in</strong>g portfolio optimization problem<br />
corresponds to this model:<br />
© 2013 ACADEMY PUBLISHER
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max<br />
⎧<br />
n<br />
m<br />
C P<br />
∑⎨xr i i<br />
+ ∑ ( βik Rik + γik Rik<br />
)<br />
⎩<br />
−1<br />
⎧⎪<br />
( I − L)<br />
wxβγ<br />
= C ra<br />
⎨<br />
⎪⎩<br />
QV ( ≥ B( α ))<br />
≥1−α<br />
i= 1 k=<br />
1<br />
st .<br />
C. Parameter Uncerta<strong>in</strong>ty<br />
Most of the parameter such as the expected returns and<br />
covariance are estimated from noisy data. Hence, these<br />
estimates are no accurate. As a result, if the model<br />
amplifies any estimation errors, the portfolios yield<strong>in</strong>g<br />
will extremely perform badly <strong>in</strong> out-of-sample tests. So it<br />
needs to solve this problem. And the robust optimization<br />
is a good choice. Generally speak<strong>in</strong>g, robust optimization<br />
aims to f<strong>in</strong>d solutions to a given optimization problems<br />
with uncerta<strong>in</strong> parameters which could achieve good<br />
objective values for all or most of realizations of the<br />
uncerta<strong>in</strong> parameters. We will assume that the estimate<br />
covariance is reasonably accurate such that there is no<br />
uncerta<strong>in</strong>ty about it. This assumption is justified s<strong>in</strong>ce the<br />
estimation error <strong>in</strong> expectation by far outweighs the<br />
estimation error <strong>in</strong> covariance, see e.g. [14]. So, <strong>in</strong><br />
decision-mak<strong>in</strong>g uncerta<strong>in</strong>ty is unknown. There are many<br />
factors that affect the decision-mak<strong>in</strong>g, <strong>in</strong>clud<strong>in</strong>g human<br />
psychology state, external <strong>in</strong>formation <strong>in</strong>put, which is<br />
usually difficult to be derived <strong>in</strong> terms of probabilistic or<br />
stochastic measurement. The well known B–S model has<br />
a number of assumptions such as the riskless <strong>in</strong>terest rate<br />
and the volatility are constant, which hardly catch human<br />
psychology state and external <strong>in</strong>formation <strong>in</strong>put although,<br />
B–S model has been improved.<br />
Now, it needs to <strong>in</strong>troduce robust optimization and<br />
portfolio selection [15]. The robust counterpart of an<br />
uncerta<strong>in</strong> mathematical program is a determ<strong>in</strong>istic worst<br />
case formulation <strong>in</strong> which model parameters are assumed<br />
to be uncerta<strong>in</strong>, but symmetrically distributed over a<br />
bounded <strong>in</strong>terval known as an uncerta<strong>in</strong>ty set U. The<br />
structure and scale of U is specified by the modeler,<br />
typically based on statistical estimates. Structure refers to<br />
the geometry or shape of the constra<strong>in</strong>t set U, such as<br />
ellipsoidal or polyhedral. Scale refers to the magnitude of<br />
the deviations of the uncerta<strong>in</strong> parameters from their<br />
nom<strong>in</strong>al values; it can be thought of as the size of the<br />
structure def<strong>in</strong><strong>in</strong>g U. A general form of the robust<br />
counterpart to an uncerta<strong>in</strong> LP is given as<br />
T<br />
max ⎡m<strong>in</strong> c x ⎤<br />
⎣<br />
( )<br />
Subject to Ax≤b, ∀( A,b,c)<br />
∈ U<br />
There are two forms for transfer the robust <strong>in</strong>to a set,<br />
l<strong>in</strong>ear or Ellipsoidal.<br />
(1) L<strong>in</strong>ear <strong>in</strong>terval<br />
In the robust optimization framework, the true value<br />
a is not certa<strong>in</strong> which is given by the follow<strong>in</strong>g equation<br />
i<br />
⎦<br />
− ^<br />
ai<br />
= ai+ a iηi, ∀ i<br />
where a −<br />
i is an estimate for a i<br />
, and a ^<br />
i is the maximum<br />
distance that a i<br />
deviated from a − i and ηi<br />
is a random<br />
⎫<br />
⎬<br />
⎭<br />
variable which is bounded by and symmetrically<br />
distributed with<strong>in</strong> the <strong>in</strong>terval[-1,1]. That is, the true<br />
value ai<br />
is symmetrically distributed with respect to i on<br />
− ^ − ^<br />
⎡<br />
⎤<br />
the <strong>in</strong>terval ai− a i,ai+<br />
ai<br />
⎢<br />
⎣<br />
⎥<br />
⎦ .<br />
(2) Ellipsoidal uncerta<strong>in</strong>ty sets are given by<br />
2<br />
⎧<br />
−<br />
⎛ ⎞ ⎫<br />
⎜ai<br />
− ai<br />
⎟<br />
⎪<br />
2<br />
a:<br />
⎝ ⎠ ⎪<br />
⎨ ∑<br />
^ 2 ≤Ω ⎬<br />
⎪ a ⎪<br />
i<br />
⎪⎩<br />
⎪⎭<br />
where Ω is a user def<strong>in</strong>ed parameter and adjusts the<br />
trade-off between robustness and optimality.<br />
Next, the problem is how to transfer the uncerta<strong>in</strong> set<br />
to a series equations or <strong>in</strong>-equations.<br />
Let J be the number of parameters. For Soyster’s and<br />
Ben-Tal and Nemirovski’s model[16],<br />
or<br />
∑<br />
i<br />
i<br />
a<br />
∑<br />
i<br />
^<br />
i<br />
−<br />
i<br />
− a<br />
a<br />
η =<br />
i<br />
Bertsimas and Sim (2004) relaxed this condition by<br />
def<strong>in</strong><strong>in</strong>g a new parameter Γ (the budget of uncerta<strong>in</strong>ty) as<br />
the number of uncerta<strong>in</strong> parameters that take their worst<br />
− ^<br />
case value ai<br />
− ai<br />
.Therefore ηi<br />
≤Γ,such that Γ ∈⎡⎣ 0, J ⎤⎦ ,<br />
then the optimal problem can be rewritten as<br />
−<br />
^<br />
⎛<br />
⎞<br />
max⎜∑ai<br />
wi + m<strong>in</strong>∑aiη<br />
iwi⎟<br />
⎝<br />
ηi<br />
⎠<br />
S.t w = 1<br />
∑<br />
∑ i<br />
i<br />
η ≤Γ<br />
wi<br />
≥0, −1≤ηi<br />
≤1, ∀ i<br />
It also can be rewritten as<br />
−<br />
^<br />
⎛<br />
⎞<br />
max⎜∑ai<br />
wi −max∑<br />
ai<br />
ηiwi<br />
⎟<br />
⎝<br />
ηi<br />
⎠<br />
S.t w = 1<br />
∑<br />
∑ i<br />
i<br />
η ≤Γ<br />
wi<br />
≥0,0≤ηi<br />
≤1, ∀ i<br />
However, this problem is not well-def<strong>in</strong>ed. Because it<br />
is difficult to obta<strong>in</strong> a different optimal solution for each<br />
return realization, there are multiple ways to specify the<br />
l<strong>in</strong>ear set. A nature choice is to construct an ellipsoidal<br />
uncerta<strong>in</strong>ty set<br />
T −<br />
Θ = r : r − μ Σ<br />
1 r − μ ≤ δ<br />
2<br />
r<br />
{ ( ) ( ) }<br />
~<br />
Accord<strong>in</strong>g to EI Ghaoui et al [17],when r has f<strong>in</strong>ite<br />
second-order moments, then, we can choice<br />
δ p<br />
= 1− p<br />
for p ∈[0,1 ) and δ = +∞<br />
for p = 1 , it means the follow<strong>in</strong>g probabilistic<br />
guarantee for any portfolio w :<br />
=<br />
J<br />
J<br />
a −<br />
© 2013 ACADEMY PUBLISHER
1584 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
~<br />
T<br />
T<br />
{ r∈Θ<br />
}<br />
r<br />
P w r ≥m<strong>in</strong>w r ≥ p<br />
The optimal problem reduces to a convex second-order<br />
cone program[18].<br />
T<br />
2 T<br />
max w μ − δ Σ<br />
1/ w 1 = 1,<br />
l ≤ w ≤ u<br />
w<br />
{ }<br />
2<br />
Accord<strong>in</strong>g to the Central Limit Theorem, it is<br />
^<br />
concluded that the sample mean μ is approximately<br />
normally distributed. That is ,it follows:<br />
^<br />
⎛ Σ ⎞<br />
μ ~ N ⎜ μ,<br />
⎟<br />
⎝ n ⎠<br />
Similarly, the ellipsoidal uncerta<strong>in</strong>ty set for the<br />
mean μ can be expressed as<br />
Θ<br />
μ<br />
−1<br />
⎪⎧<br />
^<br />
⎛ Σ<br />
^<br />
⎛ ⎞ ⎞ ⎛ ⎞ ⎪⎫<br />
2<br />
= ⎨μ<br />
: ⎜ μ − μ ⎟⎜<br />
⎟ ⎜ μ − μ ⎟ ≤ κ ⎬<br />
⎪⎩ ⎝ ⎠⎝<br />
n ⎠ ⎝ ⎠ ⎪⎭<br />
where κ = q / 1−<br />
q for some q ∈[0,1)<br />
The problem reduces to<br />
⎪⎧<br />
1/ 2<br />
^<br />
⎛ Σ<br />
^ 1/ 2<br />
⎪⎫<br />
T ⎞<br />
T<br />
max⎨w<br />
μ−κ<br />
⎜ ⎟ w −δ<br />
Σ w w 1 = 1, l ≤ w ≤ u⎬<br />
w<br />
⎪⎩<br />
⎝ n ⎠<br />
2<br />
2<br />
⎪⎭<br />
See[19] the problem is f<strong>in</strong>ally reduced to<br />
⎪⎧<br />
^<br />
^ 1 / 2<br />
⎪⎫<br />
T<br />
1 / 2<br />
T<br />
max⎨w<br />
μ − κ Ω w − δ Σ w w 1 = 1, l ≤ w ≤ u⎬<br />
w<br />
2<br />
⎪⎩<br />
2<br />
⎪⎭<br />
where<br />
Σ 1 Σ T Σ<br />
Ω = − 11<br />
n T Σ n n<br />
1 1<br />
n<br />
In this paper, firstly, we consider the uncerta<strong>in</strong> set for<br />
return mean. We def<strong>in</strong>e r′ is the estimation of real<br />
value r , the uncerta<strong>in</strong>ly set I as<br />
{ : i<br />
′ i i i<br />
′ i }<br />
I = r r −s ≤r ≤ r + s for mean μ .<br />
Accord<strong>in</strong>g to Anna[20], the robust counterpart:<br />
rx ≥ r<br />
∑<br />
m<strong>in</strong><br />
i i p<br />
can be transferred to the follow<strong>in</strong>g form:<br />
⎧∑rx ′<br />
i i<br />
−∑sm i i<br />
≥rp<br />
⎪<br />
⎨ mi<br />
≥ xi<br />
⎪<br />
⎩ si<br />
≥ 0<br />
The robust counterpart of objective function is<br />
n<br />
m<br />
⎛ ⎧<br />
C P ⎫⎞<br />
max ⎜∑⎨xr i i<br />
+ ∑ { βik Rik + γik Rik}<br />
⎬⎟<br />
x, βγ ,<br />
⎝ i= 1 ⎩ k=<br />
1<br />
⎭⎠<br />
let x αβγ<br />
is the share of stock and options.<br />
The goal is to determ<strong>in</strong>e the solution of above problem<br />
under the constra<strong>in</strong>ts.<br />
Ⅲ.MONTE CARLO SIMULATION AND EMPIRICAL EXAMPLE<br />
A. Monte Carlo Method and the Simulation Process<br />
Compar<strong>in</strong>g with other numerical methods, Monte<br />
Carlo simulation has two major advantages: first, more<br />
flexible, easy to implement and improvement; secondly,<br />
the simulation of estimation error and convergence speed<br />
<strong>in</strong> solv<strong>in</strong>g the problem has strong <strong>in</strong>dependence of<br />
dimension. European option because of its execution time<br />
is fixed, not to be executed <strong>in</strong> advance, therefore it only<br />
need to calculate the earn<strong>in</strong>gs of the option of each<br />
sample path at expiration date, which is available by<br />
Matlab programm<strong>in</strong>g. [21-23] discuss the application of<br />
the simulation methods <strong>in</strong> various area. Monte Carlo<br />
method can overcome the obstacle and we use it further<br />
to improve the accuracy of simulated price with the<br />
enhancement of reduction variate technique for more<br />
complex options whose payoff function is dependent on<br />
the underly<strong>in</strong>g asset path and sum of asset is more than<br />
one.<br />
Now, we illustrate the key steps <strong>in</strong> Monte Carlo. It is<br />
saw that to draw samples of the term<strong>in</strong>al stock price<br />
S( T ) it suffices to have a mechanism for draw<strong>in</strong>g<br />
samples from the standard normal distribution. For now<br />
we simply assume the ability to produce a sequence<br />
Z1,<br />
Z2 of <strong>in</strong>dependent standard normal random<br />
variables. Given a mechanism for generat<strong>in</strong>g the Z<br />
i<br />
, we<br />
rT<br />
can estimate E⎡<br />
−<br />
e ( ST<br />
− K )<br />
+ ⎤ us<strong>in</strong>g the follow<strong>in</strong>g<br />
⎣<br />
⎦<br />
algorithm:<br />
For i = 1, 2n<br />
generate<br />
Z<br />
i<br />
⎛⎡<br />
1 ⎤ ⎞<br />
Si<br />
T = S0<br />
exp⎜⎢<br />
r− σ +<br />
2 ⎥<br />
T σ TZi⎟<br />
⎝⎣<br />
⎦ ⎠<br />
set ( )<br />
2<br />
C = e S −K<br />
−rT<br />
set ( ) +<br />
^<br />
i<br />
set n = ( + + + )<br />
T<br />
C C C C n<br />
1 2 n<br />
/<br />
For any n ≥ 1, the estimator C n is unbiased, <strong>in</strong> the<br />
sense that its expectation is the target quantity:<br />
^<br />
⎛ ⎞<br />
− rT<br />
+<br />
E⎜Cn<br />
⎟= C = E⎡<br />
⎣e ( ST<br />
−K)<br />
⎤<br />
⎝ ⎠<br />
⎦<br />
The estimator is strongly consistent mean<strong>in</strong>g that as<br />
n →∞.<br />
In this paper, we suppose z = z()<br />
t is a random<br />
process, the change <strong>in</strong> a very small time <strong>in</strong>terval Δt<br />
is<br />
expressed as Δ z . If Δz<br />
satisfies that Δ z = ε Δ t where<br />
ε ∼ N ( 0,1)<br />
. For different time <strong>in</strong>terval Δ t , Δz<br />
are<br />
<strong>in</strong>dependent, then call z = z()<br />
t follows Wiener process.<br />
Suppose the stock price follows ds = μsdt + σ sdz ,<br />
where dz is the Standard Brown motion. In the practical<br />
^<br />
© 2013 ACADEMY PUBLISHER
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application, more accurate simulation not starts from S,<br />
but log-price ln S . Monte Carlo simulation steps:<br />
(1) To generate sample paths for underly<strong>in</strong>g asset, given<br />
the <strong>in</strong>itial value<br />
i i i i<br />
S = t 1<br />
S + t<br />
μiS Δ t<br />
t + +<br />
σiS Δ t<br />
tεt<br />
(2)To calculate option price of each sample path.<br />
(3) To average option price for each sample path.<br />
IV.EMPIRICAL EXAMPLE<br />
In order to illustrate the features and applications of<br />
this model, we make a numerical example. For simple,<br />
we only consider two stocks. And there is a call and a put<br />
option based on each stock. Suppose that the <strong>in</strong>vestment<br />
horizon is T = 1year, <strong>in</strong>clud<strong>in</strong>g 20 trad<strong>in</strong>g days <strong>in</strong> each<br />
month, so there is 240 trad<strong>in</strong>g days <strong>in</strong> total. To divide<br />
T by daily, that is Δ t =1day, equals to 1 year. The<br />
240<br />
price of each stock is supposed to follow log-normal<br />
distribution, then the price of stock i,( i = 1,2) <strong>in</strong><br />
t + 1day is:<br />
i i i i<br />
S S μ S t σ S tε<br />
ε ∼ N 0,1<br />
= + Δ + Δ , ( )<br />
+ t<br />
t 1 t i t i t t<br />
i i i<br />
Generate a path S 0<br />
, S 1<br />
S<br />
240<br />
for stock i by Monte<br />
Carlo method.<br />
Each stock will only correspond to a European call<br />
option and a European put option, asset specific<br />
parameters are as follows:<br />
μ1 = 11%, σ1 = 26.86%; μ2 = 8.05%, σ2<br />
= 16.3%<br />
Other parameters are as shown <strong>in</strong> the follow<strong>in</strong>g.<br />
The k<strong>in</strong>d of option, underly<strong>in</strong>g, market price, option<br />
price, time and strike price respectively are:<br />
For call option C 1<br />
whose underl<strong>in</strong>g is S with <strong>in</strong>itial<br />
1<br />
value S 1 ( 0 ) =15.59, the option premium C 1 ( 0 ) =2.17,<br />
the strike price is K<br />
11<br />
=14.5, the expired time is 6 month.<br />
For call option P 1<br />
whose underl<strong>in</strong>g is S 1<br />
with <strong>in</strong>itial<br />
P =1.87,<br />
value S ( ) =15.59, the option premium ( )<br />
1 0<br />
1 0<br />
the strike price is K 12<br />
=16.5, the expired time is 12<br />
month.<br />
For call option C whose underl<strong>in</strong>g is<br />
2<br />
S 1<br />
with <strong>in</strong>itial<br />
value ( ) 2<br />
0<br />
C<br />
2<br />
0 =1.32,<br />
the strike price is K =13, the expired time is 3 month.<br />
21<br />
For call option P 2<br />
whose underl<strong>in</strong>g is S 2<br />
with <strong>in</strong>itial<br />
P =1.48 ,<br />
S =13.71, the option premium ( )<br />
value S ( ) =13.71, the option premium ( )<br />
2<br />
0<br />
2<br />
0<br />
the strike price is K =15, the expired time is 9 month.<br />
22<br />
If the option j based on stock i is exercised on the<br />
l ( ≤ 240)<br />
day, the option value is<br />
i i i i<br />
( Srr<br />
01 2<br />
rl<br />
− Kij)<br />
max 0,<br />
,and <strong>in</strong> the rest of <strong>in</strong>vestment<br />
horizon, that is, <strong>in</strong> the follow<strong>in</strong>g 240 − l days,the value<br />
is treated as risk free asset,so the total value of the<br />
option <strong>in</strong> the <strong>in</strong>vestment horizon is:<br />
i i i i<br />
r( 240 −l)<br />
/ 365<br />
max ( 0, Srr<br />
0 1 2rl<br />
− Kij) e , r=<br />
5% is the risk<br />
free <strong>in</strong>terest rate.<br />
The European call option price before expiration day,<br />
for example, on the v− th day is<br />
i i i i −r l−v i<br />
max 0, Srr r − K e − c , v≤<br />
l<br />
( )<br />
( l ij) 0 1 2 0<br />
i<br />
where C is the option current price (option premium)<br />
0<br />
based on stock i.<br />
If v> l , then on the v− th day, the call option price<br />
is<br />
r<br />
⎛ ⎞<br />
365<br />
i i i i<br />
⎜e −1⎟max( 0, S0r1r2<br />
rl<br />
−Kij)<br />
⎝ ⎠<br />
Suppose that the portfolio assets real returns are<br />
μ = μ , μ , r 1 , r 1 , r<br />
2 , r<br />
2 , and the means of samples<br />
( 1 2 c p c p )<br />
return are μ ( μ′ )<br />
1 1 2 2<br />
1<br />
, μ ′<br />
2<br />
, r ′<br />
c<br />
, r ′<br />
p<br />
, r ′<br />
c<br />
, r ′<br />
p<br />
′ = with <strong>in</strong>vestment<br />
share x = ( x , x , w , w , w , w ) . We construct the model:<br />
1 2 1 2 3 4<br />
μ x μ x r w r w r w r w<br />
1 1 2 1<br />
max<br />
1 1+ 2 2+ c 1+ p 2+ c 3+<br />
p 4<br />
⎧<br />
1 1 2 1<br />
μ′ 1<br />
x1+ μ ′<br />
2<br />
x2 + r ′<br />
c<br />
w1+ r ′<br />
p<br />
w2 + r ′<br />
c<br />
w3+ r ′<br />
p<br />
w4<br />
≥0.001<br />
⎪<br />
−1<br />
⎪<br />
( I − L)<br />
wxβγ<br />
= C μa<br />
⎪<br />
−1 −1 −1 2<br />
a= eC ′ μ, b= μ′ C μ, c= eC ′ e,<br />
d = bc−a<br />
⎪<br />
⎪ ⎛b−aμ<br />
⎞ ⎛cμ−a⎞<br />
−1<br />
⎪ μa = ⎜ ⎟, μc = ⎜ ⎟,<br />
L=<br />
C μcμ′<br />
⎨ ⎝ d ⎠ ⎝ d ⎠<br />
⎪x1+ x2 + w1+ w2 + w3+ w4<br />
= 1<br />
⎪<br />
⎪μ′ x + μ ′ x + r ′ w + r ′ w + r ′ w + r ′ w −∑<br />
sm ≥r<br />
⎪<br />
⎪mi<br />
≥ xi<br />
⎪<br />
⎩si<br />
≥ 0<br />
1 1 2 1<br />
1 1 2 2 c 1 p 2 c 3 p 4 i i p<br />
where C is the covariance matrix between the assets ,<br />
the m<strong>in</strong>imum return for an <strong>in</strong>vestor is 2%.<br />
By solv<strong>in</strong>g the above model, we obta<strong>in</strong> the optimal<br />
portfolio is (0.4,-0.04,-0.1,-0.3,-0.16), the objective<br />
is0.00682456. If it is set s<br />
i<br />
= 0 , that is there is no robust<br />
of return mean, the result is 0.0070175439. It is easy to<br />
understand that under robust, <strong>in</strong>vestment is more<br />
conservative. Because the advantage of comb<strong>in</strong><strong>in</strong>g option<br />
<strong>in</strong> portfolio is option could hedg<strong>in</strong>g with risk. In order to<br />
test it, we change the variance from small to large, for<br />
example, supposeσ<br />
1<br />
= 30%; σ 2<br />
= 25% , we f<strong>in</strong>d that the<br />
objective is 0.0052984, if there is without options, the<br />
objective is 0.000215. That is, options <strong>in</strong> portfolio could<br />
hedge risks.<br />
V. CONCLUSION<br />
This paper extents the general portfolio model <strong>in</strong> two<br />
aspects. The first is to comb<strong>in</strong>ed option <strong>in</strong> the portfolio<br />
could hedge the risk, and the options can also considered<br />
as an asset <strong>in</strong> the portfolio, extend<strong>in</strong>g the general<br />
model.And we use Monte Carlo method to simulate the<br />
© 2013 ACADEMY PUBLISHER
1586 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
option prices. The second po<strong>in</strong>t is to propose the model<br />
of maximiz<strong>in</strong>g the return under constra<strong>in</strong>s of variance<br />
efficiency and shortfall preference structure <strong>in</strong> the robust<br />
counterpart, tak<strong>in</strong>g account of uncerta<strong>in</strong> <strong>in</strong>puts. It extends<br />
the general portfolio model, putt<strong>in</strong>g forward some<br />
feasible suggestions to <strong>in</strong>vestors.<br />
ACKNOWLEDGMENT<br />
This research is supported by a Project Supported by<br />
Scientific Research Fund of Hunan Prov<strong>in</strong>cial Education<br />
Department (12C0749).<br />
REFERENCES<br />
[1] Alexander, S., T.F. Coleman and Yuy<strong>in</strong>g Li, Derivative<br />
Portfolio Hedg<strong>in</strong>g Based on CVaR, Journal of Bank<strong>in</strong>g and<br />
F<strong>in</strong>ance, 34,pp.343-350, 2006.<br />
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[3] Mehment Horasanli.Hedg<strong>in</strong>g stragy for a portofolio of<br />
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[4] Pei-wang Gao. Options strategies with the risk adjustment.<br />
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[5] Gerhard Scheuenstuhl, Rudi Zagst. Integrated portfolio<br />
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[6] Wets, R.J.B., Stochastic Programm<strong>in</strong>g. In: Nemhauser,<br />
G.L.,R<strong>in</strong>nooy Kan, A.H.G., Todd, M.J., Handbooks <strong>in</strong><br />
Operations Research and Management Science,<br />
Optimization, 1,pp.573–625, (Chapter VIII), 1991.<br />
[7] Steve Zymler, Robust portfolio optimization with<br />
derivative <strong>in</strong>surance guarantees. European Journal of<br />
Operational Research, 210, pp. 410–424, 2011.<br />
[8] A.L.Soyster, Convex programm<strong>in</strong>g with set-<strong>in</strong>clusive<br />
constra<strong>in</strong>ts and applications to <strong>in</strong>exact l<strong>in</strong>ear programm<strong>in</strong>g.<br />
Operations Research, 21, pp.1154-1157, 1973.<br />
[9] BenTal, A., Nemirovski, A., Robust optimization –<br />
methodology and alications. Math. Program., Ser. B,<br />
92,pp.453–480,2002.<br />
[10] A,Nemilrovski A.Robust solutions of uncerta<strong>in</strong> l<strong>in</strong>ear<br />
programs[J].Operations Research Letters, 25( 1), pp.1-<br />
3,1999.<br />
[11] Steve Zymler. Robust Portfolio Optimization with<br />
Derivative Insurance Guarantees, 42, pp.1244-1265, 2010.<br />
[12] Ai-fan L<strong>in</strong>g, Cheng-xian Xu. Robust portfolio selection<br />
<strong>in</strong>v<strong>in</strong>g options under a ‘‘marg<strong>in</strong>al + jo<strong>in</strong>t’’ ellipsoidal<br />
uncerta<strong>in</strong>ty set. Journal of Computational and Applied<br />
Mathematics, 236, pp. 3373–3393, 2012.<br />
[13] S. Zymler, B. Rustem.Robust Portfolio Optimization with<br />
Derivative Insurance Guarantees. www.comiswf.eu.<br />
2009.4.11, pp.1-31.<br />
[14] Gerhard Scheuenstuhl, Rudi Zagst. Integrated portfolio<br />
management with options. European Journal of<br />
Operational Research,185, pp. 1477–1500,2008.<br />
[15] V.K. Chopra, W.T. Ziemba, The effect of errors <strong>in</strong> means,<br />
variances and covariances on optimal portfolio choice,<br />
Journal of Portfolio Management ,19(2),pp.6–11,1993.<br />
[16] L. El Ghaoui, M. Oks, and F. Outstry. Worst-case value-atrisk<br />
and robust portfolio optimization: A conic<br />
programm<strong>in</strong>g approach. Operations Research, 51(4), pp.<br />
543-556, 2003.<br />
[17] M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret.<br />
Applications of second-order cone programm<strong>in</strong>g. L<strong>in</strong>ear<br />
Algebra and its Applications, 284(1), pp.193-228, 1998.<br />
[18] Christ<strong>in</strong>e Gregory, Ken Darby-Dowman. Robust<br />
optimization and portfolio selection: The cost of robustness.<br />
European Journal of Operational Research 212, pp.417–<br />
428, 2011.<br />
[19] Ben-Tal, A., Nemirovski, A., Robust convex optimization.<br />
Mathematics of Operations Research 23 (4), pp. 769–805,<br />
1998.<br />
[20] S. Ceria and R. Stubbs. Incorporat<strong>in</strong>g estimation errors <strong>in</strong>to<br />
portfolio selection: Robust portfolio construction. Journal<br />
of Asset Management, 7(2), pp. 109–127, 2006.<br />
[21] Anna G.Q., Alberto z. Robust optimization of conditional<br />
value at risk and portfolio selection. Journal of Bank<strong>in</strong>g &<br />
F<strong>in</strong>ance, 32, pp. 2046–2056, 2008.<br />
[22] Wu, Jianwu,Functional verification methodology of<br />
complex electronics system based model<strong>in</strong>g and simulation.<br />
Journal of Computers, vol 5, no9, pp.1343-1347, 2010.<br />
[23] Mizouni,Simulation-based feature selection for software<br />
requirements basel<strong>in</strong>e. Journal of Software, vol 7, no7, pp.<br />
1440-1450, 2012.<br />
[24] Aijiu Chen. The Meso-level Numerical Experiment<br />
Research of the Mechanics Properties of Recycled<br />
Concrete. Journal of Software, vol 7.no 9, pp.1932-1940,<br />
2012.<br />
X<strong>in</strong>g Yu was born <strong>in</strong> 1981. From 2000.9.1 to 2004,7.1, she<br />
studied at Department of mathematics and applied mathematics<br />
of Yangtze University, received Bachelor of Science Degree,<br />
From 2004.9.1 to 2007,1, she studied at Department of<br />
mathematics and applied mathematics of Huazhong University<br />
of science and technology, and earned a Master of Science<br />
Degree. From 2007,3, she is work<strong>in</strong>g at Hunan university of<br />
humanities Science and Technology, study<strong>in</strong>g aim at f<strong>in</strong>ancial<br />
mathematics, mathematical model.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1587<br />
A Novel Water Quality Assessment Method<br />
Based on Comb<strong>in</strong>ation BP Neural Network<br />
Model and Fuzzy System<br />
M<strong>in</strong>g Xue<br />
Chang Chun Institute of Technology<br />
Chang Chun, Ch<strong>in</strong>a,130012<br />
Email: xuem<strong>in</strong>g_net@s<strong>in</strong>a.com<br />
Abstract—As the forefront of complex nonl<strong>in</strong>ear science and<br />
artificial <strong>in</strong>telligence science, artificial neural network has<br />
began to be applied <strong>in</strong> the field of water quality control and<br />
plann<strong>in</strong>g step by step. Accord<strong>in</strong>g to the fuzzy feature of<br />
water quality <strong>in</strong>formation, this paper proposes a<br />
membership degree Back-Propagation network (MDBP) for<br />
water quality assessment with comb<strong>in</strong><strong>in</strong>g fuzzy mathematics<br />
and artificial neural network. The proposed MDBP model<br />
comb<strong>in</strong>es the merits of artificial neural network method and<br />
fuzzy evaluation method, which overcomes effectively the<br />
shortcom<strong>in</strong>g of other assessment methods. With improv<strong>in</strong>g<br />
the accuracy and reliability of the assessment method, the<br />
method has a higher flexibility than other conventional<br />
approach and its programs have a better adaptability and<br />
more convenient application. The assessment method is<br />
closer to the reality with consider<strong>in</strong>g the cont<strong>in</strong>uity of the<br />
changes of water quality environment.<br />
Index Terms—Water Quality, Fuzzy Mathematics, Back-<br />
Propagation Neural Network, Assessment Method<br />
I. INTRODUCTION<br />
The water quality assessment is basic program to plan<br />
and manage water quality and important base of<br />
comput<strong>in</strong>g water environment capacity and controll<strong>in</strong>g<br />
water pollutant, which shows the total <strong>in</strong>formation of<br />
water environment quality. In practice, there are many<br />
assessment methods used to water quality assessment.<br />
For example, the <strong>in</strong>tegrated <strong>in</strong>dex approach shows the<br />
uncerta<strong>in</strong> characters of water quality changes, which<br />
holds the needs of water quality function classification.<br />
The practice shows that all of these used methods need to<br />
suppose subjective parameters and concrete assessment<br />
mode, so the assessment results always have obviously<br />
subjectivity and restra<strong>in</strong>ed applicability. In theory, the<br />
artificial neural network method with potentiality can<br />
solve the problem. As for the artificial neural theory, the<br />
function of learn<strong>in</strong>g and memoriz<strong>in</strong>g can provide the<br />
basic theory and methods for water quality assessment<br />
mode and classification problem. In the reference [1] the<br />
un-po<strong>in</strong>t pollutant sources dra<strong>in</strong>age area is assessed by<br />
us<strong>in</strong>g the method of Bayesian concepts and comb<strong>in</strong><strong>in</strong>g<br />
artificial neutral network. In reference [2-4], the Back-<br />
Propagation network model with multi-<strong>in</strong>put, multioutput<br />
and multi-layer is adopt to assess <strong>in</strong>tegrated water<br />
quality, and the qualitative description is used <strong>in</strong> water<br />
quality classification. But the shortcom<strong>in</strong>g of this method<br />
is that the output mode must be obta<strong>in</strong>ed not by learn<strong>in</strong>g<br />
but artificially load<strong>in</strong>g. Thus the assessment results can<br />
not be objective, direct and compact enough.<br />
In this paper, a new water quality assessment method<br />
is studied, which can be so much more effective and<br />
objective to overcome the shortcom<strong>in</strong>g of the present<br />
artificial neural network method. A membership degree<br />
Back-Propagation network for water quality assessment<br />
with comb<strong>in</strong><strong>in</strong>g fuzzy mathematics and artificial neural<br />
