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Journal of Computers 

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Volume 8, Number 6, June 2013 

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REGULAR PAPERS 

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Hongxia Zhang, Wei Liu, Boxue Tan, and Wenling Lu 

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JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1377 

Functional Networks Analysis from Multi 

Neuronal Spike Trains on Prefrontal Cortex of 

Rat during Working Memory Task and 

Neuronal Network Simulation 

Dexuan Qi 

Tianjin Research Centre of Basic Medical Science, Tianjin Medical University, Tianjin 300070, China 

Email: dxqi@tju.edu.cn 

Xin Tian* 

Tianjin Research Centre of Basic Medical Science, Tianjin Medical University, Tianjin 300070, China 

Email: tianx@tijmu.edu.cn 

Abstract—Functional connectivity networks on prefrontal 

cortex of rat during working memory task in vivo are 

analyzed. Neural ensemble entropy coding is applied to find 

the time interval of working memory event occurrence. The 

analysis of functional connectivity networks is carried out 

though the method of cross-covariance. And functional 

networks of the occurrence working memory event and 

resting state are obtained. The complex network topology 

parameters are calculated, the two networks satisfy the 

small-world network property as the clustering coefficients 

of them are larger than their corresponding random 

networks and their characteristic path lengths are 

approximately equal to their corresponding random 

networks. Finally, the simulations of spiking neuronal 

networks of working memory event occurrence and resting 

state are presented. Hindmarsh-Rose neuron model is 

chosen as single neuron of prefrontal cortex that connected 

by functional network of working memory event occurrence 

and resting state, receptivity. The simulation results are 

agreed with experiment data in rat prefrontal cortex during 

a working memory task. 

Index Terms—functional connectivity, neuronal entropy 

coding, spike trains, working memory, small-world network, 

neuronal network simulation 

I. INTRODUCTION 

Working memory is short-term memory, which is one 

of the most important research domain of cognitive 

science, refers to a complex cognitive tasks in the brain 

which can provide temporary storage and processing of 

the necessary information, such as learning and 

reasoning[1]-[2]. Physiological studies have found the 

neural activity of the prefrontal cortex changes in the 

Manuscript received March 7, 2012; revised September 27, 2012; 

The work was supported by grants (No. 91132722 and No. 

61074131) from the National Natural Science Foundation of China. 

*corresponding author. Tel.:+86 022 23542744 

process of new learning task, suggesting that working 

memory is mediated by continuous activities of prefrontal 

cortex neurons[3]-[8]. Therefore, understanding the 

information of neural activity is important to grasp the 

basic principle of brain function computations. 

In addition, many theories such as rate coding, time 

coding, and nonlinear coding have laid the foundation for 

further studies of neural activities[9]-[10]. Entropy is a 

measurement of uncertainty or the amount of information, 

which can quantify the information and can describe the 

characteristics of neural activity[9]-[11]. Moreover, the 

nonlinear entropy can make up for the deficiency of 

traditional linear coding methods and show the 

differences between two spike trains which have the same 

firing rates but different temporal structures. In the 

present paper, entropy coding is applied to study local 

spatiotemporal pattern of neuronal activity in the process 

of working memory task and to find the period of 

working memory event occurrence. 

The concept of brain functional connectivity first 

appeared in the electroencephalogram (EEG) study, 

which measures the statistical dependencies of the 

correlation and functional activities on the spatial 

separation of time between different brain regions. 

Functional network is the network obtained from 

deviation of statistical independence, including 

measuring their correlation, covariance, coherent 

spectrum and phase synchronization between different 

brain regions or neurons[12]. In the early 1990s, Friston 

KJ et al first proposed functional connectivity analysis on 

functional magnetic resonance imaging (fMRI) data[13], 

since then the complexity of brain networks based on 

functional connectivity imaging of EEG, 

Magnetoencephalography (MEG) or fMRI data has 

become an important research direction. For example, 

Eguiluz VM et al (2005)[14] applied the correlation 

coefficient method to measure functional connectivity of 

fMRI data, found that the human brains are small-world 

© 2013 ACADEMY PUBLISHER 

doi:10.4304/jcp.8.6.1377-1384

1378 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 

networks; Achard S and Bullmore E (2007)[15] applied 

correlation, partial correlation and partial coherence 

measurement method to study the functional connectivity 

networks between different brain regions, the results 

consistently indicate that the human brains are efficient 

small-world networks. 

Traditional EEG, MEG, fMRI, and other macro 

technology, can directly measure the integrated electrical 

activity of neuronal population, but the measurement 

results cannot be acquired with high time resolution 

(millisecond) and spatial resolution (millimeter) at the 

same time. At the micro level, individual neuron is the 

basic functional unit of the activity in the brain, its neural 

information transmission and storage is very complex and 

highly dynamic. 

Multi-channel neural discharge recording technology, 

developed in recent years, is the use of electrophysiology 

- the extracellular recording method to record the activity 

of neurons in the discharge. This new technology can also 

record the firing activity of neuronal populations of the 

different parts of a brain region or multiple brain regions. 

Therefore, the functional connectivity analysis from 

neuronal firing data of the multi-channel recording 

technology is an effective method of access to the 

functional activity of neurons, and to achieve high 

temporal resolution and spatial resolution. Yu S et al 

(2008)[17] studied the functional networks of visual 

cortex neurons; Correlation analysis method was used to 

calculate the functional connectivity matrix; The visual 

responses data were simultaneously recorded from 24 

nerve cells in visual cortex of anesthetized cats; The 

functional networks had small-world properties. In 

addition, many statistical method has been used for 

establishing statistical associations or causality between 

neurons, finding spatiotemporal correlations, or studying 

the functional connectivity in neuronal networks[18]-[24]. 

The standard method of analysis functional connectivity 

from multi spike trains is cross-correlation method[16]. 

A variety of neural network models have been 

proposed to simulate the spike potentials of neural 

population. For instance, Xiao ZG and Tian X(2010) [25] 

built small-world neural network model of hippocampal 

CA3 based on the characteristics of the hippocampal CA3 

neurons, simulated the response spike trains of neuronal 

population under three types of stimulus, and studied the 

respective neural ensemble encoding of three types of 

stimulus. Meeter M(2003)[26] built a neural nucleus 

model of hippocampus, which composed by CA1, CA3, 

dentate gyrus, and entorhinal cortex nucleus; The model 

was based on the neural information connection relation 

of hippocampus. Atallah HE and et al (2004)[27] used a 

computational neural network model to investigate how 

the hippocampus with together neocortex and basal 

ganglia operate, which can sustain cognitive and 

behavioral function in the brain. 

In the present paper, we aim to provide functional 

connectivity networks analysis on prefrontal cortex of rat 

in the process of working memory task in vivo, during the 

period of working memory event occurrence and the 

period of resting state. Neural ensemble entropy coding 

can be applied to find the period of working memory 

event occurrence and the period of resting state. The 

analysis of functional connectivity networks carried out 

though the method of cross-covariance. The complex 

network topology parameters are calculated. Finally, the 

simulations of spiking neuronal networks of working 

memory event occurrence and resting state are presented. 

Hindmarsh-Rose (HR) neuron model is chosen as single 

neuron that is connected by functional network of 

working memory event occurrence and resting state, 

receptivity. 

II. METHODS 

A. Experimental Data Acquired on Prefrontal Cortex of 

Rats during Working Memory Task in Vivo 

Experimental data were conducted with the approval 

from Animal Care and Use Committee of Tianjin 

Medical University and were in conformity to the Guide 

for the Care and Use of Laboratory Animals. 16-channel 

micro-wire electrodes were planted in rat prefrontal 

cortex and neural activities were recorded while the rats 

performed a working memory task in Y-maze. Effective 

period of 7 seconds were selected, which is deemed to be 

enough to represent the entire working memory process. 

B. Neural Ensemble Entropy Coding for Working 

Memory in Rats Prefrontal Cortex 

Entropy, especially Shannon entropy in this paper, is 

computed from inter-spike intervals (ISIs), which are 

generally regarded as an important carrier of encoded 

information. Assume there is an N-element information 

source sequence{ z 1 

, z 

2 

, ..., z n 

}; Shannon entropy is 

defined as the following (1) (Shannon CE, 1948)[28]: 

n 

E =− p log p , (1) 

i= 

1 

i 

where p 

i 

, ( i =1, 2, ..., n ), is the occurrence probability 

of each element of information source sequence. The 

algorithms of Shannon entropy for spike train from single 

neuron estimation are described as the followings: The 

Inter Spike Interval (ISI) sequence of the neural firing 

was measured and the ISI histogram was estimated; The 

ISI histogram was separated with appropriate bin base on 

the defined bin length and the characteristics of the spike 

trains; The spikes number Si 

in each bin i ( i =1, 2, ..., 

n ) was counted; The firing probability p i 

of bin i was 

calculated based on the equation of 

2 

i 

p = S / S ; 

n 

i i i 

i= 

1 

From (1) the entropy E of the firing sequence was 

calculated. 

Above entropy estimation method can be used to 

present nonlinearity of neural population activity. The 

steps of Neural ensemble entropy coding are summarized 

as: An appropriate window length L was selected and 

Shannon entropy was calculated for the individual 

neuron k , ( k =1, 2, ... , L ) in the window; The window 

© 2013 ACADEMY PUBLISHER


along the time till the end of spike trains was slid with a 

moving step; The entropy values in each window were 

estimated; All the entropy values were normalized and 

the dynamical map can be represented the neural 

ensemble activity as a response to the event. 

C. Functional Network from Neuronal Spike Train Data 

The method to determine directed network is to 

calculate the covariance between neurons, which is used 

to analyze the influences between pairs of spike trains. 

Spike trains are binned in window of 1 millisecond, and 

then 10 milliseconds time-step is applied to count the 

number of spikes of each spike train, the corresponding 

vectors are obtained. To measure whether there is an 

influence from a reference neuron (vector y ) to a target 

neuron (vector x ), (2) is applied to calculate covariance 

between neurons, 

C 

N−| d| 

N N 

1 1 

( n+ 

d) 

i n i 

n 1 N 

 

i 1 N 

 

= = i= 

1 

xy 

( d) 

= N−| d| 

N N 

 

 

 

x − x y − y d ≥0 

, (2) 

1 1 

y − y x − x d < 0 

 

 

( n−d) 

i n i 

n= 1 N i= 1 N i= 

1 

where C ( d ) is covariance between reference neuron 

xy 

(vector y ) and target neuron (vector x ), d is time lag 

between reference neuron (vector y ) and target neuron 

(vector x ), x and y are length N vectors obtained from 

corresponding spike trains of neuron. The Cxy 

( d ) will 

show a peak if there is some consistent pattern between 

vector y and vector x with a time lag d . When a peak 

occurs at a time lag d ≥ 0 in lag window of 50 

milliseconds, there is an effect from reference neuron 

(vector y ) to target neuron (vector x ) with target neuron 

delay d , the influence strength is the value of peak. If the 

peak exceeded a threshold, we can obtain a connection 

from reference neuron to target neuron with connectivity 

weigh of peak value. Each neuron is considered with no 

connectivity to itself, in other words, the main diagonal 

elements of functional connectivity matrix are zero. 

D. Complex Network Topology Parameters 

Small-world networks theory is presented by Watts DJ 

and Strogatz SH(1998)[29]. Usually two parameters are 

used to characterize the complex network characteristics. 

One is clustering coefficient ( CC ), and another is 

characteristic path length ( CPL ). Suppose there are k 

edges connected to one node; there are at most 

kk− ( 1)/2 probable exist edges among k neighbor 

nodes which are connected to k edges. The CC of one 

node is the number of actual exist edges divide by the 

number of at most probable exist edges. The CC of the 

network is defined as the average value of all nodes, as 

the followings (3). 

N 

2ei 

CC = , (3) 

k ( k −1) 

i= 

1 i i 

where N is the nodes number of the network, e i 

is the 

number of actual exist edges among k 

i 

nodes. Arbitrarily 

select two nodes in a complex network, connecting these 

two nodes with the minimum number of edges, which is 

defined as the shortest path length of these two nodes. 

The CPL of the network is defined as the average value 

of all shortest path length between node pairs, as the 

followings (4), 

N 

2 

CPL = dij 

. (4) 

nn ( + 1) i= 

1 

where d 

ij 

is the shortest path length between the two 

nodes i and j in the complex network, N is the nodes 

number of the network. 

Characteristics of small-world network are high CC 

and shorter CPL . Meanwhile the two parameters are 

high in regular networks and low in corresponding 

random networks[30]. 

E. Spiking Neuronal Network Simulation of 

Prefrontal Cortex 

Single spiking neuron model is the basis computational 

model of the neural physiological activity study. The 

Hindmarsh-Rose (HR) model was proposed by 

Hindmarsh J and Rose RM (1984)[32]. Used HR neuron 

model, the action potential can be simulated. HR model 

can be used to study single neuron spiking characteristics 

as well as the basic unit of the large-scale network. HR 

neuron model is used as network nodes in our neural 

population model. The equations of HR neuron model are 

shown in (5), (6) and (7), 

dX 3 2 

= Y − aX + bX − Z + I 

stim 

, (5) 

dt 

dY 

2 

c dX Y 

dt = − − , (6) 

dZ 

1 

r( X ( Z- g)) 

dt = − 4 

, (7) 

where X is the membrane potential of neuron, Y 

represents the fast recovery currents, Z represents slow 

adaptive currents, I stim 

is an external stimulus input 

currents, a , b , c , d , r and g are constant parameters. 

The values of these parameters are set according to [33]. 

In HR neuron model, the parameter r is related to the 

concentration of calcium ions. By adjusting the value of 

the parameter r , the neuron can be shown a different 

discharge mode. 

The prefrontal cortex neurons are mainly divided into 

two categories: excitatory neurons and inhibitory neurons; 

The anatomical sampling of the neurons in the prefrontal 

cortex has shown that about 80% of the neurons are 

excitatory neurons and the rest 20% are inhibitory 



neurons[31]. Excitatory neurons are pyramidal cells in 

morphology. The firing characteristics of excitatory 

neurons are regular spiking (RS) neurons, which present 

rapid and evident firing frequency adaptation responding 

to a continuous depolarizing current injection. Inhibitory 

neurons are interneuron cells. The firing characteristics of 

excitatory neurons are fast spiking (FS) neurons, which 

respond to long depolarizing current stimulus with higher 

firing rate and less prominent spike frequency adaptation 

than RS neurons. 

In our Spiking neuronal network simulation of 

prefrontal cortex, all HR neurons are coupled by 

functional connectivity. The equations of network model 

are shown as (8), (9), and (10): 

dX 

d 

N 

i 

3 2 

Yi aXi bXi Zi Istim 

w AijX 

j 

t j= 

1 

= − + − + + , (8) 

dYi 

dt 

= c−dX − Y , (9) 

2 

i 

dZi 

1 

= r( Xi 

− ( Zi 

- g)) 

, (10) 

dt 

4 

where the subscript i represents the neuron number, N 

is the number of neurons. In our simulation we use 

N equals to the neuron number in working memory 

experiment in rat prefrontal cortex. 

i 

w 

N 

 

j= 

1 

A X 

ij 

j 

is the 

coupling term of the neural network model, where w is 

the coupling strength of connectivity from neuron j to 

neuron i . Aij 

is an N × N martix, which represents the 

coupling matrix of the neurons when a connection exists 

between neurons i and j . 

III. RESULTS 

A. Neural Ensemble Coding from Experimental Data 

After using software of spike sorting (off-line sorter, 

Plexon, TX, USA) to separate single neuron data from 

16-channel data, we obtain 34 neurons and corresponding 

spike trains. Neuronal population spatiotemporal 

activities in rat prefrontal cortex during the performance 

of working memory task in vivo are shown in Fig. 1. 

In Fig. 1, effective period of 7 seconds is selected to 

represent the whole working memory process. The 

dynamic entropy coding method was applied to 

characterize activity of neural population response to the 

working memory event. We calculated the entropy values 

of population firing during working memory task. The 

neural firing entropy matrix is obtained in sliding window 

of 200 milliseconds with 50 milliseconds overlapping, 

representing the local entropy for each neuron. And 

neural ensemble entropy coding is shown in Fig. 2. 

Spike raster 

(neuron# 1-34) 

Figure 1. Neuronal population spatiotemporal activities in rat prefrontal 

cortex during a working memory task in vivo. The triangle " " 

indicates the time stamp. 

Entropy 


Normalized entropy 

Figure 2. Neural ensemble entropy coding in rat prefrontal cortex 

during a working memory task in vivo. The triangle " " indicates the 

time stamp. 

In Fig. 2, Normalization is achieved by dividing spike 

trains by the maximum entropy values over the time 

period. Simultaneous increase of firing rate and entropy 

demonstrate the occurrence of working memory event. 

Neuron 12, 13, 14, 15, 16, 17, 18 and 19 form a neural 

ensemble during the occurrence of working memory 

event. The triangle " " indicates the time stamp. 

B. Functional Connectivity Network 

The analyses of functional connectivity networks were 

carried out during the occurrence of working memory 

event (time interval [2.818s, 4.818s], before time stamp) 

and the period of resting state (time interval [5.000s, 

7.000s], i.e. the period of 2s after time stamp). The 

method of cross-covariance between pairs of neurons has 

been used to determine directed connectivity edges. For 

34 neurons, N( N − 1)/2, or 561 pairs of neuron have 

been calculated. And at most there are 1122 crosscovariance 

peaks greater than zero. To determine the 

threshold of the connectivity, the peaks sorted by their 

values are shown in Fig. 3. If the threshold is too low, the 

result network is a fully connected graph. However, if the 

threshold is too high, the graph has several edges. Here, 

threshold was determined with the value when the mean 

degree K ≈ ln( N) 

[34]. 



14 

12 

Working memory event occurrence 

Resting state 

Cross-covariance peaks 

10 

8 

6 

4 

Target neuron # 

2 

Threshold 

0 

0 200 400 600 800 1000 1200 

Pair index 

Figure 3. Cross-covariance peaks between neuronal pairs 

In Fig. 3, the threshold=2.0 at the point where the 

increment of the curve changes notably. If the peak 

exceeds the threshold, a directed edge of functional 

connectivity network could be obtained from the 

reference neuron to the target neuron with the 

connectivity weight of peak value. Via the analysis of 

two time intervals (the occurrence of working memory 

event in the time interval before time stamp; period of 

resting state in the time interval after time stamp), two 

corresponding functional connectivity networks were 

obtained and their connectivity matrix are shown in Fig. 4 

and Fig. 5, respectively. 

In Fig. 4 and Fig. 5, each column of the matrix 

indicates whether there is a direct connection from the 

reference neuron to the target neurons, where the neuron 

number corresponds to the column number is a reference 

neuron. The nonzero elements of the matrix indicate that 

there is a functional connection from the reference to the 

target neuron and the color shows the strength of the 

connection. Comparing the Functional connectivity 

matrix of working memory event occurrence network 

(Fig. 4) with resting state network (Fig. 5), the number of 

edges of working memory event occurrence network is 

more than the number of the latter network. And the 

mean connectivity strength shows the same, as shown in 

Table 1. 

TABLE 1 

CONNECTION NUMBER AND MEAN CONNECTIVITY 

STRENGTH OF TWO NETWORKS 

Connection 

number 

Mean connectivity 

strength 

Working memory event 

occurrence network 

402 3.93 ± 1.93 

Resting state network 67 2.55 ± 0.51 

Figure 4. Functional connectivity matrix of neurons during the 

occurrence of working memory event in vivo (time interval [2.818s, 

4.818s], before time stamp) 

Target neuron # 

Figure 5. Functional connectivity matrix of neurons during the period 

of resting state in vivo (time interval [5.000s, 7.000s], i.e. the period of 

2s after time stamp). 

In working memory event occurrence network, the 

high strength and dense connection concentrates on 

several neurons (especially on neuron 12, 13, 14, 15, 16, 

17, 18 and 19). And this phenomenon was not found in 

the latter network. It agrees with neural ensemble coding 

form experimental data that neuron 12, 13, 14, 15, 16, 17, 

18 and 19 form a neural ensemble during the period of 

working memory event occurrence. 

Fig. 6 and Fig. 7 show the topological graphs of 

working memory event occurrence network and resting 

state network, respectively. The color of the edges 

reflects the connection strength from the reference 

neurons to the target neurons, with magenta being largest 

and blue being smallest. 



Figure 6. Connectivity graph of working memory event occurrence 

network in vivo (during time interval [2.818s, 4.818s], before time 

stamp) 

C. Results of Simulation 

The neuronal spiking networks of working memory 

event occurrence and resting state were simulated. Our 

simulation model is composed of 34 neurons, of which 

the simulation time is 2000 milliseconds, respectively. In 

our Spiking neuronal network simulation of prefrontal 

cortex, all HR neurons are coupled by two functional 

connectivity networks as showing in Fig. 4 and Fig. 5. 

The Spike raster of neuronal network model simulation of 

working memory event occurrence and resting state are 

shown in Fig. 8 (a)(b), respectively. And we calculate 

neural ensemble entropy coding of the two simulation 

results as shown in Fig. 9 (a) (b), respectively. In Fig. 9 

(a)(b), normalization is achieved by dividing by the 

maximum entropy values from spike trains over the time 

period. 

In Fig. 8(a) and Fig. 9(a), Several neurons increases 

simultaneously in firing rate and increases in Entropy, 

and Neuron 10, 12, 13, 14, 15, 16 and 17 form a neural 

ensemble during the simulation of working memory event 

occurrence. In Fig. 8(b) and Fig. 9(b), there is no neural 

ensemble formed. The simulation results are agreed with 

experiment data in rat prefrontal cortex during a working 

memory task in vivo. 

(a) 

(b) 

Figure 7. Connectivity graph of resting state network in vivo (during 

time interval [5.000s, 7.000s], i.e. the period of 2s after time stamp) 

To compare characteristics of different networks, the 

CC and CPL were calculated. The CPL of the 

working memory event occurrence network is 1.678, and 

its equivalent random network is 1.657; the CC of the 

working memory event occurrence network is 0.604, and 

its equivalent random network is 0.356. The CPL of the 

resting state network is 3.045, and its equivalent random 

network is 3.683; the CC of the working memory event 

occurrence network is 0.098, and its equivalent random 

network is 0.066. The two networks satisfy the smallworld 

network property as the clustering coefficients of 

them are larger than their corresponding random 



networks. 

1 second 1 second 

Figure 8. Spike raster of neuronal network model simulation. (a) 

Neuronal network model of neurons spiking of working memory event 

occurrence. (b) Neuronal network model of neurons spiking of resting 

state. 

(a) 

Entropy 


(b) 

Entropy 


Normalized entropy 

Figure 9. Neural ensemble entropy coding of neuronal network model 

simulation. (a) Neural ensemble entropy coding of neurons spiking of 

working memory event occurrence simulation. (b) Neural ensemble 

entropy coding of resting state simulation. 



IV. CONCLUSIONS 

In the present paper, functional connectivity networks 

on prefrontal cortex of rat during working memory task in 

vivo are analyzed. Neural ensemble entropy coding is 

applied to find the time interval of working memory 

event occurrence. The neural firing entropy matrix is 

obtained in sliding window of 200 milliseconds with 50 

milliseconds overlapping, representing the local entropy 

for each neuron. Simultaneous increase of firing rate and 

entropy demonstrate the occurrence of working memory 

event (time interval [2.818s, 4.818s]). Neuron 12, 13, 14, 

15, 16, 17, 18 and 19 form a neural ensemble during the 

occurrence of working memory event. The analysis of 

functional connectivity networks carried out though the 

method of cross-covariance The analyses of functional 

connectivity networks were carried out during the 

occurrence of working memory event (time interval 

[2.818s, 4.818s], before time stamp) and the period of 

resting state (time interval [5.000s, 7.000s], i.e. the period 

of 2s after time stamp). The complex network topology 

parameters are calculated. The number of edges of 

working memory event occurrence network is more than 

the number of the latter network. And the mean 

connectivity strength shows the same. In working 

memory event occurrence network, the high strength and 

dense connection concentrates on several neurons 

(especially on neuron 12, 13, 14, 15, 16, 17, 18 and 19). 

And this phenomenon was not found in the latter network. 

It agrees with neural ensemble coding form experimental 

data that neuron 12, 13, 14, 15, 16, 17, 18 and 19 form a 

neural ensemble during the period of working memory 

event occurrence. The two networks satisfy the smallworld 

network property as the clustering coefficients of 

them are larger than their corresponding random 



networks. Finally, the simulations of spiking neuronal 

network of working memory event occurrence and resting 

state are presented. Hindmarsh-Rose (HR) neuron model 

is chosen as single neuron that connected by functional 

network of working memory event occurrence and resting 

state, receptivity. The two simulation models are 

composed of 34 neurons, of which the simulation time is 

2000 milliseconds, respectively. Several neurons 

increases simultaneously in firing rate and increases in 

Entropy, and Neuron 10, 12, 13, 14, 15, 16 and 17 form a 

neural ensemble during the simulation of working 

memory event occurrence. There is no neural ensemble 

formed during the simulation of resting state. The 

simulation results are agreed with experiment data in rat 

prefrontal cortex during a working memory task. 

ACKNOWLEDGEMENTS 

This work was supported by grants (No. 91132722 and 

No. 61074131) from the National Natural Science 

Foundation of China. 

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Dexuan Qi was born in Tianjin, China, in 1983. She 

received the Bachelor's degree in Mechanics Engineering in 

2006, from Tianjin University, Tianjin, China. She received the 

Master's degree and Doctor's degree in 2010, from Tianjin 

University, Tianjin, China. 