network is proposed, which comb<strong>in</strong>es the merits of<br />
artificial neural network method and fuzzy evaluation<br />
method, and then the model overcomes effectively the<br />
shortcom<strong>in</strong>g of other assessment methods. So the<br />
assessment method is closer to the reality with<br />
consider<strong>in</strong>g the cont<strong>in</strong>uity of the changes of water quality<br />
environment. The experiment and analysis show that the<br />
new water quality assessment method which comb<strong>in</strong>es<br />
BP neural network model and fuzzy system is effective.<br />
II. THE PRINCIPLE OF BACK PROPAGATION NEURAL<br />
NETWORK MODEL<br />
A. The Basic Structure of Back Propagation Network<br />
Model<br />
In 1985, Rumelhart and Meclelland proposed Back<br />
Propagation neural network model. Error Back<br />
Propagation usually called BP network <strong>in</strong> short, which is<br />
one of the most widely applied neural network model.<br />
[5]From the structure, BP network is typical multi-layer<br />
network which has not only <strong>in</strong>put layer nodes and output<br />
layer nodes, but also one layer or multi-layer recessive<br />
nodes. In BP network, the consecutive layers are<br />
complete connected, but no connections <strong>in</strong> different<br />
nodes of same layer. [6]<br />
The structure of the BP neural network model with<br />
three layers is shown as fig.1. In the BP neural network<br />
model, the weigh coefficients between different layers<br />
can be adjusted automatically. Except for the <strong>in</strong>put layer,<br />
the process units <strong>in</strong> other layers have nonl<strong>in</strong>ear<br />
<strong>in</strong>put/output connection. That is to say, the characteristic<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1587-1593
1588 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
functions of the process units are differentiable, which are<br />
usually S type function (Sigmoid function) f ( x ), that is<br />
1<br />
f( x)<br />
= (1)<br />
x<br />
1 + e −<br />
The study process of BP neural network <strong>in</strong>cludes<br />
forward propagation and error back-propagation. If given<br />
some <strong>in</strong>put mode, the BP network will study for every<br />
<strong>in</strong>put mode <strong>in</strong> accordance with the followed methods.<br />
The <strong>in</strong>put mode are transferred from <strong>in</strong>put layers to the<br />
hidden layer units, by which the <strong>in</strong>put mode can be<br />
processed, the new output mode will be transferred to<br />
output layer, that is called forward propagation. If the<br />
output mode is not expected, the error signals will return<br />
along the orig<strong>in</strong> route, connection weights of neurons <strong>in</strong><br />
every layer should be corrected to make the error signals<br />
least, that is error back-propagation. Forward propagation<br />
and back propagation repeatedly, until the expected<br />
output mode can be obta<strong>in</strong>ed<br />
The learn<strong>in</strong>g process of BP network beg<strong>in</strong> from a set<br />
of random weights and thresholds, any selected samples<br />
can be <strong>in</strong>put. The output can be computed by forwardback<br />
method. Usually this error is big, the new weights<br />
and thresholds of the mode must be computed over aga<strong>in</strong><br />
by the back propagation. For all of the samples, the<br />
process should be done repeatedly aga<strong>in</strong> and aga<strong>in</strong>, to get<br />
the appo<strong>in</strong>ted accuracy. In the process of network<br />
operation, the system error and s<strong>in</strong>gle mode error can be<br />
followed. If the network learn<strong>in</strong>g successfully, the system<br />
errors will decrease with <strong>in</strong>creas<strong>in</strong>g of iterative time, at<br />
last converge at a set of steady weights and thresholds.<br />
y1<br />
y2<br />
y3<br />
x1<br />
x2<br />
x3<br />
Figure 1. the BP network model structure with three layers<br />
B. The Mathematical Pr<strong>in</strong>ciple of Back Propagation<br />
Network Model<br />
The propagation formulas for BP network study are<br />
used to adjust the weights and thresholds. In fact, the<br />
network study process is a process <strong>in</strong> which weights and<br />
thresholds of network connection are revised repeatedly<br />
accord<strong>in</strong>g to the propagation formula <strong>in</strong> the direction of<br />
least error. There are some symbol conventions:<br />
O : output of nodei ;<br />
i<br />
net : <strong>in</strong>put of node<br />
j<br />
j ;<br />
w : connected weight from node i to node j ;<br />
ij<br />
θ : threshold of node<br />
j<br />
j ;<br />
y : actual output of node<br />
k<br />
k <strong>in</strong> output layer;<br />
t : expected output of node<br />
k<br />
k <strong>in</strong> output layer.<br />
Obviously, for hidden node j :<br />
net<br />
j<br />
= ∑ wijO<br />
⎫<br />
i ⎪ ⎬<br />
(2)<br />
Oj = f( netj −θ<br />
j)<br />
⎪⎭<br />
In study process of BP algorithm, the errors of every<br />
output node can be computed accord<strong>in</strong>g to the follow<strong>in</strong>g<br />
formula:<br />
1<br />
2<br />
e= ∑ ( tk<br />
− yk)<br />
(3)<br />
2 k<br />
The connection weights can be corrected accord<strong>in</strong>g to<br />
the follow<strong>in</strong>g formula:<br />
w ( t+ 1) = w ( t)<br />
+Δ w<br />
(4)<br />
ij ij ij<br />
w<br />
In the formula, () ij<br />
t wij<br />
( t+ 1)<br />
and are separately<br />
connection weights from node j to node k at time t<br />
andt + 1 Δw<br />
;<br />
ij is variation of connection weights.<br />
In order to improve the connection weights <strong>in</strong> the<br />
Δwij<br />
gradient change direction of error E, can be<br />
computed:<br />
e<br />
Δ wij<br />
=−η ∂<br />
(5)<br />
∂ w<br />
In the formula, η is ga<strong>in</strong> factor,<br />
Thus<br />
Thus<br />
jk<br />
∂e<br />
∂w<br />
jk<br />
∂e<br />
∂e<br />
∂net<br />
=<br />
∂w ∂net ∂w<br />
∂net<br />
jk k jk<br />
∂<br />
can be computed:<br />
k<br />
= ∑ wjkOj = O (6)<br />
j<br />
∂wjk<br />
∂wjk<br />
j<br />
∂<br />
δk<br />
= ∂ net k<br />
∂e<br />
Δ w =− η =−ηδ<br />
O<br />
ij k j<br />
∂wjk<br />
When comput<strong>in</strong>gδ k<br />
, it is essential to dist<strong>in</strong>guish the<br />
output layer nodes and hidden layer nodes. If node k lies<br />
<strong>in</strong> output layer, thus:<br />
∂e<br />
∂e<br />
∂yk<br />
δk<br />
= =<br />
∂netk ∂yk ∂netk<br />
Because of<br />
∂ e<br />
∂y<br />
=− ( t −<br />
k<br />
k<br />
yk)<br />
= f ′( netk<br />
)<br />
∂yk<br />
∂netk<br />
Thus<br />
δk =−( tk −yk) f′<br />
( netk)<br />
⎫⎪ ⎬ (8)<br />
Δ wjk = η( tk − yk) f′<br />
( netk)<br />
Oj⎪⎭<br />
k<br />
(7)<br />
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If node k is not the node <strong>in</strong> output layer, connection<br />
weights effect on hidden node, then δ k<br />
can be computed<br />
by the follow<strong>in</strong>g formula:<br />
That is<br />
Thus<br />
∂e ∂e ∂Ok<br />
∂e δk<br />
= = = f ′( net<br />
k)<br />
∂net ∂O ∂net ∂O<br />
k k k k<br />
∂e<br />
(9)<br />
= ∑ δmw<br />
(10)<br />
km<br />
∂Ok<br />
δ = f ′( net ) ∑ δ w<br />
(11)<br />
k k m km<br />
m<br />
The formula shows that δ <strong>in</strong> low layer can be<br />
computed by δ <strong>in</strong> the upper layer.<br />
The learn<strong>in</strong>g process of BP network beg<strong>in</strong> from a set<br />
of random weights and thresholds, any selected samples<br />
can be <strong>in</strong>put. The output can be computed by forwardback<br />
method. Usually this error is big, the new weights<br />
and thresholds of the mode must be computed over aga<strong>in</strong><br />
by the back propagation. For all of the samples, the<br />
process should be done repeatedly aga<strong>in</strong> and aga<strong>in</strong>, to get<br />
the appo<strong>in</strong>ted accuracy. In the process of network<br />
operation, the system error and s<strong>in</strong>gle mode error can be<br />
followed. If the network learn<strong>in</strong>g successfully, the system<br />
errors will decrease with <strong>in</strong>creas<strong>in</strong>g of iterative time, at<br />
last converge at a set of steady weights and thresholds. [7]<br />
C. The Study Algorithm of Back Propagation Network<br />
In BP network model, the study algorithm of BP<br />
network can be described as the follow<strong>in</strong>g rules.<br />
Step 1 Initializ<strong>in</strong>g study parameters and BP network<br />
parameters. That is to set random numbers <strong>in</strong> [ − 1,1] for<br />
Neuron threshold and connection weights <strong>in</strong> hidden<br />
layers and output layers.<br />
Step 2 Propos<strong>in</strong>g the tra<strong>in</strong><strong>in</strong>g mode of BP network.<br />
That is to select a tra<strong>in</strong><strong>in</strong>g mode from the tra<strong>in</strong><strong>in</strong>g mode<br />
set, and put the <strong>in</strong>put mode and expected output mode to<br />
the BP network.<br />
Step 3 Forward propagation process. That is to<br />
compute the output mode of the network from the No.1<br />
hidden layer for the given <strong>in</strong>put layer. If error energiz<strong>in</strong>g,<br />
execut<strong>in</strong>g the step 4, else return<strong>in</strong>g to step 2, and<br />
provid<strong>in</strong>g next tra<strong>in</strong><strong>in</strong>g mode for the algorithm.<br />
Step 4 Back propagation process. That is to correct the<br />
connection weight of every unit <strong>in</strong> different layer from<br />
output layer to the first hidden layer, and follow<strong>in</strong>g the<br />
rules:<br />
1) Comput<strong>in</strong>g the error δ k<br />
of different units <strong>in</strong> the<br />
same layer.<br />
2) Correct<strong>in</strong>g the connection weights and threshold.<br />
For connection weights, the correct<strong>in</strong>g formula is:<br />
w ( t+ 1) = w ( t)<br />
+ ηδ O (12)<br />
jk jk k j<br />
For threshold, the correction method is same as the<br />
study method of connection weights.<br />
3) Repeat<strong>in</strong>g the Above-mentioned correct<strong>in</strong>g process<br />
to get expected output mode.<br />
Step 5 Turn back to step 2, and do<strong>in</strong>g step 2 to step 3<br />
for the every tra<strong>in</strong><strong>in</strong>g mode of tra<strong>in</strong><strong>in</strong>g mode set, until<br />
every tra<strong>in</strong><strong>in</strong>g mode meet the expected output.<br />
III. THE PRINCIPLE OF BACK PROPAGATION NEURAL<br />
NETWORK MODEL<br />
A. The Basic Pr<strong>in</strong>ciple of Fuzzy Mathematics<br />
Assumed that X represents a set of some objects,<br />
which is called co doma<strong>in</strong>. For a subset A <strong>in</strong> X , it can<br />
be expressed by its characteristic function, that is<br />
⎧1<br />
x ∈ A<br />
μA( x)<br />
= ⎨<br />
(13)<br />
⎩0<br />
x ∈ A<br />
In this, μ A<br />
is a function def<strong>in</strong>ed <strong>in</strong> X , its values<br />
belong to{ 0,1 } ,which is called characteristic function of<br />
A . For x ∈ X , if μ ( x A<br />
) = 1, thus, x is element of A .<br />
But if μ ( x A<br />
) = 0, thus, x isn’t the element of A . So we<br />
can def<strong>in</strong>e fuzzy sets:<br />
In co doma<strong>in</strong> X , for any element x ∈ X , if there is a<br />
formula correspond<strong>in</strong>g real function μ A( x ) :<br />
μA( x): X → [0,1]<br />
(14)<br />
X → μA( x)<br />
Then all elements x meet<strong>in</strong>g the formula assemble a<br />
set which is a fuzzy set A <strong>in</strong> set X . For x ∈ X , μ is<br />
A<br />
membership function of A . μ A ( x ) is called membership<br />
degree from x to A .[6]<br />
The Relationship that expresses uncerta<strong>in</strong> relationship<br />
us<strong>in</strong>g fuzzy Sets is def<strong>in</strong>ed fuzzy relation. [8] Fuzzy<br />
relation R between set X andY is fuzzy subset def<strong>in</strong>ed<br />
<strong>in</strong> X × Y , its membership function is shown as:<br />
μ<br />
R<br />
: X × Y → [0,1] (15)<br />
If X is same asY , so R is called the fuzzy relation <strong>in</strong> X .<br />
If the co doma<strong>in</strong> is product of n sets Xi<br />
( i = 1,2, , n)<br />
X × X × × X , its correspond<strong>in</strong>g fuzzy relationship<br />
1 2 n<br />
R is called n dimensions fuzzy relation.<br />
If X and Y are both limited subsets,<br />
X = { x , x , , x m<br />
} , Y = { y1, y2, , y n<br />
} , thus the<br />
then<br />
1 2<br />
fuzzy relation <strong>in</strong> X<br />
R<br />
× Y can be expressed by :<br />
⎡ μR( x1, y1) μR( x1, y2) μR( x1, yn)<br />
⎤<br />
⎢<br />
μ ( x , y ) μ ( x , y ) μ ( x , y )<br />
⎥<br />
⎢<br />
<br />
⎥<br />
<br />
<br />
⎢<br />
⎥<br />
⎣μR( xm, y1) μR( xm, y2) μR( xm, yn)<br />
⎦<br />
R 2 1 R 2 2 R 2 n<br />
= ⎢ ⎥<br />
(16)<br />
The above matrix is called fuzzy matrix, its<br />
element μ ( x , y ) <strong>in</strong> the scope of 0 between 1.<br />
R i i<br />
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B. The Design of Membership Degree BP Neural<br />
Network<br />
The paper adopted a three layers BP network to build<br />
the membership degree BP network for water quality<br />
assessment. In the structure, the network has one <strong>in</strong>put<br />
layer one output layer and one hidden layer. The output<br />
layer can expressed water quality classification by one<br />
neuron, actual test<strong>in</strong>g parameters are six, so <strong>in</strong>put layer<br />
has six neurons, hidden layer has three neurons [9].<br />
In order to make the assessment more objective and<br />
certa<strong>in</strong>, this paper puts the membership degree of fuzzy<br />
mathematics <strong>in</strong>to BP network. The membership degree<br />
BP network model is built on comb<strong>in</strong><strong>in</strong>g the fuzzy system<br />
and neural network <strong>in</strong> series. In the series connection,<br />
output of neural network is <strong>in</strong>put of the fuzzy system.<br />
Membership degree can be computed, then the exact and<br />
concrete water quality classification can be put out. The<br />
membership degree BP network for water quality<br />
assessment is shown as fig. 2.<br />
In the formula, abstand , for the classification of<br />
neighbor<strong>in</strong>g two water quality samples, the membership<br />
degree to every standard water quality classification of<br />
test sample can be computed by the formula (17).<br />
IV. THE PRINCIPLE OF BACK PROPAGATION NEURAL<br />
NETWORK MODEL<br />
A.. The Model of BP Neural Network Algorithm<br />
Accord<strong>in</strong>g to the po<strong>in</strong>t of mathematics, BP algorithm is<br />
a generalized function convergence numeric method, and<br />
it has tra<strong>in</strong><strong>in</strong>g and test<strong>in</strong>g processes. The whole tra<strong>in</strong><strong>in</strong>g<br />
process <strong>in</strong>cludes forward and back propagation. After<br />
be<strong>in</strong>g built, the BP network model is tested by other<br />
samples to testify the effectiveness and validity of the<br />
model. The results show that the BP network model and<br />
its algorithm are effective. The algorithm of BP neural<br />
network is shown as <strong>in</strong> fig.3.<br />
Figure 2. The framework of BP neural network comb<strong>in</strong><strong>in</strong>g<br />
membership degree<br />
Accord<strong>in</strong>g to fuzzy mathematics theory, the standard<br />
water quality classification 1-5 as co doma<strong>in</strong> can be<br />
def<strong>in</strong>ed. For n assessment parameters of some standard<br />
water quality classification, we suppose that the<br />
membership degree to itself is zero, so a fuzzy subset E<br />
can be gotten. We suppose that the membership degree to<br />
other is zero, subset F can also be gotten. In here, the<br />
membership degree to standard water quality<br />
classification for n assessment parameters of other water<br />
quality samples must belong to[0,1] , and build<strong>in</strong>g fuzzy<br />
subset A . Therefore, the problem of assess<strong>in</strong>g water<br />
quality sample transforms <strong>in</strong>to comput<strong>in</strong>g the<br />
membership degree to two neighbor<strong>in</strong>g standard water<br />
quality classification. In this paper, the membership<br />
function is built as follow<strong>in</strong>g formula.<br />
⎧1<br />
x = a<br />
⎪<br />
ux ( ) = ⎨1 − f( x)<br />
a< x<<br />
b<br />
⎪<br />
⎩0<br />
x = b<br />
(17)<br />
Figure 3. The algorithm process of BP neural network<br />
B. The Tra<strong>in</strong><strong>in</strong>g of BP Neural Network<br />
The whole network tra<strong>in</strong><strong>in</strong>g process <strong>in</strong>cludes forward<br />
propagation and error back-propagation, the tra<strong>in</strong><strong>in</strong>g<br />
process are shown as followed.<br />
1) Assignment the weighs w_<br />
xh , w_<br />
hy between<br />
nodes and need threshold u_<br />
h, u_<br />
y , the assigned<br />
values are Nonzero Random <strong>in</strong>itial valuebetween (-1,1).<br />
2) Inputt<strong>in</strong>g <strong>in</strong>put vector X of one tra<strong>in</strong><strong>in</strong>g sample and<br />
target output vector T .<br />
3) Comput<strong>in</strong>g output vector Y .<br />
Comput<strong>in</strong>g output vector H of hidden layers:<br />
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∑<br />
neth = w _ xhih⋅X i<br />
−u _ hh<br />
⎫<br />
⎪<br />
i<br />
⎬<br />
Hh = ( neth) = 1 1+ exp( −neth)<br />
⎪⎭<br />
Comput<strong>in</strong>g output vector Y of output layers:<br />
net<br />
j<br />
= ∑ w _ hyhj ⋅Hh −u _ y ⎫<br />
j<br />
⎪<br />
h<br />
⎬<br />
Yj = ( netj) = 1 (1 + exp( −netj))<br />
⎪ ⎭<br />
4) Comput<strong>in</strong>g the difference mountδ<br />
δ<br />
j<br />
(18)<br />
(19)<br />
Comput<strong>in</strong>g difference mount of output layers<br />
δ = Y (1 −Y )( T − Y ) (20)<br />
j j j j j<br />
δ<br />
Comput<strong>in</strong>g difference mount of hidden layers<br />
h :<br />
δ = H (1 −H ) ∑ w_<br />
hy δ (21)<br />
h h h hj j<br />
j<br />
5) Comput<strong>in</strong>g correction mount of weigh dw , and<br />
correction mount of threshold du .<br />
Comput<strong>in</strong>g weigh correction mount of output layers<br />
dw _ hy , correction mount of threshold du _ y :<br />
dw _ hyhj = δ<br />
jH<br />
h ⎫⎪ ⎬ (22)<br />
du _ y<br />
j<br />
=−ηδ<br />
j ⎪⎭<br />
Comput<strong>in</strong>g weigh correction mount of hidden layers<br />
dw , correction mount of threshold du :<br />
dw _ xhih = ηδh X<br />
i ⎫<br />
⎬ (23)<br />
du _ H<br />
h<br />
=−ηδh<br />
⎭<br />
6) Updat<strong>in</strong>g weigh mount w_<br />
hy , and threshold<br />
u_<br />
y.<br />
Updat<strong>in</strong>g weigh mount of output layer w_<br />
hy and<br />
threshold u_<br />
y:<br />
w _ hyhj = w _ hyhj + dw _ hyhj<br />
⎫⎪ ⎬ (24)<br />
u_ yj = u_ yj + du_<br />
yj<br />
⎪⎭<br />
Updat<strong>in</strong>g weigh mount of hidden layer w_<br />
hy and<br />
threshold u_<br />
y:<br />
w _ xhih = w _ xhih + dw _ xhih<br />
⎫<br />
⎬ (25)<br />
u_ hh = u_ hh + du_<br />
hh<br />
⎭<br />
(c) The test<strong>in</strong>g of BP neural network<br />
After be<strong>in</strong>g build<strong>in</strong>g, the character of model must be<br />
tested by us<strong>in</strong>g the samples which are not used <strong>in</strong><br />
build<strong>in</strong>g the model, so that the Correctness and<br />
Practicality of the model can be verified.<br />
The comput<strong>in</strong>g format of the test<strong>in</strong>g process is showed<br />
as followed.<br />
1) Adopted the stable Weight matrices after tra<strong>in</strong>ed<br />
w_<br />
xh, w_<br />
hy and Threshold vector u_<br />
h, u_<br />
y.<br />
2)Input vector X of test<strong>in</strong>g samples.<br />
3)Comput<strong>in</strong>g output vector Y .<br />
Comput<strong>in</strong>g the output vector of hidden layer H :<br />
∑<br />
neth = w _ xhih⋅X i<br />
−u _ hh⎫<br />
i<br />
⎪<br />
1 ⎬<br />
Hh = f( neth)<br />
= ⎪<br />
−neth<br />
1+ exp ⎪⎭<br />
(27)<br />
Comput<strong>in</strong>g the output vector of hidden layer Y :<br />
net<br />
j<br />
= ∑ w _ hyhj⋅H h<br />
−u _ y ⎫<br />
j<br />
h<br />
⎪<br />
1 ⎬ (28)<br />
Yj = f( netj)<br />
=<br />
−net<br />
⎪<br />
j<br />
1+ exp ⎪⎭<br />
V. THE EXPERIMENT AND ANALYSIS OF BP NEURAL<br />
NETWORK FOR WATER QUALITY ASSESSMENT<br />
In the learn<strong>in</strong>g process of network, some standard<br />
water quality classification is adopted <strong>in</strong> learn<strong>in</strong>g samples.<br />
With consider<strong>in</strong>g that the range of activation function<br />
is[0,1] , and water quality classification is from the first<br />
class to the fifth class, so the five water quality<br />
classifications are only part of the whole range, and no<br />
attach<strong>in</strong>g the limited values 0 and 1.<br />
In this paper, target outputs are 0.1,0.3,0.5,0.7,0.9 ,<br />
and the output represents No.1-5 water quality<br />
classifications. As the most important parameters <strong>in</strong><br />
debugg<strong>in</strong>g the BP network, learn<strong>in</strong>g rate η = 0.68 ,<br />
Impulse coefficient α = 0.5 , then the network can be<br />
tra<strong>in</strong>ed after 1600 iterations.<br />
(a) Errors curve of learn<strong>in</strong>g process<br />
(b) Test<strong>in</strong>g result curve of network for some samples<br />
Fig. 4 The learn<strong>in</strong>g process curve of the network<br />
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Then the accuracy of the tra<strong>in</strong>ed network can be<br />
accepted. The accuracy of the tra<strong>in</strong>ed network is accepted,<br />
and the learn<strong>in</strong>g process curves are shown <strong>in</strong> fig 4.<br />
After be<strong>in</strong>g tra<strong>in</strong>ed, the BP network has held the<br />
characters of water quality classification, which can<br />
recognize the samples effectively. In experiment, the<br />
test<strong>in</strong>g results of membership degree BP network are<br />
shown as table1 & table 2.<br />
Sample<br />
Index<br />
Dissolved<br />
oxygen (mg/l)<br />
TABLE I.<br />
THE INTERMEDIATE RESULTS OF MEMBERSHIP DEGREE BP NETWORK<br />
BOD5<br />
COD Mn<br />
Total<br />
phosphorus<br />
Ammonia<br />
Nitrate<br />
Output of<br />
network<br />
Water quality<br />
classification<br />
1 5.02 2.86 4.61 0.81 0.023 4.39 0.41 Ⅱ~ Ⅲ, near Ⅲ<br />
2 8.91 0.77 1.17 0.18 0.015 0.13 0.093 Ⅰ<br />
3 6.78 3.42 3.32 0.23 0.07 0.93 0.17 Ⅰ~ Ⅱ, near Ⅰ<br />
4 7.56 0.71 0.71 0.19 0 0.1 0.096 Ⅰ<br />
5 3.54 6.15 8.05 1.36 0.05 1.00 0.62 Ⅲ~ Ⅳ, near Ⅳ<br />
6 4.13 1.33 1.24 0.46 0.02 1.1 0.22 Ⅰ~ Ⅱ, near Ⅱ<br />
7 10.22 1.33 1.26 0.17 0 0.06 0.092 Ⅰ<br />
8 6.32 4.57 5.56 0.78 0.19 0.97 0.42 Ⅱ~ Ⅲ, near Ⅲ<br />
9 9.67 1.57 3.16 0.21 0 0.31 0.1 Ⅰ~ Ⅱ, near Ⅰ<br />
10 4.96 6.58 6.55 1.1 0 0.23 0.56 Ⅲ~ Ⅳ, near Ⅲ<br />
TABLE II.<br />
THE MEMBERSHIP DEGREE TESTING RESULTS OF SAMPLES TO STANDARD WATER QUALITY<br />
Sample<br />
1 2 3 4 5 6 7 8 9 10<br />
Classification<br />
Ⅰ 0 0.939 0.696 0.971 0 0.393 0.997 0 0.92 0<br />
Ⅱ 0.425 0.061 0.304 0.029 0 0.607 0.003 0.45 0.08 0.729<br />
Ⅲ 0.575 0 0 0 0.403 0 00 0.55 0 0.271<br />
Ⅳ 0 0 0 0 0.597 0 0 0 0 0<br />
Ⅴ 0 0 0 0 0 0 0 0 0 0<br />
Fig.7 the Software structure of the prediction and warn<strong>in</strong>g system<br />
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VI. THE NEW WATER QUALITY ASSESSMENT METHOD<br />
APPLIED IN THE PREDICTION AND WARNING SYSTEM<br />
In the paper, the automatic prediction and warn<strong>in</strong>g<br />
system based on the new water quality assessment<br />
methods, which is a whole <strong>in</strong>formation system <strong>in</strong>tegrat<strong>in</strong>g<br />
computer hardware technique, communication technique,<br />
and software Intelligent analysis technology. The system<br />
<strong>in</strong>cludes monitor<strong>in</strong>g term<strong>in</strong>al, user term<strong>in</strong>al, data<br />
transmission channel and data management center. The<br />
prediction and warn<strong>in</strong>g system can provide some water<br />
quality <strong>in</strong>formation for the department to mak<strong>in</strong>g some<br />
decision. In the system, the water quality can be predicted<br />
based on hydrology and water quality data, natural and<br />
geographical environment, by the methods of software<br />
technology and theory of mathematical model. The water<br />
quality parameters predicted by the system <strong>in</strong>clude<br />
dissolved oxygen, total phosphorus, ammonia nitrogen,<br />
nitrate nitrogen, permanganate <strong>in</strong>dex and BOD 5. The<br />
software structure of system is shown as fig.7, which can<br />
be divided <strong>in</strong>to water quality database module, <strong>in</strong>tegrated<br />
<strong>in</strong>formation analysis module, assessment report<br />
generation module, water quality trend analysis module.<br />
The water quality database system <strong>in</strong>cludes both water<br />
quality database and geography <strong>in</strong>formation database.<br />
Accord<strong>in</strong>g to the above database, water quality data can<br />
be counted and evaluated. The water quality database<br />
covers monitor<strong>in</strong>g network <strong>in</strong>formation, all k<strong>in</strong>ds of<br />
water data and water composition for example total<br />
phosphorus, ammonia nitrogen, nitrate nitrogen,<br />
permanganate <strong>in</strong>dex and BOD 5 etc. The geography<br />
<strong>in</strong>formation database ma<strong>in</strong>ly <strong>in</strong>cludes all k<strong>in</strong>ds of<br />
geographical zon<strong>in</strong>g maps. Based on web, the statistics<br />
and evaluation reports can be archived, queried and<br />
published automatically. In the system, the water quality<br />
trends can be predicted base on the BP model.<br />
VII. CONCLUSIONS<br />
The new water quality assessment method proposed <strong>in</strong><br />
this paper <strong>in</strong>tegrates the fuzzy mathematics theory and<br />
artificial neural network. The theoretical analysis shows<br />
that the assessment method has theoretical feasibility and<br />
great practical utility. The new ideal and method <strong>in</strong> the<br />
paper propose a new way of water quality assessment and<br />
develop the application of artificial neural network. The<br />
experimental results and research demonstrate that the<br />
water quality assessment method has good prospects for<br />
further application and development.<br />
VIII. ACKNOWLEDGMENT<br />
This research was supported <strong>in</strong> part by JiL<strong>in</strong> prov<strong>in</strong>ce<br />
science and technology development plan project<br />
(No.20110421) and foundation of Jil<strong>in</strong> prov<strong>in</strong>ce<br />
educational committee (No.20110232). All the authors<br />
would like to thank the sponsors and the colleagues who<br />
give us good suggestions and helps dur<strong>in</strong>g the research.<br />
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[6] Zhao ZhenYu, Xu YongMao. The Base and Application of<br />
Fuzzy theory and neural network, T<strong>in</strong>g Hua Press, 1997.<br />
[7] Zaclch L. “A. Fuzzy Set”, Information and Control , 1965,<br />
Vol.8, pp. 338-353.<br />
[8] Mart<strong>in</strong> T H, Howard B D, Mark H B. Neural Network<br />
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[9] Daniel J. Fisher et al, “The Relative Acute Toxity of<br />
Cont<strong>in</strong>uous and Intermittent Exposures of Chlor<strong>in</strong>e and<br />
Brom<strong>in</strong>e to Aquatic Organism <strong>in</strong> the Presence and Absence<br />
of Ammonia”, Water Research, 1999, Vol 33 (3), pp. 760-<br />
768.<br />
[10] Simon Hayk<strong>in</strong>. Neural Networks: A Comprehensive<br />
Foundation, Beij<strong>in</strong>g, Mechanical Industry Press, 2004.<br />
[11] Sasikumar K. and Mujumdar P.P. “Fuzzy Opimization<br />
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[12] Donald H. Burn. “Water Quality Management through<br />
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Environmental Eng<strong>in</strong>eer<strong>in</strong>g, 1989, Vol 115 (5), pp. 1011-<br />
1024.<br />
[13] Tanner R. et al. “Food Cha<strong>in</strong> Organism <strong>in</strong> Hypersal<strong>in</strong>e<br />
Industrial Evaporation”, Journal of Water Environ<br />
Research, 1999, Vol 71 (4), pp. 494-501.<br />
[14] Richard N. Palmer, et al. “Optimization of Water Quality<br />
Monitor<strong>in</strong>g Networks”, Journal of Water Resources<br />
Plann<strong>in</strong>g and Management, 1985, Vol 111(4), pp. 478-493.<br />
[15] Amity K. S<strong>in</strong>halese, et al. “Nonl<strong>in</strong>ear Optimization Model<br />