She is working as post-doctor in Tianjin Research Centre of 

Basic Medical Science, Tianjin Medical University. Her 

research interests include neuronal network model, simulation 

of cortex spiking model, and functional connectivity network. 

Xin Tian was born in Shanghai, China, in 1946. She 

obtained the Bachelor's degree in 1968, from Tsinghua 

University, Beijing, China. She received the Master's degree in 

1982, from Tianjin University, Tianjin, China. She received the 

Doctor's degree in 1991, from University of New South Wales, 

Australia. 

She is currently a professor of school of Biomedical 

Engineering, Tianjin Medical University. Her research interests 

include neural information processing, encoding, nonlinear 

systems and neural computation. 



A Novel Heuristic Usage of Helpful Actions for 

Conformant-FF System 

Wei Wei, Dantong Ouyang, Tingting Zou and Shuai Lu 

College of Computer Science and Technology, Jilin University, Changchun, China 

Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, 

Changchun, China 

Email: wei_wei10@mails.jlu.edu.cn, ouyd@jlu.edu.cn, zoutingt@163.com, lus@jlu.edu.cn 

Abstract—Conformant planning is usually transformed into 

a search problem in the space of belief states, where the 

combinatorial explosion of search space has been one of the 

most intractable problems. In this paper, we present a novel 

usage of the helpful action pruning technique in the 

Conformant-FF planner. The key idea is to change the way 

it deals with helpful actions and first consider actions from 

the so-called implication path which was used by 

Conformant-FF for concluding which subgoal would be 

considered known to be true in the relaxed planning graph. 

We first point out the semantics of solving by cases, 

indicated by the implication paths of the relaxed planning 

process. In line with the semantics, we then propose our 

heuristic idea of using these implication paths further by 

attempting to collect certain groups of helpful actions such 

that executing all actions within a group can achieve some 

subgoal while executing an individual action in the group 

cannot due to incomplete information. This technique 

usually leads to the goal faster and cuts down the search 

space dramatically. We evaluate the idea experimentally. In 

a number of conformant benchmarks, our heuristic 

pruning technique outperforms helpful actions pruning in 

both planning efficiency and the size of search space. 

Index Terms—Helpful actions, Conformant-FF, Heuristic 

Pruning, Belief state 


Planning is an area of Artificial Intelligence that 

studies choosing and organizing actions to achieve some 

objectives. Over the last few years we have seen a 

significant increase of the efficiency of planning systems 

[1, 2]. There are several promising approaches in plan 

generation including planning graph analysis [3, 4], 

planning as satisfiability [5] and heuristic search 

planning [6, 7, 8]. Classical planning refers to planning 

under a restricted model which is deterministic, static, 

finite and fully observable with restricted goals and 

implicit time. However, these assumptions are often 

unrealistic when modeling real-world tasks. For instance, 

the initial state may be incompletely specified, actions 

may have non-deterministic effects or the environment 

Manuscript received July 1, 2012; revised October 6, 2012; accepted 

October 11, 2012. 

Corresponding author: Dantong Ouyang 

may be only partially observable. Several interesting 

models are obtained by relaxing some of the restrictive 

assumptions. Conformant planning is the problem of 

finding a plan that guarantees goal achievement given 

nondeterministic initial state or action effects, and no 

information can be observed at run time. A conformant 

plan is a sequence of actions that should be successful to 

achieve the goal regardless of uncertainty about the 

initial state and action effects. Therefore, conformant 

planning turns out to be considerably harder than 

classical planning [9]. Effective approaches for 

conformant planning include heuristic guidance [10, 11], 

translation in to classical ones [12], approximation-based 

planning and so on [13]. 

Heuristic search is one of the strongest trends in the 

planning community. We focus on the formulation that 

transfers a conformant planning task into a search 

problem in the belief state space. In this way, uncertainty 

about the true current world state is modeled via a belief 

state, i.e., the set of world states that we consider 

possible at this time. Then a heuristic function is derived 

from the specification of the planning instance and used 

for guiding the search through the search space. FF’s 

heuristic function based on a relaxation of the planning 

task turns out to be the most successful idea in classical 

planning. Hoffmann and Brafman extended this 

technique to conformant planning and implemented the 

well known planner Conformant-FF [14]. In a number of 

benchmarks, Conformant-FF can provide very 

informative heuristic values and shows fine scalability. 

Conformant-FF uses the same overall search 

arrangement as FF, with reasonable modifications for 

conformant setting. In Conformant-FF, belief states are 

represented by an implicit approach where the truth 

values of all the propositions in a belief state are 

determined using a CNF reasoning. FF’s relaxed 

planning process is also extended to handle conformant 

problems. For each action effect the relaxation is to 

ignore the effect’s delete list as well as all but one 

proposition of the effect’s condition. After building the 

relaxed planning graph successfully, a relaxed plan is 

extracted and the length of the relaxed plan is used to 

provide the heuristic value of the belief state. When 

solving the relaxed planning task for a belief state, 

implication relation is maintained simultaneously to 


doi:10.4304/jcp.8.6.1385-1393


capture constraints between propositions at adjacent time 

steps. Implication paths in this machinery can be used to 

check the truth value of uncertain propositions when 

building the relaxed planning graph and to determine 

actions that must be inserted to the solution during 

relaxed plan extraction. Besides the estimate of goal 

distance, Conformant-FF uses a pruning technique of 

helpful actions selecting a set of promising successors to 

each search node. 

In conformant setting, we observe that some branches 

of the search tree are usually non-independent with each 

other when expanding a belief state. All the actions on 

these branches will be involved into the final plan in 

different search iterations. In this paper, we recognize 

such branches and consider them as a group. With that 

we propose a powerful pruning technique suggested by 

implication paths when solving the relaxed planning task. 

Briefly, those actions which are inserted into the relaxed 

plan by implication paths at the first time step concern 

the unknown propositions of the current belief state and 

thus permit to remove the uncertainty. We execute these 

actions in sequence with higher priority than other 

regular helpful action provided by Conformant-FF. 

Our novel usage of helpful actions is useful in 

reducing the degree of uncertainty about the current 

belief state and get closer to the goal quickly. We run 

experiments to evaluate our idea. In a number of 

conformant benchmarks, the experimental results show 

that our pruning technique can get a much smaller search 

space than before and improves the original 

Conformant-FF system in both planning efficiency and 

the size of search space. 

The paper is organized as follows. In Section 2 we 

briefly describe the conformant planning framework we 

consider and give an overview of Conformant-FF’s 

architecture. In Section 3 we characterize the semantics 

of the implication paths in Conformant-FF firstly. Then 

we propose our idea of pruning based on the usage of 

helpful actions, and illustrate the enforced hill-climbing 

procedure adopting this pruning technique. Section 4 

gives the experimental results and our analysis. We 

conclude the paper in Section 5. 

II. BACKGROUND 

A. Conformant planning problem 

The conformant planning problem considered in this 

paper extends a subset of the ADL language with 

uncertainty about the initial state. The extensions to 

handle uncertainty about effects are conceptually 

straightforward by taking account of the 

non-deterministic effects when computing state 

transitions. 

Definition 1 (Conformant planning problem) 

A conformant planning problem P is a triple (A, I, G) 

where A corresponds the action set, I is a propositional 

CNF formula denoting the possible initial world states 

and G is an non-empty set of propositions defining the 

goal conditions. 

The initial situation is a belief state represented by a 

propositional CNF formula I. Any world state that 

satisfies this formula is a possible initial state. We use S I 

to denote the initial belief state. An action a is a pair of 

(pre(a), E(a)) where pre(a) is a set of propositions 

representing the preconditions and E(a) is a set of 

conditional effects. A conditional effect e is a triple 

(con(e), add(e), del(e)) that correspond to e’s condition, 

add list and delete list respectively. An action a is 

applicable in a world state w if pre(a) w, i.e., all of a’s 

preconditions are satisfied in w. If action a is applicable 

in w, then all conditional effects eE(a) that satisfies 

con(e) w get executed. Executing a conditional effect e 

results in the world state w- del(e)∪add(e). 

Definition 2 (Conformant plan) 

An action sequence actA* is a conformant plan for 

problem P if, no matter what initial world state one starts 

from, all actions in act are applicable at their point of 

execution and the associate run results in a goal state. 

B. Conformant-FF system 

Conformant-FF system transforms a conformant 

planning problem into a search problem in belief state 

space. A belief state S is represented by the initial belief 

state formula together with the action sequence that leads 

to S. For each belief state encountered during search, the 

sets of known, negatively known and unknown 

proposition are computed. Given a conformant planning 

problem, a belief state S reached by an action sequence 

act and a proposition p, p is known in S if p is contained 

in the intersection of the worlds in S, i.e., p is always true 

after executing act and equally p is negatively known in 

S if p is always false after executing act. A proposition p 

is unknown in S if it is neither known nor negatively 

known. The truth value of a proposition in a belief state 

can be computed by a SAT solver checking the CNF 

formula that captures the semantics of the respective 

action sequence. 

Conformant-FF’s overall architecture is identical to 

FF system, illustrated in Fig. 1. The basic search 

algorithm is enforced hill-climbing which combines local 

and systematic search. Starting from current search state 

S, enforced hill-climbing algorithm performs a 

breadth-first search for a better state S such that h(S) < 

Belief state S 

Conformant 

Planning problem 

Enforced hill-climbing 

Relaxed planning task 

Plan/“Fail” 

Heuristic value h(S) 

Helpful actions H(S) 

Figure 1. Conformant-FF’s architecture 



h(S). Here, h(S) denotes the heuristic value, and H(S) 

denotes the helpful actions, which are the considered 

actions when expanding S. If a state with lower heuristic 

value was reached, then S= S, else the hill-climbing fails, 

a complete best-first search is invoked to solve the 

problem from scratch. 

III. THE HEURISTIC TECHNIQUE OF HELPFUL ACTIONS 

During search, the considered successors of a search 

state are generated by the helpful actions in H(S). In 

classical planning, H(S) is the set of actions at the first 

level of the relaxed planning graph that add a subgoal of 

this level. In the conformant setting, H(S) is the set of 

such actions at the first level of the relaxed planning 

graph, plus those actions that are selected for an 

implication path during relaxed plan extraction. 

In this section, we propose our heuristic idea of 

helpful actions pruning, which can be used to reduce the 

search space further in the enforced hill-climbing 

procedure of Conformant-FF. The idea is derived 

according to the semantics of the relaxed planning graph 

and the implication paths. For the purpose of exposition, 

we first point out the relation between the implication 

paths of the relaxed plan and the uncertain aspect of the 

estimated belief state. 

A. Semantics of implication paths 

Consider a simplified example from the Blockworld 

domain. 

Example 1 There are four blocks, b1, b2, b3 and b4. 

Initially b2, b3 and b4 are on the table and b1 is on b2 or 

b3. The initial situation of b1 is not known, modeled as 

oneof((on b1 b2), (on b1 b3)). The goal is (on b1 table) 

and (on b4 b1). We have a simple (move b from to) 

action that can change the location of the blocks. The 

graphical sketch of this example is given in Fig. 2. 

To get the heuristic value, the relaxed task starting 

from the initial belief state is solved. In Fig. 3 we give 

the conformant relaxed planning graph built for Example 

1. Proposition layers P(t) and action layers A(t) are built 

alternatively. Propositions on the dashed area are 

unknown at their respective layers. Dashed lines denote 

implication edges between two adjacent proposition 

layers and empty actions are represented by dots. 

We find that A(0) only includes actions given by 

implication edges plus some empty actions NOOP. The 

implication edges yielded by A(0) are: 

(move b1 b2 table): (on b1 b2)(0)→(on b1 table)(1) 

(move b1 b3 table): (on b1 b3)(0)→(on b1 table)(1) 

(move b1 b2 b4): (on b1 b2)(0)→(on b1 b4)(1) 

(move b1 b3 b4): (on b1 b3)(0)→(on b1 b4)(1) 

NOOP: (on b1 b2)(0)→(on b1 b2)(1) 

NOOP: (on b1 b3)(0)→(on b1 b3)(1). 

Here, timed implication edges represent that the truth 

values of some propositions at layer t are uncertain and 

usually depend on their truth values at layer t-1. 

b1 b1 

b2 b3 b4 

table 

b4 

b1 

Initial situation 

b2 

Goal 

b3 

table 

Figure 2. An example of Blockworld 

Relaxed plan extraction starts with G 2 (S I )={(on b1 

table), (on b4 b1)}. The subgoal (on b1 table) is inserted 

at layer 1 of its first appearance. (on b1 b4) is not a 

subgoal since it does not contribute to achieve the goal. 

However, there is no action in A(0) that can guarantee 

achievement of (on b1 table). According to implication 

edges, to make (on b1 table) true at layer 1, we have to 

check the truth value of (on b1 b2) or (on b1 b3) at layer 

0. In Conformant-FF, the implication edges of subgoal 

g(t) form an Imp tree in the relaxed planning graph 

between the lowest layer and layer t. For the subgoal g(t) 

that is not proved to be true at t, it is checked if the 

current state formula implies the disjunction of the leafs 

in the Imp tree, where the leafs are all the propositions in 

the current belief state whose truth values determine the 

truth value of g at layer t. Impleafs(g(t)) is the set of such 

proposition leafs that are reachable from g(t) and then 

min_Impleafs(g(t)) is computed to be the minimal subset 

of Impleafs(g(t)). For this example, we get min_Impleafs 

((on b1 table)(1))={(on b1 b2)(0), (on b1 b3)(0)} whose 

disjunction is obviously implied by the initial state 

formula. Then we know that (on b1 table) can be 

achieved by (move b1 b2 table) or (move b1 b3 table). 

These two actions form the implication paths from 

min_Impleafs ((on b1 table)(1)) to (on b1 table)(1). To 

guarantee (on b1 table) become true at layer 1, both of 

the two actions are selected into the relaxed plan. Also 

these are collected as helpful actions. Since (on b1 b4) is 

not a necessary subgoal at layer 1, other actions of A(0) 

are not considered as helpful. 

For a subgoal g at layer t, sometimes there does not 

exists any supporting action that guarantees to always 

achieve g, i.e., any action with an effect that adds g and 

whose condition is known to hold at layer t-1. This 

complicated situation should trace back to the uncertain 

initial state. Intuitively, g has been shown that at least 

one possible world state could make it true. To achieve g, 

implication paths for g are determined from layer t going 

downwards to layer 0. All the actions that are responsible 

for the implication paths are selected at the respective 

times. min_Impleafs(g(t)) is computed by a back 

chaining loop over the implication edges ending in g(t) 

and it must be a subset of unknown propositions at layer 

0, which corresponds to the uncertain aspect of the 

estimated belief state. Checking out the disjunction of the 



P(0) 

A(0) 

P(1) 

A(1) 

P(2) 

… 

… 

(on b2 table) 

(on b3 table) 

(on b4 table) 

(on b1 b2) 

(on b1 b3) 

(move b1 b2 table) 


(move b1 b2 b4) 

(move b1 b3 b4) 

(on b1 table) 

(on b2 table) 

(on b3 table) 

(on b4 table) 

(on b1 b2) 

(on b1 b3) 

(on b1 b4) 

(move b4 table b1) 

(on b4 b1) 

(on b1 table) 

(on b2 table) 

(on b3 table) 

(on b4 table) 

(on b1 b2) 

(on b1 b3) 

(on b1 b4) 

Figure 3. The relaxed planning graph for the initial belief state 

min_Impleafs(g(t)) against the current state formula, g 

can be proved to be always true at layer t in the relaxed 

planning procedure. Each implication path from g(t) to 

one of its leaf corresponds to an action sequence that is 

executable in a particular current world state. Trying out 

all these actions in the current belief state is the only way 

to make g to be true in despite of the uncertainty arisen 

from initial state. This way, we remark that implication 

paths capture a form of solving by cases. 

In Example 1, as the situation of b1 is unknown, 

implication paths in the relaxed plan indicate that action 

(move b1 b2 table) achieves (on b1 table) if (on b1 b2) is 

true in the initial world state, otherwise action (move b1 

b3 table) achieves (on b1 table). Since b1 is only at one 

of the two locations, executing these two actions one by 

one could guarantee to make (on b1 table) true. Namely, 

given uncertainty about the initial state, to solve the task, 

a plan must be able to solve each possible initial world 

state. 

B. Pruning of helpful implication paths 

In line with our analysis of implication paths, we give 

our changing on the usage of helpful actions during 

search. To illustrate the algorithm, let us reconsider 

Example 1. After solving the relaxed planning task, we 

get the heuristic value supplied by the relaxed plan and 

collect the helpful actions. This information helps to lead 

the search procedure. The helpful actions here are (move 

b1 b2 table) and (move b1 b3 table), given by 

implication paths at the lowest level of the relaxed plan. 

These are the restricted choices to expand the estimated 

belief state. We get two successors by expanding the 

belief state with these actions. Enforced hill-climbing 

will perform an exhaustive search to select a better 

successor. In this example we find out that both 

successors generated by these two actions can give better 

heuristic evaluations. Thus to reach the subgoal (on b1 

table) for sure, search is iterated starting from the 

intermediate state and the other action is also involved 

into the final plan. 

Based on the solving by cases semantics of 

implication paths, we pursue the idea of considering 

implication paths for some subgoal as a group of actions. 

The observation that forms our basic idea is obtained 

from the back chaining process to determine implication 

paths during the extraction of relaxed plan. Actually the 

implication paths in the relaxed plan are back chained 

exactly to the uncertain part of the estimated belief state 

and branches of the implication edges are used to deal 

with different possible world states in current belief state. 

To construct a conformant plan, all the actions that refer 

to uncertainty about the current belief state are necessary. 

Like helpful actions, we restrict to actions that are part 

of the implication paths and are at the lowest layer, i.e., 

those that could be select to start the relaxed plan. 

Definition 3 Given the current belief state S, suppose 

rplan is the extracted relaxed plan, H(S) is the set of 

helpful actions and min_Impleafs(g(t)) is the determined 

minimal subset of leafs for subgoal g of step t, the set of 

implication helpful actions achieving subgoal g(t) is 

defined as follows: 

imp_H(g(t), S)={a | aH(S) and one conditional effect 

of a is responsible for an edge in rplan from 

min_Impleafs(g(t)) to g(t)}. 

We call actions from imp_H(g(t), S) to be 

responsible to achieve the subgoal g(t). Selection of 

imp_H(g(t), S) is done as a set union operation to avoid 

any superfluous action. We integrate these actions into 

an action sequence in an arbitrary order and use this 

sequence to expand the current search state. However, 

before making the action sequence, we have to address 

the problem of the interference between actions. In 

relaxed planning graph, delete effects of actions are 

ignored and the interference situation is not visible. Here 

we focus on the situation that the effect on an edge of the 

implication path may delete preconditions of action that 

has an effect on another edge. Entailment of an action 

precondition is checked against the known propositions, 

so deleting of one precondition would cause that the 

action does not work at its point of the sequence. We 

observe that conditional effects on the implication edges 

of the first layer refer to different world state. These 

effects do not interfere with each other generally since 

the possible current states are usually mutually exclusive. 

We call imp_H(g(t), S) to be executable if it can be made 

into a sequence and each action is executable at the 

respective time. As imp_H(g(t), S) is selected from 

implication paths for subgoal g, to distinguish from the 



regular helpful actions, we call them helpful implication 

paths for g(t). 

Definition 4 Given the belief state S, the set of helpful 

implication paths to S is defined as follows: 

HIP(S)={ imp_H(g(t), S) | g is a subgoal at time step 

t of the extracted relaxed plan and imp_H(g(t), S) is 

executable}. 

What we do in principle is to recognize and pick a 

group of actions that contribute to achieve a subgoal out 

of helpful actions. The notion of helpful implication 

paths shares some similarities with helpful actions. In a 

nutshell, action sequences in the set of helpful 

implication paths are usually made up of several helpful 

actions, which are deemed to have more potential for 

reaching a state with a much lower heuristic value. Thus 

helpful implication paths take precedence over other 

helpful actions during expanding. The enforced 

hill-climbing procedure that adopts the pruning 

technique is specified in Fig. 4. The input of the 

procedure is the planning problem . The 

procedure outputs the plan if the goal is achieved 

successfully, otherwise it returns “Fail” if the enforced 

hill-climbing can not get any better state before the goal 

state. 

The search procedure starts out in the initial belief 

state. Facing an intermediate search state S, the 

Search_for_better_state() procedure is invoked. During 

search, states are kept in a queue. In each iteration 

process, the first state is removed from the queue and 

evaluated. If the evaluation is lower than the current 

heuristic value, the iteration gets a better state. Otherwise, 

the removed state is expanded. Our implementation puts 

the successors generated by HIP(S) in the queue with 

higher priority beside the usual successors obtained by 

other regular helpful actions. 

Procedure EhcSearch-HIP(, plan) 

1 Initialize S to be the initial belief state; 

2 Initialize the search queue U to be empty 

3 plan= ; 

4 while h(S) != 0 do 

5 Put S in the queue U; 

6 if (Search_for_better_state(S, h(S), S, h(S ))) then 

7 add the path from S to S at the end of plan; 

8 S = S ; 

9 reset U to be empty; 

10 else 

11 output “Fail”, stop; 

12 endif 

13 endwhile 

Procedure Search_for_better_state(S, h(S), S, h(S )) 

14 while (true) do 

15 Remove the first node S in the queue; 

16 if h(S ) < h(S) then 

17 return true; 

18 endif 

19 Collect HIP(S) 

20 for each action sequence p in HIP(S) 

21 put the state generated through p to the end of U; 

22 for each of other regular helpful action a 

23 put the successor generated by a to the end of U; 

24 endwhile 

Figure 4. Enforced hill-climbing with helpful implication paths 

pruning 

Our implementation cuts down the branching factor 

further. Usually an action sequence from helpful 

implication paths could reach a search state a few steps 

away with a strictly better heuristic evaluation, which 

would be reached in several iterations when using 

helpful actions only. Thus, helpful implication paths 

offer some short cuts to better states. This way, the 

number of evaluated states is also reduced because only 

the two states that are at the beginning and end point of 

the action sequence need to get evaluated and all the 

intermediate states on this path are ignored. To take 

everything considered, we just leave other helpful 

actions behind and in this way our idea appears to be a 

tie breaking preference for the search procedure. 

In the above example, the two actions (move b1 b2 

table) and (move b1 b3 table) come from helpful 

implication paths for the subgoal (on b1 table)(1) of the 

relaxed plan. Fig. 5 illustrates our implementation of 

expanding process. Grayed parts are computations that 

are saved by our pruning. The two helpful actions are 

integrated into an action sequence to expand the initial 

belief state S I . A better belief state S 3 is generated 

immediately by this sequence. Our pruning cuts down 

the branching factor from two to one and reaches the 

subgoal (on b1 table) within one search iteration, which 

will be accomplished by the normal helpful actions in 

two iterations. Moreover, the state evaluation of S 1 is 

avoided. 

As our specific implementation collects helpful 

implication paths amongst the helpful actions, we can get 

the helpful implication paths totally for free, as another 

important side effect of the basic heuristic method, more 

strictly, as a side effect of the helpful actions for 

conformant setting. Moreover, just like helpful actions, 

helpful implication paths pruning do not preserve 

completeness as well, so the pruning technique is only 



F: (on b2 table) 

(on b3 table) 

(on b4 table) 

U: (on b1 b3) 

(on b1 table) 


(on b2 table) 

(on b3 table) 

(on b4 table) 


(on b3 table) 

(on b4 table) 

U: (on b1 b2) 

(on b1 b3) 

S 1 

h(S 1 )=2 

S 3 

h(S 3 )=1 

S I 

h(S I )=3 



(on b3 table) 

(on b4 table) 

U: (on b1 b2) 

(on b1 table) 

Figure 5. The expanding procedure for the initial belief state 

S 2 



adopted in the enforced hill-climbing search, which is 

not complete anyway, and the complete best-first search 

procedure is unchanged. In all of our test domains, the 

tasks can be solved successfully in the enforced 

hill-climbing procedure with our new pruning technique. 

IV. EXPERIMENTAL RESULTS 

We implemented the heuristic pruning technique 

presented in the previous sections and evaluated it on a 

number of conformant planning benchmarks. The 

experiments were run on a PC running Ubuntu 8.0 at 

1.90 GHz with 1 GB main memory. There are three 

heuristic setups in Conformant-FF and most of the time 

they yield similar performance. We select to use the 

state-formula heuristic function which gives the most 

precise computing. It is enough to evaluate the power of 

the pruning technique under one heuristic function setup. 

The individual domains are described below respectively. 

For each problem we provide the runtime in seconds, the 

number of evaluated states during search and the length 

of the found plan of the planning system that adopts our 

helpful implication paths pruning and the original helpful 

actions pruning, respectively. 

A. The Uts domain 

The Uts domain describes a series of tasks of universal 

transversal sequences. In this domain, one is initially 

located at any node on a graph with n nodes. Some nodes 

on the graph are connected by edges. One can execute 

the action “start” to switch to a “started” phase and make 

the current node visited. After started, one can “travel” 

through edges to change the locations and visit other 

nodes. The goal is to visit all the nodes with the initial 

location uncertain. There are three different test suites, 

k-n, l-n, r-n, corresponding to tasks with different extents 

to which the graph is connected, where the number of 

nodes in 2n. Tab. 1 provides our experimental results in 

the Uts domain. “US” indicates that the problem is 

unsolvable. 

From a quick glance, our idea improves the helpful 

actions pruning significantly. To make every node 

visited eventually, a subgoal that gets to a “started” 

phase is required at first. Since the initial location is 

unknown, one should apply a start action to each 

possible initial location. Intuitively, the number of the 

required start actions is equal to the number of nodes in a 

task. Conformant-FF recognizes these helpful actions 

and to assure the “started” subgoal, these actions are 

applied one after another until all of them are included 

into the plan. For a task with 2n nodes, the subgoal 

becomes true after 2n search iterations. In our 

implementation, all these actions form helpful 

implication paths for the “started” subgoal. Using helpful 

implication path pruning technique to expand the initial 

belief state, the subgoal becomes true in the second 

search iteration in despite of the number of nodes in the 

task. 

Our pruning technique of helpful implication paths 

leads to a decrease of evaluated states which refers to the 

TABLE I. 

RESULTS IN THE UTS DOMAIN 

Helpful implication paths Helpful actions 

T (s) S L T (s) S L 

k-01 0.00 2 4 0.01 4 4 

k-02 0.00 4 10 0.01 10 10 

k-03 0.01 6 16 0.04 16 16 

k-04 0.01 8 22 0.22 22 22 

k-05 0.02 10 28 0.83 28 28 

k-06 0.02 12 34 1.81 34 34 

k-07 0.04 14 40 4.45 40 40 

k-08 0.07 16 46 10.25 46 46 

k-09 0.12 18 52 23.58 52 52 

k-10 0.20 20 58 45.95 58 58 

l-01 0.00 2 4 0.00 4 4 

l-02 0.01 7 12 0.02 14 11 

l-03 0.01 17 24 0.03 28 22 

l-04 0.03 26 35 0.11 41 34 

l-05 0.08 40 51 0.39 56 48 

l-06 0.20 57 66 1.23 73 64 

l-07 0.42 76 86 3.03 92 82 

l-08 1.25 104 105 6.29 113 102 

l-09 2.48 129 129 16.95 136 124 

l-10 4.04 171 152 41.28 161 148 

r-01 0.00 1 US 0.00 1 US 

r-02 0.00 1 US 0.00 1 US 

r-03 0.00 8 8 0.02 17 16 

r-04 0.01 20 32 0.14 34 25 

r-05 0.04 29 37 3.23 1021 37 

r-06 0.08 28 47 18.18 4071 41 

r-07 0.26 52 53 2.63 74 45 

r-08 0.27 36 55 7.24 83 50 

r-09 0.17 40 56 13.59 112 58 

r-10 0.78 64 72 40.18 156 69 

size of search space. Most strikingly, the number of 

evaluated states is even a lot smaller than the plan length 

in some problems. This means that helpful implication 

paths contribute to find a fragment of the plan within one 

search iteration and don’t have to compute the heuristic 

values for all the states that are along the search path 

corresponding to the plan. With the number of evaluated 

states decreased, the efficiency is improved dramatically. 

Regarding runtime, our implementation is much superior 

and scales up more easily. We find that sometimes the 

plan length of our idea is a little longer due to the order 

of actions in the plan sequence. This, however, does not 

affect the plan quality seriously, since Conformant-FF 

does not guarantee to find an optimal plan anyway. 

B. The Safe domain 

In the Safe domain, there are several possible 

combinations for a safe. The right combination is one out 

of these combinations which is initially unknown. The 

goal is to get the safe door open. To assure the goal, one 

must “try” all combinations exhaustively. Tab. 2 and Tab. 

3 provides the experimental results for instances with n 

possible combinations. “-” indicates time-out, with a 

runtime cutoff 1200s. 

The plan for any problem in this domain is to try all 

combinations in some order. In Conformant-FF’s 

implementation, the number of evaluated states is equal 

to the plan length, i.e., the number of possible 

combinations in the task. For each visited state, the goal 

proposition safe-open appears at the first layer of the 

relaxed planning graph, providing all the try actions at 

first layer that have not been applied as helpful actions. 



TABLE II. 

RESULTS IN THE SAFE DOMAIN-1 

Helpful implication paths 

Helpful actions 


s5 0.00 1 5 0.00 5 5 

s10 0.01 1 10 0.03 10 10 

s30 0.14 1 30 3.87 30 30 

s50 1.34 1 50 72.87 50 50 

s70 6.06 1 70 368.74 70 70 

s100 28.22 1 100 - - - 

TABLE III. 

RESULTS IN THE SAFE DOMAIN-2 

Helpful implication paths Helpful actions -D 


s5 0.00 1 5 0.00 5 5 

s10 0.01 1 10 0.01 10 10 

s30 0.14 1 30 0.22 30 30 

s50 1.34 1 50 2.18 50 50 

s70 6.06 1 70 8.92 70 70 

s100 28.22 1 100 35.01 100 100 

Executing one of these helpful actions will get to a 

state closer to the goal. Such iterations are repeated until 

the goal is reached. Using our pruning technique, all the 

try actions are selected as helpful implication paths in the 

first search iteration. After executing the helpful 

implication paths in the initial belief state, the goal 

becomes known in the second iteration and the task is 

solved successfully. For tasks in different sizes, our idea 

can find plans by evaluating only one state. 

Regarding runtime, our implementation behaves much 

faster. The poor runtime performance of Conformant-FF 

is also due to the special structure of the Safe domain 

that no proposition becomes known until the task is 

solved. As the number of possible combinations 

increases, Conformant-FF gets in trouble with repeated 

states checking. Helpful actions -D refers to the option 

that turns the repeated states checking off, at this time the 

original planner can solve the tasks quickly. Generally, 

our pruning technique is still competitive in this domain 

with the helpful actions of Conformant-FF without 

repeated states checking. 

C. The Dispose domain 

The Dispose domain is a variation of Grid family, 

which is about picking objects and dropping them into a 

trash. Initially the locations of all the objects are 

uncertain and the location of the trash is given. One starts 

from a given location and can “move” between two 

adjacent locations. One can “pickup” an object with a 

condition that the object is at the current location. One 

can also “drop” an object into a trash if the trash is at the 

current location. The goal is to get all the objects 

disposed of in the trash. Tab. 4 shows our results in the 

Dispose domain. 

Once again, the old helpful action pruning technique 

evaluates much more states and performs a lot worse. To 

drop an object into a trash, one has to guarantee that the 

object is held in hand. Given that the initial locations of 

the objects are unknown, a conformant plan should 

execute a pickup action for each object at all the possible 

TABLE IV. 

RESULTS IN THE DISPOSE DOMAIN 

Helpful implication paths Helpful actions 


2-1 0.00 9 9 0.00 11 9 

2-2 0.00 10 14 0.01 16 14 

2-3 0.01 11 19 0.02 21 19 

2-4 0.01 12 24 0.03 26 24 

2-5 0.02 13 29 0.04 31 29 

2-6 0.02 14 34 0.08 36 34 

2-7 0.04 15 39 0.13 41 39 

2-8 0.07 16 44 0.23 46 44 

2-9 0.10 17 49 0.32 51 49 

2-10 0.13 18 54 0.49 56 54 

3-1 0.00 25 20 0.01 36 24 

3-2 0.04 26 30 0.07 46 34 

3-3 0.15 27 40 0.30 56 44 

3-4 0.41 28 50 0.80 66 54 

3-5 0.66 29 60 1.84 76 64 

3-6 1.15 30 70 2.55 86 74 

3-7 2.11 31 80 5.53 96 84 

3-8 3.26 32 90 10.98 106 94 

3-9 5.17 33 100 18.11 116 104 

3-10 8.77 34 110 32.24 126 114 

4-1 0.06 61 43 0.07 61 39 

4-2 0.78 62 60 0.79 78 56 

4-3 1.94 63 77 2.37 95 73 

4-4 5.59 64 94 7.94 112 90 

4-5 18.09 65 111 27.82 129 107 

4-6 25.84 66 128 46.22 146 124 

4-7 47.63 67 145 93.87 163 140 

4-8 73.42 68 162 156.43 180 158 

4-9 189.02 69 179 462.63 197 175 

4-10 207.30 72 183 508.43 202 180 

locations. We observed that our pruning technique 

explores a much smaller search space. As the size of the 

problem increases, heuristic evaluation becomes more 

costly and the runtime spent mostly goes into the 

computation of heuristic estimations, thus the reduction 

of search space is quite significant. Regarding plan 

length, our implementation is somewhat longer in a few 

cases. But still the quality of the found plan is satisfying. 

D. The Logistics domain 

Logistics we consider in this section is a classical 

planning domain enriched with uncertainty. A package 

can be loaded onto a truck if the package is at the same 

location as the truck. Packages are transported by trucks 

between different positions of a city. Airplanes fly 

between different cities. Instances in Tab. 5 are 

generated by choosing the initial positions of the trucks 

and airplanes, the initial positions and goal positions of 

packages randomly. The uncertainty lies in the initial 

position of each package within its origin city. 

Results from Tab. 4 show that the pruning of helpful 

implication paths is generally competitive or faster, 

compared to helpful actions. Our pruning technique 

avoids the computation of heuristic values for some 

search states which helps to save the runtime 

considerably. In the relatively small cases, the behavior 

of helpful implication path pruning is not obvious that 

much. Large cases with 10 packages, cities, trucks and 

airplanes reveal the power of the pruning strategy and 

show that our implementation scales better to large 

instances. With respect to the plan quality, our technique 



TABLE V. 

RESULTS IN THE LOGISTICS DOMAIN 

Helpful implication paths 

Helpful actions 


2-2-2 0.00 16 16 0.00 23 16 

2-2-4 0.00 23 26 0.00 34 26 

2-3-2 0.01 19 17 0.00 37 17 

2-3-3 0.01 36 24 0.01 46 24 

2-10-10 0.89 211 83 3.59 324 83 

3-2-2 0.01 23 20 0.01 29 20 

3-2-4 0.01 29 33 0.02 36 33 

3-3-2 0.01 36 28 0.02 55 28 

3-3-3 0.01 32 32 0.07 72 34 

3-10-10 3.09 427 112 10.95 435 108 

4-2-2 0.00 15 19 0.01 19 19 

4-2-4 0.01 36 40 0.08 59 40 

4-3-2 0.00 24 23 0.01 31 23 

4-3-3 0.02 48 37 0.07 70 37 

4-10-10 2.51 281 127 11.45 356 121 

is a little longer only in two problems. In most of the 

time, our pruning of helpful implication paths finds 

exactly the same conformant plan as the situation of 

helpful actions pruning. 

All in all, from the experimental results above, we 

conclude that our pruning technique has the potential to 

reduce the size of search space and consequently 

improve the runtime efficiency. In this aspect we 

consider that our idea is clearly superior to helpful 

actions technique. 

V. CONCLUSION 

In this paper, we addressed the Conformant-FF 

planner which solves conformant planning problem by 

belief state space search. The size of search space has 

been a bottleneck to this method which could be 

ameliorated by using heuristic function and pruning. 

Based on our analysis of the implication paths in the 

relaxed planning heuristic function, we proposed the 

pruning technique of helpful implications paths to reduce 

the search space further. We run a number of conformant 

benchmarks to evaluate our idea and the experimental 

results indicate that our heuristic technique has two 

advantages: 

1) An action sequence that integrates several helpful 

action branches together usually cuts down the branching 

factor of a search state. At the same time, considering 

helpful implication paths over other branches often finds 

a better state faster. 

2) Executing a helpful implication path can get to a 

better state a few steps away within one search iteration, 

which relates with recent tread on obtaining long 

sequence of actions instead of applying one by one. Thus 

the evaluations of intermediate states on the helpful 

implication path are avoided, which leads to a 

considerable improvement of runtime efficiency. 

The planner Conformant-FF still has inherent 

limitations due to its implicit representation of belief 

states and incomplete information adding to the 

relaxation. These make the planner provide inaccurate 

heuristic sometimes and get trouble in situations where 

an action may contain many conditional effects or takes 

more complicated forms. It will be significant to propose 

promising ideas to overcome those disadvantages. 

In future, we will treat nondeterministic action effects 

and explore to use a similar pruning idea to solve the 

more general setting of contingent planning, i.e. to 

handle partially observable planning problems. We also 

plan to investigate the search spaces of other 

non-classical planning settings that can be formalized as 

search problems, in particular probabilistic planning and 

temporal planning. 

ACKNOWLEDGMENT 

The authors wish to thank Professor Dantong Ouyang 

for her comments, which was helpful to improve the 

paper. This work was Supported by the National Natural 

Science Foundation of China under Grant No. 

61272208,61133011,60973089,61003101,61170092; 

Jilin Province Science and Technology Development 

Plan under Grant No. 20101501,20100185,201101039; 

Doctoral Fund of Ministry of Education of China under 

Grant No.20100061110031; 

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Wei Wei was born Dec. 28, 1984, in Jilin, 

China. She received the Master degree at 

College of Computer Science and 

Technology of Jilin University, China, in 

2007. 

She is a Ph.D candidate at College of 

Computer Science and Technology of Jilin 

University. Her main research interests include automated 

planning and reasoning. 

Dantong Ouyang was born in 1968, Jilin, China. She received 

the Ph. D degree at College of Computer Science and 

Technology of Jilin University, China, in 1998. 

She is Professor, Ph.D. supervisor, Deputy Dean of College 

of Computer Science and Technology of Jilin University. Her 

main field of expertise is model-based diagnosis and automated 

reasoning. 

Tingting Zou was born Nov. 24, 1984, in Jilin, China. She 

received the Master degree at School of Computer Science and 

Information Technology of North East Normal University, 

China, in 2007. 

She is a Ph.D candidate at College of Computer Science and 

Technology of Jilin University. Her main research interest is 

description logic. 

Shuai LU was born Jul. 11, 1981, in Jilin, China. He received 

the Ph.D degree at College of Computer Science and 

Technology of Jilin University, China, in 2010. 

He is a lecturer at College of Computer Science and 

Technology of Jilin University. Her main research interests 

include automated planning and reasoning. 



Assessing Land Ecological Security Based on BP 

Neural Network: a Case Study of Hangzhou, 

China 

Heyuan You 

College of Business Administration, Zhejiang University of Finance and Economics, Hangzhou, China 

Email: youheyuan@gmail.com 

Abstract— Due to the increasing stress on the land ecology, 

the land eco-security suffers damage. In this paper, the BP 

neural network and PSR framework were adopted to 

establish the model for assessment of land eco-security, and 

an empirical study of assessing land eco-security in 

Hangzhou was done. The results show that the city center 

district is at serious land eco-security risk; Xiaoshan district 

and Yuhang district are at high land eco-security risk; and 

others counties (cities) are at low risk or intermediate risk. 

In Hangzhou, although some measures are adopted to 

control the risk of land eco-security, the economic growth 

still has negative impact on the land ecology. The rapid 

industrialization and urbanization increase the risk of land 

eco-security. Therefore the policy constitutors should do 

something to strengthen the land ecology protection. 

Index Terms—land ecological security, pressure-state-response 

framework, BP neural network, Hangzhou 


As an essential resource for sustainable development, 

the land keeps human supplied with basic material and 

living space. In China, land use is regulated strictly by 

government since the socialist public ownership of land. 

However, in order to accelerate the economic growth, the 

local governments in China excessively exploit and 

utilize land resource [1], and the sustainable use of land 

resources is always neglected in many regions. Some 

serious problems such as soil loss, over-conversion of 

farmland to construction land, land contamination and 

deforestation threat the sustainable land use [2, 3, 4, 5]. 

The scarcity of enough protection for land leads to 

increased risk of land ecological security (eco-security) 

[6]. Consequently, the assessment of land eco-security 

necessarily is done to ascertain ecological state of land 

use system. And the characteristic analysis of land 

eco-security can reveal important information for 

adopting measures to improve the land ecology. 

The current literature that related to land eco-security 

mostly focused on the sustainable use of land resources. 

The ecological sustainability is considered as a vital 

Manuscript received July 5, 2012; revised October 21, 2012; 

accepted October 27, 2012. 

Project number: 70973047. 

Corresponding author: Heyuan You. 

feature of sustainable land use [7]. The indicator systems 

which were applied to assess the sustainable use of land 

resources included some indicators reflected land 

eco-security such as soil loss/formation ratio [8], forest 

cover [9], population density [10], and species loss [11]. 

Owing to the defects in the accurate analysis of land 

ecology, the assessment of land ecological security 

aroused researchers’ attention [6, 12]. 

Back-Propagation (BP) neural network, a method of 

training a multi-layer feed-forward artificial neural 

network with the BP algorithm can approximate any 

nonlinear function [13]. Due to its robust and 

fault-tolerance, the BP neural network is widely applied 

in predictor, optimization and classification [14, 15, 16]. 

Given the subjectivity in the assessment of land 

eco-security, especially determining the weights of 

indicators, and the fuzzy relationship among indicators, 

the BP neural network whose advantage is suitable can be 

applied to establish model for assessing land ecosecurity. 

The rest of this paper proceeds as follows: Section 2 

describes a survey of study area; Section 3 establishes the 

model for assessment of land eco-security based on BP 

neural network; Section 4 obtains the original data and 

pretreats the original date; Section 5 shows the results of 

the assessment of land eco-security of 8 districts 

(county-level cities, counties) in Hangzhou; Section 6 

summarizes the discussion and conclusion. 

II. STUDY AREA 

Hangzhou which is administered as a sub-provincial 

city, with a registered population of 6.8912 million as of 

2010, is the capital and largest city of Zhejiang province. 

Located in Eastern China, Hangzhou sits on the south 

edge of the Yangtze River Delta economic zone (Figure 

1). Hangzhou is the economic, political and cultural 

center of Zhejiang province. It is an industrial city, and is 

considered as an important manufacturing base in coastal 

area of China. The Qiantang River passes through the 

northeast to the southwest of Hangzhou, and Hangzhou 

Bay ends at Hangzhou which lies south of Shanghai. 

Hangzhou extends to the border of the hilly-country 

Anhui Province on its west and the flat-land Hangzhou 

Bay on its east. The vast majority of land in Hangzhou is 


doi:10.4304/jcp.8.6.1394-1400


hill and mountain. 

Hangzhou city is composed of 8 districts, 3 

county-level cities and 2 counties. The city center of 

Hangzhou is composed of Shangcheng district, Xiacheng 

district, Jianggan district, Gongshu district, Xihu district 

and Binjiang district. And Xiaoshan district, Yuhang 

district, Tonglu county, Chun'an county, Jiande city, 

Fuyang city and Lin'an city compose the suburban and 

rural area of Hangzhou. In empirical study, I assumed that 

the six central urban districts were one integrated region 

since the six central urban districts were small districts 

and principal affairs of districts were administered 

independently of suburban and rural area of Hangzhou 

by Hangzhou city people’s government. 

Since the rapid economic growth and large population, 

risk to land ecology in Hangzhou continual increases. 

Consideration of land eco-security in Hangzhou is 

required to preserve the land and to draw up measures 

whose purpose is sustainable utilization of land. 

Figure 1. 

Location of study area 

III. METHODS 

A. Indicator System for Assessment 

The pressure-state-response (PSR) framework has been 

widely used to describe and quantify the environment [17, 

18]. It was accepted to determine indicator to understand 

complex realities about ecology [6, 19]. In this paper, I 

focus on the pressures on the land eco-security, the 

condition of land eco-security which results from these 

pressures and the actions taken to prevent negative land 

eco-security impacts. It is apparent that PSR framework 

can be chosen as a basis for selecting the indicators that 

compose the indicator system for assessing land 

ecological security. Complied with the principles in 

selecting indicators that include substantive, simplicity, 

universality, consistency and availability, and learnt 

experience from previous literature, the initial set of 12 

indicators was selected. Then indicators were adjusted 

based on experts’ opinions who invited to evaluate the 

suitability of initial set. Some indicators in initial set 

were not selected by experts. The reasons for the experts’ 

decision were as follows. (1) Soil erosion modulus was 

not the representative factor which affected the land 

eco-security in Hangzhou since the geographical 

condition of Hangzhou. (2) Natural population growth 

rate was important indicator of the land eco-security, 

however the cultivated land area per capita and water 

resources per capita implied the impact of natural 

population growth rate on the land eco-security. (3) The 

original data of energy consumption per unit of GDP 

could not be obtained. The indicator system applied in 

study area in this paper is presented in Table 1. 

B. Grade Criterion 

It is important to grade the land eco-security and 

determine the grade criterion which used to assess the 

state of land eco-security in Hangzhou. However, there 

was no widely accepted grade criterion of land 

eco-security [6]. The land eco-security should be 

classified to correspond to local conditions. In this paper, 

the grade criterion of land eco-security was classified into 

five grades. The range of land eco-security value was 

assumed [0, 1], and it can be divided into five grades as 

no land eco-security risk (0.8, 1], low land eco-security 

risk (0.6, 0.8], intermediate land eco-security risk (0.4, 

0.6], high land eco-security risk (0.2, 0.4] and serious 

land eco-security risk (0, 0.2]. 

The land eco-security was relative. The assessment 

standards of eco-security in the literature were 

classified into four grades [12]. The numbers ranging 

from 1 to 4 were assigned to “insecure”, “relatively 

insecure”, “relatively secure” and “secure”. Two grade 

criterions of land eco-security were similar in the method 



TABLE I. 

INDICATOR SYSTEM FOR ASSESSING LAND ECO-SECURITY AND GRADE CRITERION OF LAND ECO-SECURITY 

Element Indicators Grade criterion of land eco-security 

(0.8, 1] a (0.6, 0.8] (0.4, 0.6] (0.2, 0.4] [0, 0.2] 

Pressure 

b 

Cultivated land area per capita(mu/person)x 1 

>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 

Population density(person/km 2 ) x 8 650 

Area of stable yields despite drought or excessive rain 

Response proportion (%)x 9 

>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&


Where w ij (k+1) is the new vector of weight and bias, 

w ij (k) is the current vector of weight and bias, D(k) is the 

negative gradient of wij(k) at time k, D(k–1) is the 

negative gradient of wij(k) at time k–1, η is the learning 

rate, β is the momentum constant which is a number 

between 0 and 1.The learning rate usually is trialed with 

a range of 0.1 to 0.3, if the learning rate is too high, the 

algorithm may oscillate and becomes unstable. And the 

momentum constant usually is trialed with a range of 0.9 

to 1 since the low momentum may prevent the network 

from learning. In empirical study, the values of η and β 

were selected as 0.3 and 0.94, respectively. 

The performance measure adopted in empirical study 

was mean-squared error (MSE) function. The MSE 

function is as follows: 

1 

MSE = q t −s t 

n 

2 

∑ ( ( ) ( )) 

(5) 

k 

k 

n t = 1 

Where MSE is net error. q k (t) is kth network node 

desired output of tth training pattern and s k (t) is kth 

network node actual output of tth training pattern. 

original grade criterion of land eco-security presented 

Table Ⅰ were normalized between 0 and 1. The land 

eco-security grade is determined by the particular 

combination of indicator values. Therefore the BP neural 

network should be trained to learn the nonlinear 

relationship from the learn samples. The endpoints of the 

interval of land eco-security and indicator values whose 

correspondence relationship was showed in Table Ⅲ 

were selected. Although the range of land eco-security 

values is assumed [0, 1], the values of land eco-security 

in Hangzhou that will be assessed by BP neural network 

may greater than 1 or less than 0. So as to prevent the 

assessment values of land eco-security to break the 

limitation of an interval and enhance the 

distinguishability of assessment values of land 

eco-security, some proper endpoints were selected to 

reflect the correspondence relationship between the 

indicator values and land eco-security whose value was 0. 

There are a variety of methods for normalization. In 

this empirical study, the equation for normalization is as 

follows: 

S ′ = ( S −min )/(max − min ) (6) 

n n n. value n. value n. 

value 

Where max n.value is maximal value in input vector n, 

and min n.value is minimal value in input vector n. S n is the 

original input in input vector n. S n′ is the normalized 

value of the original in input vector n. 

TABLE II. 

DESCRIPTIVE STATISTICS OF ORIGINAL DATA IN HANGZHOU 

Min. Max. Mean Std.Deviation 

x 1 0.05 0.82 0.61 0.25 

x 2 527.04 14001.76 4426.24 4454.91 

x 3 10.37 45.29 25.59 11.29 

Figure 2. 

Topological structure of BP neural network for 

assessment 

IV. ORIGINAL DATA AND PRETREATMENT 

The original indicator values of 8 districts 

(county-level cities, counties) applied to assess the land 

eco-security of Hangzhou were obtained from the 

statistical yearbooks and local municipal bureau of land 

and resources. The descriptive statistics of original 

indicator values is showed in Table Ⅱ. 

In order to improve the convergence rates and enhance 

the estimation accuracies since the feature of logsig 

transfer function. The original indicator values and 

x 4 117.55 554.03 338.03 149.02 

x 5 3.89 38.31 16.01 11.54 

x 6 14.69 76.86 51.39 26.79 

x 7 0.04 5.47 2.18 2.01 

x 8 103.00 3209.00 730.25 1037.25 

x 9 6.79 87.43 49.02 26.13 

x 10 30.58 63.27 38.04 10.73 

x 11 1.69 190.31 34.87 64.00 

x 12 1.29 8.56 3.76 2.20 



TABLE III. 

ENDPOINTS OF THE INTERVAL OF LAND ECO-SECURITY AND CORRESPONDING INDICATOR VALUES 

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 

1.4 2500 5.00 220 12 30 1.0 450 65 70 30 5 0.8 

0.8 2000 15.00 300 10 25 1.5 500 50 60 25 4 0.6 

0.7 1500 20.00 400 8 20 2.0 550 40 50 20 3 0.4 

0.6 1000 25.00 500 6 15 2.5 600 30 40 15 2 0.2 

0.5 500 30.00 600 5 10 4.0 650 20 30 10 1 0.0 

V. RESULTS 

The BP neural network that was established to assess 

the land eco-security was performed under MATLAB 

version 7.0 by using Neural Network Toolbox [20, 21]. In 

the empirical study, performance goal of the BP neural 

network was set to 0.001 or if number of epoch reaches 

2000. The learn samples which were normalized were 

input, and the Figure 3 showed that the training error falls 

down to 0.001 within 62 epochs. Therefore the BP neural 

network was accepted, and applied to assess of land 

eco-security in Hangzhou. 