for Screen<strong>in</strong>g Multipurpose Reservoir System”, Journal of<br />
Water Resources Plann<strong>in</strong>g and Management, 1999, Vol<br />
125 (4), pp. 229-233.<br />
[16] Shang Gao, Zaiyue Zhang, Cungen Cao. “A BP Neural<br />
Network Realization <strong>in</strong> the Measurement of Material<br />
Permittivity”, Vol 6, No 6 (2011): Special <strong>Issue</strong>: Recent<br />
Advances <strong>in</strong> Data M<strong>in</strong><strong>in</strong>g and Data Management.<br />
[17] P<strong>in</strong>g Zhang, XiaoHong Hao, HengJie Li et al. “Research of<br />
the Electro-hydraulic Servo System Based on RBF Fuzzy<br />
Neural Network Controller”, Vol 7, No 9 (2012): Special<br />
<strong>Issue</strong>: Advances <strong>in</strong> Information and Networks.<br />
[18] Huawang Shi, Wanq<strong>in</strong>g Li Vol 5. “Risk Evaluation Model<br />
on Enterprises’ Complex Information System: A Study<br />
Based on the BP Neural Network”, No 1 (2010): Special<br />
<strong>Issue</strong>: Recent Trends and Advances <strong>in</strong> Software<br />
Technology and Applications<br />
M<strong>in</strong>g Xue born <strong>in</strong> Jil<strong>in</strong>, Ch<strong>in</strong>a, <strong>in</strong> 1970, received the B.S., M.S.<br />
degrees from Jil<strong>in</strong> University, Ch<strong>in</strong>a, <strong>in</strong> 1990, 1995,<br />
respectively, all <strong>in</strong> Computer Science and Technology. And<br />
now she is currently a associate professor <strong>in</strong> department of<br />
electrical and <strong>in</strong>formation, Chang Chun Institute of Technology.<br />
Her current research <strong>in</strong>terests <strong>in</strong>clude computer technology,<br />
software eng<strong>in</strong>eer<strong>in</strong>g.<br />
© 2013 ACADEMY PUBLISHER
1594 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
An Isolated Dual-Input Converter for<br />
Grid/PV Hybrid Power Systems<br />
Yu-L<strong>in</strong> Juan<br />
National Changhua University of Education Department of Electrical Eng<strong>in</strong>eer<strong>in</strong>g, Changhua City, Taiwan<br />
Email: yljuan0815@cc.ncue.edu.tw<br />
Hs<strong>in</strong>-Y<strong>in</strong>g Yang, Peng-Lai Chen<br />
National Changhua University of Education Department of Electrical Eng<strong>in</strong>eer<strong>in</strong>g, Changhua City, Taiwan<br />
Email: a13816@abc.ncue.edu.tw<br />
Abstract—An isolated dual-<strong>in</strong>put power converter for a<br />
grid/photovoltaic (PV) hybrid power <strong>in</strong>door light<strong>in</strong>g system<br />
is proposed <strong>in</strong> this paper. The proposed converter can be<br />
operated <strong>in</strong> s<strong>in</strong>gle power supply mode or hybrid power<br />
supply mode. While the available PV power is <strong>in</strong>sufficient<br />
for the load demand, the proposed dual-<strong>in</strong>put converter will<br />
automatically deliver the complement power from the grid.<br />
The power complement<strong>in</strong>g is achieved by two <strong>in</strong>dependent<br />
control loops of the PV power and the grid power. F<strong>in</strong>ally, a<br />
prototype for a 36W LED light<strong>in</strong>g module is constructed to<br />
verify the validity of the proposed converter. From the<br />
experimental results, it can be seen that a smooth 24V/1.5A<br />
output power for the LED light<strong>in</strong>g module can be provided<br />
even while the PV power is <strong>in</strong>sufficient or unavailable.<br />
Index Terms—hybrid power system, dual-<strong>in</strong>put converter,<br />
PV array<br />
I. INTRODUCTION<br />
Renewable energy systems have attracted a lot of<br />
attention due to the global warm<strong>in</strong>g and fuel crisis [1]-[6].<br />
It is seen that the power consumption of office light<strong>in</strong>g<br />
systems may take 20% to 60% of total energy<br />
consumption <strong>in</strong> daily life [7]. Among the renewable<br />
energy resources, PV power has been considered as a<br />
more stable and reliable power source [8]. In most of PV<br />
power systems, the battery storage device is required to<br />
provide smoother electricity. However, the costs of<br />
<strong>in</strong>stall<strong>in</strong>g PV arrays and ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g battery pack are still<br />
considerable for consumers. In recent studies, reduc<strong>in</strong>g<br />
the consumption of grid power by comb<strong>in</strong><strong>in</strong>g renewable<br />
resources is one of the major trends. To reduce the system<br />
cost and provide a stable power supply, several types of<br />
multi-<strong>in</strong>put converters with renewable energy resources<br />
and grid power hybrid have been proposed [9]-[18]. The<br />
dependence on grid power can then be reduced and the<br />
output power quality is also rema<strong>in</strong>ed.<br />
Basically, these multi-<strong>in</strong>put converters can be<br />
classified <strong>in</strong>to three types of topology. In first type, a<br />
multi-w<strong>in</strong>d<strong>in</strong>g transformer is used to <strong>in</strong>tegrate the multi<br />
<strong>in</strong>put power sources with s<strong>in</strong>gle core [12]-[14]. In second<br />
type of converter, a pulsat<strong>in</strong>g voltage source cell (PVSC)<br />
is used as the power coupl<strong>in</strong>g component [9],[15]-[18].<br />
Because the <strong>in</strong>ductor is the ma<strong>in</strong> component <strong>in</strong> the PVSC,<br />
the major design criteria of the PVSC-type converter are<br />
the cont<strong>in</strong>uity of <strong>in</strong>ductor current and the copper loss of<br />
<strong>in</strong>ductor w<strong>in</strong>d<strong>in</strong>g. In the last type converter, a pulsat<strong>in</strong>g<br />
current source cell (PCSC) is adopted as the power<br />
coupl<strong>in</strong>g component [17],[18]. The copper loss is<br />
relatively much lower because the multi-<strong>in</strong>put power<br />
sources are coupled by capacitors [18].<br />
Figure 1. Grid/PV hybrid power system with proposed dual-<strong>in</strong>put converter<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1594-1601
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1595<br />
Figure 2. Power supply modes of the grid/PV hybrid power system<br />
The circuit diagram of the grid/PV hybrid power<br />
system with proposed dual-<strong>in</strong>put converter is shown <strong>in</strong><br />
Fig. 1. The system can be operated <strong>in</strong> s<strong>in</strong>gle power<br />
supply mode or hybrid power supply mode as shown <strong>in</strong><br />
Fig. 2. While the PV power is unavailable, the converter<br />
would be operated <strong>in</strong> s<strong>in</strong>gle power supply mode, namely,<br />
the grid supply mode. If the PV power can only provide<br />
part of the load, the converter will be operated <strong>in</strong> hybrid<br />
power supply mode for deliver<strong>in</strong>g the rest part of power<br />
from the grid to the load side. As a result, the commonly<br />
required battery pack <strong>in</strong> the stand-alone system can then<br />
be replaced by the grid to provide smooth electricity. The<br />
PV array <strong>in</strong>stallation capacity can also be reduced<br />
because additional capacity for presort<strong>in</strong>g <strong>in</strong> the battery<br />
pack is not required. Therefore, resulted system<br />
<strong>in</strong>stallation and ma<strong>in</strong>tenance costs can both be reduced. It<br />
would be very helpful to encourage consumers to<br />
purchase a PV power system as an alternative electricity<br />
system.<br />
II. OPERATION PRINCIPLE OF THE PRPOSED CONVERTER<br />
For the proposed converter shown <strong>in</strong> Fig. 1, the active<br />
switch S 1 is adopted to control the power flow from the<br />
grid to the load through the coupl<strong>in</strong>g capacitor C 1 . The<br />
other <strong>in</strong>put term<strong>in</strong>al is connected to the PV array and the<br />
PV output power is controlled by the active switch S 2 .<br />
The PV power is delivered to the load side through the<br />
coupl<strong>in</strong>g capacitor C 1 as well. Once the available power<br />
from PV array is lower than the load demand, the<br />
proposed converter would deliver the complement power<br />
from the grid to the load side accord<strong>in</strong>g to the feedback<br />
<strong>in</strong>formation about the load current. Based on the<br />
supply<strong>in</strong>g power sources, there are three power supply<br />
modes of the proposed converter as shown <strong>in</strong> Fig. 2. First,<br />
if the PV power is unavailable, the converter is operated<br />
<strong>in</strong> the grid supply mode. Then the converter would be<br />
changed <strong>in</strong>to the PV supply mode while the available PV<br />
power is higher than the load demand. F<strong>in</strong>ally, if the PV<br />
power is available but not enough for the load, the<br />
converter would be operated <strong>in</strong> the third mode, namely<br />
the hybrid supply mode.<br />
While the two sources are simultaneously deliver<strong>in</strong>g<br />
power, i.e. <strong>in</strong> the hybrid supply mode, there would be six<br />
operation modes <strong>in</strong> one switch<strong>in</strong>g cycle as shown <strong>in</strong> Fig.<br />
3. The relative waveforms <strong>in</strong> one switch<strong>in</strong>g cycle are<br />
shown <strong>in</strong> Fig. 4. It can be seen that the two active<br />
switches are controlled with <strong>in</strong>terleave phase shift<br />
technique to reduce the voltage and current ripple of the<br />
coupled capacitor. The correspond<strong>in</strong>g operation<br />
pr<strong>in</strong>ciples are described as follows:<br />
Mode1—(t 0 ≦t
1596 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
(a) Mode 1<br />
(b) Mode 2<br />
(c) Mode 3<br />
(d) Mode 4<br />
© 2013 ACADEMY PUBLISHER
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(e) Mode 5<br />
(f) Mode 6<br />
Figure 3. Equivalent circuits of the proposed converter <strong>in</strong> different operation modes<br />
Figure 4. Relative waveforms <strong>in</strong> one switch<strong>in</strong>g cycle<br />
III. POWER COMPLEMENT CONTROLLER<br />
From section II, it is seen that the power drawn from<br />
the grid is controlled by the active switch S 1 and firstly<br />
buffered <strong>in</strong> the coupl<strong>in</strong>g capacitor. Then, it would be<br />
transmitted to the load side through the <strong>in</strong>ductor L 2 . The<br />
other <strong>in</strong>put power, i.e. the PV power, is controlled by the<br />
active switch S 2 . The power processes are similar to an<br />
isolated Cuk converter. The PV power would be<br />
delivered to the load side through the transformer T 2 and<br />
coupl<strong>in</strong>g capacitor C 1 . Obviously, the two power flows<br />
are both unidirectional and transferred to the load side<br />
<strong>in</strong>dividually. Therefore, the two active switches can be<br />
<strong>in</strong>dependently used to control the power from each <strong>in</strong>put<br />
source. To achieve automatically deliver<strong>in</strong>g the<br />
complement power part from the grid to provide smooth<br />
electricity for the load, a power complement controller<br />
for the proposed converter is shown <strong>in</strong> Fig. 5. It is seen<br />
that the power complement controller is composed of two<br />
<strong>in</strong>dependent control loops for grid power and PV power<br />
respectively.<br />
Usually, a maximum power po<strong>in</strong>t track<strong>in</strong>g (MPPT)<br />
would be adopted to fully utilize the renewable PV power.<br />
Hence, the gat<strong>in</strong>g signal of the active switch S 2 is<br />
provided accord<strong>in</strong>g to the adopted MPPT strategy. The<br />
MPPT strategy is out of the scope of this study and would<br />
not be further described. Basically, either one of the wellknown<br />
current-controlled type MPPT strategies can be<br />
directly applied to this controller. And the gat<strong>in</strong>g signal<br />
of the active switch S 1 is then decided accord<strong>in</strong>g to the<br />
amount of the complement power for the load. In this<br />
paper, a well-known hill-climb<strong>in</strong>g search<strong>in</strong>g MPPT<br />
strategy is adopted <strong>in</strong> the prototype light<strong>in</strong>g system. For<br />
the control loop of PV power, the PV current is regulated<br />
to the current command for extract<strong>in</strong>g maximum PV<br />
power.<br />
© 2013 ACADEMY PUBLISHER
1598 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 5. Power complement controller diagram<br />
The active switch S 2 is driven by gat<strong>in</strong>g signal V GS2 to<br />
control the <strong>in</strong>put current from PV array. For the control<br />
loop of grid power, the ma<strong>in</strong> object is to deliver the<br />
complement power for rema<strong>in</strong><strong>in</strong>g smooth current to the<br />
LED light<strong>in</strong>g module. Therefore, the load current I o is fed<br />
back and needs to be regulated to the load current<br />
command I o * which is decided by the normal operat<strong>in</strong>g<br />
current of LED module. Then the active switch S 1 will be<br />
driven by the gat<strong>in</strong>g signal V GS1 to control the <strong>in</strong>put grid<br />
power for complement<strong>in</strong>g the power demand.<br />
IV. EXPERIMENT RESULTS<br />
To evaluate the performance and validity of proposed<br />
converter, a prototype with a 45W PV array for a 36W<br />
LED light<strong>in</strong>g module is constructed as shown <strong>in</strong> Fig. 6.<br />
The controlled is implemented by a microprocessor,<br />
HT46R23, and relative electrical parameters are shown <strong>in</strong><br />
Table I. The <strong>in</strong>put current from PV array and load current<br />
are sampled by hall sensors. Fig. 7 shows the waveforms<br />
of the grid <strong>in</strong>put current, PV <strong>in</strong>put power and the load<br />
condition. In Fig. 7(a), it can be seen that firstly the load<br />
demand is only provided by the grid because the PV<br />
power is unavailable. Then, the PV power is started to<br />
provide its maximum power, but the available PV power<br />
is still not enough for the load.<br />
Therefore, the converter is automatically changed <strong>in</strong>to<br />
hybrid supply mode for deliver<strong>in</strong>g the complement power<br />
from the grid. Once, the maximum PV power is higher<br />
than the load demand, there is no complement power<br />
required from grid. As a result, the output power for the<br />
LED module as shown <strong>in</strong> Fig. 7(b) can then be wellcontrolled<br />
at 36W/24V/1.5A. Fig. 8 shows the waveforms<br />
of the capacitor C 1 while the converter is operated <strong>in</strong><br />
hybrid supply mode with 50% PV power and 50% grid<br />
power. It can be seen that the current ripple and peak<br />
current are reduced because of adopt<strong>in</strong>g the <strong>in</strong>terleave<br />
phase shift technique. Fig. 9 shows the efficiency of the<br />
proposed converter <strong>in</strong> s<strong>in</strong>gle power supply mode with PV<br />
power or Grid power <strong>in</strong>put. The efficiency <strong>in</strong> hybrid<br />
power supply mode is measured and shown <strong>in</strong> Fig. 10,<br />
and the def<strong>in</strong>ition of the efficiency η is given as<br />
follow<strong>in</strong>g:<br />
PO<br />
η =<br />
(1)<br />
P + P<br />
PV<br />
Grid<br />
Table I. PARAMETERS OF PROTOTYPE SYSTEM<br />
Input -<br />
V Grid =110VACrms, 60 Hz<br />
V MPPT ≈45 V, I MPPT ≈1 A<br />
Output - V O =24 V, I O =1.5 A<br />
Frequency - 38.4 kHz<br />
Ferrite core<br />
Transformer<br />
Component<br />
-<br />
-<br />
EI-33<br />
L T1P /L T1S =425μH / 35.8μH<br />
A gip ≈ 0.29 mm<br />
N T2P /N T2S =32N / 16N<br />
Inductance<br />
L 1 =460μH<br />
-<br />
Component<br />
L 2 =525μH<br />
C 1 =6μF<br />
Capacitor<br />
Component<br />
- C 2 =1μF<br />
C 3 =220μF<br />
Figure 6. Prototype of proposed dual-<strong>in</strong>put power converter<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1599<br />
(a) grid <strong>in</strong>put current I GRID<br />
Figure 10. Measured Efficiency of the proposed converter <strong>in</strong> hybrid<br />
power supply mode<br />
(b) output voltage V o , output current I o and output power P o<br />
Figure 7. Measured waveforms <strong>in</strong> hybrid power supply mode<br />
The comparison of system cost between stand-alone<br />
PV power system and the proposed hybrid power system<br />
is shown <strong>in</strong> Table II. For a 36W office light<strong>in</strong>g power<br />
system with 85% efficiency works 8 hours a day, the<br />
m<strong>in</strong>imum required power capacity is 340Wh. However,<br />
the rated power of PV array is only available <strong>in</strong> 2~3 hours<br />
a day [19]. The m<strong>in</strong>imum PV array <strong>in</strong>stalled capacity for<br />
a 36W stand-alone power system is 120W. Compared<br />
with the stand-alone system, the required capacity of PV<br />
array <strong>in</strong> the proposed system is only 36W. Moreover, the<br />
energy storage device is not required neither. It is seen<br />
that the <strong>in</strong>stall<strong>in</strong>g and ma<strong>in</strong>tenance cost can then be<br />
greatly reduced.<br />
Table II. THE POWER SUPPLY SYSTEM COST COMPARISON<br />
(8HOURS/DAY AT 36W)<br />
Stand-Alone<br />
Proposed system<br />
PV System<br />
Load<strong>in</strong>g 36W 36W<br />
PV Array 120W 36W<br />
Battery bank 720Wh —<br />
Cost High Low<br />
Figure 8. Waveforms <strong>in</strong> different supply modes (V GS1&GS2 : 20V/DIV,<br />
V C1 : 5V/DIV, I C1 :4A/DIV)<br />
Figure 9. Measured Efficiency of the proposed converter <strong>in</strong> s<strong>in</strong>gle<br />
power supply modes<br />
V. CONCLUSION<br />
This paper proposed an isolated dual-<strong>in</strong>put power<br />
converter for grid/PV hybrid power conversion systems<br />
which can be operated <strong>in</strong> s<strong>in</strong>gle power supply mode or<br />
hybrid power supply mode. The power complement<br />
controller composed of two <strong>in</strong>dependent control loops for<br />
the grid and the PV power. Once the available PV power<br />
is <strong>in</strong>sufficient for the load demand, the power flow from<br />
the grid would automatically be controlled to complement<br />
the output power. F<strong>in</strong>ally, a prototype for a 36W LED<br />
light<strong>in</strong>g module is constructed to evaluate the validity and<br />
performance of the proposed converter. From the<br />
experimental results, it is seen that even while the PV<br />
power is unstable, the proposed converter can provide a<br />
smooth 24V/1.5A output power for the LED module.<br />
© 2013 ACADEMY PUBLISHER
1600 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
a prototype with a 45W PV array for a 36W LED<br />
light<strong>in</strong>g module is constructed as shown <strong>in</strong> Fig. 6.<br />
Figure 11. Prototype of the 36W LED light<strong>in</strong>g module<br />
Figure 12. Prototype of the 45W PV array<br />
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Converter Based on the Multi-w<strong>in</strong>d<strong>in</strong>g Transformer for<br />
Renewable Energy Applications,” IEEE Trans. Ind.<br />
Application., vol. 38, no. 4, pp. 1096-1104, July/August<br />
2002.<br />
[14] R. Maurya, S. P. Srivastava, and P. Agarwal, “Design &<br />
Implementation of Transformer-less Multi Output DC<br />
Power Supply,” Trans. International Review of Electrical<br />
Eng<strong>in</strong>eer<strong>in</strong>g, vol. 6, no.7, pp. 2910-2918, November 2011.<br />
[15] R. J. Wai, C. Y. L<strong>in</strong>, J. J. Liaw, and Y. R. Chang, “Newly<br />
Designed ZVS Multi-Input Converter, IEEE Trans. Ind.<br />
Electr., vol. 58 no. 2, pp. 555-566, February 2011.<br />
[16] R. Ahmadi and M. Ferdowsi, “Double-Input Converters<br />
Based on H-Bridge Cells: Derivation, Small-Signal<br />
Model<strong>in</strong>g, and Power Shar<strong>in</strong>g Analysis,” IEEE Trans.<br />
Circuits Syst. I, Reg., vol. 59, no. 4, pp. 875-888, April<br />
2012.<br />
[17] Y. Yuanmao and K. W. E. Cheng, “Level-Shift<strong>in</strong>g<br />
Multiple-Input Switched- Capacitor Voltage Copier,” IEEE<br />
Trans. Power Electr., vol. 27 no. 2, pp. 828-837, February<br />
2012.<br />
[18] Y. C. Liu and Y. M.Chen, “A Systematic Approach to<br />
Synthesiz<strong>in</strong>g Multi-Input DC-DC Converter,” IEEE Trans.<br />
Power Electron., vol. 24, no.1, pp.116-127, January 2009.<br />
[19] Kolhe M, “Techno-Economic Optimum Siz<strong>in</strong>g of a Stand-<br />
Alone Solar Photovoltaic System,” IEEE Trans. Energy<br />
Convers., vol. 24, no.2, pp.511-519, 2009<br />
Yu-L<strong>in</strong> Juan (S’08) was born <strong>in</strong><br />
Kaohsiung, Taiwan, <strong>in</strong> 1979. He<br />
received the B.S. degree <strong>in</strong> electrical<br />
eng<strong>in</strong>eer<strong>in</strong>g from National Cheng Kung<br />
University, Ta<strong>in</strong>an, Taiwan, <strong>in</strong> 2001<br />
and the M.S. degree <strong>in</strong> electrical<br />
eng<strong>in</strong>eer<strong>in</strong>g <strong>in</strong> 2003 from National<br />
Ts<strong>in</strong>g Hua University, Hs<strong>in</strong>chu, Taiwan.<br />
His current research <strong>in</strong>terests <strong>in</strong>clude<br />
power electronics, renewable energy<br />
systems, and ac motor drives.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1601<br />
Hs<strong>in</strong>-Y<strong>in</strong>g Yang was born <strong>in</strong> Taichung<br />
Taiwan, R.O.C. <strong>in</strong> 1982. He received<br />
the B. S. degree <strong>in</strong> electrical<br />
eng<strong>in</strong>eer<strong>in</strong>g from National Formosa<br />
University, Yunl<strong>in</strong>, Taiwan, <strong>in</strong> 2005<br />
and was conferred the Master of<br />
Electrical Degree by National<br />
Changhua University of Education,<br />
Changhua City, Taiwan, R.O.C. <strong>in</strong> 2007.<br />
He is currently work<strong>in</strong>g toward the<br />
Ph.D. degree <strong>in</strong> electrical eng<strong>in</strong>eer<strong>in</strong>g. His research <strong>in</strong>terests are<br />
power electronics, electronic circuit design, battery charge and<br />
microprocessor application.<br />
Peng-Lai Chen is currently work<strong>in</strong>g<br />
toward the Ph.D. degree <strong>in</strong> electrical<br />
eng<strong>in</strong>eer<strong>in</strong>g. His research <strong>in</strong>terests are<br />
power electronics, design and<br />
application.<br />
© 2013 ACADEMY PUBLISHER
1602 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Deformed Kernel Based Extreme Learn<strong>in</strong>g<br />
Mach<strong>in</strong>e<br />
Zhang Chen<br />
School of Computer Science and Technology,Ch<strong>in</strong>a University of M<strong>in</strong><strong>in</strong>g and Technology, XuZhou,221116,Ch<strong>in</strong>a<br />
Email: zc@cumt.edu.cn<br />
Xia Shi Xiong and Liu B<strong>in</strong>g<br />
School of Computer Science and Technology,Ch<strong>in</strong>a University of M<strong>in</strong><strong>in</strong>g and Technology, XuZhou,221116,Ch<strong>in</strong>a<br />
Email: xiasx@cumt.edu.cn, liub<strong>in</strong>g@cumt.edu.cn<br />
Abstract—The extreme learn<strong>in</strong>g mach<strong>in</strong>e (ELM) is a newly<br />
emerg<strong>in</strong>g supervised learn<strong>in</strong>g method. In order to use the<br />
<strong>in</strong>formation provided by unlabeled samples and improve the<br />
performance of the ELM, we deformed the kernel <strong>in</strong> the<br />
ELM by model<strong>in</strong>g the marg<strong>in</strong>al distribution with the graph<br />
Laplacian, which is built with both labeled and unlabeled<br />
samples. We further approximated the deformed kernel by<br />
means of random feature mapp<strong>in</strong>g. The experimental<br />
results showed that the proposed semi-supervised extreme<br />
learn<strong>in</strong>g mach<strong>in</strong>e tends to achieve outstand<strong>in</strong>g<br />
generalization performance at a relatively faster learn<strong>in</strong>g<br />
speed than traditional semi-supervised learn<strong>in</strong>g algorithms.<br />
Index Terms—extreme learn<strong>in</strong>g mach<strong>in</strong>e (ELM); random<br />
feature mapp<strong>in</strong>g; semi-supervised learn<strong>in</strong>g; Reproduc<strong>in</strong>g<br />
Kernel Hilbert Spaces (RKHS).<br />
I. INTRODUCTION<br />
Lately, extreme learn<strong>in</strong>g mach<strong>in</strong>e ELM has been<br />
attract<strong>in</strong>g a lot of attention from an <strong>in</strong>creas<strong>in</strong>g number of<br />
researchers [1]-[5]. It was orig<strong>in</strong>ally developed for the<br />
s<strong>in</strong>gle-hidden layer feedforward neural networks (SLFN)<br />
[6]-[8], which was extended to the “generalized” SLFNs,<br />
i.e., may not be neuron alike [9, 10]. ELM has three ma<strong>in</strong><br />
learn<strong>in</strong>g features: (1) ELM was orig<strong>in</strong>ally proposed to<br />
apply random computational nodes <strong>in</strong> the hidden layer.<br />
Thus, the hidden layer of the ELM does not need be<br />
tuned. (2) ELM <strong>in</strong>corporates the smallest tra<strong>in</strong><strong>in</strong>g error<br />
and the norm of output weights <strong>in</strong>to the objective<br />
function. Hence, it controls the complexity of decision<br />
functions by means of regularization. (3) Unlike LS-SVM<br />
and SVM that only provide one type of computational<br />
need, ELM provides a unified solution to different<br />
practical applications (e.g., regression, b<strong>in</strong>ary, and<br />
multiclass classifications).<br />
ELM is a supervised learn<strong>in</strong>g method. In many<br />
applications, however, there are little labeled data and a<br />
large amount of unlabeled data available. Semi-<br />
Supervised Learn<strong>in</strong>g (SSL) methods are proposed to<br />
solve this problem. ELM can be naturally extended to the<br />
unsupervised scenario, where the “cluster” and “manifold”<br />
assumptions are used to learn <strong>in</strong>put-output mapp<strong>in</strong>g<br />
functions. The “cluster” assumption refers to that po<strong>in</strong>ts<br />
<strong>in</strong> a data cluster have similar labels. The “manifold”<br />
assumption corresponds to high-dimensional data<br />
distributed on a low-dimensional manifold and the<br />
samples <strong>in</strong> each local region have similar labels. There<br />
are many approaches based on the “cluster” assumption,<br />
which uses techniques such as local comb<strong>in</strong>atorial<br />
searches[12], branch-and-bound algorithms[13,14],<br />
gradient descent[15], semi-def<strong>in</strong>ite programm<strong>in</strong>g [16-19],<br />
cont<strong>in</strong>uation techniques[20], non-differentiable<br />
methods[21], concave-convex procedures[22,23], and<br />
determ<strong>in</strong>istic anneal<strong>in</strong>g[24]. However, the time<br />
complexity of these methods scales at least quadratically<br />
with the dataset size, which makes them <strong>in</strong>applicable to<br />
large-scale datasets. In [25], a cutt<strong>in</strong>g plane semisupervised<br />
support vector mach<strong>in</strong>e algorithm (CutS3VM)<br />
was proposed to reduce the number of iterations, but it<br />
still takes time O(sn) to converge with guaranteed<br />
accuracy <strong>in</strong> the l<strong>in</strong>ear case, where n is the total number of<br />
samples <strong>in</strong> the dataset and s is the average number of<br />
non-zero features. S<strong>in</strong>dhwani et al.[26] proposed two<br />
k<strong>in</strong>ds of large-scale semi-supervised l<strong>in</strong>ear SVMs: the<br />
transductive modified f<strong>in</strong>ite newton l<strong>in</strong>ear L 2 -SVM (L 2 -<br />
TSVM-MFN) and the determ<strong>in</strong>istic anneal<strong>in</strong>g L 2 -SVM-<br />
MFN method (DA L 2 -SVM-MFN). L 2 -TSVM-MFN is<br />
converged after hav<strong>in</strong>g been switched many times and<br />
DA L 2 -SVM-MFN needs a number of iterations to<br />
compute the correspond<strong>in</strong>g parameters of unlabeled data.<br />
Besides the “cluster” assumption, many regularization<br />
frameworks based on the “manifold” assumption have<br />
been designed by add<strong>in</strong>g a manifold regularization term.<br />
In [27], Belk<strong>in</strong> et al. proposed a general Manifold<br />
Regularization (MR) framework for a full range of<br />