The normalized indicator values of city center district, 

Xiaoshan district, Yuhang district, Tonglu county, 

Chun'an county, Jiande city, Fuyang city and Lin'an city 

were put into the BP neural network which had been 

trained, then the values of land eco-security of 8 districts 

(county-level cities, counties) were calculated by the BP 

neural network. The result of assessment was showed in 

Table Ⅵ, and the spatial distribution of land eco-security 

of Hangzhou was presented in Figure 4. 

Figure 4. 

Spatial distribution of land eco-security of Hangzhou 

Figure 3. 

Training error trend of BP neural network 



City center 

district 

TABLE IV. 

NORMALIZED INDICATOR VALUES AND THE LAND ECO-SECURITY OF DISTRICTS IN HANGZHOU 

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 

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 

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 

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 

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 

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 

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 

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 

Lin'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 

serious land 

eco-security risk 

high land 


high land 


intermediate land 


low land 


low land 


intermediate land 


low land 


VI. DISCUSSION AND CONCLUSIONS 

Districts whose land eco-security values are above 0.4 

and below 0.8 account for 60% of the entire region. It 

indicates that the land ecology of districts in Hangzhou 

suffers damage, whereas the risk of land eco-security in 

Hangzhou is in control. Actually the local government 

adopts some measures to administer the land use and land 

ecology since the ecological consciousness. These 

measures principally refer to farmland protection, 

intensive and economical utilization of construction land, 

forests land preservation, contamination emission control, 

family planning, ect. Therefore the condition of land 

eco-security in Tonglu county, Chun'an county, Jiande 

city, Fuyang city and Lin'an city is at low risk or 

intermediate risk. 

The economic growth has negative impact on the land 

ecology of the land ecology in Hangzhou. The city center 

district has a population of 226.74 million which 

accounts for 33% of the total population of Hangzhou, 

and the city center district produces largest GDP of 

Hangzhou which accounts for over 85% of Hangzhou 

GDP. A great deal of service industry and manufacturing 

centralize the city center district. For example, biological 

medicine industry, mechanical manufacturing industry 

and food and beverage industry is geographically 

concentrated Hangzhou Economic & Technological 

Development Zone whose purpose is to attract the global 

investment. The local governments currently consider 

GDP as a most important indicator of economic progress, 

however the improvement of land ecology dose not 

directly tied to the growth of GDP. Much farmland is 

converted to construction land for industrial and 

residential uses, and high population density increases the 

ecological frangibility. 

Xiaoshan district and Yuhang district locate in the 

surrounding area fringed city center district of Hangzhou. 

The development plan of Hanghzhou proposes that 

concentrated distribution area of heavy industry locate in 

Xiaoshan district and Yuhang district. Rapid 

industrialization and urbanization increase the stress on 

the land ecology, in spite of the fact that original 

ecological condition of land in Xiaoshan district and 

Yuhang district is appropriate to maintain the relatively 

security of land ecology since the large cultivated land 

area per capital, large proportion of cultivated land, 

low population density, ect. 

One goal of this paper is to provide a method to assess 

the land eco-security. The BP neural network and PSR 

framework were adopted to establish the model for 

assessment of land eco-security. Then the original date 

was pretreated, and the training error of BP neural 

network was acceptable. The values of land eco-security 

of 8 districts (county-level cities, counties) in Hangzhou 

were evaluated by the BP neural network which was 

trained. The results showed that the city center district 

was at serious land eco-security risk; Xiaoshan district 

and Yuhang district were at high land eco-security risk; 

Tonglu county and Fuyang city were at intermediate land 

eco-security risk; Chun'an county, Jiande city and Lin'an 

city were at low land eco-security risk. This phenomenon 

reveals that although some measures are adopted to 

control the risk of land eco-security, the economic 

growth still has negative impact on the land ecology in 

Hangzhou, and the rapid industrialization and 

urbanization increase the risk of land eco-security. 

Therefore the policy constitutor should do something 

to strengthen the land ecology protection. 

The method for assessing land eco-security in this 

paper is flexible enough to be modified to applied in 

other areas according to the local factors. The purpose of 

assessment of land eco-security is not only obtaining the 

state of the land eco-security but also understanding of 

the factors affect the land eco-security. Consequently 



the similar research about land ecology in the areas 

where the land ecology may suffer damage should be 

done. 


The author wishes to thank Hangzhou municipal 

bureau of land and resources for providing the origin data. 

This work was supported in part by a grant from National 

Natural Science Foundation of China (No.70973047). 

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Heyuan You, he was born in Wenzhou 

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use simulation and land ecology management. 



Magellan: Technical Description of a New 

System for Robot-Assisted Nerve Blocks 

Joshua Morse ∗ , Mohamad Wehbe ‡ , Riccardo Taddei † , Shantale Cyr § , and Thomas M. Hemmerling § 

∗ Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada 

email: joshua.morse@mail.mcgill.ca 

‡ Department of Experimental Surgery, McGill University, Montreal, QC, Canada 

† Department of Anesthesiology, University of Pisa, Pisa, Italy 

§ Department of Anesthesia, McGill University, Montreal, QC, Canada 

Institute of Biomedical Engineering, University of Montreal, Montreal, QC, Canada 

email: thomas.hemmerling@mcgill.ca 

1 

Abstract—Nerve blocks are common procedures used to 

remove sensation from a specific region of the body via 

injection of local anesthetic. Ultrasound-guided nerve blocks 

are common-place in anesthesia, but require specialized 

training and advanced bi-manual dexterity. This paper describes 

a system designed to robotically assist in ultrasoundguided 

nerve blocks. Robot-assisted nerve blocks could allow 

for more precise needle placement, and therefore a higher 

efficacy of blocks. This system is the first step in developing a 

completely automated nerve block system, which would also 

require the incorporation of ultrasound image recognition 

of nerves and other physiological markers. 

Index Terms—Regional anesthesia, nerve blocks, robotic 

anesthesia. 


NERVE blocks are a procedure of regional anesthesia 

used to remove the sensitivity from an area of the 

body via the injection of an anesthetic drug into the nerve 

innervating the target area. Nerve blocks were first used 

in surgery in 1885 [1] and are now a common procedure 

performed routinely around the world. 

Performing regional nerve blocks requires special training. 

Anesthesiologists performing regional nerve blocks 

only on an occasional basis have a significant failure rate, 

as high as 45% [2]. Most regional blocks are performed 

using ultrasound guidance; this necessitates careful bimanual 

operation of the ultrasound probe and the nerve 

block needle. Precise movement of the needle is important 

for successful blocks. One centimeter movement in any 

direction can make the difference between a failed and a 

successful block. 

Mechanical robots have been used in surgery for more 

than 10 years, the da Vinci Surgical System (Intuitive 

Surgical, Inc., Sunnyvale, CA) being the latest. These 

mechanical robots are shown to increase precision of 

movements and improve outcome [3]. Recently, Tighe et 

al. have used the da Vinci Surgical System to perform 

successful nerve blocks in an ultrasound phantom [4]. We 

present the first robotic system, called Magellan, designed 

specifically to perform routine nerve blocks. 

II. MATERIALS AND METHODS 

The Magellan system is designed to perform robotassisted, 

ultrasound-guided nerve blocks. The system has 

4 primary components: a standard nerve block needle 

and syringe mounted via a custom clamp to a robotic 

arm (JACO robotic arm, Kinova, Montreal, QC, Canada), 

an ultrasound machine, a joystick (ThrustMaster T.Flight 

Hotas X, Guillemot Inc., New York, NY, USA), and a 

software control system. The system is designed to work 

with any ultrasound machine with a video output. The ultrasound 

video signal is captured via a USB video capture 

device (Dazzle DVC100, Pinnacle Systems, Mountain 

View, CA, USA). 

The software system is designed on a client/server model 

so that nerve blocks can be performed remotely. Both 

the client and server programs were written in C# and 

communicate using UDP/IP. The client software interfaces 

with the ultrasound machine, robotic arm, and a 

webcam (Lifecam HD, Microsoft Corporation, Redmond, 

WA, USA). The ultrasound and webcam video feeds are 

streamed from the client to the server, where they are 

displayed in a graphical user interface (GUI) created 

in LabView (National Instruments, Austin, TX, USA). 

The webcam is positioned in order to provide a direct 

view of the target nerve insertion area and the ultrasound 

probe. The server software interfaces with the joystick and 

transmits the joystick commands to the client over the IP 

network. The client and server, as well as their software 

subsystems, are detailed in Fig. 1. Further explanation 

of the individual subsystems of both applications are 

presented below. 

A. Software Control System 

1) Server Application: The Controller Subsystem implements 

an interface that decouples the precise controller’s 

driver from the system, allowing for the controller 

to be easily changed. This subsystem reads the state of 

the controller and provides it to the Server Networking 

Subsystem. 

The Server Networking Subsystem is responsible for 


doi:10.4304/jcp.8.6.1401-1405


2 

Client 

Robotic Arm API 

Safety Input Filter 

Client 

Networking 

Subsystem 

Data Logging 

Subsystem 

Video Streaming 

Software 

Server 

Joystick Controller 

Subsystem 

Server Networking 

Subsystem 

GUI 

Fig. 1. 

Logical View of the Magellan system detailing the individual software subsystems of both the client and server applications. 

Fig. 2. GUI of the Magellan system. Left: Ultrasound video feed. Right: Webcam video showing ultrasound probe and insertion area. The arm 

speed and network latency are displayed beneath the ultrasound video. 

transmitting the controller data to the client over the 

network. Furthermore, this subsystem encrypts all packets 

to be sent to the client and decrypts those received from 

the client. This subsystem also works with the client to 

monitor the latency of the network. The latency information 

is displayed prominently on the GUI in order to 

allow the user to estimate the lag between the commands 

they send using the joystick and the resulting movement 

on the video displays. The latency display is color-coded 

to provide a clear, visual indication of the latency status: 

grey for latencies less than 200 ms, yellow for latencies 

between 201 and 400 ms, and red for latencies greater 

than 400 ms. 

The GUI is detailed in Fig. 2. The GUI prominently displays 

the ultrasound video feed and the view of the target 

area, as well as the network latency and current arm speed. 

The arm speed can be toggled between three different 

modes: high, used to place the needle initially in position 

above the target area; medium, used to descend the needle 

towards the insertion point; and low, used to drive the 

needle through the skin and to the nerve sheath. The arm 

speed display is also color-coded, with green, yellow, and 

red denoting low, medium, and high speeds, respectively. 

The arm moves .15 m/s, 0.075 m/s, and 0.0425 m/s for 

high, medium, and low speeds, respectively. 



3 

2) Client Application: The Robotic Arm API subsystem 

is responsible for transmitting commands to the 

robotic arm. This subsystem also provides details on the 

location and status of the arm to the Client Networking 

Subsystem. 

The purpose of the Safety Input Filter subsystem is to 

prevent unsafe commands from being sent to the robotic 

arm: by pressing a specific button on the joystick, the 

operator puts the system into a needle insertion mode that 

limits the depth that the needle can move; these limitations 

are dependent on the target nerve. For example, for the 

popliteal nerve, maximum depth is set to 4 cm. This 

feature prevents the needle from descending below the 

maximum depth of the target nerve. This subsystem also 

scales the magnitude of movement speeds to allow for 

small and precise changes in the orientation of the needle 

in order to provide the anesthesiologist with fine control. 

Additionally, this subsystem implements the control 

scheme for the system as it is responsible for translating 

controller commands received over the network into individual 

commands to be sent to the robotic arm. 

The Client Networking Subsystem is responsible for 

handling all communications with the server application. 

This communication includes the reception of controller 

packets from the server, the monitoring of latency in the 

network, and updates about the status of the robotic arm. 

Additionally, this subsystem handles the encryption of all 

data being transmitted to the server and the decryption of 

all data received from the server. 

The Data Logging Subsystem records all data that is 

received by the client from the server. Additionally, it 

records the output of the Safety Input Filter so that all 

commands that are transmitted to the robotic arm are 

logged. 

The Video Streaming Software subsystem streams the 

local ultrasound and webcam video feeds to the server. 

B. Safety Features 

There are two safety classifications of medical robots: 

fail-safe and fault-tolerant [5]. A fail-safe robot is one 

which enters a safe state when an error occurs; a faulttolerant 

robot is one which continues to operate in the 

presence of errors [5]. This system is fail-safe as it will 

enter a state that poses no risks to the patient if any errors 

occur. 

In the event of a disconnection of any critical device (i.e., 

the joystick is disconnected from the server PC or the 

JACO arm is disconnected from the client PC), the robotic 

arm will immediately stop moving and remain stationary 

until a connection can be re-established. The motors of the 

robotic arm cannot be manually moved while powered on. 

This same protocol is followed if a network connection 

is lost between the client and server PCs. Similarly, the 

robotic arm will also stop all movement if any critical 

exceptions occur in the client or server applications. 

A second important safety consideration of a medical 

robot is the magnitude in error between the actual, measured 

position of the motors of the robot and the position 

that motors were commanded to go [5]. The JACO robotic 

arm has a relative position tolerance of 1.6 mm, meaning 

that the maximum error between the commanded and 

actual positions of the needle will be, within 1.6 mm of 

the target. Additionally, the anesthesiologist can activate a 

safety limitation which will prevent the needle from going 

below the maximum depth of the current target nerve. 

The arm features several important safety features which 

make it suitable for use in this application: it has redundant 

error checks for each joint and the control system, it 

recalculates the position of each motor every 0.01 second, 

recovers automatically in case of a system fault, has zero 

backlash on each of its six axes, and is back drivable when 

shutdown. The arm also has a maximum translational 

speed of 15 cm/s and a maximum joint rotation speed 

of 8 rpm. 

The arm is powered by a 24V DC power adapter and 

is plugged into an uninterruptable power supply (Back 

UPS XS 1300, APC, W. Kingston, RI, USA) that provides 

power to both it and the client computer in the case of 

a power failure. The arm draws between 1.7 and 10 A 

while in use and the UPS contains a battery with sufficient 

capacity to allow for a safe reversal of the procedure 

should power be lost. 

The JACO arm is connected to the client PC using a 

standard USB cable. In the case of a computer failure, the 

robotic arm also has a backup joystick that can be used 

to directly control it, independent of the client PC. This 

joystick allows full control of the arm and will operate as 

long as the arm has power. 

C. Robotic Arm 

The JACO robotic arm was developed to provide 

mechanical assistance to wheelchair-bound people and 

is certified by Health Canada as a medical device. The 

robotic arm has 6 degrees of freedom and can support 

a payload of 1.5 kg or 1 kg at full extension. The 

arm is built of carbon fiber, making it lightweight at 

5 kg. It has a reach of 90 cm at full extension and 

contains 6 independently-controlled motors. The arm can 

also operate in both a left-handed and right-handed mode. 

These features make the JACO robotic arm versatile and 

allow great flexibility in the placement of the robotic arm. 

D. Control Scheme 

In order to provide an intuitive control scheme to the 

user, each of the six primary movements available via the 

robotic arm were mapped to specific buttons and/or axes 

of the joystick. 

The left/right and forward/backward movements of the 

primary joystick handle are mapped to the same movements 

of the robotic arm. Twisting the joystick handle to 

the left or right will cause the robotic arm to rotate the 

needle in a similar fashion. The throttle control of the 

joystick is used to rotate the tip of the needle forward 

or backwards, while rotating a slider bar on the rear of 

the throttle will rotate the syringe about the point of the 



4 

needle. The hat switch is used to ascend or descend the 

needle. The trigger button informs the system that the 

nerve block procedure is beginning, and thus engages the 

safety limitations described in section II-B. Two buttons 

on the top of the joystick are used to either increase or 

decrease the speed of the robotic arm. 

E. Operational Setup 

The JACO robotic arm is mounted to the rear of the 

operating table and placed in the handedness mode that 

would provide the easiest approach to the leg that will 

receive a block: left-handedness for performing a nerve 

block on the right leg, or right-handedness for performing 

a nerve block on the left leg. 

The ultrasound machine is placed so that the probe 

can be manipulated manually to locate and identify the 

target nerve. The ultrasound machine’s video output is 

connected to the client PC using a composite video cable 

and a USB video capture device. For all local tests 

performed with the system, the same PC was used as 

both the client and server. The PC and joystick were 

installed on a mobile cart which was placed close to the 

mannequin. The webcam was then placed with a clear 

view of the intended position and connected to the PC. 

III. TESTING & RESULTS 

The Magellan system was tested on an ultrasound 

nerve phantom (Blue Phantom Select Series Peripheral 

Nerve Block Ultrasound Training Model, Blue Phantom, 

Redmond, WA, USA). This nerve phantom is designed to 

realistically mimic human tissue, both physically and in 

an ultrasound image. These tests were made to ensure that 

the control scheme was easy to use and that the needle 

could be placed in the correct location by the robotic arm. 

An experiment was conducted to record and analyze the 

first 20 nerve blocks performed on the nerve phantom. 

These trials were performed by an anesthesiologist who 

had never previously used the Magellan nor been formally 

trained in its control scheme. In this experiment, the 

anesthesiologist verbally guided an assistant to maneuver 

the ultrasound probe until the nerve was located and 

identified on the ultrasound screen and then directed the 

needle, using the joystick, from a resting position, to the 

proper insertion position, and then directly into the nerve. 

Success was defined as the introduction of the tip of the 22 

gauge needle into the nerve. The trial times are shown in 

Fig. 3. The success rate for the first 20 trials on the nerve 

phantom was 90% with an average time of 95.2 s with a 

standard deviation of 49.9 s. The data was analyzed using 

linear regression and a trend line with a slope of -5.5 s 

was found, denoting that the anesthesiologist was able to 

perform a block 5.5 seconds faster with each successive 

attempt that was made. The failures in these trials were 

identified to be due to improperly aligning the tip of the 

needle with the center of the ultrasound probe. Further 

tests performed by another anesthesiologist resulted in a 

100% success rate. 

Fig. 3. Blue: block times for first 20 phantom trials of the Magellan 

system. Black: trend line and equation. 

IV. CONCLUSION 

We present the first mechanical robotic system 

specifically designed to perform nerve blocks using a 

joystick and computer control center. Using the Magellan, 

a 90-100% success rate was achievable using a standard 

nerve block phantom. In addition, a rather steep learning 

curve was determined indicating great ease of learning to 

operate the nerve block needle using a joystick with rapid 

improvement of the operation times of the Magellan. 

A study of anesthesia residents studying regional 

anesthesia techniques showed a success rate of 89% 

for ultrasound-guided nerve blocks after performing 

40 blocks on patients [6], showing a similar success 

rate between the nerve phantom tests performed with 

Magellan and success rates by anesthesia students. 

Clinical tests will show whether the success rates 

achieved in dummy testing can be confirmed in human 

testing; further research needs to focus on automated 

nerve recognition, as well as automated nerve block 

performance – without human intervention. Combining 

these two approaches, a completely automated nerve 

block system will be possible. 


The authors would like to acknowledge the Department 

of Anesthesia in the Montreal General Hospital for their 

financial support of this project. 

REFERENCES 

[1] W. S. Halsted, “Practical comments on the use and abuse of 

cocaine,” New York Medical Journal, vol. 42, pp. 294–299, 1885. 

[2] P. Marhofer and V. Chan, “Ultrasound-guided regional anesthesia: 

current concepts and future trends,” Anesthesia & Analgesia, vol. 

104, no. 5, pp. 1265–1269, 2007. 

[3] D. Willis, M. Gonzalgo, M. Brotzman, Z. Feng, B. Trock, and L. Su, 

“Comparison of outcomes between pure laparoscopic vs robotassisted 

laparoscopic radical prostatectomy: a study of comparative 

effectiveness based upon validated quality of life outcomes,” BJU 

international, 2011. 

[4] P. Tighe, S. Badiyan, I. Luria, A. Boezaart, and S. Parekattil, 

“Robot-assisted regional anesthesia: A simulated demonstration,” 

Anesthesia & Analgesia, vol. 111, no. 3, pp. 813–816, 2010. 

[5] P. Kazanzides, “Safety design for medical robots,” in Engineering 

in Medicine and Biology Society, 2009. EMBC 2009. Annual 

International Conference of the IEEE, Sept. 2009, pp. 7208 –7211. 



5 

[6] C. Luyet, G. Schupfer, M. Wipfli, R. Greif, M. Luginb&, U. Eichenberger 

et al., “Different learning curves for axillary brachial plexus 

block: Ultrasound guidance versus nerve stimulation,” Anesthesiology 

research and practice, vol. 2010, p. 309462, 2010. 

Thomas M. Hemmerling received the MD 

degree from the Faculty of Medicine, University 

of Saarland, Germany, in 1990. He leads 

the ITAG laboratory, Department of Anesthesia, 

McGill University. He is currently an 

Associate Professor in the department of Anesthesia 

at McGill University and the Institute 

of Biomedical Engineering at the University 

of Montreal, Montreal, Canada. His research 

interests are automated and robotic anesthesia. 

Joshua Morse is currently an undergraduate 

student in the Department of Computer Engineering 

at McGill University, Montréal, QC, 

Canada. 

In 2010, he joined the Intelligent Technology 

in Anesthesia Group (ITAG) as a research 

assistant. His research interests include robotic 

anesthesia, telemedicine and bioinformatics. 

Mohamad Wehbe received the B.Sc. degree 

in biomedical engineering from the American 

University of Science and Technology, Beirut, 

Lebanon, and the M.Sc. degree in biomedical 

engineering from the École Polytechnique de 

Montréal, Montréal, QC, Canada, in 2006 and 

2009, respectively. 

In 2010, he joined the department of 

Experimental Surgery at McGill University, 

Montréal, QC, where he started working toward 

the Ph.D. degree in the Intelligent Technology 

in Anesthesia Group (ITAG). His research interests are focused 

on intelligent biomedical devices and robotic anesthesia. 

Riccardo Taddei received the MD degree 

from the Faculty of Medicine and Surgery, 

University of Pisa, Pisa, Italy in 2008. 

During 2011, he worked as a research fellow 

in the Department of Anesthesia in the 

Montreal General Hospital, McGill University, 

Montreal, Canada. He is currently a third year 

resident in the department of Anethesiology 

and Intensive Care in Cisanello Hospital, University 

of Pisa. His research interests include 

automation in anesthesia. 

Shantale Cyr holds a PhD degree from the 

University of Montreal, Montreal, Canada. 

Since 2007, she has worked as a research 

associate in the ITAG laboratory, Department 

of Anesthesia in the Montreal General Hospital, 

McGill University, Montreal, Canada. Her 

research interests include closed-loop anesthesia, 

device design and user interaction and 

telemedicine. 



State Assignment for Finite State Machine 

Synthesis 

Meng Yang 

State Key Lab of ASIC and Systems, Fudan University, Shanghai, China 

Email: mengyang@fudan.edu.cn 

Abstract—This paper proposes simulated annealing based 

algorithm for the synthesis of a finite state machine to 

determine the optimal state assignment with less area and 

power dissipation. The algorithm has two annealing stages. 

In the first rough annealing stage it tries to search in global 

scope by the proposed rough search method. In the second 

focusing annealing stage it tries to search in local scope by 

using proposed focusing search methods intending changing 

solution slightly. In both stages, the experience of past 

solution is utilised by combing the best solution in the past 

and the current solution. The experiments performed on a 

large suite of benchmarks have established the fact that the 

proposed method outperforms the published GA-based 

algorithms. The results have shown the effectiveness of the 

proposed method in achieving optimal state assignment for 

finite state machine. 

Index Terms—state assignment, finite state machine, 

optimisation algorithm, simulated annealing algorithm 


As the mobile applications are emerging, the power 

consumption of the circuits has become a major concern. 

Numerous researches have been investigated concerning 

the power issues [1-3]. Finite state machine (FSM) is 

mathematical model of the sequential circuits with 

discrete inputs, internal states and discrete outputs. The 

problem of finding an optimal state assignment is NPhard 

[4]. As a result, the synthesis of an FSM plays an 

important role. 

The genetic algorithm (GA) technique [5] has been 

successfully applied to a variety of computationally 

complex problems since it has a large search space. Many 

investigations have shown that GA can find good state 

assignments. Almaini, et al [6] have demonstrated that 

the GA method produced significantly simpler solutions. 

In [7] multi objective GA (MOGA) has been used to 

optimise area and power simultaneously. Xia and 

Almaini [8] have used GAs to optimise both area and 

power with good tradeoffs. Pradhan, et al [3] report on 

the application of power gating in the higher level of 

system design in the form of finite state machine (FSM) 

synthesis. In [9] Chattopadhyay has used GAs to obtain 

power optimised two- and multilevel FSM realisations. 

Chattopadhyay [10] considers D flip-flops to store the 

state bits and investigates the avenue of GAs to achieve 

area reduction under flip-flop and output polarity 

selection. 

Other than GA based methods, a number of heuristic 

algorithms have been proposed, which are based on 

different cost functions estimating the effect of state 

assignment on logic minimisation. It has shown a new 

comprehensive method in [11] consisting of an efficient 

state minimisation and state assignment technique. Goren, 

et al [12] present a heuristic for state reduction of 

incompletely specified finite state machines. The 

proposed heuristic is based on a branch-and-bound search 

technique and identification of sets of compatible states 

of a given incompletely specified finite state machine 

specification. In [13], the usage of a stochastic search 

technique inspired by simulated annealing is explored to 

solve the state assignment problem. 

Generally speaking, it is relatively easy to find state 

assignments to minimise the area only or the power 

dissipation only. However, it is known that minimisation 

of either the power or logic complexity could be at the 

expense of the other and in most cases it is hard to find a 

solution that is optimum in both domains. For large 

circuits, there are millions or possibly billions of 

assignments [14] and hence to find the state assignment 

for the minimisation of power consumption and area at 

the same time is computationally difficult. Besides, GA 

selects the next generation via a ranking system, which is 

not always necessary but takes significant runtime. In this 

paper, in order to reduce the computational time but at the 

same time retain the quality if the solution, simulated 

annealing based algorithm is proposed to solve FSM 

problem with low-power and small-area requirements. 

The remainder of the paper is organised as follows. 

Section II gives terminology of state assignment of the 

FSM. The two annealing stage simulated annealing 

approach is given in Section III. Section IV discusses the 

comparison results in details with respect to other 

approaches. Conclusions are then given in Section V. 

II. TERMINOLOGY 

An FSM can be characterised by a 5-tuple (I, O, M, X, 

Y) where I and O are the sets of primary inputs and 

primary outputs, M is the internal states, X and Y are the 

output and the next state functions, respectively. An FSM 

with M states requires a minimum of S state variables for 

the assignment, where S = ⎡log 

2 M ⎤ and ⎡g ⎤ is the 

smallest integer equal to or greater than g. The number of 

logically unique assignments for an FSM N is given as 

follows. 


doi:10.4304/jcp.8.6.1406-1410


S 

(2 −1)! 

N = (1) 

S 

(2 − M )! S! 

The FSM is commonly represented by a state transition 

table (STT). Given the input transition probability of an 

FSM, its state transition probability can be computed. 

The state transition probability tp ij between state s i and 

state s j occurs in an arbitrarily long sequence and is given 

as follows. 

tp = P p 

(2) 

ij 

The steady state probabilities P i can be obtained via 

Gaussian elimination methods to solve the set of linear 

equations as in (3) and (4). 

i 

i = M 1 

∑ − 

i 

i= 

0 

ij 

P = 1 

(3) 

j = M 

∑ − 1 

Pj 

j= 

0 

P = p 

(4) 

i 

The power consumption [15] of a sequential circuit is 

proportional to its switching activity which can be 

represented as in (5), where C is the capacitance of the 

output for the node, V dd is the supply voltage, f clk is the 

clock frequency and E is the expected switching activity. 

ji 

1 2 

P = CVdd 

fclk 

E 

(5) 

2 

Since the register capacitance is fixed and cannot be 

affected, therefore the E is considered as part of the cost 

function in terms of power consumption. 

i = M 

∑∑ 

− 1 j= 

M −1 

i= 

0 j= 

0 

E = tp ij dist i j 

(6) 

where dist i,j represents the hamming distance between the 

coding of state s i and state s j and tp ij is the total state 

transition probability from state s i and state s j as defined 

in (2). 

III. SIMULATED ANNEALING BASED ALGORITHM 

The problem of finding the state assignment for the 

minimisation of power consumption and area is 

computationally difficult. GA has been successfully 

applied to a variety of computationally difficult problems. 

It has been shown that it can produce good results in a 

reasonable computation time. The basic idea of GA is 

initially to generate a breeding pool of potential solutions 

to a problem. These solutions are encoded as 

chromosomes, and each chromosome is subjected to an 

evaluation function which assigns fitness depending on 

the quality of the solution it encodes. Existing solutions 

are recombined by crossover operator. Mutation operator 

makes random changes in a few randomly selected 

chromosomes in order to prevent premature convergence 

by maintaining the diversity of the population. The GA 

uses a tournament selection method via population 

ranking system to reproduce new generation. As a result, 

, 

the ranking system itself takes significant computational 

time. However, in most cases only the best solution at last 

is required, therefore the entire ranking is not always 

necessary. Furthermore, if some parents are not excellent 

enough, these solutions have little chance to join the 

competition in GA. 

Simulated annealing (SA) algorithm on the other hand 

is another method to solve problems such as 3D packing 

problem [16] and single container loading problem [17]. 

It starts with high temperature. The inspiration of the 

algorithm demand an interesting feature related to the 

temperature variation to be embedded in the operational 

characteristics of the algorithm. This necessitates a 

gradual reduction of the temperature as the simulation 

proceeds. The algorithm starts initially with a high value 

temperature, and then it is decreased at each step 

following some annealing schedule. However there are 

several significant disadvantages of traditional SA, such 

as its slow search speed. Hence, in order to overcome the 

mentioned shortcomings, following simulated annealing 

based algorithm is proposed. 

A. Solution Representation 

Let the state-code array for an M-state FSM be 

S 0 , S1, 

, S M −1 

, where M is the number of FSM states. 

The solution representation is an array of size equal to the 

number of states in the FSM. Each entry in the array is an 

integer between 0 and M-1. Take a ten-state machine 

S 0 , S1, 

S 2 , S3, 

S 4 , S5 

, S 6 , S 7 , S8 

, S9 

for example. One 

possible representation is 9, 6, 8, 2, 3, 0, 4, 1, 5, 7, which 

is shown in Figure 1. 

Figure 1. State assignment for ten-state machine. 

B. Rough Annealing Stage 

The proposed simulated annealing is designed 

purposely into two stages as the temperature schedules. In 

the rough annealing stage, it tends to alter the solution 

with bigger changes at high temperature, consequently 

escape local optima. The rotation swap method randomly 

selects the cutting line from the representation. The 

cutting line is treated as a mirror. Copy the state 

assignments in the left part of the mirror to the right part 

of the mirror. Similarly, the right part is copied to the left 

part. Figure 2 shows an example of exchange method. 

C. Focusing Annealing Stage 

The focusing annealing stage differs to the previous 

annealing stage, which tends to alter the solution with 

smaller changes at low temperature, consequently to 

achieve an effective convergence. In this stage, it 

randomly selects a state assignment and its neighbouring 

state assignment from the representation and swaps these 

two state assignments. These two states can be close to 

each other, as shown in Figure 3, or apart from each other, 

as shown in Figure 4. 



new solution. State entry 9, 2, 3, and 7 from the best 

solution form part of new solution. State entry 8, 3, 9, 2, 4 

and 6 from current solution form the other part of new 

solution. Modification of the new solution is carried out 

to make sure that duplicated state entry 2, 3, and 9 do not 

appear in the solution. By doing so, unassigned state 

entry 0, 1 and 5 are filled in. 

Figure 2. Exchange method. 

Figure 3. Swap method for two states close to each other. 

Figure 4. Swap method for two states apart from each other. 

D. Crossover 

Crossover operator is designed to escape the local 

optimum in the GA. In this paper crossover operator is 

adapted in the simulated annealing to generate a new 

solution by combining the best solution with the current 

solution. Consequently, some potential parts of the 

solution can be inherited from the previous solution. 

It operates as a position-based crossover [18]. An array 

of binary bits is initialised randomly, in which the length 

of the array equals to the length of the representation. 

When 1s appear in the array, copy the states from the best 

solution to new solution. When 0s appear in the array, 

copy the states from the current solution to new solution. 

Since each entry of state assignment solution is unique, 

continuous check is required avoiding the repetition of 

the same states which is not allowed. If state entry is 

duplicated, the first unassigned state entry is assigned. 

Figure 5 shows an example of relay operator to generate 

Figure 5. Crossover operator. 

E. Cost Function 

By minimising (6), low power dissipation could be 

achieved. Unfortunately, this may lead to area overhead, 

resulting in power overhead in the combinational part of 

the circuit. Therefore, objectives of area and power 

should be optimised simultaneously. The total cost 

function is C total = γC area + (1-γ) E, where C area is area 

function, E is power function and γ is a parameter 

specifying the tradeoff of E with respect to C area . 

F. Proposed Algorithm 

To begin with, an initiation solution is randomly 

produced. The annealing approach is divided into rough 

annealing and focusing annealing, which is identified by 

Temperature threshold T threshold . In the rough annealing 

stage the temperature is high and uses exchange method. 

In the focusing annealing stage the temperature is low 

and uses swap methods. The solution is evaluated by the 

cost function. The solution is accepted according to a 

probability P = exp (-∆C/T), where ∆C is the difference 

cost between new solution and current solution, T is the 

temperature. P is between 0 and 1. If the solution is 

improved and kept according to P, the new solution will 

be compared with the best recorded solution to decide 

whether updating the best record is necessary. If new 

solution is rejected instead, this solution is then ignored 

and reverses the current solution. Outer loop updates the 

temperature. The temperature schedules at each outer 

iteration. In the inner loop it generates possible solutions 

at each temperature. The algorithm terminates when 

reaching the lowest temperature and the output will be the 

best record. The pseudo code is shown in Algorithm 1. 



Algorithm 1: Two stage Simulated Annealing 

Inputs: Temperature coefficient α 

Number of state variables N 

Exit temperature T 0 

Temperature threshold T threshold 

Outputs: The best solution S best 

begin 

initialise a solution S current and temperature T 

while (T < T 0 ) { // outer loop 

k = 0 

while (k < N 3 ) { // inner loop 

if (T > T threshold ) S new = generate solution via 

exchange method 

else 

S new = generate solution via swap methods 

k= k + 1 

r = random (0, 1) 

∆C = cost (S new ) – cost (S current ) 

if (r < exp (–∆C/T)) { 

S current = S new 

if (cost (S best ) > cost (S current )) 

S best = S current 

} 

} // end of inner loop 

T =αT 

} // end of outer loop 

Output the best solution S best 

IV. EXPERIMENTAL RESULTS 

The algorithm has been implemented in C++ and the 

results have been obtained on a personal computer with 

an INTEL CPU 2.4 GHz and 4 GB RAM. A Gaussian 

elimination method is used to find the total transition 

probabilities according to the STT of an FSM. 

ESSPRESSO is used to minimise the circuit for each state 

assignment. The product terms from this minimisation 

determine the number of cubes for that assignment. 

Switching activity is calculated by (6). T, T threshold and T 0 

are set to 10000, 100 and 0.1, respectively. In order to 

balance the required solution quality and computational 

time, temperature schedule coefficient α is selected to 

0.95 and 0.8 in the rough annealing stage and focusing 

annealing stage, respectively. Based on the numerous 

experimental results, when γ is 0.3, it performs the best 

trade-off between area and power consumption. 

The results are given in Table I, in which the first 

column shows the name of the circuit, the second column 

shows the number of states for the given circuit in the 

first column. Next three columns show comparison 

results among GA [8], MOGA [7] and the proposed 

method in terms of CPU time. The proposed method can 

convergence quicker than results compared to GA 

method in [8]. MOGA minimises the logical expressions 

via communication with ESSPRESSO, resulting that it 

takes significant more time than the proposed method. 

It can be seen in Table II that on average the proposed 

method produces results requiring 13.2% fewer product 

terms and 44.1% less switching activity compared to 

results obtained from NOVA [19]. Methods used in [20] 

and [21] achieve good power reduction but paying 

penalty of area consumption. MOGA [7] and GA [8] 

perform well in both area and power. The proposed 

algorithm outperforms other methods in both area saving 

and less power consumption in the tested suite. 

TABLE I. 

RECENTLY PUBLISHED RESULTS IN TERMS OF CPU TIME 

Circuits States GA[8] (s) MOGA[7] Ours (s) 

bbara 10 0.17 0h and 8 mins 0.12 

cse 16 0.59 3hs and 9 mins 1.1 

donfile 24 0.77 6hs and 4 mins 1.58 

keyb 19 1.61 3hs and 32 mins 0.87 

modulo12 12 0.13 5hs and 56 mins 0.15 

planet 48 2.75 25hs and 23 mins 2.77 

s1 20 4.37 6hs and 0 min 3.94 

styr 30 4.44 6hs and 5 mins 2.57 

ex1 20 3.26 6hs and 7 mins 2.68 

ex4 14 0.27 6hs and 1 mins 0.38 

opus 10 0.21 0h and 40 mins 0.22 

Total 606 18.57 69h and 5 mins 16.38 

V. CONCLUSIONS 

In the paper, two-stage simulated annealing based 

algorithm approach to the state assignment problem is 

proposed with the aim of minimising area and power 

dissipation for sequential circuits. By using designed twostage 

annealing approach, the algorithm is able to find the 

best assignment with fast convergence, which has 

reduced switching activity to minimise the power 

dissipation and the area simultaneously. By combing the 

best and current solutions, it utilises the experience of 

past solutions, overcoming the problem that ranking 

system in GA selection takes significant runtime. As a 

result, the algorithm outperforms the existing GA-based 

FSM state-encoding strategies achieving 13.2% fewer 

product terms and 44.1% less switch compared to NOVA 

and is therefore more suitable for area/power-optimised 

realisation of FSMs. 


This work was supported by a grant (No. 11MS011) 

from State Key Lab of ASIC and System, China. 

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[5] J. H. Holland, Adaptation in Natural and Artificial Systems, 

University of Michigan Press, 1975. 

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algorithm,” IEE Proc. Comput. Digit. Tech., vol. 142, pp. 

279-286, 1995. 

[7] B. A. Al Jassani, N. Urquhart, A. E. A. Almaini, “State 

assignment for sequential circuits using multi-objective 

genetic algorithm,” IET Proc Comput. Digit. Tech., vol. 5, 

pp. 296-305, 2011. 

[8] Y. Xia, and A. E. A. Almaini, “Genetic algorithm based 

state assignment for power and area optimisation,” IET 

Proc Comput. Digit. Tech., vol. 149, pp. 128–133, 2002. 

[9] S. Chattopadhyay and P. Reddy, “Finite state machine state 

assignment targeting low power consumption,” IET Proc 

Comput. Digit. Tech., vol. 151, pp. 61–70, 2004. 

[10] S. Chattopadhyay, “Area conscious state assignment with 

flip flop and output polarity selection for finite state 

machine synthesis genetic algorithm approach,” Comput. J., 

vol. 48, pp. 443-450, 2005. 

[11] W. T. Shiue, “Novel state minimization and state 

assignment in finite state machine design for low power 

portable devices,” Integration. VLSI J., vol. 38, pp. 549- 

570, 2005. 

[12] S. Goren and F. J. Ferguson, “On state reduction of 

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Electr. Eng., vol. 33, pp. 58-69, 2007. 

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stochastic search aided with simulated annealing,” America 

J. Eng. Appl. Sci., vol. 2, pp. 710-714, 2009. 

[14] T. A. Dolotta, and E.J. McCluskey, “The coding of internal 

states of sequential circuits,” IEEE Trans. Electron. 

Comput., vol. EC-13, pp. 549-562, 1964. 

[15] S. Chattopadhyay, and P. N. Reddy, “Finite state machine 

state assignment targeting low power consumption,” IET 

Proc Comput. Digit. Tech., vol. 151, pp. 61-70, 2003. 

[16] Y. Q. Sheng, A. Takahashi, S. Ueno, “2-Stage Simulated 

Annealing with Crossover Operator for 3D-Packing 

Volume Minimization,” Proceedings of the 17th Workshop 

on Synthesis And System Integration of Mixed Information 

Technologies, pp. 227-232, 2012. 

[17] H. T. Wang; Z. J. Wang; J. Luo, “A simulated annealing 

algorithm for single container loading problem,” 

Proceedings of the 9th Intl. Conf. on Service Systems and 

Service Management, pp. 551-556, 2012. 

[18] A. E. A. Almaini, N. Zhuang, and F. Bourset, 

“Minimisation of multioutput Reed–Muller binary decision 

diagrams using hybrid genetic algorithm,” IEE Electron. 

Lett., vol. 31, pp. 1722-1723, 1995. 

[19] T. Villa, and A. Sangiovanni-Vincentelli, “NOVA: state 

assignment of finite state machine for optimal two-level 

logic implementation,” IEEE Trans. Comput. Aided Des. 

Integr. Circuits Syst., vol. 9, pp. 905-924, 1990. 

[20] S. K. Hong, I. C. Park, S. H. Hwang, and C. M. Kyung, 

“State assignment in finite state machines for minimal 

switching power consumption,” IEE Electron. Lett., vol. 30, 

pp. 627-629, 1994. 

[21] S. J. Wang, and M. D. Horng, “State assignment of finite 

state machines for low power applications,” IEE Electron. 

Lett., vol. 32, pp2323-2324, 1996. 

Meng Yang received Bachelor of 

Engineering (Honor) degree in Electrical 

Engineering from Shanghai University, 

Shanghai, China, in 1999. He received 

Master of Science with distinction in 

Electronics and Communication 

Engineering and Ph.D. in Electronics from 

School of Engineering Edinburgh Napier 

University, Edinburgh, UK, in 2002 and 2006, respectively. 

Currently he is a lecturer of Department of Microelectronics, 

School of Information Science and Technology, Fudan 

University, Shanghai, China. His research interests include 

algorithms in FPGA design automation, logic synthesis, and 

dynamic reconfigurable FPGA automation design. He has 

published more than 30 research papers. 

Dr. Yang is a member of IET and Chairman of Young 

Member Section of IET Shanghai Branch. 

TABLE II. 

EXPERIMENTAL RESULTS SHOWING POWER AND AREA IN COMPARISON 

Circuits 

NOVA[19] MOGA[7] GA[8] Hong[20] Wang[21] This paper 

area Power area power area Power Area power area power area Power 

bbara 24 0.495 22 0.49 22 0.317 26 0.295 26 0.279 22 0.277 

bbsse 30 1.5 28 0.663 27 0.783 31 0.856 31 0.776 27 0.758 

cse 46 0.604 43 0.39 43 0.355 50 0.292 48 0.239 43 0.250 

donfile 28 1.75 22 1.375 36 1.6 40 1.083 45 1.125 22 1.458 

keyb 48 1.466 46 0.98 46 0.674 52 0.647 58 0.556 46 0.533 

modulo12 12 1 10 0.75 12 0.583 12 0.583 12 0.5 10 0.568 

planet 87 2.831 81 2.49 86 2.424 101 1.153 103 0.984 81 1.680 

s1 80 1.698 43 1.37 66 1.48 85 1.131 91 1.175 43 1.188 

sand 97 1.085 94 0.585 89 0.765 110 0.604 109 0.61 92 0.666 

styr 94 1.278 78 1.1 88 0.943 101 0.578 99 0.553 78 0.578 

ex1 44 1.358 48 0.78 52 0.842 49 0.755 47 1.135 48 0.754 

ex4 19 1.316 13 0.568 14 0.421 16 0.495 18 0.957 13 0.476 

opus 16 0.812 15 0.49 15 0.556 17 0.524 17 0.712 15 0.471 

train11 9 0.619 10 0.414 10 0.339 9 0.36 10 0.714 10 0.302 

Total 634 17.812 553 12.445 606 12.082 699 9.356 714 10.315 550 9.959 

Improved% 0% 0% -13% -30% -4% -32% 10% -47% 13% -42% -13.2% -44.1% 



A Rotation-based Data Buffering Architecture for 

Convolution Filtering in a Field Programmable 

Gate Array 

Zhijian Lu 

College of Computer Science and Technology Harbin Engineering University, Harbin, China 

Email: luzhijian@hrbeu.edu.cn 

Yanxia Wu, Zhenhua Guo, Guochang Gu 

College of Computer Science and Technology Harbin Engineering University, Harbin, China 

Email: {wuyanxia, guozhenhua, guguochang}@hrbeu.edu.cn 

Abstract—Convolution filtering applications range from 

image recognition and video surveillance. Two observations 

drive the design of a new buffering architecture for convolution 

filters. First, the convolutional operations are inherently 

local; hence every pixel of the output feature maps is calculated 

by the neighboring pixels of the input feature maps. 

Even though the operation is simple, the convolution filtering 

is both computation-intensive and memory-intensive. 

For real-time applications, large amounts of on-chip memories 

are required to support massively parallel processing 

architectures. Second, to avoid access to external memories 

directly, the data that are already stored in on-chip memories 

should be used as many times as possible. Based on these 

two observations, we show that for a given throughput 

rate and off-chip memory bandwidth, a rotation-based data 

buffering architecture provide the optimum area-utilization 

results for a particular design point, which are commonly 

used applications in recognition area. 

Index Terms—convolution filtering, Field Programmable 

Gate Arrays (FPGAs), data buffering 


Convolution filters are the computational models that 

are widely used in recognition and video processing domains 

[1][2][3][4]. The computation of convolution requires 

not only the high computational capability but also 

large memory bandwidth, especially when high-definition 

images and videos have to be processed in real-time. In 

these applications, convolution filtering plays an essential 

role [5][6]. Generally, external memories are used to contain 

input image pixels, but the memory bandwidth cannot 

satisfy the requirement of the optimal throughput directly. 

Hence intermediate buffers by means of on-chip 

memories are adopted to avoid access to external memories 

directly [7][8]. To load as many pixel values as needed 

to the convolution filter in one cycle, multiple memory 

ports are attached to intermediate data buffers. Once a 

pixel value is loaded, it can be reused for the corresponding 

successive convolutions to avoid accessing it from 

off-chip memories repetitively. As a result, the requirements 

for off-chip memory bandwidth are reduced. 

Convolution architecture with a complete convolution 

architecture is adopted in [7], where a set of linear shift 

registers are used to move a window over the input 

image. The input image is divided in rows, each with a 

fixed length according to the input image row length, and 

the height according to the convolution window height. 

Each pixel in the input image needs to be loaded only 

once to the intermediate data buffer and with a fixed minimum 

external memory bandwidth. In case the size of 

input image or convolution window become large, FPGA 

implementations become very expensive, which will cost 

a significant amount of FPGA resources [7][8]. 

There are alternative buffering architectures that internal 

buffers only store a small portion of pixels [7][9]. 

Each group of shift registers in the convolution window 

receives the pixels belonging to consecutive rows of input 

image. Compared with the aforementioned methods, a 

great shift register reduction is achieved. However, multiple-dataflow 

is needed to feed data to the internal buffer. 

Pixels in the input image need to be read repetitively 

from external memories depending on the size of convolution 

window. And to keep the maximum throughput 

rate, this leads to a sharp increase in terms of external 

memory bandwidth requirement. 

In this paper, we are concerned with the implementation 

of convolution filters in FPGA and we design a alternative 

buffering architecture for convolution filters that 

shows good balance between on-chip resource utilization 

and external memory bus bandwidth. 

II. ROTATION-BASED DATA BUFFERING ARCHITECTURE 

Yanxia Wu is the corresponding author. 


doi:10.4304/jcp.8.6.1411-1416


Figure 1. Conceptual view of an convolver and an image 

In this section, we will first introduce the convolution 

filtering implementation strategy. The advantages and 

disadvantages of existing implementation architectures 

will be discussed. Then we will present the rotation-based 

data buffering architecture. In Fig. 1, we show the conceptual 

view of a convolution filter moving over an 

input image, which will be used in the following 

sections. 

A. Convolution Filter Implementation Strategy 

The convolution of an image is defined by equation 

1: 

 

∑ ∑ , ∙ , 

, 

R 

S 

Input Image 

/ / 

/ / 

(1) 

 

where , is the convolved pixel on the output image, 

, is the pixel value from the input image, and , is 

the convolution kernel weight. To calculate the convolution 

, , each pixel , from a window of input 

 

image centered on , is multiplied by the corresponding 

convolution kernel of weights, and then the 

products are accumulated to produce the output value. 

 

Because the two-dimensional convolution , of each 

pixel , requires the values of its 1 immediate 

neighbors before being able to process that pixel, more 

columns than needed will be read within the same transaction. 

Each output pixel requires multiplyaccumulations, 

all of which can be performed in parallel. 

To accelerate the computation of convolution filter, multiple 

data in a convolution window need to be accessed 

simultaneously, so the calculations can be performed in 

parallel. 

B. Multiple Dataflow Single Convolution Architecture 

(MDSCA) 

In order to eliminate the shift register arrays in [7], 

multiple dataflow single convolution architectures are 

adopted in [8][10]. In these architectures, small portion of 

image pixels are loaded to the convolution filter. However, 

with fewer shift register arrays, the pixels can no 

longer be loaded to the convolution window in zigzag 

order. Instead of that, pixels belonging to consecutive 

rows are read into the shift register simultaneously. 

Groups of FIFOs are included to feed the pixels to the 

shift registers. After one column of pixels are fed into the 

convolution filter, the convolution window moves to a 

next position. 

Fig. 2 shows a multiple dataflow single convolution 

architecture using an input/output bus, which can completely 

eliminate the shift register arrays in [7]. The convolution 

window pixel registers receive the pixels belonging 

to consecutive rows of the original image through 

stacks. Multiple dataflow single convolution architecture 

requires much larger bandwidth than the single dataflow 

architecture. The shift register arrays are completely 

eliminated. Extra memory bandwidth is used to reduce 

the number of shift registers. To compute a single cycle 

convolution, one new pixel per row is needed at 

every cycle. The total of pixels transferred and one 

result produced means that a bandwidth of 1 bytes 

per cycle is needed. 