learn<strong>in</strong>g problems from unsupervised and semisupervised,<br />
to supervised. The MR framework adds an<br />
additional penalty term to the traditional regularization,<br />
from which the Laplacian Regularization Least Square<br />
Classification (LapRLSC) and the Laplacian SVM<br />
(LapSVM) methods are derived and have been shown to<br />
be efficient <strong>in</strong> semi-supervised learn<strong>in</strong>g problems.<br />
Additionally, the Discrim<strong>in</strong>atively Regularization Least<br />
Square Classification (DRLSC) method and the Sparse<br />
Regularized Least Square Classification (S-RLSC)<br />
algorithm[29] were proposed, which improves the MR<br />
framework further. Although these frameworks can<br />
handle semi-supervised learn<strong>in</strong>g problems and the<br />
analytic solutions can also be derived, they still <strong>in</strong>volve<br />
© 2013 ACADEMY PUBLISHER<br />
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JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1603<br />
expensive computation when tra<strong>in</strong><strong>in</strong>g large-scale data<br />
sets.<br />
To improve the performance of the ELM, it is essential<br />
to use the <strong>in</strong>formation provided by both labeled and<br />
unlabeled samples. We construct the deformed kernel for<br />
the ELM, which is adapted to the geometry of the<br />
underly<strong>in</strong>g distribution. Based on the deformed kernel,<br />
we propose a deformed kernel-based extreme learn<strong>in</strong>g<br />
mach<strong>in</strong>e (DKELM) to provide a unified solution for<br />
regression, b<strong>in</strong>ary, and multiclass classifications (like<br />
ELM). To address large-scale data tra<strong>in</strong><strong>in</strong>g, we<br />
approximate the deformed kernel by random feature<br />
mapp<strong>in</strong>g, so that the proposed DKELM does not need<br />
parameter tun<strong>in</strong>g and has less computational complexity,<br />
as well as a natural out-of-sample extension for novel<br />
examples. We demonstrate the relationship between the<br />
traditional kernel-based learn<strong>in</strong>g approach and ELM, and<br />
our approach can be used by other kernel-based methods<br />
and a sequence of fast learn<strong>in</strong>g algorithms can be derived.<br />
The rest of this paper is organized as follows. Some<br />
previous works are <strong>in</strong>troduced <strong>in</strong> Section II. The method<br />
of construct<strong>in</strong>g and approximat<strong>in</strong>g the deformed kernel is<br />
discussed <strong>in</strong> Section III. In Section IV, we first<br />
demonstrate the relationship between the traditional<br />
kernel-based learn<strong>in</strong>g approach and ELM, and propose<br />
the deformed kernel based extreme learn<strong>in</strong>g mach<strong>in</strong>e.<br />
The experiments us<strong>in</strong>g benchmark real-world data sets<br />
are reported <strong>in</strong> Section V. F<strong>in</strong>ally, we conclude this paper<br />
<strong>in</strong> Section VI.<br />
II. BRIEF OF THE EXTREME LEARNING MACHINE<br />
The output function of ELM for generalized SLFNs <strong>in</strong><br />
the case of one output node case is<br />
(1)<br />
where<br />
is the vector of the weights<br />
between a hidden layer of L nodes and the output node.<br />
Note that<br />
is the output (row)<br />
vector of the hidden layer with respect to the <strong>in</strong>put x. In<br />
fact, maps the data from the d-dimensional <strong>in</strong>put<br />
space to the L-dimensional hidden-layer feature space<br />
(ELM feature space) H. Different from traditional<br />
learn<strong>in</strong>g algorithms [11], ELM is meant to m<strong>in</strong>imize the<br />
tra<strong>in</strong><strong>in</strong>g error as well as the norm of the output weights [7]<br />
M<strong>in</strong>imize: and (2)<br />
where H is the hidden-layer output matrix, which is<br />
denoted by<br />
where , and is a<br />
kernel function.<br />
If a feature mapp<strong>in</strong>g h(x) is known, we have<br />
(5)<br />
where is a nonl<strong>in</strong>ear piecewise cont<strong>in</strong>uous<br />
function satisfy<strong>in</strong>g ELM universal approximation<br />
capability theorems [7],[30] and are<br />
randomly generated accord<strong>in</strong>g to any cont<strong>in</strong>uous<br />
probability distribution. The output function of ELM<br />
classifier is<br />
or<br />
where<br />
classes.<br />
(4)<br />
, (6)<br />
, (7)<br />
and m is the number of<br />
III. DEFORMING THE KERNEL BY WARPING AN RKHS<br />
For a Mercer kernel K: X X , there is an<br />
associated RKHS of functions X with the<br />
correspond<strong>in</strong>g norm . Given a set of l labeled<br />
examples and a set of u unlabeled examples<br />
, where and , the classical<br />
kernel-based learn<strong>in</strong>g approach is based on solv<strong>in</strong>g the<br />
regularization problem given by<br />
, (8)<br />
where V is some loss function, such as the squared loss<br />
for RLS and the h<strong>in</strong>ge loss function<br />
for SVM; is the norm of the<br />
classification function <strong>in</strong> the reproduc<strong>in</strong>g kernel Hilbert<br />
space , and controls the complexity of function .<br />
The Representer Theorem [27] states that a solution can<br />
be found <strong>in</strong> the form<br />
. In order to<br />
avoid confusion, we list ma<strong>in</strong> notations of this paper <strong>in</strong><br />
Table I.<br />
TABLE I.<br />
. (3)<br />
As with SVM for the b<strong>in</strong>ary classification, to m<strong>in</strong>imize<br />
the norm of the output weights is actually used to<br />
maximize the distance of the separat<strong>in</strong>g marg<strong>in</strong>s of the<br />
two different classes <strong>in</strong> the ELM feature space: .<br />
The norm controls the complexity of the function <strong>in</strong> the<br />
ambient space, which will be elaborated later.<br />
If a feature mapp<strong>in</strong>g h(x) is unknown to users, the<br />
output function of ELM classifier is<br />
Notation<br />
m<br />
NOTATIONS<br />
Explanation<br />
The <strong>in</strong>put d-dimensional Euclidean space<br />
is the<br />
tra<strong>in</strong><strong>in</strong>g data matrix. are labeled po<strong>in</strong>ts,<br />
and are unlabeled po<strong>in</strong>ts.<br />
The number of classes that the samples belong<br />
to<br />
is the 0-1 label matrix.<br />
is the label vector of , and all<br />
components of are s except one be<strong>in</strong>g .<br />
is the discrim<strong>in</strong>ative<br />
vector function. The <strong>in</strong>dex of the class which x<br />
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1604 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
belongs to is that of the component with the<br />
maximum value.<br />
Kernel function of variables and<br />
Kernel matrix<br />
. Its columns are the<br />
coefficients of the kernel function to represent<br />
the discrim<strong>in</strong>ative function .<br />
Norm <strong>in</strong> the Hilbert space<br />
Inner product <strong>in</strong> the Hilbert space<br />
tr(M)<br />
The trace of the matrix M , that is, the sum of<br />
the diagonal elements of the matrix M.<br />
span{ } subspace expanded by<br />
In the implementation of this kernel-based learn<strong>in</strong>g<br />
approach, we often use the Radial Basis Function or<br />
Gaussian (RBF) as kernel, and the kernel k def<strong>in</strong>es a<br />
unique RKHS. S<strong>in</strong>ce the Gaussian kernel is isotropic, it<br />
has a spherical symmetry. That is, it generally does not<br />
conform to the particular geometry of the underly<strong>in</strong>g<br />
classes. In other words, the underly<strong>in</strong>g data structure is<br />
obviated. F<strong>in</strong>ally, it is unable to provide an accurate<br />
decision surface. To address these limitations, it is crucial<br />
to def<strong>in</strong>e a new kernel that is adapted to the geometry of<br />
the data distribution well.<br />
Instead of solv<strong>in</strong>g (8) like a traditional kernel-based<br />
learn<strong>in</strong>g approach, we modify (or deform) the orig<strong>in</strong>al<br />
kernel <strong>in</strong> order to adapt it to the underly<strong>in</strong>g distribution<br />
geometry. Def<strong>in</strong><strong>in</strong>g a new deformed kernel , the new<br />
problem to be solved becomes<br />
, (9)<br />
(8) and (9) solved with different kernels, and thus <strong>in</strong><br />
different .<br />
The solution of (9) is<br />
, (10)<br />
that should be appropriate for real sett<strong>in</strong>g.<br />
To “deform” the orig<strong>in</strong>al kernel and adapt it to the<br />
geometry of the underly<strong>in</strong>g distribution, let be a l<strong>in</strong>ear<br />
space with positive semi-def<strong>in</strong>ite <strong>in</strong>ner product, and let<br />
be a bounded l<strong>in</strong>ear operator. Def<strong>in</strong><strong>in</strong>g<br />
to be the space with the same functions as and its<br />
<strong>in</strong>ner product def<strong>in</strong>es<br />
, (11)<br />
It is proved <strong>in</strong> [27] that is a valid . In this<br />
specific problem, it is required that and should<br />
depend on the data. Therefore, let be , and def<strong>in</strong>e<br />
as the evaluation map<br />
.Us<strong>in</strong>g a symmetric positive semidef<strong>in</strong>ite<br />
matrix , the semi-norm on can be written<br />
as<br />
. With such a norm, the regularization<br />
problem <strong>in</strong> (9) becomes<br />
(12)<br />
where <strong>in</strong>cludes both labeled and unlabeled data<br />
and the matrix encodes smoothness w.r.t. the graph or<br />
manifold.<br />
Let<br />
and substitute it <strong>in</strong>to (12), we have<br />
(13)<br />
where<br />
is a free parameter that controls<br />
the “deformation” of the orig<strong>in</strong>al kernel. Thus, Equation<br />
(13), <strong>in</strong> fact, is a graph-based semi-supervised learn<strong>in</strong>g<br />
problem based on the manifold assumption; it can be<br />
<strong>in</strong>directly set out us<strong>in</strong>g (12) and solved us<strong>in</strong>g (10).<br />
To utilize the geometry <strong>in</strong>formation of the data<br />
distribution, a graph can be constructed us<strong>in</strong>g labeled<br />
and unlabeled pixels. The graph Laplacian of is a<br />
matrix def<strong>in</strong>ed as , where is the<br />
adjacency matrix. The elements are measures of the<br />
similarity between pixels and , and the diagonal<br />
matrix D is given by<br />
. The graph<br />
Laplacian L measures the variation of the function<br />
along the graph built upon all labeled and unlabeled<br />
samples. By fix<strong>in</strong>g , the orig<strong>in</strong>al (undeformed)<br />
kernel is obta<strong>in</strong>ed.<br />
Next, we discuss the computation of the deformed<br />
kernel . In [27], the result<strong>in</strong>g new kernel was computed<br />
explicitly <strong>in</strong> terms of labeled and unlabeled data. It is<br />
proved that<br />
and<br />
(14)<br />
Thus, the two spans are same and we have<br />
where the coefficients depend on x, let<br />
.<br />
We can compute at x:<br />
(17)<br />
(15)<br />
(16)<br />
Where<br />
and g is the<br />
vector given by components<br />
. Therefore, it can be derived from (17)<br />
that<br />
(I+MK) (18)<br />
where K is the kernel matrix<br />
, = and is the<br />
identity matrix. F<strong>in</strong>ally, we obta<strong>in</strong> the follow<strong>in</strong>g explicit<br />
form for<br />
(19)<br />
where<br />
. It satisfies the Mercer’s<br />
conditions, be<strong>in</strong>g a valid kernel. If<br />
, the<br />
deformed kernel is degenerated <strong>in</strong>to the orig<strong>in</strong>al<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1605<br />
(undeformed) kernel. When is s<strong>in</strong>gular, one adds a<br />
small ridge term to and uses a cont<strong>in</strong>uity argument.<br />
IV. ELM BASED ON DEFORMED KERNEL<br />
In regularization problem (8), if yi is an m-dimensional<br />
label vector with the elements 0 or 1, where m is the<br />
number of classes, and xi belongs to the k-th class, then<br />
the k-th component of yi takes the value 1 and the rest<br />
components take the value 0. The correspond<strong>in</strong>g vector<br />
function is def<strong>in</strong>ed as<br />
. Then<br />
the extended regularization problem estimates an<br />
unknown vector function by m<strong>in</strong>imiz<strong>in</strong>g<br />
where.<br />
(20)<br />
Next, we discuss the computation of the deformed<br />
kernel , accord<strong>in</strong>g to<br />
,<br />
where<br />
is the kernel<br />
matrix over labeled and unlabeled samples, we have to<br />
compute a matrix <strong>in</strong>version of size .<br />
Note that this <strong>in</strong>version scales exponentially with the<br />
number of samples. If the number of labeled and<br />
unlabeled samples is huge, it is difficult to compute. So<br />
we further approximate the kernel matrix K, lett<strong>in</strong>g<br />
and<br />
, then ,<br />
and<br />
, so we achieve<br />
In (20), if we <strong>in</strong>troduce a deformed kernel<br />
problem to be solved becomes<br />
, the<br />
(21)<br />
where<br />
, .<br />
The solution of (21) is<br />
, where<br />
Based on what is <strong>in</strong>troduced above, the regularization<br />
problem for DKELM with multioutput nodes can be<br />
formulated as<br />
(22)<br />
The solution of the optimization problem (22) is given<br />
by<br />
,<br />
where is the identity matrix. .<br />
Let<br />
and<br />
and<br />
, so<br />
,where<br />
is the deformed kernel<br />
matrix over labeled po<strong>in</strong>ts.<br />
If the number of labeled samples is not huge, the<br />
output function is<br />
, (23)<br />
if the number of labeled samples is huge, accord<strong>in</strong>g to<br />
the Sherman-Morrison-Woodbury(SMW) formula for<br />
matrix <strong>in</strong>version, we have<br />
, (24)<br />
where<br />
is the label matrix<br />
with elements or , and ( ) is an m-<br />
dimensional label vector with the elements 0 or 1. In a<br />
semi-supervised case, the number of labeled samples is<br />
small, so (40) should be used to compute the output<br />
function.<br />
, (25)<br />
where , .<br />
Correspond<strong>in</strong>gly, <strong>in</strong> a semi-supervised case, the output<br />
function of DKELM with a s<strong>in</strong>gle output is<br />
(26)<br />
where is an l dimensional label vector given by:<br />
.<br />
The formula (25) and (26) all <strong>in</strong>volve the <strong>in</strong>version of<br />
a matrix of order , as long as L is large enough, the<br />
generalization performance of DKELM is not sensitive to<br />
the dimensionality of the feature space (L) and good<br />
performance can be reached, which will be verified later<br />
<strong>in</strong> Section 5. The DKELM algorithm is summarized <strong>in</strong><br />
the Table II.<br />
TABLE II.<br />
THE DESCRIPTION OF DKELM ALGORITHM BASED ON DEFORMED<br />
KERNEL<br />
DKELM Algorithm based on deformed kernel<br />
Input: l labeled examples , u unlabeled examples .<br />
Output: Estimated function .<br />
Step 1: Construct data adjacency graph with (l+u) nodes us<strong>in</strong>g k nearest<br />
neighbors or a graph kernel. Choose edge weights Wij, for<br />
example, for b<strong>in</strong>ary weights or heat kernel weights<br />
.<br />
Step 2: Compute graph Laplacian matrix: , where is a<br />
diagonal matrix given by<br />
.<br />
Step 3: Choose a kernel function . Choose , C and L (the<br />
number of sample po<strong>in</strong>ts), randomly generate .<br />
Step 4: if the number of the tra<strong>in</strong><strong>in</strong>g data sets is very large ,<br />
compute ,<br />
, select (25) for<br />
comput<strong>in</strong>g the deformed kernel; Otherwise, use (19) .<br />
Step 5: Select (23) for comput<strong>in</strong>g the output function of DKELM<br />
© 2013 ACADEMY PUBLISHER
1606 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
with multioutputs or select (26) for comput<strong>in</strong>g the output<br />
function of DKELM with s<strong>in</strong>gle output (m=1).<br />
Step 6: Output .<br />
Like ELM, DKELM has the unified solutions for<br />
regression, b<strong>in</strong>ary and multiclass classification. But we<br />
ma<strong>in</strong>ly discuss DKELM for the classification problems <strong>in</strong><br />
this paper.<br />
A DKELM classifier with a s<strong>in</strong>gle-output node (m = 1):<br />
For multiclass problems, among all the multiclass labels,<br />
the predicted class label of a given test<strong>in</strong>g sample is<br />
closest to the output of a DKELM classifier. The decision<br />
function of the DKELM classifier is<br />
. (27)<br />
For the b<strong>in</strong>ary classification, the decision function of<br />
DKELM classifier is<br />
. (28)<br />
A DKELM classifier with multioutput nodes (m > 1) is:<br />
For multiclass cases, the predicted class label of a given<br />
test<strong>in</strong>g sample is the <strong>in</strong>dex number of the output node,<br />
which has the highest output value for the given test<strong>in</strong>g<br />
sample. The decision function of the DKELM classifier is<br />
. (29)<br />
The predicted class label of sample x is<br />
*<br />
label( x) arg max fi<br />
( x)<br />
i{1,..., m}<br />
. (30)<br />
The deformed kernel <strong>in</strong> both cases is computed by<br />
,<br />
which is applied to moderate scale tra<strong>in</strong><strong>in</strong>g samples, or<br />
,<br />
(31)<br />
which is applied to large scale tra<strong>in</strong><strong>in</strong>g samples, where<br />
, .<br />
V. EXPERIMENTS<br />
In this section, we will validate the performance of the<br />
proposed DKELM algorithm on a number of real-world<br />
data sets. In particular, we studied the sensitivity of<br />
DKELM to the number of labeled samples. All the<br />
experiments are performed with MATLAB 7.0.1<br />
environment on a 3.10GHZ Intel CoreTM i5-2400 with<br />
3-GB RAM.<br />
A. Data Sets<br />
We used different scale data sets from the UCI<br />
mach<strong>in</strong>e learn<strong>in</strong>g repository (satellite, Ionosphere), and<br />
another benchmark repository (Extended Yale B, USPS).<br />
For the satellite data sets, there are multiple class labels;<br />
we used their first two classes only. For USPS, we<br />
randomly selected 250 data po<strong>in</strong>ts from each class for our<br />
experiments. The basic <strong>in</strong>formation about these data sets<br />
is summarized <strong>in</strong> Table III.<br />
TABLE III.<br />
DESCRIPTION OF THE DATA SETS<br />
Data Size (n) Feature (d) Class<br />
SatelliteC1-C2 2236 36 2<br />
Ionosphere 351 34 2<br />
Extended Yale B 2114 1024 38<br />
USPS 2500 256 10<br />
B. Parameter selection and experimental sett<strong>in</strong>gs<br />
Comparisons are made with four important<br />
classification methods: CutS 3 VM[25], L 2 -TSVM-<br />
MFN[26], DA L 2 -SVM-MFN[26] and S-RLSC<br />
algorithm[29]. In our experiments, b<strong>in</strong>ary edge weights<br />
are chosen and the neighborhood size k is set to be 12 for<br />
all the data sets. DKELM algorithm needs to choose the<br />
feature mapp<strong>in</strong>g, the cost parameter C and the number of<br />
hidden nodes L, s<strong>in</strong>ce ELM algorithm achieves good<br />
generalization performance as long as L and C are large<br />
enough[30]. Thus we let C =500. The regularization<br />
parameters and are split <strong>in</strong>to the ratio 1:9, and we<br />
let , , which is<br />
set <strong>in</strong> the same way as <strong>in</strong> [27]. We select Gaussian<br />
functions as the hidden-node output functions.<br />
We test L 2 -TSVM-MFN with multiple switch<strong>in</strong>gs and<br />
DA L 2 -SVM-MFN with parameter and<br />
on all datasets. We also test CutS3VM with parameters<br />
, and set <strong>in</strong> the balanc<strong>in</strong>g constra<strong>in</strong>t to the<br />
true ratio of the positive po<strong>in</strong>ts <strong>in</strong> the unlabeled set. The<br />
S-RLSC methods also have regularization parameters<br />
and . Let , , and also use the<br />
Gaussian kernel function. In our experiments, we also set<br />
CA=0.005, CI=0.01 and for all data sets, which<br />
is set <strong>in</strong> the same way as <strong>in</strong> [29].<br />
For each data set , 15% of the data po<strong>in</strong>ts are left for<br />
out-of-sample extension experiment. We denote by the<br />
rest data po<strong>in</strong>ts of the data set . In each class of , we<br />
randomly label l data po<strong>in</strong>ts to tra<strong>in</strong> every algorithm. For<br />
DKELM, S-RLSC, L 2 -TSVM-MFN, DA L 2 -SVM-MFN<br />
and CutS 3 VM, the tra<strong>in</strong><strong>in</strong>g set consists of the whole ,<br />
<strong>in</strong>clud<strong>in</strong>g the labeled and the unlabeled data po<strong>in</strong>ts. For<br />
L 2 -TSVM-MFN, DA L 2 -SVM-MFN and CutS 3 VM,<br />
multiclass datasets are learned us<strong>in</strong>g a one-versus-rest<br />
approach.<br />
C. Experimental results<br />
For simplicity, we used DKELM with a s<strong>in</strong>gle output<br />
and 800 hidden nodes; the recognition result of all the<br />
algorithms is shown <strong>in</strong> Table 4–6, respectively. For each<br />
dataset, classification accuracy and tra<strong>in</strong><strong>in</strong>g time<br />
averaged over 20 <strong>in</strong>dependent trials. The number of l (<strong>in</strong><br />
each class) of the labeled data po<strong>in</strong>ts varies from 5 to 250<br />
for the Satellite data set, from 5 to 150 for the Ionosphere<br />
and from 5 to 40 for the Extended Yale B data set.<br />
In Tables 4–6, for several values of m, the best<br />
classification results are <strong>in</strong> boldface for each fixed value<br />
of m. As can be seen from the tables, the classification<br />
accuracy is lower for all algorithms when l is small. With<br />
the <strong>in</strong>crease of labeled data, the discrim<strong>in</strong>ative ability of<br />
the DKELM algorithm is much better than the other<br />
algorithms, s<strong>in</strong>ce it utilizes the manifold structure of<br />
labeled and unlabeled samples. The recognition result of<br />
the S-RLSC algorithm is very close to that of the<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1607<br />
DKELM algorithm, but it runs much slower than our<br />
algorithm. For the Satellite and Ionosphere data sets, the<br />
performance of the DKELM algorithm is worse than that<br />
of Extended Yale B data set, s<strong>in</strong>ce the manifold structure<br />
is less salient than that of face images. As can be seen<br />
from Table 6, the recognition accuracy of the L2-TSVM-<br />
MFN, DA L 2 -SVM-MFN and CutS3VM classifiers<br />
decreases with the <strong>in</strong>crease of the number of classes,<br />
s<strong>in</strong>ce these classifiers are constructed with a one-versusrest<br />
approach, which has a great <strong>in</strong>fluence on the<br />
accuracy. Moreover, this k<strong>in</strong>d of multiclass classification<br />
approach also <strong>in</strong>creases the runn<strong>in</strong>g time of these<br />
algorithms. With the <strong>in</strong>crease of the number of the feature<br />
dimensions of data sets, the runn<strong>in</strong>g time of the<br />
CutS3VM <strong>in</strong>creases dramatically, s<strong>in</strong>ce its time<br />
complexity depends on the average number of non-zero<br />
features. In contrast, as can be seen from Table IVandVI,<br />
the speed of the DKELM algorithm is not sensitive to the<br />
number of classes and the feature dimensions of data sets.<br />
It can perform well by means of the <strong>in</strong>tr<strong>in</strong>sic geometry of<br />
data distribution.<br />
TABLE IV.<br />
PERFORMANCE COMPARISON OF ALL T<br />
Numb<br />
er of<br />
labele<br />
d<br />
data<br />
po<strong>in</strong>ts<br />
l<br />
DKELM<br />
Accuracy<br />
(%)<br />
SATELLITE DATA SET<br />
S-RLSC<br />
Accurac<br />
y(%)<br />
L 2-TSVM-<br />
MFN<br />
Accuracy<br />
(%)<br />
HE ALGORITHMS FOR THE<br />
DA L 2-<br />
SVM-<br />
MFN<br />
Accuracy<br />
(%)<br />
CutS 3 VM<br />
Accuracy<br />
(%)<br />
l =5 57.62 62.78 56.48 61.02 73.59<br />
l =10 78.45 79.79 69.83 70.73 74.46<br />
l =50 85.68 83.47 71.95 75.28 82.85<br />
l =250 89.21 87.86 75.82 76.29 84.46<br />
Numb<br />
er of<br />
labele<br />
d<br />
data<br />
po<strong>in</strong>ts<br />
l<br />
DKELM<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
S-RLSC<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
L 2-TSVM-<br />
MFN<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
DA L 2-<br />
SVM-<br />
MFN<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
CutS 3 VM<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
l =5 52.782 328.579 3.782 12.652 1.190<br />
l =10 55.273 328.647 3.894 11.676 0.976<br />
l =50 54.374 330.152 2.957 10.016 0.620<br />
l =250 52.962 322.674 2.365 5.625 0.569<br />
Numb<br />
er of<br />
labele<br />
d<br />
data<br />
po<strong>in</strong>ts<br />
l<br />
DKELM<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
S-RLSC<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
L 2-TSVM-<br />
MFN<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
DA L 2-<br />
SVM-<br />
MFN<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
CutS 3 VM<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
l =5 21.704 168.579 0.618 5.724 0.554<br />
l =10 25.753 168.647 0.772 5.676 0.377<br />
l =50 23.176 170.152 0.252 4.534 0.324<br />
l =250 22.802 162.674 0.246 3.165 0.232<br />
Number<br />
of<br />
labeled<br />
data<br />
po<strong>in</strong>ts l<br />
TABLEVI<br />
PERFORMANCE COMPARISON OF ALL THE ALGORITHMS FOR THE<br />
EXTENDED YALE B DATA SET<br />
DKELM<br />
Accura<br />
cy(%)<br />
S-RLSC<br />
Accurac<br />
y(%)<br />
L 2-TSVM-<br />
MFN<br />
Accuracy<br />
(%)<br />
DA L 2-<br />
SVM-<br />
MFN<br />
Accuracy<br />
(%)<br />
CutS 3 VM<br />
Accuracy<br />
(%)<br />
l =5 61.25 64.41 55.17 38.47 63.93<br />
l =10 82.05 83.18 62.76 58.71 69.82<br />
l =20 94.52 93.10 67.72 68.49 75.91<br />
l =30 95.42 95.24 71.35 73.59 79.56<br />
l =40 97.44 97.12 75.25 76.84 80.13<br />
Number<br />
of<br />
labeled<br />
data<br />
po<strong>in</strong>ts l<br />
DKELM<br />
Tra<strong>in</strong><strong>in</strong><br />
g<br />
Time(s)<br />
S-RLSC<br />
Tra<strong>in</strong><strong>in</strong>gTi<br />
me(s)<br />
L 2-TSVM-<br />
MFN<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
DA L 2-<br />
SVM-<br />
MFN<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
CutS 3 VM<br />
Tra<strong>in</strong><strong>in</strong>g<br />
Time(s)<br />
l =5 87.589 452.644 60.427 361.928 75.249<br />
l =10 88.670 455.972 58.958 273.536 69.162<br />
l =20 86.465 452.177 49.514 247.923 65.368<br />
l =30 87.259 454.921 42.943 190.380 58.532<br />
l =40 89.694 452.228 35.519 163.476 54.348<br />
The out-of-sample extension result of the algorithms<br />
on larger USPS data sets is shown <strong>in</strong> Fig. 1. We perform<br />
the DKELM algorithm us<strong>in</strong>g 500 hidden nodes. As can<br />
be seen from Fig.1, the DKELM algorithm has best<br />
recognition results over any other algorithm. So our<br />
proposed DKELM algorithm tends to have better<br />
scalability and achieve best generalization performance at<br />
a relatively faster learn<strong>in</strong>g speed.<br />
TABLEV.<br />
PERFORMANCE COMPARISON OF ALL THE ALGORITHMS FOR THE<br />
IONOSPHERE DATA SET<br />
Numb<br />
er of<br />
labele<br />
d<br />
data<br />
po<strong>in</strong>ts<br />
l<br />
DKELM<br />
Accuracy<br />
(%)<br />
S-RLSC<br />
Accurac<br />
y(%)<br />
L 2-TSVM-<br />
MFN<br />
Accuracy<br />
(%)<br />
DA L 2-<br />
SVM-<br />
MFN<br />
Accuracy<br />
(%)<br />
CutS 3 VM<br />
Accuracy<br />
(%)<br />
l =5 57.62 72.78 66.52 60.81 73.89<br />
l =10 74.79 73.45 69.42 71.67 74.56<br />
l =50 87.68 83.47 81.14 77.21 85.25<br />
l =250 90.21 87.86 85.73 86.39 86.43<br />
Figure 1. Out-of-sample extension classification results on the USPS<br />
data set<br />
VI CONCLUSIONS<br />
© 2013 ACADEMY PUBLISHER
1608 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
In this paper, we first extended the traditional kernelbased<br />
learn<strong>in</strong>g problem to multiclass cases <strong>in</strong> an Extreme<br />
Learn<strong>in</strong>g Mach<strong>in</strong>e context. To enhance the performance<br />
of ELM, a deformed kernel was proposed, which can<br />
make use of underly<strong>in</strong>g <strong>in</strong>formation from both labeled<br />
and unlabeled samples. To speed up our algorithm, we<br />