C. Single Dataflow Complete Convolution Architecture 

(SDCCA) 

To avoid directly access to external memories, FPGA 

on-chip memories are used as intermediate data buffers 

[7]. In Fig. 3, a single dataflow complete convolution 

architecture, makes use of on-chip shift register arrays to 

move a window over the input image. To extract 

pixels from input image, a single dataflow strategy has 

been adopted. Pixels are fed from external memories in a 

zigzag order, until 1 complete lines and the first 

pixels in the next line are contained within a series of 

linear shift registers. From that moment on, all the pixels 

belonging to the first convolution window are 

available for the processing element. Each time a new 

pixel is loaded, the convolution window moves to a new 

position until the entire image has been visited. The 

throughput of this architecture is one clock per pixel. In 

[7], 1 sets of shift registers with a length of , 

are employed to keep data before moving them to the 

convolution filter, and sets of registers, each with 

shift registers, are used for the convolution filter. These 

shift registers, which enable arbitrary size convolution 

filter to work with a single data stream, require no more 

than one pixel per clock external memory bandwidth. 

Pixels in the input image need to be read only once. The 

side-effect of this architecture is that in order to make this 

single data stream architecture work, 1 complete 

rows must be read from external memory first, therefore 

storing these data within a set of shift registers would be 

very expensive in FPGA implementation when the size of 

input image or the size of convolution filter is large. 

D. Rotation-based Multiple dataflow Buffering Architecture 

(RMDBA) 

In order to reuse data that are already stored in on-chip 

buffers as many times as possible, we proposed a rotation-based 

data buffering architecture. Fig.4 illustrates 

continuous convolution filter in a row-wise direction, 

where the two adjacent filter windows share 1 columns. 

The architecture of these sliding windows includes 

R contiguous convolution filter windows, which share 

1 columns in the row-wise direction. If the calculations 

of these convolution kernels are performed at the 

same time, a much higher level of data reusing will be 



F 

I 

F 

O 

S 

shift 

registers 

off-chip memory 

and FIFO 

. 

. 

. 

. 

. 

. 

F 

I 

F 

O 

. 

. 

. 

S 

shift 

registers 

. 

. 

. 

convolution filter array 

F 

I 

F 

O 

S 

shift 

registers 

Figure 2. Multiple dataflow single convolution architecture 

off-chip memory and FIFO 

S 

shift 

registers 

(N-S) Shift registers 

. 

. 

. 

. 

. 

. 

. 

. 

. 

S 

shift 

registers 

. 

. 

. 

. 

. 

. 


(N-S) Shift registers 

S 

shift 

registers 

achieved compared with the multiple dataflow single 

convolution architecture. Fig. 5 illustrates the rotationbased 

multiple dataflow architecture we proposed. The 

number of shift register arrays is extended to Y to hold all 

the pixels in the area as depicted in Fig. 4. Unlike 

the multiple dataflow single convolution architecture and 

the single dataflow complete convolution architecture, the 

pixel data in each set of shift register array are not simultaneously 

fed to the convolution filter window, but in a 

serial type instead. One register in the shift register group 

is useable in each cycle, and a rotationally selfincrementing 

counter is used to address the register in the 

output. Consequently, pixels in all of a same row in the 

input, belonging to adjacent windows in the row-wise 

direction, are available to the convolution filter in each 

cycle. After cycles, all the data in the place have 

Figure 3. Single dataflow complete convolution architecture 

been sent to the convolution filter, and then shift register 

arrays will be updated. A new row of data will be moved 

in from the FIFO and moves the area to next position 

effectively. The architecture for the convolution filter 

using rotation-based data buffering architecture is not the 

same as the aforementioned architectures. For each 

convolution window, input pixels are fed column-bycolumn, 

therefore one-column convolution line can be 

calculated, and it will take cycles to complete all the 

calculation for each convolution window. When neighboring 

windows are available, entire R one-column convolution 

can be processed simultaneously. 

In order to achieve the throughput rate of 1 cycle/pixel, 

multiple dataflow must be loaded to update the convolution 

window. Compared with the multiple dataflow single 



Figure 4. R simultaneous convolution windows in a area 

off-chip memory 

. . . . . . 

F 

I 

F 

O 

F 

I 

F 

O 

column 1 column S-1 column S column Y 

F 

I 

F 

O 

F 

I 

F 

O 

. . . 

. . . 

R . . . 1 

R . . . 1 

R . . . 1 

R . . . 1 

. . . . . . 


Figure 5. Rotation-based data buffering architecture 

convolution architecture the window in the rotation-based 

architecture is updated every cycle. In this case, shift 

registers can move every cycles. pixels in all will be 

loaded from off-chip memories every cycles. So the 

external memory bandwidth is / pixels/clock. This 

means that for most convolution filter applications approximately 

twice of the external memory bandwidth 

requirement is needed. 

III. ARCHITECTURE SELECTION 

In this section, we will consider an input image size of 



1280720 with 8 bits/pixel and a convolution kernel size 

of 77 as a case study. The operation will fetch image 

pixels from external memories, and store back to external 

memories after the convolution operation. In addition to 

this we will use a memory bus word length of 256-bits 

and a burst length (BL) of 8 words (i.e. 16 pixels). In 

Table I, we have summarized the main features of the two 

and the proposed architectures: area-utilization measured 

in terms of register pixels and memory pixels. Flip-flop 

count was obtained by multiplying the number of shift 

registers and memory pixels by bit per pixel; 

TABLE 1. 

FEATURES OF DIFFERENT CONVOLUTION FILTER FOR A WINDOW 

architecture 

register 

pixels 

memory pixels 

throughput 

(cycles/pixel) 

ff count 

bandwidth (pixels/cycle) 

MDSCA 1 5496 7 

SDCCA 

1 

 

1 49336 1 

RMDBA 1 2392 1.9 

TABLE 2. 

AREA UTILIZATION OF DIFFERENT ARCHITECTURES FOR VARIOUS CONVOLUTION FILTER WINDOW SIZE 

filter size 

MDSCA SDCCA RMDBA 

flip-flop count flip-flop count flip-flop count 

33 456 16536 760 

55 840 32936 1512 

77 5496 49336 2392 

99 1800 65736 3400 

11 11 2376 82136 4536 

13 13 3016 98536 5800 

15 15 3720 114936 7192 

17 17 4488 131336 8712 

19 19 5320 147736 10360 

throughput, given in terms of cycles/pixel; and external 

memory bandwidth requirements, given in terms of pixels/cycle. 

We used different FPGA resources to implement 

FIFOs and shift registers depending on specific 

FPGA devices. 

For comparison, the area-utilization will be evaluated 

in terms of flip-flops. The last two columns of Table I 

show the results of flip-flop count and external memory 

bandwidth requirement for the case study. The SCPB 

architecture shows the most area-efficient feature at the 

cost of much more requirement of the external memory 

bandwidth. 

In order to choose the optimum architecture for a particular 

design point, a suitable metric that consists in 

maximizing the throughput with respect to the amount of 

resources will be used. The evaluation metric was proposed 

in [10] that the product throughput in terms of cycles/pixel 

times flip-flop number is the metric. For a particular 

design point, the architecture will minimize the 

metric value and maximize the degree of area efficiency. 

We used the same concept in our architecture. Table 2 

shows the corresponding product of flip-flop count and 

throughput for convolution window size from 3 to 19 for 

the three architectures. We assumed a same output 

memory bandwidth of 1 pixel/cycle. In Fig. 6, we show 

the aforementioned metric comparisons and the remaining 

variable are the same described for the case study. In 

the bar diagram in Fig. 6, we can observe that RMDBA 

architecture is superior to the rest of the architecture for 

window size 7, and for the other window size MDSCA is 

superior. Window size 5 and 7 are the most frequently 

used convolution window in practical applications. As the 

size of input image gets larger, tradeoffs must be made, 

depending on different FPGA resources and available offchip 

memory bandwidth. 


In this paper, we proposed a rotation-based data buffering 

architecture for convolution filtering in FPGA. Compared 

with the direct implementation of the prior-arts, the 

new technique requires less FPGA resources and lowers 

off-chip memory bandwidth and retains the optimum 

throughput for a particular design point, therefore it is suitable 

for low-cost FPGA implementation. 

ACKNOWLEDGEMENTS 

This work is supported by the National Natural Science 

Foundation of China No. 61003036 and the Natural 

Science Foundation of Heilongjiang Province of China 

under Grant No. QC2010049 and Fundamental Research 

Funds for the Central Universities (No. HEUCFT1202, 

No. HEUCF100606). 



Figure 6. Bar diagram comparing the area efficiency metric for different architectures and for window sizes from 3x3 to 19x19 using the parameters of 

the case study. The lower the bar, the more efficient. 

REFERENCE 

[1] Gonzalez, R.C. and R.E. Woods, “Digital Image Processing,” 

Prentice Hall Press, 2002 

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[3] Z. Wang and X. Sun, “Orthogonal Maximum Margin Projection 

for Face Recognition,” Journal of Computers, 2(7): 

pp.377-383, 2012 

[4] B. Zhu and W. Jin, “Radar Emitter Signal Recognition 

Based on EMD and Neural Network,” Journal of Computers, 

6(7): pp.1413-1420, 2012 

[5] Hecht, V. and K. Ronner, “An Advanced Programmable 

2D-convolution Chip for Real Time Image Processing,” 

IEEE International Sympoisum on Circuits and Systems, 

pp.1897-1900, 1991 

[6] Leblebici, Y., et al., “A Fully Pipelined Programmable Real-time 

(3×3) Image Filter Based on Capacitive Thresholdlogic 

gates,” Proceedings of IEEE International Symposium 

on Circuits and Systems, vol.3, pp. 2072-2075, 1997 

[7] Bosi, B., G. Bois, and Y. Savaria, “Reconfigurable Pipelined 

2-D Convolvers for Fast Digital Signal Processing,” 

IEEE Transactions on Very Large Scale Integration (VLSI) 

Systems, 7(3): pp. 299-308, 1999 

[8] Liang, X., J. Jean, and K. Tomko, “Data Buffering and Allocation 

in Mapping Generalized Template Matching on 

Reconfigurable Systems,” The Journal of Supercomputing, 

19(1): pp. 77-91, 2001 

[9] Nakajima, M., et al., “A 40GOPS 250mw Massively Parallel 

Processor Based on Matrix Architecture,” IEEE International 

Solid-State Circuits Conference, pp.1616-1625, 

2006 

[10] Cardells-Tormo, F. and P.L. Molinet, “Area-efficient 2-D 

Shift-variant Convolvers for FPGA-based Digital Image 

Processing,” IEEE Workshop on Signal Processing Systems 

Design and Implementation, pp. 209-213, 2005 

Zhijian Lu is a Ph.D. student in College of Computer Science 

and Technology of Harbin Engineering University, Harbin, China. 

His current research interest includes neural network, reconfigurable 

computing and image processing. 

Yanxia Wu is Associate Professor in College of Computer Science 

and Technology of Harbin Engineering University, Harbin, 

China. Her current research interests include safe compiler, reconfigurable 

compiler and computer architecture. 

Zhenhua Guo is a Ph.D. student in College of Computer Science 

and Technology of Harbin Engineering University, Harbin, China. 

His current research interest includes reconfigurable computing 

and embedded system. 

Guochang Gu is Professor in College of Computer Science and 

Technology of Harbin Engineering University, Harbin, China. His 

main research interests include embedded systems and safe compiler. 



AT-Mine: An Efficient Algorithm of Frequent 

Itemset Mining on Uncertain Dataset 

Le Wang a,b ,Lin Feng a,b, *, and Mingfei Wu a,b 

a School of Computer Science and Technology, Faculty of Electronic Information and Electrical Engineering, Dalian 

University of Technology, Dalian, Liaoning, China 116024. 

b 

School of Innovation and Experiment, Dalian University of Technology, Liaoning, China 116024. 

Email: lelewater@gmail.com; fenglin@dlut.edu.cn; merphy.wmf@gmail.com 

Abstract—Frequent itemset/pattern mining (FIM) over 

uncertain transaction dataset is a fundamental task in data 

mining. In this paper, we study the problem of FIM over 

uncertain datasets. There are two main approaches for FIM: 

the level-wise approach and the pattern-growth approach. 

The level-wise approach requires multiple scans of dataset 

and generates candidate itemsets. The pattern-growth 

approach requires a large amount of memory and 

computation time to process tree nodes because the current 

algorithms for uncertain datasets cannot create a tree as 

compact as the original FP-Tree. In this paper, we propose 

an array based tail node tree structure (namely AT-Tree) to 

maintain transaction itemsets, and a pattern-growth based 

algorithm named AT-Mine for FIM over uncertain dataset. 

AT-Tree is created by two scans of dataset and it is as 

compact as the original FP-Tree. AT-Mine mines frequent 

itemsets from AT-Tree without additional scan of dataset. 

We evaluate our algorithm using sparse and dense datasets; 

the experimental results show that our algorithm has 

achieved better performance than the state-of-the-art FIM 

algorithms on uncertain transaction datasets, especially for 

small minimum expected support number. 

Index Terms—data mining, frequent itemset, frequent 

pattern, uncertain dataset 


Frequent itemsets mining (FIM) over transaction 

dataset is an important and common topic in data mining. 

The algorithm Apriori [1] was first proposed to discover 

frequent itemsets from market basket data. Since then, 

FIM algorithms were constantly proposed for various 

application domains, such as those for complete frequent 

itemsets [1, 2, 3, 4, 5, 6, 7], for maximal frequent itemsets 

[8, 9, 10, 11, 12], for closed frequent itemsets [13, 14, 15] 

and for frequent sequential patterns [16] and high uitlity 

itemsets [17, 18, 19, 20]. These algorithms concern 

precise transaction datasets, that is, all items can be 

described with a certain value. However, many real-world 

applications generate or require uncertain transaction 

datasets in which items can only be described with an 

existential probability. For example, some diseases can 

Manuscript received January 12, 2013; revised February. 11, 2013; 

accepted March 1, 2011. 

This work was supported by National Natural Science Foundation of 

P.R. China (61173163, 51105052), Program for New Century Excellent 

Talents in University (NCET-09-0251); and Liaoning Provincial 

Natural Science Foundation of China (Grant No. 201102037). 

Corresponding Author: Lin Feng; E-mail: fenglin@dlut.edu.cn. 

not be definitely diagnosed by a set of symptons - they 

can only be ascertained as a probability value; the 

locations of a moving object obtained through RFID or 

GPS devices are not precise [21, 22]; the shopping habits 

mined from an e-commerce website are also probability 

values for predicting what a customer will buy in the 

future. 

TABLE I. 

AN EXAMPLE OF UNCERTAIN DATASET 

TID Transaction itemset 

T 1 (a: 0.8), (b: 0.7), (d: 0.9), (f: 0.5) 

T 2 (c: 0.8), (d: 0.85), (e: 0.4) 

T 3 (c: 0.85), (d: 0.6), (e: 0.6) 

T 4 (a: 0.9) , (b: 0.85), (d: 0.65) 

T 5 (a: 0.95), (b: 0.7), (d: 0.8) , (e: 0.7) 

T 6 (b: 0.7), (c: 0.65), (f: 0.45) 

Table 1 shows an example of uncertain transaction 

dataset, each transaction of which represents that a 

customer might buy a certain item with a probability. The 

value associated with each item is called the existential 

probability of the item. For instance, the first transaction 

T 1 in Table 1 shows that a customer might purchase “a”, 

“b”, “d” and “f” with 80%, 70%, 90% and 50% chances 

in the future respectively. 

In recent years, FIM over uncertain datasets has 

become an important topic in data mining [23, 24, 25, 26, 

27, 28, 29, 30, 31, 32]. The existing algorithms can be 

classified into two main categories: the level-wise 

approach and the pattern-growth approach. The 

algorithms U-Apriori [31], MBP [28] and IMBP [26] 

employ the level-wise approach, and all these algorithms 

generate candidates and require multiple scans of the 

dataset. The algorithms UH-Mine [30], UFP-Growth [30], 

and UF-Growth [25, 29] employ the pattern-growth 

approach. UH-Mine is based on the algorithm H-Mine [5]; 

UF-Growth is based on the classical algorithm FP- 

Growth [2] and employs the same method as FP-Growth 

for mining frequent itemsets on uncertain transaction 

itemsets. Both UH-Mine and UF-Growth cannot create a 

tree as compact as FP-Tree for maintaining transaction 

itemsets, thus they require a large amount of memory and 

computational time to process tree nodes, especially on 


doi:10.4304/jcp.8.6.1417-1426


large datasets. UFP-Growth [30] also builds the UFP- 

Tree in the same manner as FP-Growth, and the UFP- 

Tree is as compact as the original FP-Tree. However 

UFP-Mine generates candidates, and identifies frequent 

itemsets by additional scan of dataset. 

So our thought is to build a tree as compact as the 

original FP-Tree and avoid generating candidates. To 

achieve this goal, we propose a tree structure named AT- 

Tree (Array based Tail node Tree) and a new algorithm 

named AT-Mine. AT-Mine needs just two scans of 

dataset. In the first scan, it finds frequent items and 

arranges them in descending order of support number. In 

the second scan, it constructs an AT-Tree using 

transaction itemsets like the method of FP-Growth, while 

maintains the probability information of each transaction 

to a tail node and an array. Then AT-Mine can directly 

mine frequent itemsets from AT-Tree without additional 

scan of datasets. The experimental results show that AT- 

Mine is more efficient than the algorithms MBP, UF- 

Growth and CUFP-Mine. 

The contributions of this paper are summarized as 

follows: 

(1) We propose a new tree structure named AT-Tree 

(Array based Tail node Tree) for maintaining 

important information related to an uncertain 

transaction dataset; 

(2) We also give an algorithm named AT-Mine for 

FIM over uncertain transaction datasets based on 

AT-Tree; 

(3) Both sparse and dense datasets are used in our 

experiments to compare the performance of the 

proposed algorithm against the state-of-the-art 

algorithms based on level-wise approach and 

pattern-growth approach, respectively. 

The rest of this paper is organized as follows: Section 

2 is the description of the problem and definitions; 

Section 3 describes related works; Section 4 describes our 

algorithms AT-Mine; Section 5 shows the experimental 

results; and Section 6 gives the conclusion and discussion. 

II. 

PROBLEM DEFINITIONS 

Let D = {T 1 , T 2 , …, T n } be an uncertain transaction 

dataset which contains n transaction itemsets and m 

distinct items, i.e. I= {i 1 , i 2 , …, i m }. Each transaction 

itemset is represented as {i 1 :p 1 , i 2 :p 2 , …, i v :p v }, where {i 1 , 

i 2 , …, i v } is a subset of I, and p u (1≤u≤v) is the existential 

probability of item i u in a transaction itemset. The size of 

dataset D is the number of transaction itemsets and is 

denoted as |D|. An itemset X = {i 1 , i 2 , …, i k }, which 

contains k distinct items, is called a k-itemset, and k is the 

length of the itemset X. 

We adopt some definitions similar to those presented 

in the previous works [1, 23, 28, 29, 30, 31, 32]. 

Definition 1: The support number (SN) of an itemset X in 

a transaction dataset is defined by the number of 

transaction itemsets containing X. 

Definition 2: The probability of an item i u in transaction 

T d is denoted as p(i u ,T d ) and is defined by 

p( i , T ) = p 

(1) 

u d u 

For example, in Table 1, p({a},T 1 ) = 0.8, p({b},T 1 ) = 

0.7, p({d},T 1 ) = 0.9, p({f},T 1 ) = 0.5. 

Definition 3: The probability of an itemset X in a 

transaction T d is denoted as p(X, T d ) and is defined by 

p( XT , 

d) = ∏ pi ( , ) 

iu 

X, 

X T u 

T 

∈ ⊂ 

d 

d 

(2) 

For example, in Table 1, p({a, b},T 1 ) = 0.8×0.7 = 0.56, 

p({a, b},T 4 ) = 0.9×0.85=0.765, p({a, b},T 5 ) = 

0.95×0.7=0.665. 

Definition 4: The expected support number (expSN) of 

an itemset X in an uncertain transaction dataset is denoted 

as expSN(X) and is defined by 

expSN( X ) = ∑ P( X , T ) 

Td⊇X, 

T d 

d∈D 

(3) 

For example, expSN({a, b}) = p({a, b},T 1 ) + p({a, 

b},T 4 ) + p({a, b},T 5 ) = 0.56+0.765+ 0.665 = 1.99. 

Definition 5: Given a dataset D, the minimum expected 

support threshold η is a predefined percentage of |D|; 

correspondingly, the minimum expected support number 

(minExpSN) is defined by 

minExpSN = | D | × η 

(4) 

In the papers [23, 25, 26, 29, 30, 31], an itemset X is 

called a frequent itemset if its expected support number is 

not less than the value minExpSN. Mining frequent 

itemsets from an uncertain transaction dataset means 

discovering all itemsets whose expected support numbers 

are not less than the value minExpSN. 

Definition 6: The minimum support threshold λ is a 

predefined percentage of |D|; correspondingly, the 

minimum support number (minSN) in a dataset D is 

defined by 

minSN = | D | × λ 

(5) 

III. RELATED WORK 

Most of algorithms of FIM on uncertain datasets can 

be classified into two main categories: the level-wise 

approach and the pattern-growth approach. The main idea 

of the level-wise algorithms comes from Apriori [1] 

which is the first level-wise algorithm for FIM. It is to 

iteratively generate candidate (k+1)-itemsets from 

combinations of frequent k-itemsets (k≥1), and calculate 

expected support numbers of candidates by one scan of 

dataset. Its main shortcoming is that it needs multiple 

scans of dataset and generates candidate itemsets. 

The main idea of the pattern-growth approach comes 

from the algorithm FP-Growth [2] which is the first 

pattern-growth algorithm. It is also an iteration approach, 

but it does not mine frequent itemsets by the combination 

method like Apriori. It finds all frequent items under the 

condition of frequent k-itemset X, and generates frequent 

(k+1)-itemsets by the union of each one of those frequent 

items and X (k≥1). It maintains all transaction itemsets to 

a FP-Tree [2] with two scans of dataset. It will generate a 

conditional tree (which is also called prefix FP-Tree or 

sub FP-Tree) for each frequent itemset X. Thus it will 

find all frequent items under the condition of X by 

scanning this conditional tree instead of the whole dataset. 



FP-Tree is created by the following rules: (1) transaction 

itemsets are rearranged in descending order of support 

numbers of items and are inserted to a FP-Tree; (2) 

transaction itemsets will share the same node when the 

corresponding items are the same. 

A. Level-wise Approach 

In 2007, the algorithm U-Apriori was proposed for 

discovering frequent itemsets from uncertain datasets 

[31]. It is based on the algorithm Apriori. U-Apriori is a 

classical level-wise algorithm for FIM on uncertain 

datasets. It starts by finding all frequent 1-itemsets with 

one scan of dataset. Then in each iteration, it first 

generates candidate (k+1)-itemsets using frequent k- 

itemsets (k ≥1), and then identifies real frequent itemsets 

from candidates with one scan of dataset. The iteration 

goes on until there is no new candidate. One important 

shortcoming of U-Apriori is that it generates candidates 

and requires multiple scans of datasets; and the situation 

may become worse with the increase of the number of 

long transaction itemsets or decrease of the minimum 

expected support threshold. 

In 2011, Wang et al. [28] proposed the algorithm 

MBP for FIM on uncertain datasets. The authors 

proposed one strategy to speed up the calculation of the 

expected support number of a candidate itemset: MBP 

will stop calculating the expected support number of a 

candidate itemset if the itemset can be determined to be 

frequent or infrequent in advance. Thus it can achieve a 

better performance than the algorithm U-Apriori. 

In 2012, Sun et al. [26] modified the algorithm MBP, 

and gave an approximate algorithm (called IMBP) for 

FIM on uncertain datasets. The performance of IMBP 

outperforms MBP in terms of running time and memory 

usage. However its accuracy is not stable, and becomes 

lower on dense datasets. 

B. Pattern-growth Approach 

In 2007, Leung et al. [29] proposed a tree-based 

algorithm UF-Growth for FIM on uncertain transaction 

dataset. Firstly, it also constructs a UF-Tree using 

transaction itemsets like the method of FP-Growth; 

secondly, it mines frequent itemsets from the UF-Tree by 

the pattern-growth approach. It creates a UF-Tree by two 

scans of dataset. In the first scan, it finds all frequent 1- 

itemsets, arranges frequent 1-itemsets in descending order 

of support numbers and maintains them in a header table. 

In the second scan, removes infrequent items from each 

transaction itemset, re-arranges the remaining items of 

each transaction itemset in order of the header table, and 

inserts the sorted itemset to a global UF-Tree. It only 

merges nodes that have the same item and the same 

probability when transaction itemsets are inserted to a 

UF-Tree. For example, for two transaction itemsets 

{a:0.50, b:0.70, c:0.23} and {a:0.55, b:0.80, c:0.23}, 

they will not share the node “a” when they are inserted to 

a UF-Tree by lexicographic order because the 

probabilities of item “a” are not equal in these two 

itemsets. Thus UF-Growth requires a large amount of 

memory to store UF-Tree. 

Leung et al. [25] improved the algorithm UF-Growth 

to reduce the size of UF-Tree. The improved algorithm 

considers that the items with the same k-digit value after 

the decimal point have the same probability. For example, 

when two transaction itemsets {a:0.50, b:0.70, c:0.23} 

and {a:0.55, b:0.80, c:0.23} are inserted to a UF-Tree 

by lexicographic order, they will share the node “a” if k is 

set as 1 because both probability values of the two item 

“a” are considered to be 0.5; if k is set as 2, they will not 

share the node “a” because the probabilities of “a” are 

0.50 and 0.55 respectively. The smaller k is, the lesser 

memory the improved algorithm requires. However, the 

improved algorithm still cannot build a UF-Tree as 

compact as the original FP-Tree; moreover, it may lose 

some frequent itemsets. 

UH-Mine [30] is a pattern-growth algorithm. The 

main difference between UH-Mine and UF-Growth is 

that UF-Growth adopts a prefix tree structure while UH- 

Mine adopts a hyperlinked array based structure called H- 

struct [5] (which can also be considered as a tree). UH- 

Mine requires two scans of dataset for creating the 

structure H-struct: in the first scan, it creates a header 

table which maintains sorted frequent 1-items; in the 

second scan, it removes infrequent items from each 

transaction itemset, re-arranges the remaining items in the 

order of the header table, and inserts the sorted 

transaction itemset into an H-struct tree without sharing 

nodes with other transaction itemsets. The header table 

maintains the hyperlink of all nodes with the same item 

name when the itemsets are inserted into an H-struct tree. 

It will achieve a good performance on small datasets. 

However, the H-struct does not share any node and is not 

a compact tree, and this will impact the performance of 

FIM, especially for large datasets. 

The authors of the paper [30] also extend the classical 

algorithm FP-Growth to get the algorithm UFP-Growth 

for FIM on uncertain datasets. UFP-Growth firstly 

generates candidates by the UFP-Tree, and then identifies 

frequent itemsets through additional scan of datasets. Its 

performance is also impacted by the generation of 

candidate itemsets. 

C. The Algorithm CUFP-Mine 

In 2011, Lin et al. [23] proposed the algorithm CUFP- 

Mine for FIM on uncertain transaction datasets. CUFP- 

Mine creates a tree named CUFP-Tree to maintain 

transaction itemsets. A CUFP-Tree is created by two 

scans of dataset. In the first scan, it creates a header table 

for maintaining sorted frequent 1-itemsets; in the second 

scan, when an item Z i in transaction itemset Z ({Z 1 , Z 2 ,…, 

Z i ,.., Z m }) is inserted into a tree, CUFP-Mine generates all 

supersets of item Z i using items Z 1 , Z 2 ,…, Z i , and 

maintains all supersets and their corresponding 

probabilities to a node corresponding to Z i . CUFP-Mine 

only accumulates the probability of each superset if there 

is a corresponding node on the tree for item Z i . The idea 

of CUFP-Mine is that it finds frequent itemsets through 

scanning supersets of each node and calculating expected 

support number of each superset. CUFP-Mine generates 

all combinations of items in an itemset, and maintains 

these combinations to tree nodes. Thus CUFP-Mine 

requires a large amount of computation time and memory 



when the length of itemsets is not very short or on large 

datasets. 

IV. THE ALGORITHM AT-MINE 

The proposed algorithm AT-Mine mainly consists of 

two procedures: (1) creating an AT-Tree; (2) mining 

frequent itemsets from the AT-Tree. We describe the 

structure of an AT-Tree in Section 4.1, give an example 

of the construction of an AT-Tree in Section 4.2, and 

elaborate the algorithm AT-Mine with an example in 

Section 4.3. 

A. Structure of an AT-Tree 

Definition 9: Let itemset X = {i 1 , i 2 , i 3 , …, i u } be a sorted 

itemset, and the item i u is called tail-item of X. When the 

itemset X is inserted into a tree T in accordance with its 

items’ order, the node N on the tree that represents this 

tail-item is defined as tail node of itemset X, and other 

nodes that represent items i 1 , i 2 , …, i u-1 are defined as 

normal nodes. The itemset X is called tail-node-itemset 

for node N. 

Definition 10: Let an itemset X contain itemset Y. When 

itemset X is added to a prefix tree of itemset Y, the 

probability of itemset Y in itemset X, p(Y, X), is defined 

as the base probability of itemset X on the tree T, and is 

denoted as BP(X, Y): 

BP YX , = pYX ( , ) 

(8) 

( ) 

Figure 1. Structure of nodes on an AT-Tree 

The node structure on an AT-Tree is illustrated in 

Figure 1. There are two types of nodes: one is normal 

node, as shown in Figure 1(a), where Name is the item 

name of each node; the other type is tail node, as shown 

in Figure 1(b), where Tail_info is the supplemental 

information that includes 4 fields: (1) bp: a list that keeps 

base probability values of all tail-node-itemsets; (2) len: 

the length of the tail-node-itemset; (3) Arr_ind: a list of 

index values of an array each element of which records 

probability values of items in each sorted transaction 

itemset (see Substep 5.2 in Section 4.2.1 and Step 5 in 

Section 4.2.2, etc.); (4) Item_ind: a list of index values of 

an array that records probability values of each item in a 

sorted transaction itemset (see Substep 10.5 and 10.7 in 

Section 4.3.2, etc., Item_ind is just used in a sub AT- 

Tree). 

B. Construction of an AT-Tree 

The structure of AT-Tree is designed to efficiently 

store the related information on tail nodes. It is 

constructed by two scans of dataset. In the first scan, a 

header table is created to maintain sorted frequent items. 

In the second scan, the probability values of frequent 

items in each transaction itemsets are stored to a list 

according to the order of the header table; the list is then 

added to an array (and its corresponding sequence 

number in the array is denoted as ID); the frequent items 

in each transaction itemset are inserted to an AT-Tree 

according to the order of the header table; the length of 

the itemset and the number ID are stored to the 

corresponding tail node. When the transaction itemsets 

are added to an AT-Tree, they are rearranged in 

descending order of support numbers of items, and share 

the same node/nodes if their prefix items/itemsets are 

identical. Thus the AT-Tree is as compact as the original 

FP-Tree. Moreover, AT-Tree does not lose probability 

information with respect to the distinct probability values 

of the transaction itemsets. 

B.1 The construction algorithm of a global AT-Tree 

A global AT-Tree is the first AT-Tree that maintains 

itemset information of the whole dataset. The 

construction algorithm is described as follows: 

CreateTree(D, η ) 

INPUT: An uncertain database D consisting of n 

transaction itemsets and a predefined minimum expected 

support threshold η . 

OUTPUT: An AT-Tree T. 

Step 1: Calculate the minimum expected support number 

minExpSN, i.e. minExpSN = | D | × η ; count the 

expected support number and support number of 

each item by one scan of dataset. 

Step 2: Put those items whose expected support numbers 

are not less than minExpSN to a header table, and 

sort the items in the header table according to the 

descending order of their support numbers; finish 

the algorithm if the header table is null. 

Step 3: Initially set the root node of the AT-Tree T as null. 

Step 4: Remove the items that are not in the header table 

from each transaction itemset, and sort the 

remaining items of each transaction itemset 

according to the order of the header table, and get a 

sorted itemset X. 

Step 5: If the length of itemset X is 0, process the next 

transaction itemset; otherwise insert the itemset X 

into the AT-Tree T by the following substeps: 

Substep 5.1: Store the probability value of each 

item in itemset X sequentially to a list; save the 

list to an array (which is denoted as ProArr); 

the corresponding sequence number of the list 

in the array is denoted as ID. 

Substep 5.2: If there has not been a tail node for the 

itemset X, create a tail node N for this itemset, 

where N.Tail_info.len is the length of itemset X, 

and N.Tail_info.Arr_ind={ID}; otherwise, 

append the sequence number ID to 

N.Tail_info.Arr_ind. 

Step 6: Process the next transaction itemset. 



Figure 2. Construction of an AT-Tree 

TABLE II. 

PROBABILITY LIST (PROARR) 

ID probabilities 

1 {0.9, 0.7, 0.8} 

2 {0.85, 0.8, 0.4} 

3 {0.6, 0.85, 0.6} 

4 {0.65, 0.85, 0.9} 

5 {0.8, 0.7, 0.95, 0.7} 

6 {0.7, 0.65} 

B.2 An Example of Constructing a Global AT-Tree 

The uncertain dataset in Table 1 is used as an example 

here to illustrate the construction of the AT-Tree. This 

dataset concludes 6 transaction itemsets and 6 distinct 

items. The minimum support threshold is set as 20%. 

Step 1: Calculate the minimum expected support number 

as 1.2 (6*20%); count the expected support number 

and support number of each item by one scan of 

database. 

Step 2: Create a header table, as shown in Figure 2(a). 

Each link in the header table records all nodes of a 

corresponding item on a tree (not shown in the 

Figures for simplicity). 

Step 3: Initially set the root node of an AT-Tree as null. 

Step 4: Remove the infrequent item “f” from the 

transaction itemset T 1 , and sort the remaining items 

according to the order of the header table, the 

resulting is {d:0.9, b:0.7, a:0.8}. 

Step 5: Maintain probability value of each item to a list 

{0.9, 0.7, 0.8}, and append the list to an array ProArr, 

as shown in Table 2; the corresponding ID of the list in 

the array ProArr is 1; then insert the first sorted 

itemset into the AT-Tree, and the resulting AT-Tree is 

shown in Figure 2(b). On the tail node “a”, “3” 

represents the length of the tail-node-itemset (len), and 

“{1}” represents the index number of the array 

ProArr in Table 2. 

Step 6: Process the next transaction T 2 , get the sorted 

transaction itemset {d:0.85, c:0.8, e:0.4}. Since the 

path “root-d” can be shared, insert a normal node 

“c” and a tail node “e”. The resulting AT-Tree is 

shown in Figure 2(c). 

Step 7: Process the next transaction T 3 , get the sorted 

transaction itemset {d:0.6, c:0.85, e:0.6}. Since the 

path “root-d-c-e” can be shared and the node “e” on 

the path is a tail node, just append the corresponding 

ID in ProArr of Table 2 to the Tail_info.Arr_ind of 

the tail node “e”. The resulting AT-Tree is shown in 

Figure 2(d). 

Step 8: Process the remaining transactions one by one. 

The resulting AT-Tree is shown in Figure 2(e). 

C. Mining Frequent Itemsets from a Global AT-Tree 

After an AT-Tree is constructed, the algorithm AT- 

Mine can directly mine frequent itemsets from the tree 

without additional scan of dataset. The details of the 

mining approach are described below. 

C.1 The Mining Algorithm 

The algorithm AT-Mine is similar to the algorithm 

FP-Growth: it creates and processes sub trees (prefix 

trees or conditional trees) recursively. But the condition 

of generating frequent itemsets is different from FP- 

Growth. The detailed steps of the mining algorithm are as 

follows: 

Mining (T, H, minExpSN) 

INPUT: An AT-Tree T, a header table H, and a 

minimum expected support number minExpSN. 

OUTPUT: The frequent itemsets (FIs). 

Step 1: Process the items in the header table one by one 

from the last item by the following steps (denote the 

currently processed item as Z). 

Step 2: Append item Z to the current base-itemset (which 

is initialized as null); each new base-itemset is a 

frequent itemset. 

Step 3: Let Z.links in the header table H contain k nodes 

whose item name is Z; we denote these k nodes as N 1 , 

N 2 , …, N k ; because item Z is the last one in the 

header table, all these k nodes are tail nodes, i.e., 

each of these nodes contains a Tail_info. 

Substep 3.1: Create a sub header table subH by 

scanning the k branches from these k nodes to 

the root. 

Substep 3.2: If the sub header table is null, go to 

Step 4. 

Substep 3.3: Create sub AT-Tree subTree = 

CreateSubTree(Z.link, subH). 

Substep 3.4: Mining(subTree, subH, minExpSN). 

Step 4: Remove item Z from the base-itemset. 

Step 5: For each of these k nodes (which we denote as N i , 

1≤i≤k), modify its Tail_info by the following 

substeps: 

Substep 5.1: Alter N i .Tail_info.len values: 

N i .Tail_info.len = N i .Tail_info.len -1. 

Substep 5.2: Move N i .Tail_info to the parent of 

node N i . 

Step 6: Process the next item of the header table H. 

Subroutine: CreateSubTree(link, subH) 

INPUT: A list link which records tree nodes with the 

same item name, and a header table subH. 

OUTPUT: An AT-Tree subT. 



Step 1: Initially set the root node of the tree subT as null. 

Step 2: Process each node in the list link by the following 

steps (denote the currently processed node as N). 

Step 3: Get the tail-node-itemset of node N (denote it as 

itemset X). 

Step 4: Remove those items that are not in the header 

table subH from itemset X, and sort the remaining 

items in itemset X according to the order of the 

header table subH. 

Step 5: If the length of the sorted itemset (denoted as k) 

is 0, process the next node of the list link; otherwise 

insert the sorted itemset X into the AT-Tree subT by 

the following substeps: 

Substep 5.1: Get the original sequential ID of each 

item of the itemset X in the corresponding list 

of ProArr: item_ind = {d 1 , d 2 , .., d k } (k is the 

length of itemset X). 

Substep 5.2: Make a copy of N.Tail_info; denote the 

copy as nTail_info. 

Substep 5.3: Alter nTail_info as the following: 

(1) nTail_info.len = k. 

(2) nTail_info. Item_ind = item_ind. 

(3) if nTail_info.bp is null, set nTail_info.bp[j] 

to be the probability of item Z, i.e. 

ProArr[nTail_info.Arr_ind[j]]; otherwise, 

set nTail_info.bp[j] to be the product of 

nTail_info.bp[j] and the probability of item 

Z (1 ≤ j ≤ bp.size; the array ProArr is 

created when the global tree is created in 

Substep 5.1 in Section 4.2.1). 

C.2 An Example of Mining Frequent Itemsets from a 

Global AT-Tree 

Figure 3. An Example of mining frequent itemsets from uncertain 

dataset 

The global AT-Tree in Figure 2(e) and its 

corresponding header table H in Figure 2(a) are used as 

an example here to illustrate the detailed processes of 

mining frequent itemsets. The minimum expected support 

number is 1.2. 

Step 1: Process the item “e” in the header table H by the 

following steps 2-3. 

Step 2: Append item “e” to the current base-itemset 

(which is initialized as null), and generates a new 

frequent itemset {e}. 

Step 3: Scan the branches containing the node “e” to 

create sub header table: 

Substep 3.1: In Figure 2(e), there are 2 nodes “e”. 

From the path “root-d-b-a-e” and Table 2, the 

expected support numbers of itemsets {ed}, {eb} 

and {ea} are calculated as 0.56 (0.7*0.8), 0.49 

(0.7*0.7) and 0.665 (0.7*0.95), respectively; 

from the path “root-d-c-e”, the expected 

supports of itemset {ed} and {ec} are 

calculated as 0.7 (0.4*0.85+0.6*0.6) and 0.83 

(0.4*0.8+0.6*0.85). 

Substep 3.2: Because the total expected support 

numbers of itemset {ed} is bigger than 1.2, the 

sub header table is not null, create a sub tree 

(prefix tree or conditional tree) for the baseitemset 

{e}, and get a new frequent itemset 

{ed}. 

SubStep 3.3: Remove the item “e” from the baseitemset, 

pass the Tail_info of nodes “e” to their 

parents, and modify Tail_info.len as 

Tail_info.len -1; the result is shown in Figure 

3(a). 

Step 4: Process the next item “c” in the header table H by 

the following steps 5-6. 

Step 5: Append item “c” to base-itemset, and get a new 

frequent itemset {c}. 

Step 6: Scan the branches containing node “c” to create 

the sub header table: 

Substep 6.1: In Figure 3(a), there are 2 nodes “c”. 

From the path “root-d-c” and Table 2, the 

expected support numbers of itemset {cd} is 

calculated as 1.19 (0.8*0.85+0.85*0.6); from 

the path “root-b-c”, the expected support of 

itemset {cb} is calculated as 0.455 (0.65*0.7). 


numbers of itemsets {cd} and {cb} are smaller 

than 1.2, the sub header table is null. 

SubStep 6.3: Remove the item “c” from the baseitemset, 

pass the Tail_info of nodes “c” to their 

parents; the result is shown in Figure 3(b). 

Step 7: Process the next item “a” in the header table in 

Figure 2(a) as the following steps 8-10. 

Step 8: Append item “a” to the base-itemset, and get a 

new frequent itemset {a}. 

Step 9: Scan the branches containing node “a” to create 

the sub header table: 

Substep 9.1: In Figure 3(b), there is one node “a”. 

From the path “root-d-b-a” and Table 2, the 

expected support numbers of itemsets {ad} and 

{ab} are calculated as 2.065 

(0.8*0.9+0.9*0.65+0.95*0.8) and 1.99 

(0.8*0.7+0.9*0.85+0.95*0.7). 


numbers of itemsets {ad} and {ab} are not 

smaller than 1.2, the sub header table subH is 

{d:2.065:3, b:1.99:3}. 

Step 10: Create a sub tree for the base-itemset {a} by the 

following substeps: 

Substep 10.1: Initially set the root node of the sub 

tree subT as null. 

Substep 10.2: Get the itemset {db} from the tailnode-itemset 

of the tail node “a” in Figure 3(b). 

Substep 10.3: Sort the itemset {db} in the order of 

the header table subH. 

Substep 10.4: Make a copy of Tail_info.Arr_ind, 



and denote it as arr_ind={1, 4, 5}. 

Substep 10.5: Get the list indexes (original 

sequential ID in a list) of items “d” and “b” in 

the list ProArr[1], which are 1 and 2 

respectively, and denote it as item_ind={1, 2}. 

Substep 10.6: Get the probability values of itemset 

{a} in ProArr[1] and ProArr[4] and ProArr[5] 

respectively, and denote them as bp={0.8, 0.9, 

0.95}; this is the corresponding base 

probabilities in the sub tree subT. 

Substep 10.7: Add the sorted itemset {db} to subT; 

maintain arr_ind, item_ind, bp and the length 

of the itemset {db} to the tail node in subT; the 

result is shown in Figure 3(c). 

Substep 10.8: Process the tree subT recursively, and 

get a new sub tree for the base-itemset {ab}, as 

shown in Figure 3(d). Lastly, get frequent 

itemsets {ab}, {abd} and {ad} when processing 

the sub tree of itemset {a}. 

Step 11: Go on processing the remaining items in header 

table H. 

V. EXPERIMENTAL RESULTS 

In this section, we evaluate the performance of the 

proposed algorithm AT-Mine. 

Summarizing the related works in Section 3, we can 

conclude that the algorithm MBP is the state-of-the-art 

algorithm employing the level-wise approach, UP- 

Growth is the state-of-the-art algorithm employing the 

pattern-growth approach and CUFP-Mine is a new 

proposed algorithm. So we compare AT-Mine with the 

algorithms UF-Growth, CUFP-Mine and MBP on both 

types of datasets: the sparse transaction datasets and 

dense transaction datasets. All algorithms were written in 

Java programming language. The configuration of the 

testing platform is as follows: Windows XP operating 

system, 2G Memory, Intel(R) Core(TM) i3-2310 CPU @ 

2.10 GHz; Java heap size is 1G. 

TABLE III. 

DATASET CHARACTERISTICS 

Dataset |D| |I| ML SD (%) Type 

T20I6D 

300K 

300,000 1000 20 2 sparse 

kosarak 990,002 41,271 8 0.02 sparse 

connect 67,557 129 43 33.33 dense 

mushroom 8,124 119 23 19.33 dense 

Table 3 shows the characteristics of 4 datasets used in 

our experiments. “|D|” represents the total number of 

transactions; “|I|” represents the total number of distinct 

items; “ML” represents the mean length of all transaction 

itemsets; “SD” represents the degree of sparsity or 

density. The synthetic dataset T20I6D300K came from 

the IBM Data Generator [1] and the datasets kosarak, 

connect and mushroom were obtained from FIMI 

Repository [33]; These four datasets originally do not 

provide probability values for each item of each 

transaction itemset; as suggested by literatures [23, 25, 28, 

29], we assign a existential probability of range (0, 1] to 

each item. The runnable programs and testing datasets 

can be downloaded from the following address: 

http://code.google.com/p/at-tree/downloads/list. 

A. Evaluation on Sparse Datasets 

Tables 4-5 show the total number of tree nodes 

generated by AT-Mine, UF-Growth and CUFP, and the 

number of candidate itemsets generated by MBP, 

respectively, on the sparse datasets. As shown in Tables 

4-5, UF-Growth creates much more tree nodes than AT- 

Mine. This is because that UF-Growth just merges the 

nodes that have the same item name and the same 

probability. CUFP-Mine is out of memory on these two 

sparse datasets because it generates too many supersets; 

UF-Growth is out of memory on kosarak when the 

threshold is set 0.01% because it generates too many tree 

nodes; MBP is out of memory when the threshold is set 

0.03% because it generates too many candidates. Thus we 

can infer that AT-Mine has a better performance than 

other three algorithms in terms of memory usage. 

TABLE IV. 

DETAILS ANALYSIS ON THE DATASET T20I6D300K 

η (%) 

trees nodes (#) candidates (#) 

AT-Mine UF-Growth MBP 

0.15 4,978,327 7,556,250 374,271 

0.13 5,101,077 8,629,034 391,413 

0.11 5,438,410 10,282,811 419,770 

0.09 6,310,746 12,978,032 467,217 

0.07 8,474,124 17,477,552 594,050 

0.05 13,189,900 24,946,139 999,799 

Running time (s) 

TABLE V. 

DETAILS ANALYSIS ON THE DATASET KOSARAK 

η (%) 



0.1 2,020,568 14,471,137 172,399 

0.09 2,208,231 15,724,272 252,348 

0.07 2,542,835 19,210,453 419,272 

0.05 3,058,380 24,651,644 793,554 

0.03 4,580,785 38,083,667 

0.01 18,829,877 

Memory 

Overflow 

Memory 

Overflow 

10000 

1000 

100 

AT-Mine 

MBP 

UF-Growth 

CUFP-Mine (Memory Overflow) 

10 

0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 

Minimum expected support threshold (%) 



(a) 

On the dataset T20I6D300K 


1000 

100 

10 


MBP 

UF-Growth 


0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 

(b) 


On the dataset kosarak 

Figure 4. Running time comparison on sparse datasets 

Figure 4 shows the running time of three algorithms 

on two sparse datasets. CUFP-Mine is out of memory on 

these two sparse datasets. As shown in Figure 4, the time 

performance of our algorithm outperforms UF-Growth, 

MBP and CUFP-Mine under different minimum expected 

support thresholds. This is because that CUFP-Mine 

generates too many supersets and UF-Growth generates 

too many tree nodes and MBP generates many candidates, 

as shown in Tables 4-5. The time performance of MBP is 

dependent on the length of candidate itemsets, the length 

of transaction itemsets, and the size of dataset: the higher 

these values are, the lower the time performance of MBP 

will be. Thus the time performance of MBP decreases 

sharply with the decreasing of the threshold. Figure 4 

indicates that AT-Mine has achieved a better time 

performance; moreover, its time performance is more 

stable on sparse dataset. 

B. Evaluation on Dense Datasets 

In this section, we test the performance of our 

proposed algorithm on dense datasets connect and 

mushroom. 

TABLE VI. 

DETAILS ANALYSIS ON THE DATASET CONNECT 

η (%) 



15.0 36,823 32,204,274 5,981 

14.0 89,118 33,739,243 6,962 

13.0 98,842 35,332,360 7,786 

12.0 116,290 48,046,639 8,565 

11.0 130,423 106,626,725 12,754 

10.0 153,913 163,809,762 19,162 

Tables 6-7 show the total number of tree nodes 

generated by AT-Mine and UF-Growth, and the number 

of candidate itemsets generated by MBP, on the dense 

datasets. As shown in Tables 6-7, UF-Growth creates too 

many tree nodes. For example, on the dataset connect, 

UF-Growth generates 163,809,762 nodes while AT-Mine 

generates 153,913 nodes when the minimum expected 

support threshold is 10%. This is because that UF- 

Growth just merges the nodes that have the same item 

name as well as the same probability, and it is a very 

dense and long dataset. Thus we can infer that our 

algorithm has achieved better performance than UF- 

Growth in terms of memory usage. MBP not only 

maintains candidates, but also maintain the dataset while 

our algorithms only maintain tree nodes using compact 

trees. 

Figure 5 shows the running time of three algorithms 

on the dense datasets connect and mushroom. CUFP- 

Mine is out of memory on these two dense datasets. As 

shown in Figure 5, the time performance of our algorithm 

prevails over UF-Growth, MBP and CUFP-Mine under 

different minimum expected support thresholds. This is 

because that CUFP-Mine generates too many supersets 

and UF-Growth generates too many tree nodes and MBP 

generates many candidates, as shown in Tables 6-7. 

Figure 5 shows that the time performance of AT-Mine 

obviously outperforms that of other algorithms on these 

two dense datasets; moreover, our time performance is 

also more stable on the dense datasets. 


TABLE VII. 

DETAILS ANALYSIS ON THE DATASET MUSHROOM 

η (%) 

trees nodes (#) candidates(#) 


7.0 12,041 1,011,721 1,917 

6.0 14,420 1,344,369 2,501 

5.0 16,243 1,947,609 3,460 

4.0 18,685 2,760,249 5,024 

3.0 25,884 4,125,745 8,222 

2.0 37,395 8,076,099 16,764 

10000 

1000 

100 


MBP 

UF-Growth 


10 

15.0 14.5 14.0 13.5 13.0 12.5 12.0 11.5 11.0 10.5 10.0 


(a) 

On the dataset connect 




60 

50 

40 

30 

20 

10 

0 


MBP 

UF-Growth 


7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 

(b) 


On the dataset mushroom 

Figure 5. Running time comparison on dense datasets 

VI. CONCLUSION AND DISCUSSION 

In this paper, we propose a novel tree structure named 

AT-Tree to maintain transaction itemsets of an uncertain 

dataset, and a corresponding algorithm named AT-Mine 

to mine frequent itemsets. AT-Mine requires two scans of 

dataset to create an AT-Tree. In the first scan, it creates a 

header table to maintain sorted frequent items in the 

descending order of support numbers of items. In the 

second scan, it maintains probability values of frequent 

items in each transaction itemsets to an array; it inserts 

frequent items in each transaction itemsets to an AT-Tree; 

it maintains probability information of each transaction 

itemsets to the tail node. So the AT-Tree is as compact as 

the original FP-Tree, and it does not lose the probability 

information of each transaction itemsets. Thus, AT-Mine 

can find frequent itemsets from AT-Tree without 

additional scan of dataset. 