further approximated the deformed kernel by means of<br />
random feature mapp<strong>in</strong>g. Our algorithm does not need<br />
kernel parameter tun<strong>in</strong>g. The experimental results have<br />
shown that the DKELM algorithm achieves better<br />
generalization performance at a relatively faster learn<strong>in</strong>g<br />
speed than traditional semi-supervised classification<br />
algorithms. In the future, we will further optimize our<br />
proposed framework and study the sparse regularization<br />
problems <strong>in</strong> our framework.<br />
ACKNOWLEDGMENTS<br />
This work was supported by the National Natural<br />
Science Foundation of Ch<strong>in</strong>a under Grant Nos. 50674086.<br />
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Mach<strong>in</strong>e for Regression and Multiclass Classification<br />
IEEE Transactions on Systems, Man, and Cybernetics-<br />
PART B: Cybernetics, Vol. 42, no. 2, 513 – 529,2012.<br />
[31] Huang et al. Extreme learn<strong>in</strong>g mach<strong>in</strong>es: a<br />
survey .International Journal of Mach<strong>in</strong>e Learn<strong>in</strong>g and<br />
Cybernetics. pp:107–122,2011.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1609<br />
Zhang Chen is current a Ph.D<br />
candidate at Ch<strong>in</strong>a University of<br />
M<strong>in</strong><strong>in</strong>g and Technology(CUMT),<br />
Ch<strong>in</strong>a. She received her MS degree<br />
<strong>in</strong> Computer Application<br />
Technology from CUMT <strong>in</strong> 2004,<br />
and her BS degree <strong>in</strong> Computer<br />
Science from CUMT <strong>in</strong> 2001. She<br />
is currently a lecture at school of Computer Science and<br />
Technology, CUMT. Her research <strong>in</strong>terest is computation<br />
<strong>in</strong>telligence and mach<strong>in</strong>e learn<strong>in</strong>g et al.<br />
Xia Shi Xiong is born <strong>in</strong> 1962,<br />
Ph.D. He is a professor at school<br />
of Computer Science and<br />
Technology <strong>in</strong> CUMT. He has<br />
published more than 60 research<br />
papers <strong>in</strong> journals and<br />
<strong>in</strong>ternational conferences. His<br />
research <strong>in</strong>terest is Wireless sensor<br />
networks and <strong>in</strong>telligent<br />
<strong>in</strong>formation process<strong>in</strong>g et al.<br />
Liu B<strong>in</strong>g is current a Ph.D<br />
candidate at Ch<strong>in</strong>a University of<br />
M<strong>in</strong><strong>in</strong>g and Technology(CUMT),<br />
Ch<strong>in</strong>a. She received her MS degree<br />
<strong>in</strong> Computer Application<br />
Technology from CUMT <strong>in</strong> 2005,<br />
and her BS degree <strong>in</strong> Computer<br />
Science from CUMT <strong>in</strong> 2002. She is<br />
currently a lecture at school of Computer Science and<br />
Technology, CUMT. His research <strong>in</strong>terest is computation<br />
<strong>in</strong>telligence and mach<strong>in</strong>e learn<strong>in</strong>g et al.<br />
© 2013 ACADEMY PUBLISHER
1610 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Optimal Sleep Schedul<strong>in</strong>g Scheme for Wireless<br />
Sensor Networks Based on Balanced Energy<br />
Consumption<br />
Shan-shan Ma<br />
College of Computer Science and Technology, Ch<strong>in</strong>a University of M<strong>in</strong><strong>in</strong>g and Technology, Xuzhou, 221116, Ch<strong>in</strong>a<br />
Email: ssma@cumt.edu.cn<br />
Jian-sheng Qian, Yan-j<strong>in</strong>g Sun<br />
College of Information and Electrical Eng<strong>in</strong>eer, Ch<strong>in</strong>a University of M<strong>in</strong><strong>in</strong>g and Technology, Xuzhou, 221116, Ch<strong>in</strong>a<br />
Abstract—Node schedul<strong>in</strong>g scheme of sensor nodes is one of<br />
the most important method to solve the energy-constra<strong>in</strong>ed<br />
wireless sensor networks. Because there are the defects that<br />
high computational complexity of exact location <strong>in</strong>formation<br />
and the energy consumption unbalance of location-unaware<br />
<strong>in</strong> traditional schemes. Aim<strong>in</strong>g at these problems, an optimal<br />
sleep schedul<strong>in</strong>g scheme based on balanced energy<br />
consumption (ECBS) was proposed <strong>in</strong> this paper.<br />
Account<strong>in</strong>g the residual energy, the precision for node<br />
redundancy evaluat<strong>in</strong>g was improved by us<strong>in</strong>g the distance<br />
<strong>in</strong>formation between the sensor and its neighbors. The<br />
numerical experiments results illustrate that our schedul<strong>in</strong>g<br />
scheme may improve the energy efficiency and extends the<br />
network lifetime while ensure the coverage requirement.<br />
Index Terms—wireless sensor networks; node schedul<strong>in</strong>g<br />
algorithm; energy balance; Location-Unaware<br />
I. INTRODUCTION<br />
Rapid advances <strong>in</strong> micro-electro-mechanical systems<br />
and wireless communication have led to the deployment<br />
of large scale wireless sensor networks (WSNs). The<br />
potential applications of sensor networks are highly<br />
varied, such as environmental monitor<strong>in</strong>g like<br />
temperature, humidity, seismic events, vibrations, and so<br />
on. But the energy source of WSNs often consists of a<br />
battery with a limited energy budget; and it is difficult or<br />
impossible to replace the power supplies for sensor nodes<br />
after deployed .So lifetime is the key performance<br />
measure for WSNs [1]. Sensors are usually deployed<br />
densely to prolong the network lifetime. But a<br />
high-density network will waste a lot of energy and<br />
cause severe problems such as redundancy, radio<br />
channel contention. A broadly-used method is to<br />
place nodes <strong>in</strong> sleep mode by schedul<strong>in</strong>g sensor nodes to<br />
work alternatively. But select<strong>in</strong>g the optimal sens<strong>in</strong>g<br />
ranges for all the sensors is a well-known NP-hard<br />
problem [2]. Random putt<strong>in</strong>g nodes to sleep mode for<br />
fixed time <strong>in</strong>terval [3 and 4] would cause the network to<br />
synchronize and may generate some bl<strong>in</strong>d po<strong>in</strong>ts that<br />
cannot be monitored by any sensors [5,6] . Based on the<br />
location of sensor nodes, some schedule schemes are<br />
known as GAF [7], PEAS [8], SSC [9], etc. Us<strong>in</strong>g the<br />
geography (location, direction, or distance) with global<br />
position system (GPS) or the directional antenna<br />
technology may ensure the coverage and connectivity<br />
effectively. But the costs of GPS or other complicated<br />
hardware devices are too high for t<strong>in</strong>y sensors. Due to<br />
the limited process<strong>in</strong>g and memory capabilities, it is not<br />
realistic to take the sensor nodes equipped with<br />
specialized hardware components such as GPS <strong>in</strong>to mass<br />
production [10]. Furthermore, most applications may not<br />
suit equip with GPS, such as underground, etc. Nodes<br />
schedul<strong>in</strong>g schemes without location <strong>in</strong>formation are<br />
more valuable <strong>in</strong> practical.<br />
Without accurate geography <strong>in</strong>formation, however, it is<br />
very hard to check whether a sensor’s sens<strong>in</strong>g area can be<br />
completely covered by other sensors. Fortunately, most<br />
applications may not require complete coverage of the<br />
monitored area. Fewer researchers have proposed the<br />
node schedul<strong>in</strong>g schemes without the accurate location<br />
<strong>in</strong>formation. Gao et al [11] propose a mathematical model<br />
to describe the redundancy <strong>in</strong> randomly deployed sensor<br />
networks. The results <strong>in</strong>dicate that: a sensor requires<br />
about 11 neighbors to get a 90% probability of be<strong>in</strong>g a<br />
complete redundant sensor. If we only require a sensor’s<br />
90% sens<strong>in</strong>g area to be covered by its neighbors, 5<br />
neighbors are necessary. Based on this theoretical<br />
analysis, a Lightweight Deployment-Aware Schedul<strong>in</strong>g<br />
(LDAS) scheme to turn off redundant sensors has been<br />
proposed [12]. LDAS uses a weighted random vot<strong>in</strong>g<br />
method to decide who will be eligible to fall asleep. But<br />
LDAS only consider a sensor’s 1-hop neighbors which<br />
can cause larger redundancy coverage. Younis proposed<br />
two distributed protocols (LUC-I and LUC-P) rely on<br />
distance between one-hop neighbors along with<br />
advertised tow-hop neighborhood <strong>in</strong>formation [13]. In<br />
[14], Li-Hs<strong>in</strong>g et al presented range-based sleep<br />
schedul<strong>in</strong>g (RBSS) protocol, an optimal sensor selection<br />
patter to ensure the coverage quality. These methods can<br />
effectively reduce network energy consumption without<br />
any location or directional <strong>in</strong>formation. But none of them<br />
take the balance of energy consumption <strong>in</strong>to account. The<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1610-1617
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1611<br />
unbalanced energy consumption means that the nodes<br />
<strong>in</strong>equality sleeps. It leads to the number of nodes<br />
premature death, and then speed up those nodes died <strong>in</strong><br />
this region, called as “funnel<strong>in</strong>g effect”. Thus the “energy<br />
hole” are formed and the network lifetime is reduced<br />
[15~18] . Ideally, all of the nodes deployed <strong>in</strong> the region<br />
should be consumed their energy at the same time as<br />
possible. The residual energy of the entire network is<br />
almost zero when the network is death.<br />
In this paper, we propose an optimal sleep schedul<strong>in</strong>g<br />
scheme (ECBS) which relies on approximate neighbor<br />
distances and two-hop neighbors’ <strong>in</strong>formation but no<br />
location <strong>in</strong>formation. Simulation results <strong>in</strong>dicate that our<br />
scheme not only prolongs the network lifetime, but also<br />
improves energy efficiency. The reset of the paper is<br />
organized as follows. Section II <strong>in</strong>troduces the system<br />
model and problem statement. Section III presents and<br />
analyzes the algorithm. In section IV, we present our<br />
experimental results for performance evaluation. F<strong>in</strong>ally,<br />
section V gives a summary and conclusion.<br />
the wireless communication module to send the data is on<br />
the transmitt<strong>in</strong>g circuit and the power amplify<strong>in</strong>g circuit.<br />
And the ma<strong>in</strong>ly energy consumption to receive the data<br />
focus on the receiv<strong>in</strong>g circuit. Under the reasonable SNR<br />
condition, the transmission energy consumption to send k<br />
bit data is:<br />
ET<br />
( k, d)<br />
= ⎨<br />
⎪⎩<br />
2<br />
⎧ ⎪ Eelec × k+ ε<br />
fs<br />
× k× d d < dcross over<br />
4<br />
Eelec × k+ ε<br />
mp<br />
× k× d d ≥dcross over<br />
and the reception energy consumption is<br />
E = E × k .<br />
R<br />
elec<br />
Among the formulas, E elec is the energy consumption<br />
coefficient for the radio electronics, ε fs and ε mp are the<br />
energy consumption coefficients for a power amplifier<br />
under different condition. Radio parameters are set as<br />
tableⅠ. We only consider the data aggregation, while<br />
ignore other process<strong>in</strong>g energy consumption. The energy<br />
for perform<strong>in</strong>g data aggregation is 5nJ/bit/signal.<br />
II. SYSTEM MODEL AND PROBLEM STATEMENT<br />
A. System Model<br />
We consider sensor nodes for which r t is the<br />
transmission range and r s is the sens<strong>in</strong>g range. And our<br />
analysis is based on the follow<strong>in</strong>g assumes: (1) sensors<br />
are stationary and are deployed randomly with<strong>in</strong> an area;<br />
(2) A sensor’s sens<strong>in</strong>g range is a circle area; (3) all<br />
sensors are supposed to have the same sens<strong>in</strong>g range and<br />
no two sensors can be deployed exactly at a same<br />
location; (4) no geography <strong>in</strong>formation is available; (5) a<br />
node can estimate the approximately distance between<br />
itself and a neighbor based on the received signal<br />
strength[19],and fusion, conflict and retransmission are<br />
not taken <strong>in</strong>to account when data transmitt<strong>in</strong>g; (6)<br />
r t ≥2r s , under this condition, coverage implies<br />
connectivity[20].<br />
Def<strong>in</strong>ition 1 (Neighbor nodes): the neighbor set of sensor<br />
i is def<strong>in</strong>ed as<br />
Ni () = { j∈ℵ| di (, j) ≤2 rs<br />
, i∈ℵ, j≠i } . Where<br />
ℵ represents the sensor set <strong>in</strong> the deployment region.<br />
d(i,j) denotes the distance between sensor i and j.<br />
Def<strong>in</strong>ition 2 1-hop neighbor of sensor i:<br />
N1 () i = { j∈N()| i d(, i j) ≤rs<br />
, i∈ℵ }.<br />
Def<strong>in</strong>ition 3 Half-hop neighbor of sensor i:<br />
ND( i) = { j ∈N( i) | d( i, j) ≤0.5 rs<br />
, i ∈ℵ}<br />
.<br />
Def<strong>in</strong>ition 4 Network lifetime: the runn<strong>in</strong>g time of the<br />
network meet<strong>in</strong>g the required coverage.<br />
B. Energy Dissipation<br />
In our simulations, we use the same energy parameters<br />
and radio model as discussed <strong>in</strong> [21] which are used<br />
widely. In the model, the ma<strong>in</strong>ly energy consumption of<br />
TABLE I.<br />
RADIO PARAMETERS<br />
Parameter<br />
Value<br />
Threshold distance(dcrossover)(m) 87<br />
E elec (nJ/bit) 50<br />
ε fs (pJ/bit/m 2 ) 10<br />
ε mp (pJ/bit/m 4 ) 0.0013<br />
Initial energy(J) 0.05<br />
Data packet size(bits) 4000<br />
C. Problem Statement<br />
Assume that N nodes are distributed <strong>in</strong> a field, and<br />
the number of the active nodes is N A . Then the sleep ratio<br />
of the network is def<strong>in</strong>ed as:<br />
N − N<br />
A<br />
Q = (1)<br />
N<br />
The sleep ratio is one of the standards for measur<strong>in</strong>g<br />
the efficiency of energy consumption. When the total<br />
number of nodes <strong>in</strong> the network is fixed, the higher the<br />
sleep ratio, the better the energy can be saved. If θ is the<br />
desired coverage rate of the network, the objective of<br />
sleep schedul<strong>in</strong>g scheme is to maximize the lifetime and<br />
the sleep ratio of the network while ensue the coverage<br />
rate of active nodes meet the θ requirement.<br />
III. OPTIMAL SLEEP SCHEDULING SCHEME<br />
A. Coverage Redundancy Determ<strong>in</strong>es<br />
© 2013 ACADEMY PUBLISHER
1612 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Figure 1.<br />
Supposed that sensor i has a neighbor sensor j. S i and<br />
S j denote the circle sens<strong>in</strong>g area covered by node i and j<br />
respectively. d ij is the distance between node i and j. And<br />
S denotes the sens<strong>in</strong>g area that is covered by node i<br />
i∩ j<br />
and j, as shown <strong>in</strong> Figure 1. Refer to [22], we can get<br />
that:<br />
⎧<br />
2<br />
d<br />
2<br />
ij<br />
dij<br />
⎪2rs arccos −dijrs 1− d ≤2<br />
2 ij<br />
rs<br />
Si∩<br />
j<br />
=<br />
(2)<br />
⎨ 2rs 4rs<br />
⎪⎩<br />
0<br />
otherwise<br />
So from formula (2), we can get that when the distance<br />
between node i and j is less than or equal to 0.5r, the<br />
redundant coverage area S<br />
i∩<br />
j<br />
is more than about 68.5%<br />
of S i . When the distance of node i and node j is more than<br />
1.75r, the area S i∩<br />
j<br />
is very small, about 0.052 S i.<br />
These results can be used <strong>in</strong> our nodes schedul<strong>in</strong>g. If<br />
d ij ≥1.75r, the effects that node i to node j will be ignored<br />
<strong>in</strong> this paper.<br />
If θ is the percentage of the redundant area covered by<br />
all the neighbors of node i. Refer to paper [22, 23], θ can<br />
be expressed as<br />
∪<br />
θ =<br />
S ∩ S<br />
S<br />
=<br />
Si<br />
= 1 −<br />
m<br />
Si<br />
j<br />
(1 − )<br />
S<br />
− S<br />
S<br />
S i∩j<br />
j i<br />
j∈N() i i N()<br />
i<br />
j=<br />
1<br />
i<br />
i<br />
∏ ∩ (3)<br />
S<br />
N()<br />
i<br />
is the area that covered by sensor i but not<br />
covered by its neighbors. Then, if node i has a neighbor<br />
node k and d ik ≤0.5r. Based on formula (2) and (3), the θ<br />
of node i can be expressed as<br />
m<br />
Si<br />
j<br />
θ ≥1− 0.32 • ∏(1 −<br />
∩ )<br />
(4)<br />
S<br />
j=<br />
1<br />
j≠k<br />
Suppose node j is a neighbor node of node i. Based<br />
on the above def<strong>in</strong>ition, the distance between node i and j<br />
satisfy the condition: 0
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1613<br />
the condition to sleep, it enters the pre-sleep state with a<br />
random short time T w. If the node received other<br />
sensor’s sleep-message at the pre-sleep state, it will<br />
return the active state. Otherwise, it broadcasts itself<br />
sleep-message after wait<strong>in</strong>g T w time and then goes to<br />
sleep state; fall asleep for a period of time Ts.<br />
Based on the classic LEACH cluster protocol, time is<br />
divided <strong>in</strong>to fixed-length time periods called rounds.<br />
Each round beg<strong>in</strong>s with a competition phase, <strong>in</strong> which<br />
every node determ<strong>in</strong>es whether it can be active or sleep.<br />
Then those active sensors enter <strong>in</strong>to cluster<strong>in</strong>g and<br />
sens<strong>in</strong>g. We detail the steps as follows.<br />
Step1: Networks <strong>in</strong>itialization. We assumed that all<br />
sensors are active <strong>in</strong>itially. Each sensor broadcasts<br />
messages to estimate the distance between itself and its<br />
every neighbor and then record these <strong>in</strong>formation.<br />
Accord<strong>in</strong>g to the QoS demand (the coverage rate θ) of<br />
network, s<strong>in</strong>k broadcasts the system message <strong>in</strong>clud<strong>in</strong>g<br />
the two parameters HT and AT. Where HT is the<br />
m<strong>in</strong>imum number of active neighbors with one half-hop<br />
neighbor and AT is the m<strong>in</strong>imum number of neighbor<br />
nodes that have no half-hop neighbor. For example, the<br />
network coverage (θ) is required to 85%. Accord<strong>in</strong>g to<br />
tableⅡ, we can set HT = 5 and AT = 8. While the<br />
coverage rateθis more than 90%, we can set HT = 6<br />
and AT = 9.<br />
Start<br />
cluster heads broadcast hello messages and other active<br />
nodes select the closest head to jo<strong>in</strong>.<br />
Step 4: Sens<strong>in</strong>g.<br />
Step 5: The current round end and return step 2.<br />
IV. SIMULATION RESULTS<br />
We focus on the construction of one cover and assume<br />
that 1000 nodes are deployed randomly <strong>in</strong> a 100<br />
meter×100 meter square. Each sensor has a sens<strong>in</strong>g range<br />
of 15 meters. The transmitt<strong>in</strong>g, receiv<strong>in</strong>g (idl<strong>in</strong>g), and<br />
sleep<strong>in</strong>g power consumption ratio is 20:4:0.01[21]. We<br />
conducted simulations with matlab simulator for<br />
compar<strong>in</strong>g among two sleep schedul<strong>in</strong>g methods: LDAS<br />
and our proposed scheme (ECBS).<br />
A. Coverage Effectiveness<br />
Set θ≥90%. Run LDAS and ECBS at the same<br />
condition to compare. We sampled on the No.100 round<br />
respectively as shown <strong>in</strong> Figure 4 (only active sensors are<br />
marked to see clearly). Only 58 nodes are active <strong>in</strong><br />
our algorithm, but 150 nodes are on-duty by LDAS<br />
algorithm. And Figure 5 shows the coverage condition<br />
with the active nodes on No.100 round by different<br />
algorithm. It can be easy to see that the fewer numbers of<br />
active nodes are needed <strong>in</strong> our algorithm to meet the<br />
same coverage required and the sensors distribute more<br />
uniform <strong>in</strong> Figure 4(b). However, there is more<br />
redundancy coverage <strong>in</strong> Figure 5(a).<br />
Ni>HT<br />
N<br />
Keep active<br />
Y<br />
Ndi>0<br />
N<br />
Y<br />
Ni>AT<br />
N<br />
The maximal residual<br />
energy of sensor <strong>in</strong> ND<br />
> Ei<br />
N<br />
Y<br />
Sensor i sleep<br />
Y<br />
Sensor j with the<br />
m<strong>in</strong>imum residual<br />
energy <strong>in</strong> ND sleep<br />
100<br />
90<br />
(a)<br />
LDAS<br />
80<br />
End<br />
70<br />
60<br />
Figure 3<br />
The schedul<strong>in</strong>g process of an active sensor i<br />
Step 2: Nodes-schedul<strong>in</strong>g. At the beg<strong>in</strong>n<strong>in</strong>g of each<br />
round, each active node determ<strong>in</strong>es whether it is a<br />
redundancy sensor or not. The schedul<strong>in</strong>g scheme is<br />
detailed <strong>in</strong> Figure 3. Where N i is the number of sensor<br />
i ’s active neighbors, and N di is the number of sensor i’s<br />
half-hop neighbors, ND is the set of sensor i’s half-hop<br />
neighbors, E i is the residual energy of sensor i.<br />
Step 3: Cluster<strong>in</strong>g. Active nodes randomly select nodes<br />
as cluster heads based on LEACH algorithm. Then the<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
0 10 20 30 40 50 60 70 80 90 100<br />
(b) ECBS<br />
Figure 4 The distribution of active nodes on No.100 round<br />
© 2013 ACADEMY PUBLISHER
1614 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
covered by those active nodes at some time.<br />
As shown <strong>in</strong> Figure 6, the network coverage is<br />
reduc<strong>in</strong>g with the network runn<strong>in</strong>g us<strong>in</strong>g both the two<br />
algorithms. The higher the network coverage required,<br />
the shorter survival time of the network. Dur<strong>in</strong>g the <strong>in</strong>itial<br />
operation, the two algorithms have ma<strong>in</strong>ta<strong>in</strong>ed a higher<br />
coverage rate. But with the operation of network, more<br />
and more nodes exhausted their energy, the network<br />
coverage also decreased. Furthermore, the coverage rate<br />
of ECBS is always higher than LDAS at the same round<br />
dur<strong>in</strong>g the whole runn<strong>in</strong>g time.<br />
100<br />
80<br />
(a)<br />
LDAS<br />
the number of active nodes<br />
160<br />
140<br />
120<br />
100<br />
80<br />
60<br />
40<br />
θ=90%,LDAS<br />
θ=85%,LDAS<br />
θ=90%,ECBS<br />
θ=85%,ECBS<br />
60<br />
20<br />
network coverage<br />
1<br />
0.95<br />
0.9<br />
0.85<br />
0.8<br />
0.75<br />
0.7<br />
0.65<br />
40<br />
20<br />
0<br />
-20 0 20 40 60 80 100 120<br />
(b)<br />
ECBS<br />
Figure 5 The coverage condition on No.100 round<br />
0.6<br />
θ=90%,LDAS<br />
θ=85%,LDAS<br />
0.55<br />
θ=90%,ECBS<br />
θ=85%,ECBS<br />
0.5<br />
0 200 400 600 800 1000 1200 1400 1600 1800<br />
runn<strong>in</strong>g rounds<br />
Figure 6 Comparisons of network coverage ratio<br />
The network coverage (η) is the ratio of the area<br />
covered by those active nodes to the whole monitor<strong>in</strong>g<br />
area dur<strong>in</strong>g the nodes schedul<strong>in</strong>g scheme runn<strong>in</strong>g<br />
process.<br />
Aactive<br />
∩ A<br />
η () t =<br />
(5)<br />
A<br />
A is the whole monitor<strong>in</strong>g area, and A active is the area<br />
0<br />
0 200 400 600 800 1000 1200 1400 1600 1800<br />
runn<strong>in</strong>g round<br />
Figure 7 Comparisons of active nodes<br />
Figure 7 shows the number of active nodes dur<strong>in</strong>g the<br />
network runn<strong>in</strong>g. As can be seen from Figure 7 and<br />
Figure 6, the number of active nodes by ECBS is always<br />
less than the number that used by LDAS when the<br />
coverage ratio meet<strong>in</strong>g the requirement. Because there<br />
are more active nodes <strong>in</strong> the early operation by LDAS,<br />
too much energy were consumed. The active nodes<br />
decreased with more and more nodes run out of their<br />
energy. And the coverage percentage dropped from 98%<br />
to 50% quickly. But the number of active nodes used by<br />
ECBS algorithm is kept stability <strong>in</strong> the whole runn<strong>in</strong>g<br />
process. Us<strong>in</strong>g the less active nodes to meet a high<br />
coverage, thus the energy has been saved and the lifetime<br />
has been prolonged.<br />
B. Network Lifetime<br />
Accord<strong>in</strong>g to the def<strong>in</strong>ition 4 <strong>in</strong> this paper, network<br />
lifetime is the runn<strong>in</strong>g time of the network meet<strong>in</strong>g the<br />
required coverage. As illustrated <strong>in</strong> Figure 8, the network<br />
lifetime is only 70 rounds with no schedul<strong>in</strong>g scheme. Set<br />
θ≥90%, us<strong>in</strong>g LDAS schedul<strong>in</strong>g scheme the lifetime is<br />
850 rounds and the first dead node occurred on No.104<br />
round. But by ECBS schedul<strong>in</strong>g scheme, the lifetime<br />
extends to 1520 rounds and the first dead node occurred<br />
on No.382 round. Set θ≥85%, the lifetime is 1020 rounds<br />
and the first dead node occurred on No.117 round by<br />
LDAS. But by ECBS algorithm, the lifetime extends to<br />
1750 rounds and the first dead node occurred on No.402<br />
round. ECBS algorithm can prolong the network lifetime<br />
efficiently. And the lower required coverage, the longer<br />
the network lifetime.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1615<br />
∑ N<br />
Ei<br />
() t<br />
i=<br />
1<br />
mE<br />
() t =<br />
N<br />
(6)<br />
The energy variance function is:<br />
=<br />
D () t =<br />
E<br />
∑ N i E<br />
i 1<br />
[ E () t − m () t ] 2<br />
N<br />
(7)<br />
C. Energy Efficiency<br />
Figure 8 Comparison of network lifetime<br />
The average energy<br />
0.05<br />
0.045<br />
0.04<br />
0.035<br />
0.03<br />
0.025<br />
0.02<br />
0.015<br />
0.01<br />
θ=90%,LDAS<br />
θ=85%,LDAS<br />
θ=90%,ECBS<br />
θ=85%,ECBS<br />
0.005<br />
0<br />
0 200 400 600 800 1000 1200 1400 1600 1800<br />
runn<strong>in</strong>g round<br />
Figure 10 comparison of the average residual energy<br />
×10 -5 Figure 11 comparison of the energy Variance<br />
30<br />
25<br />
θ=90%,LDAS<br />
θ=85%,LDAS<br />
θ=90%,ECBS<br />
θ=85%,ECBS<br />
Figure 9 Comparison of sleep ratio<br />
As mentioned above, the sleep ratio is an important<br />
parameter to describe the situation of sav<strong>in</strong>g energy<br />
dur<strong>in</strong>g the operation. When meet<strong>in</strong>g the coverage<br />
requirement, the higher the sleep ratio, the better the<br />
energy can be saved. Figure 9 shows that the sleep ratios<br />
of ECBS are always higher than that of LDAS algorithm<br />
and ma<strong>in</strong>ta<strong>in</strong> stability <strong>in</strong> the whole runn<strong>in</strong>g time.<br />
Moreover with different coverage requirement, the sleep<br />
ratios of LDAS are also much different. The higher the<br />
network coverage requires the lower sleep ratio. But the<br />
sleep ratios of our algorithm have a little change.<br />
Figure10 shows the average residual energy of network<br />
dur<strong>in</strong>g operation. It confirms that the residual energy of<br />
ECBS is always higher than that of LDAS on the same<br />
round.<br />
Sleep ratio can only demonstrate the total condition of<br />
energy consumed, but not measure the balance of energy<br />
consumed. In this paper, the average residual energy and<br />
the energy variance function are used to measure that the<br />
energy consumed is balanced or not at some time [25].<br />
Consider<strong>in</strong>g the two values, the larger the average<br />
residual energy and the smaller the energy variance, the<br />
better balance of the energy consumed <strong>in</strong> the network.<br />
The average residual energy function is:<br />
Energy variance<br />
20<br />
15<br />
10<br />
5<br />
0<br />
0 200 400 600 800 1000 1200 1400 1600 1800<br />
runn<strong>in</strong>g round<br />
From Figure 10 and Figure 11, it can be seen that the<br />
ECBS algorithm has a better balance of energy consumed.<br />
By LDAS algorithm, the m E (t) decreased more rapidly<br />
and the D E (t) were larger. The experiment data shows that<br />
us<strong>in</strong>g LDAS algorithm some nodes still rema<strong>in</strong>ed more<br />
than 90% energy even when the network died. But us<strong>in</strong>g<br />
ECBS algorithm, the maximal ratio of the residual energy<br />
to the <strong>in</strong>itial energy was about 40% when the network<br />
died. It also <strong>in</strong>dicates that LDAS algorithm exits the<br />
problem that energy consumes uneven. Thus it will lead<br />
to some nodes run out their energy earlier. And then<br />
energy hole are formed so as to make the network dy<strong>in</strong>g<br />
prematurely. Ideally each node <strong>in</strong> a network runn<strong>in</strong>g out<br />
its energy at the same time will obta<strong>in</strong> the optimal energy<br />
efficiency.<br />
© 2013 ACADEMY PUBLISHER
1616 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
V. CONCLUSION<br />
Energy sav<strong>in</strong>g <strong>in</strong> WSNs has attracted a lot of attention<br />
<strong>in</strong> the recent years. Extensive research has been<br />
conducted to address these limitations by develop<strong>in</strong>g<br />
schemes that can improve resource efficiency. In this<br />
paper, we have <strong>in</strong>troduced an optimal energy-efficient<br />
sleep schedul<strong>in</strong>g scheme for WSNs. Without accurate<br />
geography <strong>in</strong>formation, the two-hop neighbors are<br />
considered. Simulation results show that our schedul<strong>in</strong>g<br />
scheme has improved the sleep ratio and extended the<br />
network lifetime. But <strong>in</strong> the simulation experiments, we<br />
discovered that there is approximately 17% residual<br />
energy when the network died. Consider<strong>in</strong>g the death<br />
spread from the border of the monitor region to the<br />
central, we believe that there is still space to improve. So,<br />
one of our future works is to f<strong>in</strong>d a solution to alleviate<br />
the <strong>in</strong>equality sleep of the boundary nodes.<br />
ACKNOWLEDGMENTS<br />
This work was supported under the National Science<br />
Foundation of Ch<strong>in</strong>a (50904070, 51104157); The Ch<strong>in</strong>a<br />
Postdoctoral Science Foundation (20100471412).<br />
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[23] Fan Gao-juan, Sun Li-juan, Wang Ru-chuan, et al,<br />
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[24] Fan Gao-juan, Wang Ru-chuan, Huang Hai-p<strong>in</strong>g, et al,<br />
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[25] Jiang Chang-jiang, Shi Wei-ren, Tang Xian-lun, et al,<br />
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[26] Shao-feng Jiang, M<strong>in</strong>g-hua Yang, Han-tao Song, et al, “An<br />
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© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1617<br />
Shan-shan Ma, was born <strong>in</strong> 1978, is<br />
currently a lecturer <strong>in</strong> Ch<strong>in</strong>a University<br />
of M<strong>in</strong><strong>in</strong>g and Technology. She received<br />
the B.S. <strong>in</strong> Electronic and Information<br />
Technology from Ch<strong>in</strong>a University of<br />
M<strong>in</strong><strong>in</strong>g and Technology, Xuzhou, Ch<strong>in</strong>a,<br />
<strong>in</strong> 2000 and the M.S. <strong>in</strong> Communication<br />
and Information Eng<strong>in</strong>eer<strong>in</strong>g from Ch<strong>in</strong>a<br />
University of M<strong>in</strong><strong>in</strong>g and Technology,<br />
Xuzhou, Ch<strong>in</strong>a, <strong>in</strong> 2003. She is currently pursu<strong>in</strong>g the Ph. D.<br />
degree at Computer Application Technology <strong>in</strong> College of<br />
Computer Science and Technology, University of M<strong>in</strong><strong>in</strong>g and<br />
Technology, from 2007. Her research <strong>in</strong>terests <strong>in</strong>clude wireless<br />
sensor network and <strong>in</strong>formation process<strong>in</strong>g.<br />
Yan-J<strong>in</strong>g Sun, was born <strong>in</strong> 1977, is<br />
currently a professor <strong>in</strong> Ch<strong>in</strong>a University<br />
of M<strong>in</strong><strong>in</strong>g and Technology. He received<br />
his Ph.D. degree <strong>in</strong> Communication and<br />
Information System from Ch<strong>in</strong>a<br />
University of M<strong>in</strong><strong>in</strong>g and Technology <strong>in</strong><br />
2007. His research <strong>in</strong>terest <strong>in</strong>cludes<br />
wireless sensor network and embedded<br />
real-time system.<br />
Jian-sheng Qian, was born <strong>in</strong> 1964, is a<br />
professor and Ph.D. candidate tutor <strong>in</strong><br />
Ch<strong>in</strong>a University of M<strong>in</strong><strong>in</strong>g and<br />
Technology currently. He received the<br />
Ph. D degree <strong>in</strong> Control Theory and<br />
Control Eng<strong>in</strong>eer<strong>in</strong>g from Ch<strong>in</strong>a<br />
University of M<strong>in</strong><strong>in</strong>g and Technology,<br />
Ch<strong>in</strong>a, <strong>in</strong> 2003. His research <strong>in</strong>terest<br />
<strong>in</strong>cludes m<strong>in</strong>e communication and<br />
wireless sensor network.<br />
© 2013 ACADEMY PUBLISHER
1618 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Identity Based Proxy Re-encryption From BB1<br />
IBE<br />
J<strong>in</strong>dan Zhang 1 , Xu An Wang 2 and Xiaoyuan Yang 2<br />
1 Department of Electronic Information<br />
Xianyang Vocational Technical College, 712000, P. R. Ch<strong>in</strong>a<br />
2 Key Laboratory of Information and Network Security<br />
Eng<strong>in</strong>eer<strong>in</strong>g University of Ch<strong>in</strong>ese Armed Police Force, 710086, P. R. Ch<strong>in</strong>a<br />
wangxahq@yahoo.com.cn<br />
Abstract— In 1998, Blaze, Bleumer, and Strauss proposed a<br />
k<strong>in</strong>d of cryptographic primitive called proxy re-encryption.<br />
In proxy re-encryption, a proxy can transform a ciphertext<br />
computed under Alice’s public key <strong>in</strong>to one that can<br />
be opened under Bob’s decryption key. In 2007, Matsuo<br />
proposed the concept of four types of proxy re-encryption<br />
schemes: CBE (Certificate Based Public Key Encryption)<br />
to IBE (Identity Based Encryption) (type 1), IBE to IBE<br />
(type 2), IBE to CBE (type 3), CBE to CBE (type 4). In this<br />
paper, we f<strong>in</strong>d that if we allow the PKG to use its masterkey<br />
<strong>in</strong> the process of generat<strong>in</strong>g re-encryption key for proxy<br />
re-encryption <strong>in</strong> identity based sett<strong>in</strong>g, many open problems<br />
can be solved. We give the new security models for proxy reencryption<br />
<strong>in</strong> identity based sett<strong>in</strong>g, especially consider<strong>in</strong>g<br />
PKG’s <strong>in</strong>volv<strong>in</strong>g <strong>in</strong> the re-encryption key generation process<br />
and PKG’s master-key’s security. We construct the new<br />
IND-ID-CPA and the first IND-ID-CCA2 secure proxy reencryption<br />
schemes based on BB1 IBE. We also prove their<br />
security by <strong>in</strong>troduc<strong>in</strong>g some new techniques which maybe<br />
have <strong>in</strong>dependent <strong>in</strong>terest. At last, we compare our new<br />
schemes with exist<strong>in</strong>g ones, the results show that our scheme<br />
can achieve high security levels and are very efficient for<br />
re-encryption and, which are very important for practical<br />
applications.<br />
Index Terms— Cryptography, Identity based proxy reencryption,<br />
PKG, BB1 IBE, Security proof.<br />
I. INTRODUCTION<br />
The concept of proxy re-encryption(PRE) comes from<br />
the work of Blaze, Bleumer, and Strauss <strong>in</strong> 1998[2].<br />
The goal of proxy re-encryption is to securely enable<br />
the re-encryption of ciphertexts from one key to another,<br />
without rely<strong>in</strong>g on trusted parties. In 2005, Ateniese et<br />
al proposed a few new PRE schemes and discussed its<br />
several potential applications such as e-mail forward<strong>in</strong>g,<br />
law enforcement, cryptographic operations on storagelimited<br />
devices, distributed secure file systems and outsourced<br />
filter<strong>in</strong>g of encrypted spam [1]. S<strong>in</strong>ce then, many<br />
excellent schemes have been proposed[10], [25], [20],<br />
[26], [15], [27], [11], [29]. In ACNS’07, Green et al.<br />
proposed the first identity based proxy re-encryption<br />
schemes(IDPRE) [15]. In ISC’07, Chu et al. proposed<br />
The second author is the correspond<strong>in</strong>g author. This paper is an<br />
extended work of [34], [35] and supported by the National Natural<br />
Science Foundation of Ch<strong>in</strong>a under contract no. 61103230, 61103231,<br />
61272492, 61202492, Natural Science Foundation of Shaanxi Prov<strong>in</strong>ce<br />
and Natural Science Foundation of Eng<strong>in</strong>eer<strong>in</strong>g University of Ch<strong>in</strong>ese<br />
Armed Police Force.<br />
the first IND-ID-CCA2 IDPRE schemes <strong>in</strong> the standard<br />
model, they constructed their scheme based on Water’s<br />
IBE. But unfortunately Shao et al. found a flaw <strong>in</strong> their<br />
scheme and they fixed this flaw by propos<strong>in</strong>g an improved<br />
scheme [29]. In Pair<strong>in</strong>g’07, Matsuo proposed another<br />
few more PRE schemes <strong>in</strong> identity based sett<strong>in</strong>g [27].<br />
Interest<strong>in</strong>gly, they proposed the concept of four types of<br />
PRE: CBE(Certificate Based Public Key Encryption) to<br />
IBE(Identity Based Encryption)(type 1), IBE to IBE(type<br />
2), IBE to CBE (type 3), CBE to CBE (type 4)[27], which<br />
can help the ciphertext [33], [24] circulate smoothly <strong>in</strong><br />
the network. They constructed two PRE schemes: one<br />
is the hybrid PRE from CBE to IBE, the other is the<br />
PRE from IBE to IBE. Both of the schemes are now<br />
be<strong>in</strong>g standardized by P1363.3 workgroup [28]. Recently,<br />
Tang et al. extended the concept of identity based proxy<br />
re-encryption, they proposed a concept of <strong>in</strong>ter-doma<strong>in</strong><br />
identity based proxy re-encryption which aimed to construct<strong>in</strong>g<br />
proxy re-encryption scheme between different<br />
doma<strong>in</strong>s <strong>in</strong> identity based sett<strong>in</strong>g [31].<br />
A. Ma<strong>in</strong> Idea and Contribution<br />
Our contributions are ma<strong>in</strong>ly as follow<strong>in</strong>g: If we follow<br />
the pr<strong>in</strong>cipal that all the work PKG can do is just<br />
generat<strong>in</strong>g private keys for IBE users, it is <strong>in</strong>deed difficult<br />
for construct<strong>in</strong>g PRE based on BB 1 IBE. But if we allow<br />
PKG generat<strong>in</strong>g re-encryption keys for PRE by us<strong>in</strong>g its<br />
master − key, we can easily construct PRE based on a<br />
variant of BB 1 IBE.<br />
On the Role of PKG <strong>in</strong> IBPRE and Related Primitives.<br />
We challenge the traditional idea of PKG is only<br />
responsible to generate private keys. Traditionally when<br />
cryptographers design IBE and other related schemes, they<br />
assume the PKG can only generate the private keys to<br />
the users. The idea situation is that after PKG generat<strong>in</strong>g<br />
private keys for the whole users, the PKG is shut up<br />
to avoid “s<strong>in</strong>gle-po<strong>in</strong>t failure” problem. But we remark<br />
that this idea situation can not work <strong>in</strong> the practical<br />
application, we can not predicate all the future users<br />
of the system when it was set up. Furthermore, <strong>in</strong> the<br />
IBE systems, there are also requirements of revocation<br />
of the identity, which will necessary <strong>in</strong>volved the PKG.<br />
Thus many usable IBE systems let their PKG be onl<strong>in</strong>e<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1618-1626
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1619<br />
24/7/365. From a practical po<strong>in</strong>t, for PRE <strong>in</strong> the identity<br />
based sett<strong>in</strong>g, <strong>in</strong>volv<strong>in</strong>g PKG <strong>in</strong> generat<strong>in</strong>g re-encryption<br />
key can generically help the proxy improve its efficiency,<br />
which is very important for practical IBPRE systems,<br />
after all, re-encryption is the ma<strong>in</strong> operation <strong>in</strong> the PRE<br />
systems. More importantly, <strong>in</strong>volv<strong>in</strong>g PKG <strong>in</strong> generat<strong>in</strong>g<br />
some “valued ephemeral” maybe br<strong>in</strong>g unexpected benefits<br />
to exist<strong>in</strong>g identity based primitives. For example,<br />
<strong>in</strong> identity based broadcast encryption, some “valued<br />
ephemeral” given by the PKG maybe be very useful<br />
for the receivers for decryption, Note the length of this<br />
“valued ephemeral” is just constant, <strong>in</strong>stead of l<strong>in</strong>ear with<br />
the receivers, thus improve the efficiency greatly. Also<br />
note this feature can not be shared with the normal public<br />
key broadcast encryption schemes.<br />
B. Organization<br />
We organize our paper as follow<strong>in</strong>g. In Section I-<br />
I, we give some prelim<strong>in</strong>aries which are necessary to<br />
understand our paper. We propose our new proxy reencryption<br />
scheme based on a variant of BB 1 IBE and<br />
prove its security <strong>in</strong> SectionIII. In Section IV, we give<br />
the comparison results with previous IBPRE schemes. We<br />
give our conclusions <strong>in</strong> the last Section V.<br />
II. PRELIMINARIES<br />
In the follow<strong>in</strong>g, we sometimes use notations described<br />
<strong>in</strong> this section without notice. We denote the concatenation<br />
of a and b by a||b, denote random choice from a set<br />
S by R ←− S.<br />
A. Bil<strong>in</strong>ear groups<br />
Let G and G 1 be multiplicative cyclic groups of prime<br />
order p, and g be generator of G. We say that G 1 has an<br />
admissible bil<strong>in</strong>ear map e : G×G → G 1 . if the follow<strong>in</strong>g<br />
conditions hold.<br />
1) e(g a , g b ) = e(g, g) ab for all a, b.<br />
2) e(g, g) ≠ 1.<br />
3) There is an efficient algorithm to compute e(g a , g b )<br />
for all a, b and g.<br />
B. Assumptions<br />
Def<strong>in</strong>ition 1: For randomly chosen <strong>in</strong>tegers a, b, c R ←−<br />
Z ∗ p, a random generator g R ←− G, and an element R R ←− G,<br />
we def<strong>in</strong>e the advantage of an algorithm A <strong>in</strong> solv<strong>in</strong>g<br />
the Decision Bil<strong>in</strong>ear Diffie-Hellman(DBDH) problem as<br />
follows:<br />
Adv G dbdh (A) =| P r[A(g, g a , g b , g c , e(g, g) abc ) = 0]<br />
−P r[A(g, g a , g b , g c , R) = 0] |<br />
where the probability is over the random choice of generator<br />
g ∈ G, the randomly chosen <strong>in</strong>tegers a, b, c, the<br />
random choice of R ∈ G, and the random bits used by<br />
A. We say that the (k, t, ɛ)-DBDH assumption holds <strong>in</strong> G<br />
if no t-time algorithm has advantage at least ɛ <strong>in</strong> solv<strong>in</strong>g<br />
the DBDH problem <strong>in</strong> G under a security parameter k.<br />
C. Identity Based Encryption<br />
An Identity Based Encryption(IBE) system consists of<br />
the follow<strong>in</strong>g algorithms.<br />
1) SetUp IBE (k). Given a security parameter k, PKG<br />
generate a pair (parms, mk), where parms denotes<br />
the public parameters and mk is the master − key.<br />
2) KeyGen IBE (mk, parms, ID). Given the<br />
master − key mk and an identity ID with parms,<br />
generate a secret key sk ID for ID.<br />
3) Enc IBE (ID, parms, M). Given a message M and the<br />
identity ID with parms, compute the encryption of<br />
M, C ID for ID.<br />
4) Dec IBE (sk, parms, C ID ). Given the secret key sk,<br />
decrypt the ciphertext C ID .<br />
III. IBPRE BASED ON A VARIANT OF BB 1 IBE<br />
A. Our Def<strong>in</strong>ition for IBPRE<br />
In this section, we give our def<strong>in</strong>ition and security<br />
model for identity based PRE scheme, which is based<br />
on [15], [31].<br />
Def<strong>in</strong>ition 2: An identity based PRE scheme is tuple<br />
of algorithms (Setup, KeyGen, Encrypt, Decrypt, RK-<br />
Gen, Reencrypt):<br />
• Setup(1 k ). On <strong>in</strong>put a security parameter, the algorithm<br />
outputs both the master public parameters<br />
which are distributed to users, and the master secret<br />
key (msk) which is kept private.<br />
• KeyGen(params, msk, ID). On <strong>in</strong>put an identity<br />
ID ∈ {0, 1} ∗ and the master secret key, outputs a<br />
decryption key sk ID correspond<strong>in</strong>g to that identity.<br />
• Encrypt(params, ID, m). On <strong>in</strong>put a set of public<br />
parameters, an identity ID ∈ {0, 1} ∗ and a pla<strong>in</strong>text<br />
m ∈ M, output c ID , the encryption of m under the<br />
specified identity.<br />
• RKGen(params, msk, sk ID1 , sk ID2 , ID 1 , ID 2 ).<br />
On <strong>in</strong>put secret keys msk, sk ID1 , sk ID2 , and i-<br />
dentities ID ∈ {0, 1} ∗ , PKG, the delegator and the<br />
delegatee <strong>in</strong>teractively generat the re-encryption key<br />
rk ID1→ID 2<br />
, the algorithm output it.<br />
• Reencrypt(params, rk ID1→ID 2<br />
, c ID1 ). On <strong>in</strong>put<br />
a ciphertext c ID1 under identity ID 1 , and a reencryption<br />
key rk ID1→ID 2<br />
, outputs a re-encrypted<br />
ciphertext c ID2 .<br />
• Decrypt(params, sk ID , c ID ). Decrypts the ciphertext<br />
c ID us<strong>in</strong>g the secret key sk ID , and outputs m<br />
or ⊥.<br />
Remark 1: This def<strong>in</strong>ition is different from the Def<strong>in</strong>ition<br />
of IBPRE <strong>in</strong> the work of [27]. We <strong>in</strong>sist this is a<br />
more natural and general Def<strong>in</strong>ition for PRE from IBE to<br />
IBE. This def<strong>in</strong>ition is consistent with the work of [15],<br />
[31].<br />
B. Our Security Models for IBPRE<br />
In PRE from IBE to IBE, there is no necessary to<br />
consider the malicious PKG attack, so we omit PKG <strong>in</strong><br />
our security model when consider<strong>in</strong>g delegator security<br />
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1620 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
and delegatee security.<br />
Delegator Security.<br />
In PRE from IBE to IBE, we consider the case that proxy<br />
and delegatee are corrupted.<br />
Def<strong>in</strong>ition 3: (DGA-IBE-IND-ID-CPA) A PRE<br />
scheme from IBE to IBE is DGA 1 -IBE-IND-ID-CPA<br />
secure if the probability<br />
P r[{(ID ⋆ , sk ID ⋆) ← KeyGen(·)}<br />
{(ID x , sk IDx ) ← KeyGen(·)},<br />
{(ID h , sk IDh ) ← KeyGen(·)},<br />
{R hx ← RKGen(msk, sk IDh , sk IDx , ·)},<br />
{R xh ← RKGen(msk, sk IDx , sk IDh , ·)},<br />
{R hh ← RKGen(msk, sk IDh , sk IDh , ·)},<br />
{R xx ← RKGen(msk, sk IDx , sk IDx , ·)},<br />
{R ⋆h ← RKGen(msk, sk ID ⋆, sk IDh , ·)},<br />
{R ⋆x ← RKGen(msk, sk ID ⋆, sk IDx , ·)},<br />
(m 0 , m 1 , St) ← A Orenc (ID ⋆ , {sk IDx },<br />
{R xh }, {R hx }, {R hh }, {R xx }, {R ⋆h }, {R ⋆x }),<br />
d ⋆ R<br />
←− {0, 1}, C ⋆ = Encrypt(m d ⋆, ID ⋆ ),<br />
d ′ ← A Ørenc (C ⋆ , St) : d ′ = d ⋆ ]<br />
is negligibly close to 1/2 for any PPT adversary A. In<br />
our notation, St is a state <strong>in</strong>formation ma<strong>in</strong>ta<strong>in</strong>ed by A<br />
while (ID ⋆ , sk ID ⋆) is the target user’s pubic and private<br />
key pair generated by the challenger which also chooses<br />
other keys for corrupt and honest parties. For other honest<br />
parties, keys are subscripted by h and we subscript corrupt<br />
keys by x. Oracles O renc proceeds as follows:<br />
• Re-encryption O renc : on <strong>in</strong>put (pk i , ID j , C pki ),<br />
where C pki is the ciphertext under the public key pk i<br />
, pk i were produced by Keygen CBE , ID j were produced<br />
by Keygen IBE , this oracle responds with ‘<strong>in</strong>valid’<br />
if C pki is not properly shaped w.r.t. pk i . Otherwise<br />
the re-encrypted first level ciphertext C ID =<br />
ReEnc(KeyGen P RO (sk i , ID j , mk, parms), ID j ,<br />
parms, C pki ) is returned to A.<br />
Delegatee Security.<br />
In PRE from IBE to IBE, we consider the case that proxy<br />
and delegator are corrupted.<br />
Def<strong>in</strong>ition 4: (DGE-IBE-IND-ID-CPA) A PRE<br />
scheme from IBE to IBE is DGE 2 -IBE-IND-ID-CPA<br />
1 DGA means Delegator<br />
2 DGE means Delegatee.<br />
secure if the probability<br />
P r[{(ID ⋆ , sk ID ⋆) ← KeyGen(·)}<br />
{(ID x , sk IDx ) ← KeyGen(·)},<br />
{(ID h , sk IDh ) ← KeyGen(·)},<br />
{R hx ← RKGen(msk, sk IDh , sk IDx , ·)},<br />
{R xh ← RKGen(msk, sk IDx , sk IDh , ·)},<br />
{R hh ← RKGen(msk, sk IDh , sk IDh , ·)},<br />
{R xx ← RKGen(msk, sk IDx , sk IDx , ·)},<br />
{R h⋆ ← RKGen(msk, sk IDh , sk ID ⋆, ·)},<br />
{R x⋆ ← RKGen(msk, sk IDx , sk ID ⋆, ·)},<br />
(m 0 , m 1 , St) ← A Orenc (ID ⋆ , {sk IDx }, {R xh },<br />
{R hx }, {R hh }, {R xx }, {R h⋆ }, {R x⋆ }),<br />
d ⋆ R<br />
←− {0, 1}, C ⋆ = Encrypt(m d ⋆, ID ⋆ ),<br />
d ′ ← A Ørenc (C ⋆ , St) : d ′ = d ⋆ ]<br />
is negligibly close to 1/2 for any PPT adversary A. The<br />
notations <strong>in</strong> this game are same as Def<strong>in</strong>ition 3.<br />
PKG Security.<br />
In PRE from IBE and IBE, PKG’s master key can not<br />
leverage even if the delegator, the delegatee and proxy<br />
collude.<br />
Def<strong>in</strong>ition 5: (PKG-OW) A PRE scheme from IBE to<br />
IBE is one way secure for PKG if the probability<br />
P r[{(ID x , sk IDx ) ← KeyGen(·)},<br />
{(ID h , sk IDh ) ← KeyGen(·)},<br />
{R hx ← RKGen(msk, sk IDh , sk IDx , ·)},<br />
{R xh ← RKGen(msk, sk IDx , sk IDh , ·)},<br />
{R hh ← RKGen(msk, sk IDh , sk IDh , ·)},<br />
{R xx ← RKGen(msk, sk IDx , sk IDx , ·)},<br />
mk ′ ← A Orenc ({sk IDx }, {sk IDh }, {R xh },<br />
{R hx }, {R hh }, {R xx }, {parms}) : mk = mk ′ ]<br />
is negligibly close to 0 for any PPT adversary A. The<br />
notations <strong>in</strong> this game are same as Def<strong>in</strong>ition 3.<br />
C. Our Proposed IND-Pr-sID-CPA Secure IBPRE<br />
Scheme Based on a Variant of BB 1 IBE<br />
• The underly<strong>in</strong>g IBE scheme: We give a variant of<br />
BB 1 -IBE scheme as follows:<br />
Let G be a bil<strong>in</strong>ear group of prime order p (the<br />
security parameter determ<strong>in</strong>es the size of G). Let<br />
e : G × G → G 1 be the bil<strong>in</strong>ear map. For now, we<br />
assume public keys (ID) is element <strong>in</strong> Zp. ∗ We later<br />
extend the construction to public keys over {0, 1} ∗<br />
by first hash<strong>in</strong>g ID us<strong>in</strong>g a collision resistant hash<br />
H : {0, 1} ∗ → Z p . We also assume messages to be<br />
encrypted are elements <strong>in</strong> G. The IBE system works<br />
as follows:<br />
1) SetUp IBE (k). Given a security parameter k,<br />
select a random generator g ∈ G and random<br />
elements g 2 = g t1 , h = g t2 ∈ G. Pick a random<br />
α ∈ Zp. ∗ Set g 1 = g α ,mk = g2 α , and params =<br />
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(g, g 1 , g 2 , h). Let mk be the master-secret key<br />
and let params be the public parameters.<br />
KeyGen IBE (mk, params, ID). Given<br />
mk = g2 α and ID with params, the<br />
PKG picks random s 0 , s 1 ∈ Zp, ∗ choose<br />
a hash function ˜H : Zp ∗ × {0, 1} ∗ → Zp<br />
∗<br />
and computes u 0 = ˜H(s0 , ID),<br />
u 1 = ˜H(s 1 , ID). Set sk ID = (d 0 , d 1 , d ′ 0) =<br />
(g2 α (g1 ID h) u0 , g u0 , (g2 α (g1 ID h) u1 )). The PKG<br />
preserves (s 0 , s 1 ).<br />
Enc IBE (ID, params, M). To encrypt a message<br />
M ∈ G 1 under the public key ID ∈ Zp,<br />
∗<br />
pick a random r ∈ Zp ∗ and compute C ID =<br />
(g r , (g1 ID h) r , Me(g 1 , g 2 ) r ).<br />
Dec IBE (sk ID , params, C ID ). Given ciphertext<br />
C ID = (C 1 , C 2 , C 3 ) and the secret key<br />
sk ID = (d 0 , d 1 ) with prams, compute M =<br />
C 3e(d 1,C 2)<br />
e(d .<br />
0,C 1)<br />
delegation scheme:<br />
KeyGen PRO (sk R , params, ID, ID ′ ). The<br />
PKG computes u ′ 1 = ˜H(s 1 , ID ′ ) and randomly<br />
selects k 1 , k 2 , k 3 ∈ Zp ∗ and sets<br />
rk ID→ID ′ = (rk 1 , rk 2 , rk 3 , rk 4 ) =<br />
( αID′ +t 2+k 1<br />
k 3(αID+t 2)<br />
+ k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ) and<br />
sends them to the proxy via secure channel.<br />
We must note that the PKG computes a different<br />
(k 1 , k 2 , k 3 ) for every different user pair<br />
(ID, ID ′ ).<br />
Check(params, C ID , ID). Given the delegator’s<br />
identity ID and C ID = (C 1 , C 2 , C 3 )<br />
with params, compute v 0 = e(C 1 , g1 ID h) and<br />
v 1 = e(C 2 , g). If v 0 = v 1 then output 1.<br />
Otherwise output 0.<br />
ReEnc(rk ID→ID ′, params, C ID , ID ′ ).<br />
Given the identities ID, ID ′ , rk ID→ID ′ =<br />
(rk 1 , rk 2 , rk 3 , rk 4 ) = ( αID′ +t 2+k 1<br />
k 3(αID+t 2)<br />
+<br />
k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ) with params, the<br />
proxy re-encrypt the ciphertext C ID <strong>in</strong>to<br />
C ID ′ as follows. First it runs “Check”, if<br />
output 0, then return “Reject”. Else computes<br />
C 2ID ′ = (C 1, ′ C 2, ′ C 3, ′ C 4, ′ C 5, ′ C 6, ′ C 7) ′ =<br />
αID ′ +t 2 +k 1<br />
k<br />
(C 1 , C 2 , C 3 , C<br />
(αID+t 2 ) +k2<br />
2 , rk 2 , rk 3 , rk 4 ).<br />
Dec1 IBE (sk ID ′, params, C 2ID ′). Given<br />
a re-encrypted ciphertext C 2ID ′ =<br />
(C 1, ′ C 2, ′ C 3, ′ C 4, ′ C 5, ′ C 6, ′ C 7) ′ and the secret key<br />
sk ID = (d 0 , d 1 , d ′ 0) with params, computes<br />
C<br />
M =<br />
3e(C ′ 5, ′ C 4)<br />
′<br />
e(C 2 ′ , C′ 6 )e(C′ 1 , C′ 7 )e(d′ 0 , C′ 1 )<br />
C<br />
=<br />
3e(rk ′ 2 , C 4)<br />
′<br />
e(C 2 ′ , rk 3)e(C 1 ′ , rk 4)e(d ′ 0 , C′ 1 )<br />
Dec2 IBE (sk ID ′, params, C 1ID ′). Given a<br />
normal ciphertext C ID ′ = (C 1 , C 2 , C 3 ) and the<br />
secret key sk ID ′ = (d 0 , d 1 , d ′ 0) with prams,<br />
compute M = C3e(d1,C2)<br />
e(d . 0,C 1)<br />
We<br />
Remark<br />
computes<br />
pair<br />
+t 2+k<br />
3(αID+t<br />
same<br />
not secure<br />
Security<br />
Theorem<br />
our<br />
IND-sID-CPA<br />
collud<strong>in</strong>g.<br />
Proof:<br />
construct<br />
On<br />
output<br />
= g<br />
<strong>in</strong>teract<strong>in</strong>g<br />
Initialization.<br />
with<br />
<strong>in</strong>tends<br />
Setup.To<br />
rithm<br />
h<br />
params<br />
<strong>in</strong>g<br />
g2 a<br />
Phase<br />
•<br />
•<br />
can verify its correctness as follow<strong>in</strong>g<br />
C 3e(rk ′ 2 , C 4)<br />
′<br />
e(C 2 ′ , rk 3)e(C 1 ′ , rk 4)e(d ′ 0 , C′ 1 )<br />
Me(g 1 , g 2 ) r e(g k3u′ 1 , (g<br />
ID<br />
=<br />
1 h) r( αID′ +t 2 +k 1<br />
k 3 (αID+t 2 ) +k2) )<br />
e((g1 IDh)r<br />
, g u′ 1 k2k3 )e(g r , g k1u′ 1)e(g2 α(gID′<br />
1 h) u′ 1, g r )<br />
= Me(g 1, g 2 ) r e(g k3u′ 1 , (g<br />
ID<br />
1 h) k2r )e(g k3u′ 1 , (g<br />
ID ′<br />
1 h) r<br />
e((g1 IDh)r<br />
, g u′ 1 k2k3 )e(g r , g k1u′ 1)e(g2 α(gID′<br />
= Me(g 1, g 2 ) r<br />
e(g2 α, = M<br />
gr )<br />
2: In our scheme, we must note that the P-<br />
a different (k 1 , k 2 , k 3 ) for every different<br />
(ID, ID ′ ). Otherwise, if the adversary knows<br />
1<br />
2) 2 for five different pairs (ID, ID ′ ) but<br />
k 1 , k 2 , k 3 , α, t 2 , he can compute (α, t 2 ), which<br />
at all.<br />
Analysis<br />
1: Suppose the DBDH assumption holds,<br />
scheme proposed <strong>in</strong> Section III-C is DGA-IBEsecure<br />
for the proxy and the delegatee’s<br />
Suppose A can attack our scheme, we<br />
an algorithm B solves the DBDH problem <strong>in</strong><br />
<strong>in</strong>put (g, g a , g a2 , g b , g c , T ), algorithm B’s goal<br />
1 if T = e(g, g) abc and 0 otherwise. Let<br />
, g 2 = g b , g 3 = g c . Algorithm B works by<br />
with A <strong>in</strong> a selective identity game as follows:<br />
The selective identity game beg<strong>in</strong>s<br />
A first outputt<strong>in</strong>g an identity ID ∗ that it<br />
to attack.<br />
generate the system’s parameters, algo-<br />
B picks α ′ ∈ Z p at random and def<strong>in</strong>es<br />
= g1 −ID∗ g α′ ∈ G. It gives A the parameters<br />
= (g, g 1 , g 2 , h). Note that the correspond-<br />
master − key, which is unknown to B, is<br />
= g ab ∈ G ∗ .<br />
1<br />
“A issues up to private key queries on<br />
ID i ”. B selects randomly r i , r ′ ∗<br />
i ∈ Z p<br />
and k ′ ∈ Z p , sets sk IDi = (d 0 , d 1 , d ′ 0) =<br />
−α ′<br />
ID<br />
(g i −ID ∗<br />
2 (g (IDi−ID∗ )<br />
1 g a ) ri −1<br />
ID<br />
, g i −ID ∗<br />
2 g ri ,<br />
−α ′<br />
ID<br />
g i −ID ∗<br />
2 (g (IDi−ID∗ )<br />
1 g a ) r′ i). We claim sk IDi<br />
is a valid random private key for ID i .<br />
b<br />
To see this, let ˜r i = r i −<br />
ID−ID<br />
and<br />
∗<br />
˜r i ′ = r′ i − b<br />
ID−ID<br />
. Then we have that<br />
∗<br />
−α ′<br />
ID<br />
d 0 = g i −ID ∗<br />
2 (g (IDi−ID∗ )<br />
1 g α′ ) ri =<br />
g2(g a (IDi−ID∗ )<br />
1 g α′ ) ri− b<br />
ID−ID∗<br />
= g2(g a IDi<br />
1 h) ˜ri .<br />
−1<br />
ID<br />
d 1 = g i −ID ∗<br />
2 g ri = g ˜ri .<br />
−α ′<br />
d ′ ID<br />
0 = g i −ID ∗<br />
2 (g (IDi−ID∗ )<br />
1 g α′ ) r′ i<br />
=<br />
g2(g a (IDi−ID∗ )<br />
1 g α′ ) r′ i − b<br />
ID−ID∗<br />
= g2(g a IDi<br />
1 h) ˜r i ′ .<br />
“A issues up to rekey generation queries on<br />
(ID, ID ′ )”.<br />
The challenge B chooses a randomly x ∈ Zp,<br />
∗<br />
2)<br />
KG<br />
3)<br />
αID ′<br />
k<br />
the<br />
is<br />
4)<br />
D.<br />
• The then<br />
1)<br />
G.<br />
is to<br />
g a 1<br />
1)<br />
2)<br />
2)<br />
3)<br />
3)<br />
4)<br />
5)<br />
k 3 )e(g k3u′ 1 , g<br />
k 1 r<br />
1 h) u′ 1, g r )<br />
k 3 )<br />
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1622 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
sets rk ID→ID ′ = x and returns it to A. He<br />
computes w = (gH 1 (ID) h) x<br />
and sends it to the<br />
(g H 1 (ID) h)<br />
proxy. We observe that<br />
rk 1 = αID′ + t 2 + k 1<br />
k 3 (αID + t 2 ) + k 2<br />
but from the simulation, α = a and t 2 = α ′ −<br />
aID ∗ , so we can get<br />
rk 1 = aID′ + α ′ − aID ∗ + k 1<br />
k 3 (aID + α ′ − aID ∗ ) + k 2<br />
Let rk 1 = x, we can get<br />
k 1 = k 3 (aID + α ′ − aID ∗ )(x − k 2 )<br />
−(aID ′ + α ′ − aID ∗ )<br />
= [k 3 (x − k 2 )a(ID − ID ∗ )<br />
−a(ID ′ − ID ∗ )] + k 3 α ′ (x − k 2 ) − α ′<br />
So the challenge B simulates as follows. He<br />
chooses a randomly k 2 , k 3 ∈ Z ∗ p, sets<br />
x =<br />
ID′ − ID ∗<br />
k 3 (ID − ID ∗ ) + k 2,<br />
k 1 = α ′ ( ID′ − ID ∗<br />
ID − ID ∗ ) − α′<br />
searches <strong>in</strong> User-key-list<br />
for item (ID ′ , α ′ , r, r ′ )(we assume<br />
sk ID ′ = (d 0 , d 1 , d ′ 0) =<br />
−α ′<br />
−1<br />
ID ′ −ID ∗<br />
ID<br />
(g<br />
′ −ID ∗<br />
2 (g (ID′ −ID ∗ )<br />
1 g a ) r , g2 g r ,<br />
−α ′<br />
ID<br />
g<br />
′ −ID ∗<br />
2 (g (ID′ −ID ∗ )<br />
1 g a ) r′ ) and computes<br />
rk 1 =<br />
rk 2 = g<br />
ID ′ − ID ∗<br />
k 3 (ID − ID ∗ ) + k 2,<br />
−k 3<br />
ID ′ −ID ∗<br />
2 g k3r′<br />
−k 2 k 3<br />
ID ′ −ID ∗<br />
rk 3 = g2 g k2k3r′ ,<br />
α ′ ( ID′ −ID ∗<br />
ID−ID ∗ )−α′<br />
ID<br />
rk 4 = g<br />
′ −ID ∗<br />
2 g (α′ ( ID′ −ID ∗<br />
ID−ID ∗ )−α ′ )r ′<br />
returns them to A. We can see<br />
C ′ 3e(rk 2 , C ′ 4)<br />
e(C ′ 2 , rk 3)e(C ′ 1 , rk 4)e(d ′ 0 , C′ 1 )<br />
can be reduced to<br />
Me(g 1 , g 2 ) r<br />
e(g α 2 , gr )<br />
= M<br />
Thus our simulation is <strong>in</strong>dist<strong>in</strong>guishable from<br />
the real algorithm runn<strong>in</strong>g. Thus our simulation<br />
is <strong>in</strong>dist<strong>in</strong>guishable from the real algorithm<br />
runn<strong>in</strong>g.<br />
• “A issues up to re-encryption queries on<br />
(C ID , ID, ID ′ )”. The challenge B runs<br />
ReEnc(rk ID→ID ′, C ID , ID, ID ′ ) and returns<br />
the results.<br />
4) Challenge When A decides that Phase1 is over,<br />
it outputs two messages M 0 , M 1 ∈ G. Algorithm<br />
B picks a random bit b and responds with the<br />
ciphertext C = (g c , (g α′ ) c , M b · T ). Hence if T =<br />
e(g, g) abc = e(g 1 , g 2 ) c , then C is a valid encryption<br />
of M b under ID ∗ . Otherwise, C is <strong>in</strong>dependent of<br />
b <strong>in</strong> the adversary’s view.<br />
5) Phase2 A issues queries as he does <strong>in</strong> Phase 1<br />
except natural constra<strong>in</strong>ts.<br />
6) Guess F<strong>in</strong>ally, A outputs a guess b ′ ∈ {0, 1}.<br />
Algorithm B concludes its own game by outputt<strong>in</strong>g<br />
a guess as follows. If b = b ′ , then B outputs 1<br />
mean<strong>in</strong>g T = e(g, g) abc . Otherwise it outputs 0<br />
mean<strong>in</strong>g T ≠ e(g, g) abc .<br />
When T = e(g, g) abc then A’s advantage for break<strong>in</strong>g<br />
the scheme is same as B’s advantage for solv<strong>in</strong>g DBDH<br />
problem.<br />
Theorem 2: Suppose the DBDH assumption holds,<br />
then our scheme proposed <strong>in</strong> Section III-C is DGE-<br />
IBE-IND-sID-CPA secure for the delegator and proxy’s<br />
collud<strong>in</strong>g.<br />
Proof: The security proof is same as the above<br />
theorem except that it does not allow “A issues up to<br />
rekey generation queries on (ID, ID ∗ )”, for B does not<br />
know the private key correspond<strong>in</strong>g to ID ∗ .<br />
Theorem 3: Suppose the DBDH assumption holds,<br />
then our scheme proposed <strong>in</strong> Section III-C is PKG-OW<br />
secure for the delegator, delegatee and proxy’s collud<strong>in</strong>g.<br />
Proof: We just give the <strong>in</strong>tuition for this<br />
theorem. The master-key is g2 α , and delegator’s private<br />
key is sk ID = (g2 α (g1 ID h) u0 , g u0 , (g2 α (g1 ID h) u1 )),<br />
the delegatee’s private key is sk ID ′ =<br />
(g2 α (g1 ID′ h) u0 , g u0 , (g2 α (g1 ID′ h) u1 )) , the proxy reencryption<br />
key is rk ID→ID ′ = ( αID′ +t 2+k 1<br />
k 3(αID+t 2)<br />
+<br />
k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ). Because the re-encryption key<br />
rk ID→ID ′ is uniformly distributed <strong>in</strong> (Zp, ∗ G, G, G), and<br />
the orig<strong>in</strong>al BB 1 IBE is secure, we can conclude that<br />
g2<br />
α can not be disclosed by the proxy, delegatee and<br />
delegator’s collud<strong>in</strong>g.<br />
E. Toward Chosen Ciphertext Security<br />
As we all know, just consider<strong>in</strong>g IND-sID-CPA security<br />
is not enough for many applications. We consider<br />
construct IND-Pr-ID-CCA secure IBPRE based on a<br />
variant of BB 1 IBE. There are two ways to construct<br />
IND-Pr-ID-CCA secure IBPRE. One way is consider<strong>in</strong>g<br />
CHK transformation to hierarchal variant of BB 1 IBE<br />
to get IND-Pr-sID-CCA secure IBPRE or get IND-Pr-<br />
IDKEM-CCA secure IBPRE. The other way is consider<strong>in</strong>g<br />
variant of BB 1 IBE <strong>in</strong> the random oracle model.<br />
From a practical viewpo<strong>in</strong>t, we construct an IND-Pr-ID-<br />
CCA secure IBPRE based on a variant of BB 1 IBE <strong>in</strong><br />
the random oracle model.<br />
F. Our Proposed IND-Pr-ID-CCA Secure IBPRE Scheme<br />
Based on a Variant of BB 1 IBE<br />
Let G be a bil<strong>in</strong>ear group of prime order p(the security<br />
parameter determ<strong>in</strong>es the size of G). Let e : G × G →<br />
G 1 be the bil<strong>in</strong>ear map. Identities are represented us<strong>in</strong>g<br />
dist<strong>in</strong>ct arbitrary bit str<strong>in</strong>gs <strong>in</strong> {0, 1} l . The messages (or<br />
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session keys) are bit str<strong>in</strong>gs <strong>in</strong> {0, 1} l of some fixed length<br />
l. We require the availability of five hash functions viewed<br />
as random oracles:<br />
• A hash function H 1 : {0, 1} ∗ → Z ∗ q ;<br />
• A hash function H 2 : G 1 × {0, 1} l → G;<br />
• A hash function H 3 : G 1 → {0, 1} l ;<br />
• A hash function H 4 : {0, 1} ∗ ×G×G×G×{0, 1} l →<br />
G;<br />
1) SetUp. To generate IBE system parameters, first<br />
select three <strong>in</strong>tegers α, β, γ ∈ Z p at random. Set<br />
g 1 = g α , g 2 = g t1 and h = g t2 <strong>in</strong> G, and<br />
compute v 0 = e(g, g) αβ . The public system parameters<br />
params and the masterkey are given by:<br />
params = (g, g 1 , g 3 , v 0 ), masterkey = (α, β, γ).<br />
Strictly speak<strong>in</strong>g, the generator need not be kept<br />
secret, but s<strong>in</strong>ce it will be used exclusively by the<br />
authority, it can be reta<strong>in</strong>ed <strong>in</strong> masterkey rather<br />
than published <strong>in</strong> params.<br />
2) Extract. To generate a private key d ID for an<br />
identity ID ∈ {0, 1} ∗ , us<strong>in</strong>g the masterkey, the<br />
PKG picks random s 0 , s 1 ∈ Zp, ∗ choose a hash<br />
function ˜H : Zp ∗ × {0, 1} ∗ → Zp ∗ and computes<br />
u 0 = ˜H(s 0 , ID), u 1 = ˜H(s 1 , ID). It outputs:<br />
d ID = (d 0 , d 1 ) = (g2 α (g H2(ID)<br />
1 h) u0 , g u0 ,<br />
g2 α (g H2(ID)<br />
1 h) u1 ). The PKG preserves (s 0 , s 1 ).<br />
3) Encrypt. To encrypt a message M ∈ {0, 1} l for<br />
a recipient {0, 1} ∗ , the sender chooses a randomly<br />
δ ∈ G and computes s = H 2 (δ, M), k = v0, s C 1 =<br />
g s , C 2 = h s g H1(ID)s<br />
1 , C 3 = δ·k, C 4 = M ⊕H 3 (δ),<br />
C 5 = H 4 (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 ) s , and then<br />
outputs C = (C 1 , C 2 , C 3 , C 4 , C 5 ).<br />
4) ReKeyGen. The PKG computes u ′ 1 = ˜H(s 1 , ID ′ )<br />
and randomly selects k 1 , k 2 , k 3 ∈ Zp,<br />
∗<br />
sets rk ID→ID ′ = ( αH1(ID′ )+t 2+k 1<br />
k 3(αH 1(ID)+t 2)<br />
+<br />
k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ) and sends it to the<br />
proxy via secure channel. We must note that the<br />
PKG computes a different (k 1 , k 2 , k 3 ) for every<br />
different user pair (ID, ID ′ ).<br />
5) ReEnc. Given the identities (ID, ID ′ ),<br />
rk ID→ID ′ = (rk 1 , rk 2 , rk 3 , rk 4 ) =<br />
( αH1(ID′ )+t 2+k 1<br />
k 3(αH 1(ID)+t 2)<br />
+ k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ),<br />
C ID = (C 1 , C 2 , C 3 , C 4 , C 5 ) with params, the<br />
proxy re-encrypts the ciphertext C ID <strong>in</strong>to C ID ′ as<br />
follows.<br />
a) First it computes v 0 = e(C 5 , g) and v 1 =<br />
e(H 4 (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 ), C 1 ). If<br />
v 0 ≠ v 1 , the ciphertext is rejected.<br />
b) Else computes C ID ′ =<br />
(C ′ 1, C ′ 2, C ′ 3, C ′ 4, C ′ 5, C ′ 6, C ′ 7, C ′ 8) =<br />
(C 1 , C 2 , C 3 , C rk1<br />
2 , rk 2 , rk 3 , rk 4 , C 4 ).<br />
6) Decrypt.<br />
a) To decrypt a normal ciphertext C =<br />
(C 1 , C 2 , C 3 , C 4 , C 5 ) us<strong>in</strong>g the private key<br />
d ID = (d 0 , d 1 , d ′ 0), it computes v 0 = e(C 5 , g)<br />
and v 1 = e(H 4 (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖<br />
C 4 ), C 1 ). If v 0 ≠ v 1 , the ciphertext is rejected.<br />
The recipient computes k = e(C1,d0)<br />
e(C 2,d 1)<br />
. It then<br />
computes δ =<br />
C3<br />
k , M = H 4(δ) ⊕ C 4 . It<br />
computes s ′ = H 2 (δ, M) and verifies that<br />
C 1 = g s′ , C 2 = h s′ g H1(ID)s′<br />
1 , if either checks<br />
fails, returns ⊥, otherwise returns M.<br />
b) To decrypt a re-encrypted ciphertext C ID ′ =<br />
(C 1, ′ C 2, ′ C 3, ′ C 4, ′ C 5, ′ C 6, ′ C 7, ′ C 8) ′ us<strong>in</strong>g the<br />
private key d ID = (d 0 , d 1 , d ′ 0), the recipient<br />
computes k =<br />
C ′ 3 e(rk2,C′ 4 )<br />
e(C 2 ′ ,rk3)e(C′ 1 ,rk4)e(d′ 0 ,C′ C3<br />
1<br />
C ′ 3 e(C′ 5 ,C′ 4 )<br />
e(C ′ 2 ,C′ 6 )e(C′ 1 ,C′ 7 )e(d′ 0 ,C′ 1 ) =<br />
). It then computes<br />
δ =<br />
k , M = H 3(δ) ⊕ C 8. ′ It computes<br />
s ′ = H(δ, M) and verifies that C 1 = g s′ ,<br />
C 2 = h s′ g H1(ID)s′<br />
1 , if either check fails,<br />
returns ⊥, otherwise returns M.<br />
G. Security Analysis<br />
Theorem 4: Suppose the DBDH assumption holds,<br />
then our scheme proposed <strong>in</strong> Section III-F is DGA-<br />
IBE-IND-ID-CCA secure for the proxy and delegatee’s<br />
collud<strong>in</strong>g.<br />
Proof: Let A be a p.p.t. algorithm that has nonnegligible<br />
advantage <strong>in</strong> attack<strong>in</strong>g the scheme proposed <strong>in</strong><br />
Section III-F. We use A <strong>in</strong> order to construct a second algorithm<br />
B which has non-negligible advantage at solv<strong>in</strong>g<br />
the DBDH problem <strong>in</strong> G. Algorithm B accepts as <strong>in</strong>put<br />
a properly-distributed tuple (g, g a , g b , g c , R) and outputs<br />
1 if R = e(g, g) abc . We now describe the algorithm B,<br />
which <strong>in</strong>teracts with algorithm A as follow<strong>in</strong>g.<br />
B simulates the random oracles H 1 , H 2 , H 3 , H 4 as<br />
follows.<br />
1) H 1 : {0, 1} ∗ → Zq ∗ . On receipt of a new query for<br />
ID ≠ ID ∗ , return t ← R Zq<br />
∗ and record (ID, t);<br />
On receipt of a new query for ID ∗ , select randomly<br />
T ∈ Zq ∗ , return T and record (ID ∗ , T ).<br />
2) H 2 : G 1 × {0, 1} l :→ Zq ∗ . On a new query (δ, M),<br />
returns s ← R G and record (δ, M, s).<br />
3) H 3 : G 1 :→ {0, 1} l . On receipt of a new query δ,<br />
select p ← {0, 1} l and return p. Record the tuple<br />
(δ, p).<br />
4) H 4 : {0, 1} ∗ × G × G × G × {0, 1} l :→ G. On<br />
receipt of a new query (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 ),<br />
select z ∈ Zq ∗ and return g z ∈ G, record (ID ‖<br />
C 1 ‖ C 2 ‖ C 3 ‖ C 4 , z, g z ).<br />
Our simulation proceeds as follows:<br />
1) Setup. B generates the scheme’s master parameter<br />
as follow<strong>in</strong>g. First it lets g 1 = g a , g 2 =<br />
g b , g 3 = g c , algorithm B picks α ∈ Z p at<br />
random and def<strong>in</strong>es h = g −T<br />
1 g α′ ∈ G B lets<br />
params = (G 1 , H 1 , H 2 , H 3 , H 4 , g, g 1 , g 2 , g 3 , h)<br />
and gives params to A.<br />
2) F<strong>in</strong>d/Guess. Dur<strong>in</strong>g the F<strong>in</strong>d stage, there are<br />
no restrictions on which queries A may issue.<br />
The scheme permits only a s<strong>in</strong>gle consecutive reencryption,<br />
therefore, dur<strong>in</strong>g the GUESS stage, A<br />
is restricted from issu<strong>in</strong>g the follow<strong>in</strong>g queries:<br />
a) (extract, ID ∗ ) where ID ∗ is the challenge<br />
identity.<br />
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b) (decrypt, ID ∗ , c ∗ ) where c ∗ is the challenge<br />
ciphertext.<br />
c) Any pair of queries (rkextract, ID ∗ , ID i ),<br />
(decrypt, ID i , c i )<br />
where<br />
c i =Reencrypt(rk ID∗ →ID i<br />
, c ∗ ).<br />
In the Guess stage, let ID ∗ be the target i-<br />
dentity, and parse the challenge ciphertext c ∗ as<br />
(C1 ∗ , C2 ∗ , C3 ∗ , C4 ∗ , C5 ∗ ). In both phases, B responds<br />
to A’s queries as follows.<br />
• On (extract, ID), where(<strong>in</strong> the Guess)stage<br />
ID ≠ ID ∗ , B selects randomly<br />
r i ∈ Zp, ∗ sets sk IDi = (d 0 , d 1 ) =<br />
−α ′<br />
H<br />
(g 1 (ID i )−T<br />
1 g α′ ) ri , g2 g ri ).<br />
We claim sk IDi is a valid random private key<br />
b<br />
for ID i . To see this, let ˜r i = r i −<br />
H .<br />
1(ID i)−T<br />
Then we have that<br />
2 (g (H1(IDi)−T )<br />
d 0 = g<br />
−α ′<br />
H 1 (ID i )−T<br />
2 (g (H1(IDi)−T )<br />
g2(g a (H1(IDi)−T )<br />
1 g α′ ) ri− b<br />
H 1 (ID i )−T<br />
g2(g a H1(IDi)<br />
1 h) ˜ri .<br />
−1<br />
H(ID<br />
d 1 = g i )−T<br />
2 g ri = g ˜ri .<br />
−1<br />
d ′ H(ID<br />
0 = g i )−T<br />
2 g ri = g ˜ri .<br />
−1<br />
H 1 (ID i )−T<br />
1 g α′ ) ri =<br />
• On (rkextract, ID, ID ′ ), do the same as A<br />
handl<strong>in</strong>g re-encryption key query <strong>in</strong> Phase 13<br />
<strong>in</strong> the above theorem.<br />
• On (decrypt, ID, c) where (<strong>in</strong> the Guess stage)<br />
(ID, c) ≠ (ID ∗ , c ∗ ), check whether c is<br />
a level-1 (non re-encrypted) or level-2 (reencrypted)<br />
ciphertext. In the Guess stage, parse<br />
c ∗ as (C1 ∗ , C2 ∗ , C3 ∗ , C4 ∗ , C5 ∗ ).<br />
For a level-1 ciphertext, B parses c as<br />
(C 1 , C 2 , C 3 , C 4 , C 5 ) and:<br />
a) Looks up the value (ID ‖ C 1 ‖ C 2 ‖<br />
C 3 ‖ C 4 ) <strong>in</strong> the H 4 table, to obta<strong>in</strong> the<br />
tuple (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 , z, g z ). If<br />
(ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 ) is not <strong>in</strong> the<br />
table, or if (<strong>in</strong> the Guess stage) C 5 = C5 ∗ ,<br />
then B returns ⊥ to A.<br />
b) Looks up the value (δ, M, s) <strong>in</strong> the H 2<br />
table. Checks whether there exist an item<br />
of (δ, M, s) such that S = g zs . If not, B<br />
returns ⊥ to A.<br />
c) Computes k = e(C1,d0)<br />
e(C , checks that δ = C 2,d 1) k .<br />
If not, B returns ⊥ to A.<br />
d) Checks that C 4 = H 3 (δ) ⊕ M. If not, B<br />
returns ⊥ to A.<br />
e) Otherwise, B returns M to A.<br />
For a level-2 ciphertext, B parses c as<br />
(C 1, ′ C 2, ′ C 3, ′ C 4, ′ C 5, ′ C 6, ′ C 7, ′ C 8) ′ and:<br />
a) Computes<br />
k =<br />
=<br />
C ′ 3e(C ′ 5, C ′ 4)<br />
e(C ′ 2 , C′ 6 )e(C′ 1 , C′ 7 )e(d′ 0 , C′ 1 )<br />
C ′ 3e(rk 2 , C ′ 4)<br />
e(C ′ 2 , rk 3)e(C ′ 1 , rk 4)e(d ′ 0 , C′ 1 )<br />
=<br />
b) Checks that δ = C k<br />
. If not, B returns ⊥ to<br />
A.<br />
c) Checks that C 2 = h s g H1(ID)s<br />
1 . If so, return<br />
M. Otherwise, return ⊥.<br />
• On (reencrypt, C ID , ID, ID ′ ). B runs<br />
ReEnc(rk ID→ID ′, C ID , ID, ID ′ ) and returns<br />
the results.<br />
At the end of the F<strong>in</strong>d phase, A outputs<br />
(ID ∗ , M 0 , M 1 ), with the condition that A has not<br />
previously issued (extract, ID ∗ ). At the end of the<br />
Guess stage, A outputs its guess bit i ′ .<br />
3) Choice and Challenge. At the end of the F<strong>in</strong>d<br />
phase, A outputs (ID ∗ , M 0 , M 1 ). B forms the<br />
challenge ciphertext as follows:<br />
a) Choose δ ∈ G 1 and p ∈ {0, 1} n randomly,<br />
and <strong>in</strong>sert (δ, p) <strong>in</strong> H 3 table.<br />
b) Insert (δ, M b , , g 3 , δ · R, M b ⊕ p) to H 2 table.<br />
c) Choose z ∈ Z p randomly, and <strong>in</strong>sert<br />
((g 3 , g3 α′ , δ ·R, M b ⊕p), z, g z ) <strong>in</strong> the H 4 table.<br />
B outputs the challenge ciphertext<br />
(C1 ∗ , C2 ∗ , C3 ∗ , C4 ∗ , C5 ∗ ) = (g 3 , g3 α′ , δ · R, M b ⊕ p, g3)<br />
z<br />
to A and beg<strong>in</strong>s the GUESS stage.<br />
4) Forgeries and Abort conditions The adversary<br />
may forge C 5 on (C 1 , C 2 , C 3 , C 4 ), but from the<br />
security of BLS short signature [7], this probability<br />
is negligible.<br />
Theorem 5: Suppose the DBDH assumption holds,<br />
then our scheme proposed <strong>in</strong> Section III-F is DGE-<br />
IBE-IND-ID-CCA secure for the delegator and proxy’s<br />
collud<strong>in</strong>g.<br />
Proof: The security proof is same as the above<br />
theorem except that it does not allow “A issues up to<br />
rekey generation queries on (ID, ID ∗ )”, for B does not<br />
know the private key correspond<strong>in</strong>g to ID ∗ .<br />
Theorem 6: Suppose the DBDH assumption holds,<br />
then our scheme proposed <strong>in</strong> Section III-F is PKG-OW<br />
secure for the delegator, proxy and delegatee’s collud<strong>in</strong>g.<br />
Proof: The security proof is same as the proof for<br />
Theorem 3.<br />
IV. COMPARISON<br />
In this section, we give our comparison results with<br />
other identity based proxy re-encryption schemes[15],<br />
[11], [27], [29]. We compare our schemes with other<br />
schemes from two ways. First we concern about schemes’<br />
security, then we concern about schemes’ efficiency.<br />
Notations: In Table I, we denote with/without random<br />
oracle as W/O RO, assumption as Assum, security model<br />
as SecMod, collud<strong>in</strong>g attackers as Collud<strong>in</strong>g, underly<strong>in</strong>g<br />
IBE as UnderIBE, stand model as Std, , proxy as P,<br />
DGA as delegator, DGE as delegatee. P and DGA means<br />
that proxy colludes with delegator, P or DGA means that<br />
proxy or delegator is malicious adversary but they never<br />
collude. SymEnc-Sec means the security of symmetric<br />
encryption.<br />
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TABLE I.<br />
IBPRE SECURITY COMPARISON<br />
Scheme Security W/O RO Assum SecMod Collud<strong>in</strong>g UnderlyIBE Remark<br />
GA07A[15] IND-Pr-ID-CPA RO DBDH Sec.3.1[15] P and DGA BF IBE Weak<br />
or P and DGE<br />
GA07B[15] IND-Pr-ID-CCA RO DBDH Sec.3.1[15] P and DGA BF IBE Strong<br />
or P and DGE<br />
M07B [27] IND-Pr-sID-CPA Std DBDH Sec.4.2[27] P or DGA BB 1 IBE Weak<br />
or DGE<br />
CT07[11] IND-Pr-ID-CPA Std DBDH Sec.4.2[11] P and DGA Waters’ IBE Weak<br />
or P and DGE<br />
SXC08[29] IND-Pr-ID-CCA Std DBDH Sec.2.6[29] P and DGA Waters’ IBE Strong<br />
or P and DGE<br />
OursCIII-C IND-Pr-sID-CPA Std DBDH III-B P and DGA Variant of Weak<br />
or P and DGE BB 1 IBE<br />
OursDIII-F IND-Pr-ID-CCA RO DBDH III-B P and DGA Variant of Strong<br />
or P and DGE BB 1 IBE<br />
TABLE II.<br />
IBPRE EFFICIENCY COMPARISON<br />
Scheme Enc Check Reenc Dec Ciph-Len<br />
1stCiph 2-ndCiph 1stCiph 2-ndCiph<br />
GA07A[15] 1t e + 1t p 0 1t p 2t p 1t p 2|G| + 2|G e| 1|G| + 1|G e|<br />
GA07B[15] 1t p + 1t e 2t p 2t e + 2t p 1t e + 2t p 2t e + 2t p 1|G| + 1|G e| 1|G| + 1|G T |<br />
+2|m| + |id| +1|G e| + |m|<br />
M07B [27] 1t p + 2t e 2t p 1t p 2t p 2t p 2|G e| + 1|G T | 2|G e| + 1|G T |<br />
CT07[11] 3t e + 1t p + 1t s 1t v 2t e 2t e + 10t p + 1t v 2t e + 3t p 9|G| + 2|G T | 3|G| + |G T |<br />
+|vk| + |s| +|vk| + |s|<br />
SXC08[29] 3t e + 1t p + 1t s 1t v 2t e + 1t s 2t e + 10t p + 2t v 2t e + 3t p + 1t v 9|G| + 2|G T | 3|G| + |G T |<br />
+2|vk| + 2|s| +1|vk| + 1|s|<br />
OursCIII-C 2t e + 1t p 2t p 1t e 4t p 2t p 6|G| + |G T | 2|G| + |G T |<br />
OursDIII-F 3t e + 1t me 2t p 1t e 4t p + 1t e + 1t me 2t p + 1t e + 1t me 7|G| + m 4|G| + m<br />
From Table I, we can know that our IBPRE scheme<br />
based on a variant of BB 1 IBE scheme is the most<br />
secure IBPRE. M07B scheme is the weakest IBPRE for<br />
it can only achieve IND-Pr-sID-CPA under separated<br />
proxy or delegator or delegatee attack.<br />
In Table II, we denote encryption as Enc, reencryption<br />
as Reenc, decryption as Dec, ciphertext as<br />
Ciph and ciphertext length as Ciph-Len. t p , t e and t me<br />
represent the computational cost of a bil<strong>in</strong>ear pair<strong>in</strong>g, an<br />
exponentiation and a multi-exponentiation respectively,<br />
while t s and t v represent the computational cost of a<br />
one-time signature sign<strong>in</strong>g and verification respectively.<br />
|G|, |Z q |, |G e | and |G T | denote the bit -length of an<br />
element <strong>in</strong> groups G, Z q , G e and G T respectively.<br />
Here G and Z q denote the groups used <strong>in</strong> our scheme,<br />
while G e and G T are the bil<strong>in</strong>ear groups used <strong>in</strong> GA07,<br />
CT07, SXC08 schemes, i.e., the bil<strong>in</strong>ear pair<strong>in</strong>g is<br />
e : G e × G e → G T . F<strong>in</strong>ally, |vk| and |s| denote the<br />
bit length of the one-time signature’s public key and a<br />
one-time signature respectively.<br />
From Table II, Our schemes 3 , GA07 4 and M07B<br />
schemes are much more efficient than CT07 and SXC08<br />
scheme due to their underly<strong>in</strong>g IBE is Waters’ IBE.<br />
And for the proxy, CT07 and SXC08 scheme are much<br />
3 Our first level ciphertext maps second level ciphertext and second<br />
level ciphertext maps first level ciphertext <strong>in</strong> [15], [11], [29]. Sometimes<br />
<strong>in</strong> our schemes we use e : G × G → G 1 or e : G 1 × G 1 → G T , <strong>in</strong><br />
the former cases, G maps to G e, G 1 maps G T , <strong>in</strong> the latter case, G 1<br />
maps to G e, G T maps G T .<br />
4 GA07 and SXC08 are multi-hop IBPRE but we just consider their<br />
s<strong>in</strong>gle-hop variant.<br />
more efficient than others for their special paradigm, our<br />
IBPRE scheme is more efficient than GA07B scheme<br />
and our other schemes, we th<strong>in</strong>k this is important for<br />
resist<strong>in</strong>g DDos attack aga<strong>in</strong>st the proxy.<br />
V. CONCLUSIONS AND OPEN PROBLEMS<br />
In 2007, Matsuo proposed the concept of four types<br />
of PRE schemes: CBE to CBE, IBE to CBE, CBE to<br />
IBE and IBE to IBE [27]. In Matsuo’s scheme, they<br />
allow the PKG to help the delegator and the delegatee<br />
to generate re-encryption key. We explore this feature<br />
further, if we allow PKG to generate re-encryption keys<br />
by directly us<strong>in</strong>g master − key, many open problems can<br />
be solved. Consider<strong>in</strong>g the standardization of BB 1 IBE<br />
and its broad applications, we give new identity based<br />
proxy re-encryption schemes based on BB 1 IBE, and<br />
prove its security <strong>in</strong> our new stronger security models.<br />
Furthermore, our schemes are very efficient for the reencryption<br />
process, which is the most heavy-load part of<br />
PRE.<br />
ACKNOWLEDGEMENT<br />
The authors would like to thank Dr. Jian Weng, Dr. Jun<br />
Shao, Dr. Licheng Wang, Dr. Fagen Li, Dr. Qiang Tang<br />
for many helpful discussions and the anonymous referees<br />
for helpful comments.<br />
© 2013 ACADEMY PUBLISHER
1626 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
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[30] Q. Tang, P. Hartel and W Jonker. Inter-doma<strong>in</strong> identitybased<br />
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[31] Q. Tang. Type-based proxy re-encryption and its construction.<br />
In INDOCRYPT 2008, volume 5365 of LNCS, pages<br />
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[32] Q. Wu, W. Wang. New identity-based broadcast encryption<br />
with constant ciphertexts <strong>in</strong> the standard model. In Journal<br />
of Software, 1929-1936 Volume 6, Number 10, 2011.<br />
[33] X. A. Wang, X. Y. Yang, J. R. Hu. CCA-Secure Identity<br />
Based Proxy Re-encryption Based on a Variant of BB1<br />
IBE. The 2010 Second International Conference on<br />
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Comput<strong>in</strong>g (NSWCTC 2010), IEEE Press, (Vol.2) 509-<br />
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[34] Y. D<strong>in</strong>g, X. A. Wang. Identity Based Proxy Re-encryption<br />
Based on a Variant of BB1 Identity Based Encryption. The<br />
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(NSWCTC 2010), IEEE Press, (Vol.2) 509-513, 2010.<br />
[35] L. D. Zhou, M. A. Marsh, F. B. Schneider, and A. Redz.<br />
Distributed bl<strong>in</strong>d<strong>in</strong>g for ElGamal re-encryption. TR 1924,<br />
Cornell CS Dept., 2004.<br />
J<strong>in</strong>dan Zhang was born <strong>in</strong> April. 27th, 1983. She<br />
obta<strong>in</strong>ed her master degree from University of Shaanxi<br />
Science and Technology. Now she is a lecturer <strong>in</strong> Xianyang<br />
Vocational Technical College. Her ma<strong>in</strong> research<br />
<strong>in</strong>terests <strong>in</strong>cludes cryptography, and <strong>in</strong>formation hid<strong>in</strong>g.<br />
Xu An Wang was born <strong>in</strong> Feb. 23th, 1981. He obta<strong>in</strong>ed<br />
his master degree from University of Ch<strong>in</strong>ese Armed<br />
Police Force. Now he is an associate professor <strong>in</strong> the same<br />
University. His ma<strong>in</strong> research <strong>in</strong>terests <strong>in</strong>cludes public key<br />
cryptography and <strong>in</strong>formation security.<br />
Xiaoyuan Yang was born <strong>in</strong> Nov. 12th, 1959. He<br />
obta<strong>in</strong>ed his master and bachelor degree from Xidian<br />
University. Now he is a professor <strong>in</strong> the Eng<strong>in</strong>eer<strong>in</strong>g<br />
University of Ch<strong>in</strong>ese Armed Police Force.<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1627<br />
Corn Moisture Measurement us<strong>in</strong>g a<br />
Capacitive Sensor<br />
Hongxia Zhang, Wei Liu*, Boxue Tan, Wenl<strong>in</strong>g Lu<br />
School of Electrical and Electronic Eng<strong>in</strong>eer<strong>in</strong>g, Shandong University of Technology, Zibo, Ch<strong>in</strong>a, 255049<br />
Abstract—Corn<br />
moisture content is the ma<strong>in</strong> factor of<br />
effect<strong>in</strong>g corn safe transportation and storage, and is also an<br />
<strong>in</strong>dispensable measurement part when it is<br />
used to feed,<br />
food and <strong>in</strong>dustry. Due to large particle size, corn will<br />
produce large gap dur<strong>in</strong>g measur<strong>in</strong>g moisture content.<br />
Because air has much <strong>in</strong>fluence on dielectric constant of the<br />
device, moisture content is not precision. In all k<strong>in</strong>ds of corn<br />
moisture<br />
measurement<br />
methods,<br />
capacitance<br />
method<br />
becomes the ma<strong>in</strong> method with simple structure, low cost<br />
and onl<strong>in</strong>e measurement.<br />
This paper designs a sensor for<br />
measur<strong>in</strong>g the<br />
corn moisture<br />
that uses a capacitance<br />
detection circuit based on the relationship between the<br />
capacitance and the dielectric constant of the corn. In<br />
addition, different operat<strong>in</strong>g modes of the detection circuit<br />
are analyzed. The relationship between the moisture content<br />
of corn and the sensor capacitance is obta<strong>in</strong>ed through<br />
experiment and a b<strong>in</strong>ary cubic equation is obta<strong>in</strong>ed by the<br />
least squares fitt<strong>in</strong>g method.<br />
Index Terms—corn<br />
moisture<br />
sensor, detection circuit<br />
measurement,<br />
capacitive<br />
I. INTRODUCTION<br />
The moisture component of a corn cell is essential for<br />
ma<strong>in</strong>ta<strong>in</strong><strong>in</strong>g its life activities. Furthermore, the moisture<br />
content must not be too high or too low. Higher moisture<br />
contents will cause corn mildew and other biochemical<br />
reactions. Lower moisture contents may destroy organic<br />
material and damage the dry matter. Hence, the<br />
measurement of moisture levels is important for the safe<br />
storage of corn [1,2] .<br />
The traditional method for measur<strong>in</strong>g moisture content<br />
uses an oven which leads to high accuracy but because it<br />
is time-consum<strong>in</strong>g and <strong>in</strong>volves a complicated procedure,<br />
it is not suitable for field use. Various techniques for<br />
<strong>in</strong>direct test<strong>in</strong>g methods have been studied for replac<strong>in</strong>g<br />
the traditional oven method at home and abroad, e.g. the<br />
use of conductance, capacitance, X-rays, neutrons, and<br />
microwaves. These methods allow quick measurements<br />
and are easily applied under field conditions [3] . The most<br />
common method is the capacitive method which has<br />
advantages of low cost, small volume and fast detection,<br />
although it lacks high precision.<br />
S<strong>in</strong>ce the 1960s, many countries’ researchers attached<br />
great importance to the development of gra<strong>in</strong> moisture<br />
measurement technology. Along with the measurement<br />
methods of gra<strong>in</strong> moisture emerged, advanced gra<strong>in</strong><br />
moisture measurement methods and the <strong>in</strong>struments are<br />
be<strong>in</strong>g promotion at home and abroad. TABLE I and TABLE<br />
II show the company produced the measur<strong>in</strong>g corn gra<strong>in</strong><br />
moisture <strong>in</strong>struments.<br />
TABLE I<br />
MOISTURE METER PRODUCED BY FOREIGN COMPANY<br />
Capacitance<br />
method<br />
Conductance<br />
method<br />
Decompression<br />
Infrared method<br />
Microwave method<br />
Carlfee Hugh<br />
method<br />
Capacitance<br />
method<br />
Conductance<br />
method<br />
F<strong>in</strong>land Humicoy company produced the<br />
WILE100 moisture meter [4]<br />
Japan KETT <strong>in</strong>stitute developed high frequency<br />
capacitive moisture meter<br />
European control company produced the CM - 4<br />
type moisture meter<br />
A Japanese enterprise produced VME type<br />
moisture meter<br />
British <strong>in</strong>frared eng<strong>in</strong>eer<strong>in</strong>g company produced<br />
the SM4 <strong>in</strong>frared moisture meter<br />
Japan QianYe <strong>in</strong>stitute produced the IR-AM300<br />
<strong>in</strong>frared moisture meter<br />
A Japan company produced the FD - 230, FD -<br />
310 and FD - 600 <strong>in</strong>frared moisture meter<br />
The battery motor manufactur<strong>in</strong>g produced<br />
onl<strong>in</strong>e microwave moisture meter<br />
A Germany company produced cont<strong>in</strong>uous<br />
moisture meter<br />
Japan Kyoto electronic company produced the<br />
MKA - 3 type moisture meter<br />
TABLE II<br />
MOISTURE METER PRODUCED BY DOMESTIC COMPANY<br />
Infrared method<br />
East food <strong>in</strong>spection produced the SC – 5F corn<br />
moisture meter<br />
J<strong>in</strong>an detect<strong>in</strong>g <strong>in</strong>strument company produced ly -<br />
8 capacitive moisture meter and LDS – 1G gra<strong>in</strong><br />
moisture meter<br />
Shanghai Q<strong>in</strong>gpu test<strong>in</strong>g <strong>in</strong>strument company<br />
produced LDS-IF , LDS-2,LDS – IA and LDS -<br />
ID<br />
Tianj<strong>in</strong> science and technology company produced<br />
SFY-60 corn rapid moisture meter<br />
Beij<strong>in</strong>g technology company produced high<br />
frequency capacitive gra<strong>in</strong> moisture meter<br />
81W1PM-8188 and gra<strong>in</strong> moisture meter BHC1 -<br />
PM818<br />
Beij<strong>in</strong>g huatai <strong>in</strong>strument technology company<br />
produced JCY13 / SFY -60d moisture meter<br />
Wuhan electronic <strong>in</strong>strument produced LSKC - 4<br />
type gra<strong>in</strong> moisture meter<br />
Hunan <strong>in</strong>strument factory balance <strong>in</strong>strument<br />
factory produced <strong>in</strong>serted l<strong>in</strong>k type moisture meter<br />
Hunan <strong>in</strong>strument factory balance <strong>in</strong>strument<br />
factory developed SCT - 3 moisture meter<br />
Xi’an light m<strong>in</strong>istry of light <strong>in</strong>dustry developed 3<br />
YBSIA four beam <strong>in</strong>frared moisture meter<br />
Guangdong test analysis and wuhan comb<strong>in</strong>e<br />
automation <strong>in</strong>strument developed WSHT - 102<br />
type <strong>in</strong>frared moisture meter<br />
Ts<strong>in</strong>ghua university developed near <strong>in</strong>frared<br />
moisture measurement <strong>in</strong>strument has completed<br />
the pr<strong>in</strong>ciple prototype<br />
*Correspond<strong>in</strong>g Author: weikey@sdut.edu.cn<br />
© 2013 ACADEMY PUBLISHER<br />
doi:10.4304/jcp.8.6.1627-1631
1628 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
Microwave<br />
method<br />
Neutron method<br />
Jil<strong>in</strong> prov<strong>in</strong>ce developed WSY - 100 microwave<br />
corn moisture meter<br />
Nanj<strong>in</strong>g university developed SHD - 1 type of<br />
neutron moisture gauge<br />
II. THEORY<br />
The absolute permittivity divided by the permittivity of<br />
free space is small for samples because of the air gaps<br />
between particles <strong>in</strong> the conta<strong>in</strong>er. Therefore, we adopt a<br />
coaxial cyl<strong>in</strong>der arrangement <strong>in</strong> the design of the<br />
capacitive sensor to ensure the plates’ effective area is<br />
large enough. The electrodes of the sensor are<br />
asymmetrical <strong>in</strong> that the <strong>in</strong>ner electrode is enveloped by<br />
the external one. This geometry is very effective <strong>in</strong><br />
prevent<strong>in</strong>g human body <strong>in</strong>duction. The design of the<br />
capacitive sensor is shown <strong>in</strong> Figure 1.<br />
The corn sample is placed <strong>in</strong> the media cavity between<br />
the two plate sensors. Changes <strong>in</strong> relative permittivity<br />
correspond<strong>in</strong>g to different corn moisture contents cause<br />
variations <strong>in</strong> capacitance allow<strong>in</strong>g the moisture content to<br />
be estimated.<br />
L<br />
R 1<br />
R 2<br />
external electrode<br />
media cavity<br />
<strong>in</strong>ner electrode<br />
Figure 1. capacitive sensor schematic<br />
The cyl<strong>in</strong>der height is L ; the external surface radius of<br />
<strong>in</strong>ner cyl<strong>in</strong>der is R<br />
1<br />
; the <strong>in</strong>ner surface radius of external<br />
cyl<strong>in</strong>der is R<br />
2<br />
. If L >> R2 − R1<br />
, the edge effect of<br />
cyl<strong>in</strong>drical ends can be ignored.<br />
The capacitance of the sensor can be calculated from<br />
the formula [5] :<br />
C<br />
2πε<br />
L<br />
ln R R<br />
= (1)<br />
2 1<br />
Permittivity is understood to represent the relative<br />
complex permittivity. The permittivity relative to free<br />
space, or the absolute permittivity divided by the<br />
permittivity of free space [6] .<br />
ε<br />
r<br />
ε<br />
ε<br />
= (2)<br />
0<br />
After the sample is placed <strong>in</strong>to the sensor the<br />
capacitance [7] is:<br />
C<br />
2πε ε L<br />
r 0<br />
= (3)<br />
R2<br />
It can be seen from the above formula that the changes<br />
of capacitance and relative dielectric constant of corn are<br />
l<strong>in</strong>early related. S<strong>in</strong>ce relative dielectric constant will<br />
change with corn moisture content, the latter can be<br />
obta<strong>in</strong>ed from the measured capacitance.<br />
When the corn relative dielectric constant changes<br />
capacitance changes<br />
∆<br />
ε r<br />
Sensitivity for constant<br />
So<br />
∆C<br />
and ∆ε<br />
r<br />
ln<br />
R<br />
( ε<br />
r<br />
+ ∆ε<br />
r ) L<br />
−10<br />
∆ C = × 10<br />
R2<br />
1.8ln<br />
R<br />
ε<br />
rL<br />
− × 10<br />
R2<br />
1.8ln<br />
R<br />
1<br />
1<br />
1<br />
1<br />
−10<br />
∆ε<br />
rL<br />
× 10<br />
R2<br />
1.8ln<br />
∆C<br />
R1<br />
K = =<br />
∆ε<br />
∆ε<br />
r<br />
L<br />
= × 10<br />
R2<br />
1.8ln<br />
R<br />
r<br />
−10<br />
−10<br />
(4)<br />
(5)<br />
is l<strong>in</strong>ear relationship. For moisture<br />
content corn M , when the corn moisture content<br />
changes ∆ M , relative dielectric constant changes ∆ ε<br />
r<br />
,<br />
causes the capacitance change is ∆ C ,therefore<br />
is l<strong>in</strong>ear relationship.<br />
∆C<br />
also ∆M<br />
III. MEASUREMENT CIRCUIT<br />
Hardware structure diagram of corn moisture<br />
measurement system is shown <strong>in</strong> figure 2. The ma<strong>in</strong> parts<br />
are the ma<strong>in</strong> control circuit, capacitance detection circuit,<br />
temperature detection circuit and RS232 communication<br />
circuit.<br />
Capacitive sensor<br />
Temperature<br />
detection circuit<br />
Capacitance<br />
detection circuit<br />
M S P 4 3 0 F1<br />
3 5<br />
scre e n<br />
R S 232<br />
Communication<br />
circuit<br />
Figure2 Measur<strong>in</strong>g system structure diagram<br />
Epistatic mach<strong>in</strong>e<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1629<br />
The work<strong>in</strong>g pr<strong>in</strong>ciple of moisture measurement<br />
system is: capacitance detection circuit and temperature<br />
detection circuit will set detected signal to the s<strong>in</strong>gle-chip<br />
microcomputer. The s<strong>in</strong>gle-chip microcomputer will<br />
received signal process<strong>in</strong>g as shown on the screen.<br />
The capacitance and changes of capacitance are very<br />
small <strong>in</strong> the capacitive sensor. Hence, detection circuits<br />
are needed to measure the t<strong>in</strong>y capacitance <strong>in</strong>crements.<br />
Usually we translate the t<strong>in</strong>y capacitance <strong>in</strong>crements <strong>in</strong>to<br />
a s<strong>in</strong>gle value function of voltage, current or frequency.<br />
There are many transformed capacitance circuits, such as<br />
capacitance charg<strong>in</strong>g and discharg<strong>in</strong>g circuit, FM circuit,<br />
operational amplifiers circuit, common communication<br />
bridge method, diode double T ac electric bridge, pulse<br />
width modulation circuit and so on.<br />
In the present work we use charg<strong>in</strong>g and discharg<strong>in</strong>g of<br />
capacitance sensor and transform<strong>in</strong>g capacitance <strong>in</strong>to<br />
voltage. The capacitance of the sensor can be obta<strong>in</strong>ed<br />
accord<strong>in</strong>g to the voltage<br />
The process of capacitance charge is<br />
VC<br />
= V ⎛<br />
i ⎜1−<br />
e −<br />
⎝<br />
t<br />
RC<br />
Where t denotes charg<strong>in</strong>g time, and RC denotes the<br />
time constant. The process of capacitance discharged:<br />
When C was charged until t<br />
1<br />
, C beg<strong>in</strong> to discharg<strong>in</strong>g.<br />
The process of capacitance discharge is<br />
C<br />
⎞<br />
⎟<br />
⎠<br />
(6)<br />
( = )<br />
C t t<br />
1<br />
t<br />
RC<br />
V ′ = V e −<br />
(7)<br />
The measurement circuit uses the theory of capacitor<br />
charg<strong>in</strong>g and discharg<strong>in</strong>g which make the output signal<br />
change with the capacitance of the sensor. We can get the<br />
DC voltage signal correspond<strong>in</strong>g to the changed sensor<br />
capacitor through difference amplifier, the same phase<br />
ratio amplifier and low-pass filter. Capacitive sensor<br />
detection circuit, equivalent detection circuit of the<br />
capacitance charg<strong>in</strong>g and equivalent detection circuit of<br />
the capacitance discharg<strong>in</strong>g can be seen from Figure 3 to<br />
Figure 5.<br />
C<br />
C<br />
Multiple<br />
s w itc h<br />
Periodic<br />
switch<br />
signals<br />
V C C<br />
R<br />
R<br />
Balance<br />
circuit<br />
Balance<br />
circuit<br />
R1<br />
R 1<br />
R 1<br />
-<br />
+<br />
R1<br />
A<br />
Figure 3. Capacitive sensor detection circuit<br />
R1<br />
R 1<br />
R 1<br />
-<br />
+<br />
R1<br />
A<br />
R1<br />
R1<br />
R1<br />
R1<br />
-<br />
+<br />
-<br />
+<br />
R1<br />
A<br />
R1<br />
A<br />
L o w -pass filter<br />
L o w -pass filter<br />
Output<br />
signal<br />
Output<br />
signal<br />
Figure 4. Equivalent detection circuit of the capacitance charg<strong>in</strong>g<br />
R<br />
C<br />
Balance<br />
circuit<br />
R1<br />
R 1<br />
R 1<br />
-<br />
+<br />
R1<br />
A<br />
R1<br />
R1<br />
-<br />
+<br />
R1<br />
A<br />
L o w -pass filter<br />
Output<br />
signal<br />
Figure 5. Equivalent detection circuit of the capacitance discharg<strong>in</strong>g<br />
VI. EXPERIMENT AND DATA ANALYSIS<br />
Configuration pr<strong>in</strong>ciple is important. If the default<br />
moisture content is lower than the orig<strong>in</strong>al sample corn<br />
moisture content , we can dry corn gradually through the<br />
oven to reduce the corn moisture content. If the default<br />
moisture is higher than the orig<strong>in</strong>al sample moisture, we<br />
can add water to improve corn gra<strong>in</strong> moisture content.<br />
Calculation formula for about add<strong>in</strong>g water weight [8]<br />
M = M<br />
1<br />
H2 − H1<br />
1−<br />
H<br />
Among formula, the M is added water weight. M1 is<br />
corn orig<strong>in</strong>al sample weight. H1 is orig<strong>in</strong>al sample<br />
moisture content. H2 is the default moisture content.<br />
Dur<strong>in</strong>g the process of corn sample preparation, if the<br />
default moisture value m<strong>in</strong>us corn orig<strong>in</strong>al sample<br />
moisture value is less than 10% [9] , the water can be onetime<br />
jo<strong>in</strong>ed. TABLE III shows operation method of<br />
shak<strong>in</strong>g jar of time and preparation. If greater than 10%,<br />
add water twice.Time about shak<strong>in</strong>g jar and operation<br />
method such as shown <strong>in</strong> TABLE IV<br />
The first<br />
n day<br />
n=1<br />
TABLE III<br />
SHAKING TIME IF LESS Than 10%<br />
Wett<strong>in</strong>g time(t/hour)<br />
one-time jo<strong>in</strong>ed water 60<br />
t=1 15<br />
t=2 15<br />
t=3 15<br />
t=3~24 15<br />
n=2 15<br />
n=3 15<br />
n=4 15<br />
The first<br />
n day<br />
n=1<br />
n=2<br />
2<br />
Shak<strong>in</strong>g time(s)<br />
TABLE IV<br />
SHAKING TIME IF GREATER THAN 10%<br />
Wett<strong>in</strong>g time(t/hour)<br />
Half of total 60<br />
t=1 15<br />
t=2 15<br />
t=3 15<br />
t=3~24 15<br />
Another half of total 60<br />
t=1 15<br />
t=2 15<br />
t=3 15<br />
t=3~24 15<br />
Shak<strong>in</strong>g time(s)<br />
(8)<br />
© 2013 ACADEMY PUBLISHER
1630 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013<br />
n=3 15<br />
n=4 15<br />
n=5 15<br />
x ′ − x ′<br />
′ 2 1<br />
10<br />
=<br />
xn<br />
′ − x1<br />
′<br />
r<br />
(10)<br />
Twelve corn samples were placed <strong>in</strong> jars of 1L.<br />
Accord<strong>in</strong>g to the above two k<strong>in</strong>ds of operation methods<br />
prepared conta<strong>in</strong><strong>in</strong>g different moisture values of the corn<br />
samples. The sealed jars were stored <strong>in</strong> the laboratory of<br />
shady place. If the sample went bad, we must allocate the<br />
same corn samples to do the experiment.<br />
Place corn samples <strong>in</strong> the lab (laboratory temperature<br />
can be adjusted) and choose a temperature (through the<br />
temperature measurement circuit ). Us<strong>in</strong>g dry method<br />
measure a group of corn sample moisture content value,<br />
at the same time us<strong>in</strong>g the capacitive corn moisture<br />
measurement system collect capacitance value and<br />
voltage value related temperature. The data collection<br />
procedure as follows:<br />
1) Use dry method measure moisture content of a<br />
group of corn sample and record moisture value.<br />
2) At the same time a sample group will be placed <strong>in</strong><br />
the cyl<strong>in</strong>der of capacitive sensor. Press the reset<br />
button and start measur<strong>in</strong>g. After a period of time,<br />
the results of voltage value about sensor capacitance<br />
and temperature will be recorded.<br />
3) Weigh the sample and then put <strong>in</strong>to measurement,<br />
repeat steps 2 and record the results.<br />
4) Each group samples need to repeat measurement 5<br />
times.<br />
5) Another group of corn samples, repeat steps (1) - (4).<br />
Then configurate the same twelve groups of corn<br />
samples <strong>in</strong> lab (temperature changed) and repeat the<br />
above steps. Due to the limitation of the laboratory<br />
conditions, choose the five different temperatures. The<br />
measured data are saw <strong>in</strong> the appendix.<br />
In the process of data collection, the measurement of<br />
the personnel subjective reason, or the external condition<br />
of the objective causes, the results of each measurement<br />
can have <strong>in</strong>dividual measurement results and the real<br />
value a lot of deviation. For each group of corn samples<br />
more measured value, need to use some methods to<br />
remove or modify the deviation of measured value, the<br />
experiment us<strong>in</strong>g statistics discrim<strong>in</strong>ant method of Dixon<br />
(Dixon) criterion [10] get rid of deviation of measured<br />
value.<br />
Assum<strong>in</strong>g there are normal measur<strong>in</strong>g population<br />
x, x … x , arrangement for<br />
distribution of a sample 1 2<br />
, ,<br />
n<br />
the sample x ′ , , 1<br />
x ′<br />
2<br />
… x ′<br />
n<br />
, by from big to small,<br />
accord<strong>in</strong>g to the value of n can structure as shown below<br />
statistics,<br />
If n=3~7,<br />
x ′<br />
n<br />
− x ′<br />
n−1<br />
r10<br />
=<br />
x ′ − x ′<br />
n<br />
1<br />
(9)<br />
If n=8~10,<br />
If n=11~13,<br />
If n=14~30,<br />
If rij r ′<br />
ij<br />
x ′<br />
n<br />
− x ′<br />
n−1<br />
r11<br />
=<br />
x ′ − x ′<br />
r ′ =<br />
11<br />
n<br />
2<br />
x ′<br />
2<br />
− x ′<br />
1<br />
x ′ − x ′<br />
n−1 1<br />
x ′<br />
n<br />
− x ′<br />
n−2<br />
r21<br />
=<br />
x ′ − x ′<br />
r ′ =<br />
r<br />
21<br />
22<br />
n<br />
2<br />
x ′<br />
3<br />
− x ′<br />
1<br />
x ′ − x ′<br />
n−1 1<br />
x ′<br />
n<br />
− x ′<br />
n−2<br />
=<br />
x ′ − x ′<br />
n<br />
x ′<br />
3<br />
x ′<br />
1<br />
r ′<br />
−<br />
22<br />
=<br />
x ′ − x ′<br />
3<br />
n−2 1<br />
> and r D ( a,<br />
n)<br />
x ′<br />
n can be judged as abnormal value.<br />
r r ′<br />
If<br />
ij ij<br />
ij<br />
< and r D ( a,<br />
n)<br />
ij<br />
(11)<br />
(12)<br />
(13)<br />
(14)<br />
(15)<br />
(16)<br />
> (Dixon coefficient),<br />
′ > , x ′<br />
1<br />
can be judged as<br />
abnormal value. Otherwise, there is no abnormal value<br />
judgment.<br />
Experimental data obta<strong>in</strong>ed is discrete data, each set<br />
of data can not always avoid measurement error, need to<br />
use data fitt<strong>in</strong>g method to get data reflect the change<br />
trend of the whole of the approximate function. This<br />
paper collected the corn sample data based on the<br />
pr<strong>in</strong>ciple of least square fitt<strong>in</strong>g method, i.e., look<strong>in</strong>g for a<br />
fitt<strong>in</strong>g curve y = s (x) to approximate show discrete data<br />
that coord<strong>in</strong>ate relationship of function.<br />
All the experiments were carried out at room<br />
temperature and take no account of effects of<br />
temperature changes. Us<strong>in</strong>g the detection circuit to<br />
measure the capacitance of samples and the dry<strong>in</strong>g<br />
method to measure moisture content, we obta<strong>in</strong>ed the<br />
© 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1631<br />
curve of moisture content versus capacitance as shown <strong>in</strong><br />
Figure 6 .<br />
Us<strong>in</strong>g the least squares method we obta<strong>in</strong>ed the b<strong>in</strong>ary<br />
cubic equation l<strong>in</strong>k<strong>in</strong>g the capacitance x(nF) and moisture<br />
content y(%) on the basis of the experimental data. The<br />
equation is shown as follow<br />
moisture content(%)<br />
32<br />
30<br />
28<br />
26<br />
24<br />
22<br />
20<br />
18<br />
16<br />
y x x x<br />
3 2<br />
= −0.000054149 − 0.0089798 + 0.63413 + 11.4539 (17)<br />
14<br />
0 10 20 30 40 50 60 70 80<br />
capacitance(nF)<br />
Figure 6. Plot of corn moisture content versus capacitance (the<br />
cont<strong>in</strong>uous l<strong>in</strong>e is the fitt<strong>in</strong>g curve)<br />
From Figure 6, we conclude that capacitance <strong>in</strong>creases<br />
with <strong>in</strong>creas<strong>in</strong>g corn moisture content.<br />
V. CONCLUSIONS<br />
The relationship between moisture content and<br />
capacitance was obta<strong>in</strong>ed <strong>in</strong> 8 groups of experiments. The<br />
moisture content of the samples can be determ<strong>in</strong>ed on the<br />
basis of capacitance measured by the detection circuit.<br />
The error is smaller than <strong>in</strong> the dry<strong>in</strong>g method. We<br />
conclude that the accuracy <strong>in</strong> measur<strong>in</strong>g moisture content<br />
by the capacitive sensor circuit is high and that the<br />
method is appropriate for accurate assessment of the<br />
moisture content <strong>in</strong> corn.<br />
ACKNOWLEDGMENT<br />
The authors gratefully acknowledge assistance from Dr.<br />
Mike Hey from the University of Nott<strong>in</strong>gham, and also<br />
give thanks to the M<strong>in</strong>istry of Shandong Education<br />
(J09LG17), who provided part of the research fund<strong>in</strong>g.<br />
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general chairs and/or program chairs who are appo<strong>in</strong>ted as the Guest Editors of the Special <strong>Issue</strong>. Special <strong>Issue</strong> for a Conference/Workshop is<br />
typically made of 10 to 15 papers, with each paper 8 to 12 pages of length.<br />
Guest Editors are <strong>in</strong>volved <strong>in</strong> the follow<strong>in</strong>g steps <strong>in</strong> guest-edit<strong>in</strong>g a Special <strong>Issue</strong> based on a Conference/Workshop:<br />
• Select<strong>in</strong>g a Title for the Special <strong>Issue</strong>, e.g. “Special <strong>Issue</strong>: Selected Best Papers of XYZ Conference”.<br />
• Send<strong>in</strong>g us a formal “Letter of Intent” for the Special <strong>Issue</strong>.<br />
• Creat<strong>in</strong>g a “Call for Papers” for the Special <strong>Issue</strong>, post<strong>in</strong>g it on the conference web site, and publiciz<strong>in</strong>g it to the conference attendees.<br />
Information about the Journal and <strong>Academy</strong> <strong>Publisher</strong> can be <strong>in</strong>cluded <strong>in</strong> the Call for Papers.<br />
• Establish<strong>in</strong>g criteria for paper selection/rejections. The papers can be nom<strong>in</strong>ated based on multiple criteria, e.g. rank <strong>in</strong> review process plus<br />
the evaluation from the Session Chairs and the feedback from the Conference attendees.<br />
• Select<strong>in</strong>g and <strong>in</strong>vit<strong>in</strong>g submissions, arrang<strong>in</strong>g review process, mak<strong>in</strong>g decisions, and carry<strong>in</strong>g out all correspondence with the authors.<br />
Authors should be <strong>in</strong>formed the Author Instructions. Usually, the Proceed<strong>in</strong>gs manuscripts should be expanded and enhanced.<br />
• Provid<strong>in</strong>g us the completed and approved f<strong>in</strong>al versions of the papers formatted <strong>in</strong> the Journal’s style, together with all authors’ contact<br />
<strong>in</strong>formation.<br />
• Writ<strong>in</strong>g a one- or two-page <strong>in</strong>troductory editorial to be published <strong>in</strong> the Special <strong>Issue</strong>.<br />
More <strong>in</strong>formation is available on the web site at http://www.academypublisher.com/jcp/.
Deformed Kernel Based Extreme Learn<strong>in</strong>g Mach<strong>in</strong>e<br />
Chen Zhang, Shixiong Xia, and B<strong>in</strong>g Liu<br />
Optimal Sleep Schedul<strong>in</strong>g Scheme for Wireless Sensor networks Based on Balanced Energy<br />
Consumption<br />
Shan-shan Ma, Jian-sheng Qian, and Yan-j<strong>in</strong>g Sun<br />
Identity Based Proxy Re-encryption From BB1 IBE<br />
J<strong>in</strong>dan Zhang, Xu An Wang, and Xiaoyuan Yang<br />
Corn Moisture Measurement us<strong>in</strong>g a Capacitive Sensor<br />
Hongxia Zhang, Wei Liu, Boxue Tan, and Wenl<strong>in</strong>g Lu<br />
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(Contents Cont<strong>in</strong>ued from Back Cover)<br />
Intrusion Detection Based on Improved SOM with Optimized GA<br />
Jian-Hua Zhao and Wei-Hua Li<br />
Fault Diagnosis System for NPC Inverter based on Multi-Layer Pr<strong>in</strong>cipal Component Neural Network<br />
Danjiang Chen, Y<strong>in</strong>zhong Ye, and Rong Hua<br />
Pulse Wave K Value Averag<strong>in</strong>g Computation and Pathological Diagnosis<br />
Li Yang, J<strong>in</strong>xue Sui, and Yunan Hu<br />
Multi-Step Prediction Algorithm of Traffic Flow Chaotic Time Series based on Volterra Neural<br />
Network<br />
Lisheng Y<strong>in</strong>, Yigang He, Xuep<strong>in</strong>g Dong, and Zhaoquan Lu<br />
Adaptive Track<strong>in</strong>g Control for Nonaff<strong>in</strong>e Nonl<strong>in</strong>ear Systems with Zero Dynamics<br />
Hui Hu and Peng Guo<br />
Improved Feasible SQP Algorithm for Nonl<strong>in</strong>ear Programs with Equality Constra<strong>in</strong>ed Sub-Problems<br />
Zhijun Luo, Guohua Chen, Simei Luo, and Zhib<strong>in</strong> Zhu<br />
F<strong>in</strong>ite Element Analysis Based Design of Mobile Robot for Remov<strong>in</strong>g Plug Oil Well<br />
Xiaojie Tian, Yonghong Liu, Rongju L<strong>in</strong>, Baop<strong>in</strong>g Cai, Zengkai Liu, and Rui Zhang<br />
Contour Error Coupled-Control Strategy based on L<strong>in</strong>e Interpolation and Curve Interpolation<br />
Guoyong Zhao, Hongj<strong>in</strong>g An, and Q<strong>in</strong>gzhi Zhao<br />
Research of Leaf Quality Based on Snowflake Theory<br />
Lihui Zhou, Jiajia Sun, Juanjuan An, and Jun Long<br />
Oscillation Criteria for Second Order Nonl<strong>in</strong>ear Neutral Perturbed Dynamic Equations on Time<br />
Scales<br />
Xiup<strong>in</strong>g Yu, Hua Du, and Hongyu Yang<br />
Improved Quantum Ant Colony Algorithm based on Bloch Coord<strong>in</strong>ates<br />
Xiaofeng Chen, X<strong>in</strong>gyou Xia, and Ruiyun Yu<br />
Image Fusion Method Based on Directional Contrast-Inspired Unit-L<strong>in</strong>k<strong>in</strong>g Pulse Coupled Neural<br />
Networks <strong>in</strong> Contourlet Doma<strong>in</strong><br />
Xi Cai, Guang Han, and J<strong>in</strong>kuan Wang<br />
The Critical Legal Contention under the Challenge of Information Age and the Predom<strong>in</strong>ant Social<br />
Interests Concern for Develop<strong>in</strong>g Intelligent Vehicle Telematics <strong>in</strong> the United States<br />
Fa-Chang Cheng and Wen-Hs<strong>in</strong>g Lai<br />
MPC Controller Performance Evaluation and Tun<strong>in</strong>g of S<strong>in</strong>gle Inverted Pendulum Device<br />
Chao Cheng, Zhong Zhao, and Haixia Li<br />
A Metadata-driven Cloud Comput<strong>in</strong>g Application Virtualization Model<br />
Yunpeng Xiao, Guangxia Xu, Yanb<strong>in</strong>g Liu, and Bai Wang<br />
Robust Portfolio Optimization with Options under VE Constra<strong>in</strong>t us<strong>in</strong>g Monte Carlo<br />
X<strong>in</strong>g Yu<br />
A Novel Water Quality Assessment Method Based on Comb<strong>in</strong>ation BP Neural Network Model and<br />
Fuzzy System<br />
M<strong>in</strong>g Xue<br />
An Isolated Dual-Input Converter for Grid/PV Hybrid Power Systems<br />
Yu-L<strong>in</strong> Juan, Hs<strong>in</strong>-Y<strong>in</strong>g Yang, and Peng-Lai Chen<br />
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