Experiments were performed on sparse and dense 

datasets. We compared our proposed algorithm with 

some state-of-the-art level-wise and pattern-growth 

algorithms. The experimental results show that the 

proposed algorithm has better performance on dense 

datasets and large sparse datasets, and their time 

performance is stable on both dense and sparse datasets 

along with the decreasing of the minimum expected 

support threshold. 

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A Solution for Privacy-Preserving Data 

Manipulation and Query on NoSQL Database 

Guo Yubin a , Zhang Liankuan b , Lin Fengren a , Li Ximing a,∗ 

a College of Informatics, South China Agricultural University, Guangzhou 510640, China 

Email: {guoyubin,linfengren,liximing}@scau.edu.cn 

b College of Science, South China Agricultural University, Guangzhou 510640, China 

Email: zhangliankuan@scau.edu.cn 

Abstract— Privacy of data owners and query users is vital in 

modern clouding data management. Many researches have 

been done on cloud security, but most of them are focused on 

the privacy of data owners or of query users separately. How 

to protect the privacy of the data owners and users simultaneously 

is a great challenge. In this paper, a solution of data 

storage and query protocol based on classical homomorphic 

encryption scheme is given to preserve privacy of both data 

owners and query users. Our main efforts are put on NoSQL 

database which is less structural than relational database. 

Storage and indexing structure on NoSQL database, query 

protocol are proposed, and algorithms for updating and 

querying are also given. To implement our solution, Berkley 

DB, an excellent storage solution for NoSQL database is 

chosen and data are encrypted/decrypted using Elgamal 

and Paillier encryption system, using basic Java package. 

Experiments are done under different parameters in order 

to achieve better efficiency. 

Index Terms— NoSQL; cloud data management; privacy 

preserving 

need to query data from cloud, but the query might 

disclose sensitive information, behavior patterns of the 

user. For example, when Alice searches a website, such as 

Facebook, for friends who share the similar backgrounds 

(e.g., age, education, home address) with her, she should 

not disclose the query that involves her own details to the 

cloud. Privacy of data owners and query users are defined 

as data privacy and user privacy respectively. 


Today cloud computing and data outsourcing provide 

much convenience for kinds of enterprises. For instance, 

enterprises can concentrate on their main business while 

outsourcing their complex data management and query 

service to service providers in cloud. These service 

providers in cloud focus on data management, and provide 

high quality service. But in such kind of computing 

pattern, a bottleneck, privacy preserving of data owners 

and query users, seriously restricts progress of cloud 

computing. 

Consider environment illustrated in Fig. 1, data owners 

outsource their data and query services, but the data is 

private assets of them and should be protected against 

the service providers and querying users in some extent. 

On one hand, data owner can update, query and authorize 

access of data, while the service providers in cloud should 

know nothing about especially detailed data, and query 

users should know not more than the exact answers for 

what she/he is querying. On the other hand, query users 

Partially supported by National Science Foundation of China 

(61103232, 61272402, 61202294),Guangdong Provice Nature Science 

Foundation (10351806001000000, 10151064201000028), Guangdong 

Science Technology Plan Project (2010B010600046, 2011B090400325), 

Guangzhou Science Technology Plan Project (12C42101606). 

* Contact author. 

Figure 1: Architecture of Data Service on Cloud 

A. Related works 

For data privacy, the most general solution in recently 

research papers are encryption that means data deposited 

to service provider must be encrypted to avoid information 

leakage. Agrawal et al [5] proposed an order 

preserving encryption scheme (OPES) by which indexes 

can be built directly on ciphertext. OPES can handle 

directly (without decryption) any interesting SQL query 

types, except SUM and AVG. But order preserving would 

leak information about data, and is not a good solution 

to privacy preserving. Hacigumus et al [9] proposed to 

handle SUM and AVG using homomorphic encryption 

function in the database context. Ayman Mousa et al. [14] 

uses classic REA, a symmetric encryption algorithm, to 

encrypted data respectively, and in this way the query processing 

performance is assured, but information leakage 

and query privacy are not considered. Privacy homomorphism 

[17] is encryption transformations which map a 

set of operations on cleartext to another set of operations 

on ciphertext. In essence, privacy homomorphism enables 

complex computations (such as distances) based solely on 

ciphertext, without decryption. Unfortunately, as pointed 


doi:10.4304/jcp.8.6.1427-1432


out by Mykletun and Tsudik [15], its encryption scheme 

is insecure, demonstrated by its vulnerability to a basic 

ciphertext-only attack. However, for encrypted database, 

efficiency of query processing is a great challenge. 

In [8], [10], [11], user privacy is considered together 

with data privacy. Yonghong Yu and Wenyang Bai discussed 

how to enforce data privacy and user privacy 

over outsourced database service in [18]. Hu et al. [11] 

proposed a solution based on secure traversal framework 

and privacy homomorphism based encryption scheme. 

Yong Hu et.al in [12] constructed an intelligent analysis 

model for outsourced software. And secure protocols 

for processing k-nearest-neighbor queries (kNN) on R- 

tree index is given. In the authors following work [10], 

they integrated indexing techniques with secure multiparty 

computation (SMC) based protocols to construct 

a secure index traversal framework. In this framework, 

the service provider cannot trace the index traversal path 

of a query during evaluation, and thus keep privacy of 

users. Their protocols for query are complex, and hard 

to implement. The thought of composed key in index is 

directly prompted by Tingjian Ge’s work [8]. In his paper, 

keyword are composed together to improve the efficiency 

of aggregation operations in database. It is intuitively that 

addition of keywords in block is dramatically efficient 

than adding them one by one. But the authors have not 

considered range or single key search. As to protecting 

data privacy and user privacy, we use the block structure 

to hide real structure of keys in index. And key search is 

efficient for key comparison can be done k−in−1 where 

the k is key number in a single block, that is decided by 

block and key size. 

B. Our contribution 

For data privacy and user privacy, a solution of data 

storage, manipulation and query is presented in this paper. 

In main database files, data are stored in key/value pair 

which is a typical NoSQL storage structure and are encrypted 

with Elgamal homomorphic encryption scheme. 

Keys in index are ciphertext of combinations of real keys 

in big blocks (in our experiments, one block is set to 

1024 bits), which are encrypted with Paillier encryption 

scheme [16] which is an additive homomorphic cryptosystem. 

When a key is queried, comparison can be done 

on ciphertext in blocks that improves efficiency of query. 

Protocols of data manipulation and query among data 

owner, service provider and querying user is given. Algorithm 

for data updating and querying are implemented to 

verify usefulness of the solution. As to implementation of 

our solution, Berkley DB, a typical key/value pair model 

database, is chosen to construct a prototype system. It is 

an excellent storage solution for NoSQL database for its 

high efficiency and convenience. 

C. Outline of the paper 

The rest of the paper is organized as follows. Section 

II provides background information on homomorphic 

encryption scheme, NoSQL database and index. Section 

III describes the query protocol and main algorithms, 

security analysis is also given in the section. Performance 

and analysis of experiments results are shown in section 

IV. Finally, section V gives conclusions and future works. 

II. PRELIMINARY 

A. Homomorphic Encryption 

Homomorphic encryption allows specific types of computations 

to be carried out on ciphertext and obtains 

an encrypted result which is ciphertext of the result 

of operations performed on the plain text. The additive 

homomorphic property of a homomorphic cryptosystem 

is Enc(a) × Enc(b) = Enc(a + b) , where a and 

b are two plain text message blocks, and Enc is the 

encryption function that takes a plaintext message block 

(and an encryption key) and returns the ciphertext block. 

Thus, in the above equation, + operates on the plain 

text, and × operates on the ciphertext. An example of 

such an encryption scheme is the Paillier system. Elgamal 

encryption scheme [6], [7] is multiplicative homomorphic 

with Enc(a) × Enc(b) = Enc(a ∗ b) where a, b, Enc 

and × share the same meanings with formula above, 

and operation + is multiple operation on the plaintext. 

The Legion of the Bouncy Castle [1] provided open 

source libraries of Java and c# Cryptography Architecture. 

Both Paillier and ElGamal encryption scheme have 

great practical implications on the outsourcing of private 

computations, such as, in the context of cloud computing 

and outsourcing [13]. 

B. NoSQL database and index 

NoSQL database is defined as the next Generation 

Databases mostly because of the following characteristics: 

being non-relational, distributed, open-source and horizontally 

scalable [2]. The concept NoSQL is prompted 

by Carlo Strozzi in 1998 [3], and the current NoSQL 

movement beginning from 2009 often more characteristics 

apply such as: schema-free, easy replication support, 

simple API, eventually consistent / BASE (not ACID), 

a huge amount of data and more. From NoSQL Data 

Modeling Techniques [4] data model for NoSQL Database 

can be cataloged into key/value or tuple store, Bigtable 

style databases, Document databases, and graph 

databases. Berkeley DB is a robust solution on which 

to build a NoSQL system, and the storage system of its 

key/value pair is more efficient than other database. That 

is the reason for us to choose it as our base database in 

our experiments. 

III. SOLUTION FOR STORAGE AND UPDATING 

In this section some symbols are defined for simplification. 

owner means data owner, sp is service provider 

in cloud, and user data user for query. We use Paillier 

crypto-system to encrypt keys and values in NoSQL 

database. System parameter is taken as n. Enc(m, pk) 

is the function to encrypt plaintext m with public key 



pk, and Dec(c, sk) function to decrypt ciphertext c with 

private key sk. Denote the public key and secret key of 

data owner as (pk owner , sk owner ). Denote the public key 

and secret key of user user i as (pk useri , sk useri ). All data 

are encrypted using homomorphic encryption algorithm, 

each one of owner, sp and user publishes his public key 

and uses the private key to decrypt ciphers. 

A. data storage 

In our solution, data are stored in database, and in 

key/data model. That means each tuple is composed of 

one key and one data, the key and data are encrypted 

respectively. To construct indices of data, several keys 

are composited together to form a 1024 binary bits block. 

Number of keys in one block is determined by length of 

key. Let l be length of key, then the number of keys in one 

block is ⌊(1024)/(l+1)⌋ and one bit is added to each key 

to deal with overflow.. Let k 1 , k 2 , . . . , k m be keys which 

will be combined together, then the key block in index k 

can be computed as follows: 

Algorithm 1: Index constructing algorithm 

Input: key, pointer* 

Output: index file f 

1 f= New(file ); 

2 l= length of key; 

3 n = int(1024/(l + 1)); 

4 while not end of input do 

5 i = 0; 

6 m 1 = m 2 = 0; 

7 while i


Algorithm 2: Data inserting algorithm 

Input: < key, value > //a new tuple that is inserting 

into the database 

Output: 

1 //Insert a new tuple 

< Enc(key, pk owner ), Enc(key, pk owner ) > into 

database.; 

2 T =< Enc(key, pk owner ), Enc(value, pk owner ) >; 

3 Attach 

T =< Enc(key, pk owner ), Enc(value, pk owner ) > 

to the end of main database file; 

4 //index maintaining; 

5 for each index do 

6 Construct its new keys key ′ ; 

7 t =< 

Enc(key ′ , pk owner ), Enc(key, pk owner ) >; 

8 if the last data block of index file is not full then 

9 (c key , c value )= ciphertext of last block ; 

10 c key = c l+1 

key + Enc(key, pk owner) mod n 2 ; 

11 c value = c l+1 

value + Enc(value, pk owner) 

mod n 2 ; 

12 Write (c key , c value ) back to file; 

13 else 

14 Attach T =< 

Enc(key, pk owner ), Enc(value, pk owner ) > 

to the end of index file. 

15 Send the index back to sp and replace old one ; 

Algorithm 3: Data deleting algorithm 

Input: t =< 

Enc(key, pk owner ), Enc(value, pk owner ) >, 

database(main file and indices) 

Output: database(main file and indices) after 

deletion 

1 Select 

t =< Enc(key, pk owner ), Enc(value, pk owner )) > 

in main file and indices.; 

2 //deleting from main database file, is done by sp; 

3 Select the last tuple of main database file as t 1 ; 

4 Replace t with t 1 ; 

5 //deleting from index; 

6 for each index do 

7 Construct key key ′ ; 

8 Let t =< 

Enc(key ′ , pk owner ), Enc(key, pk owner ) >; 

9 Find the block b t in which t is the ith key; 

10 Find the last key block b l in in which key t l is 

in b l ; 

11 b t = b t /t i∗(l+1) ∗ t i∗(l+1) 

l 

mod n 2 ; 

12 b l = b l /t l mod n 2 ; 

13 Send the index file to sp and replace old one; 

Figure 3: An example of querying 

We know, the query algorithm is oblivious for data user. 

The data user encrypted additive reverse of queried key 

at first, and send it to service provider. Then the service 

provider extends it into queried block, and chooses proper 

index to multiple the queried block with a key block, and 

as follows, the product is sent to data owner one by one. 

When the data owner receives the product, it decrypts 

the cipher and decomposes the plaintext to find which 

one is 0, which means the according key in the block 

is equal to queried key. The serial numbers of the key 

are sent back to the service provider, service provider 

can get the key in main data file and get queried data 

for the data owner. This process will terminated when the 

queried key is found or all blocks in the index is searched. 

To database applications, querying is the most common 

operation. In our solution, all of the three roles, service 

provider, data owner and data user must participant in 

the querying process. To preserve both data owner and 

user privacy, querying process is more complex than in 

traditional database system. Fig. 4 presents the querying 

protocol in detail. 

D. Security analysis 

Figure 4: Query protocol 

In this protocol, data user prompts a query by encrypting 

additive inverse of queried key with public key of data 

owner and sends it to the service provider. The second 

step starts when the service provider receives a query 

request. The service provider chooses proper index, and 

then a 1024 bits big integer M is composed by repeating 

the queried key several times. Then multiplies M by each 

key block respectively, and sends the results to data owner. 

When the data owner receives the products, he decrypts 

the cipher and decomposes the plaintext to find 0 in each 



product. This procedure can be ended when the key is 

found or all products are searched. Then the serial number 

of equal key is sent back to the service provider, and all 

the queried data are sent to the data owner. At last step, 

the data owner decrypts the data with his owner private 

key and encrypts it with public key of the data user and 

sent the result to him. 

During the query process, additive reverse of the 

queried keyword is encrypted before sending to the service 

provider, and the queried data is sent by data owner, 

therefore the service provider can get no information 

about what the data user is querying on the database. 

Security can also be enforced by adding disturbing data 

when the data owner requests query data from service 

provider. And as to the data owner, during the query 

process, only product of the queried block and index key 

blocks are received and decrypted to find the order of 

equal ones, while the queried key is kept invisible. The 

data owner do not know which index is chosen and cannot 

deduce what the data user is querying. It is obvious that 

we cannot complete query without leaking no information 

about the user and what she is querying. At least, queried 

result must be sent back to her. What we really want to do 

and can do is to limit the information leakage as much as 

possible. From the analysis above, we can see, confidence 

of data owner can surely be protected for homomorphic 

encryption scheme is used. Data privacy and user privacy 

are all kept by the scheme we propose to some extent. 

Figure 5: Query efficiency on data quantity, and length of 

key 

length. In this figure thread number is x axis, and there 

3 curves are with different key length. It is oblivious 

that the best value of thread number is 4. When thread 

is few, computing power of CPU cannot be fully used. 

And when threads are too much, communication and 

context change decrease the efficiency of the solution. 

Thread number is vital for most service providers in 

clouds. And parallel process of key words comparison can 

improve query performance drastically. In our prototype 

system, block comparison is divided into several parts 

simply, query efficiency can be heightened further with 

sophisticated technology of parallel programming. Note 

that thread number is a hardware-depended parameter. 

A. Setup 

IV. EXPERIMENTS 

Our experiments are conducted on BDB database 

system on Windows 7. We implements the generalized 

Paillier system with basic Java package, and the Elgamal 

scheme is from open source library of bouncy castle 

[1]. All experiments of the solution are implemented in 

Java with JDK 1.7 and the prototype system are run on 

personal computer with Intel 2Ghz processor and 2GB 

memory. 

B. Experiments design and analysis 

A series of experiments have been done to test efficiency 

of our solution. Some vital parameters, like 

quantity of data, thread number, and length of key, have 

been changed to find difference. Fig. 5 illustrates query 

efficiency of our solution. In this figure, x axis is number 

of tuples which is set to be 20000, 30000, 40000, 50000, 

75000 and 100000, while y axis is average time used 

for a single value query. And we can get 3 curves when 

the length of key is set to 5, 10 and 20 decimal bits 

respectively. (as in binary, it should be 1, 2, and 4 bytes 

approximately.) On the whole, query efficiency is much 

better when length of key is not so long. The reason 

lies in that when the key is short, more keys can be put 

into one single block, therefore a comparison on block is 

equivalent to much more comparisons on single key. 

In Fig. 6, tuple number is set to 50,000, to illustrate 

query efficiency variation on thread number and key 

Figure 6: Query efficiency on thread number and key 

length 

Fig. 7 illustrates efficiency variation according to thread 

number and tuple number when the key size is fixed to 10. 

From the figure, we can see, query time increases more 

quickly when tuples are more than 50,000. And it means 

performance of our solution is more better to middle scale 

database. 

V. CONCLUSION 

Homomorphic encryption scheme provides a good solution 

to privacy preservation for database system. We 

present a storage solution for NoSQL database using homomorphic 

encryption algorithms. Protocol of data querying 

is proposed, and algorithms for data manipulation are 

given also. In indices, keys are composed into big blocks 

to improve the performance of encryption and decryption, 

therefore accelerate the process of data manipulation and 



Figure 7: Query efficiency on thread number and tuple 

number 

query. Although Paillier and Elgamal encryption scheme 

is not so efficient comparing to symmetric encryption 

schemes like DES and SHA. But it is good enough for 

some cases that users pay more attention on information 

security than computation performance. 

Future work includes improving efficiency of the system 

and extending system functionality, such as extended 

query on range, aggregation, and join. 

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GuoYubin Received Ph. D. from South China University of 

Technology in 2007. She is now lecturer in South China 

Agricultural University. Her research interests include Database 

theory and technology, cryptography and network computing. 

Zhang Liankuan Received Ph. D. from South China Agricultural 

University in 2012. He is now lecturer in South China 

Agricultural University. His research interests include Database 

theory, technology and network computing. 

Lin Fengren He is now Bachelor student in South China 

Agricultural University. His research interests include Database 

theory and technology. 

Li Ximing Received Ph.D. degree from College of Informatics, 

South China Agricultural University, Guangzhou, Guangdong, 

China, in 2011. His current research interests include computer 

theory and cryptography. 



Predicate Formal System based on 1-level 

Universal AND Operator and its Soundness 

Yingcang Ma 

School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi, 710048, China 

School of Electronics and information, Northwestern Polytechnical University, Xi’an, Shaanxi, 710048, China 

Email: mayingcang@126.com 

Huacan He 

School of Computer Science, Northwestern Polytechnical University, Xi’an, Shaanxi, 710048, China 

Email: hehuac@nwpu.edu.cn 

Abstract—The aim of this paper is solving the predicate 

calculus formal system based on 1-level universal AND 

operator. Firstly, universal logic and propositional calculus 

formal deductive system UL − h∈ (0, 1] are introduced. Secondly, 

a predicate calculus formal deductive system ∀ UL − h∈ (0, 

1] 

based on 1-level universal AND operator is built. Thirdly, 

the soundness theorem and deduction theorem of system 

∀ UL − h∈ (0, 

1] are given, which ensure that the theorems are 

tautologies and the reasoning rules are valid in 

system ∀ h (0 1] . 

UL − ∈ , 

Index Terms—universal logic, predicate calculus formal 

system, universal AND operator 


How to deal with various uncertainties and evolution 

problems have been critical issues for further 

development of artificial intelligence [1,2]. Mathematical 

logic is too rigid and it can only solve certainty problems, 

therefore, non-classical logic and modern logic develop 

rapidly, for example, fuzzy logic and universal logic. 

Considerable progresses have been made in logical 

foundations of fuzzy logic in recent years, especially for 

logic system based on t-norm and its residua [3]. Some 

well-known logic systems have been built up, such as, the 

basic logic (BL) [4, 5] introduced by Hajek; the monoidal 

t-norm based logic [6, 7] introduced by Esteva and Godo; 

a formal deductive system L* introduced by Wang [8-10], 

Universal logic proposed by He [11], and so on. 

Universal logic is a new continuous-valued logic 

system in studying flexible world’s logical rule, which 

uses generalized correlation and generalized 

autocorrelation to describe the relationship between 

propositions, more studies can be found in [12-14]. For a 

logic system, the formalization’s studies are very 

important, which include propositional calculus and 

predicate calculus. The propositional calculus formal 

systems are studied in [15-18]. But the studies of 

predicate calculus formal systems of universal logic are 

relatively rare, so we will mainly study the predicate 

calculus formal system in this paper, which can enrich the 

formalization’s studies of universal logic. 

Some predicate calculus formal deductive systems are 

built for fuzzy logic systems, for example, the predicate 

calculus formal deductive systems of Schweizer-Sklar t- 

norm in [19, 20]. The predicate calculus formal deductive 

systems of universal logic have been studies in [21-24], 

which mainly focus on the 0-level universal AND 

operator. In this paper, we focus on the formal system of 

universal logic based on 1-level universal AND operator. 

We will build predicate formal system ∀UL − h∈ (0, 

1] for 1- 

level universal AND operator, and its soundness and 

deduction theorem are given. 

The paper is organized as follows. After this 

introduction, Section II contains necessary background 

knowledge about BL and UL. Section III we will build the 

predicate calculus formal deductive system ∀ UL − h∈ (0, 

1] for 

1-level universal AND operator. In Section IV the 

soundness and deduction theorem of system ∀ UL − h∈ (0, 

1] 

will be given. The final section offers the conclusion. 

II. PRELIMINARIES 

A. The Basic Fuzzy Logic BL and BL-algebra 

The languages of BL [3] include two basic connectives 

→ and & , one truth constant 0 . Further connectives are 

defined as follows: 

ϕ ∧ ψ is ϕ & ( ϕ → ψ) 

, 

ϕ ∨ ψ is (( ϕ →ψ) →ψ) ∧( ψ →ϕ) → ϕ) 

, 

¬ ϕ is ϕ → 0 , 

ϕ ≡ ψ is ( ϕ →ψ) & ( ψ → ϕ) 

. 

The following formulas are the axioms of BL: 

(i) ( ϕ →ψ) →(( ψ → χ)( ϕ → χ)) 

(ii) ( ϕ & ψ) 

→ ϕ 

(iii) ( ϕ & ψ) → ( ψ & ϕ) 

(iv) ϕ &( ϕ →ψ) →( ψ &( ψ → ϕ)) 

(v) ( ϕ →( ψ → χ)) →(( ϕ& 

ψ) → χ) 

(vi) (( ϕ & ψ) → χ) →( ϕ →( ψ → χ)) 


doi:10.4304/jcp.8.6.1433-1440


(vii) (( ϕ →ψ) → χ) →((( ψ →ϕ) → χ) → χ) 

(viii) 0 → ϕ 

The deduction rule of BL is modus ponens. 

Definition 1 [3] A BL-algebra is an algebra 

L = ( L,∩,∪,∗,⇒, 01) , with four binary operations and 

two constants such that ( L,∩,∪, 01) , is a lattice with the 

greatest element 1 and the least element 0 (with respect to 

the lattice ordering ≤ ), ( L,∗, 1) is a commutative 

semigroup with the unit element 1, i.e. ∗ is commutative, 

associative and 1∗ x = x for all x, the following 

conditions hold for all x, yz , : 

(i) z ≤( x⇒ y) 

iff x ∗z ≤ y 

(ii) x ∩ y = x∗( x⇒ 

y) 

(iii) ( x⇒ y) ∪( y⇒ x) = 1. 

B. Universal Logic 

Universal logic was proposed by He [11], which thinks 

that all things in the world are correlative, that is, they are 

either mutually exclusive or mutually consistent, and we 

call this kind of relation generalized correlation. 

The basic principles of universal logic show as follows: 

A core objective. The objective is that any one of 

modern logics should include one or some dialectical 

contradictions, and which should exclude the logical 

contradictions. And different advanced logics have 

different dialectical contradictions. 

Two basic methods. There are two ways to include 

dialectical contradictions (or uncertainty) in general. 

Firstly, the logical scope narrows to the sub-space that 

adapts to just include the dialectical contradictions (or 

uncertainty). Secondly, the logic system express the 

impact of the dialectical contradictions (or uncertainties) 

through continuously variable flexible parameters and 

functions in the logic operation model. 

Three Break directions. There are three different 

break directions for the constraints of various modern 

logics relative to that of standard logic: the number of 

truth value of proposition, the dimension of truth value 

space, and the completeness of information reasoning. 

Four logical elements. There are four logical elements 

to construct a logical system: domain, propositional 

connectives, quantifiers and reasoning rules. Universal 

logic discussed the possible forms of these elements, and 

put forward their general expression. 

Universal logic includes four ways to contain 

dialectical contradictions (uncertainties) as follows: 

1) The establishment of flexible domain. 

The uncertainty firstly presents in the uncertainty of 

truth value of proposition. From the view of truth value 

domain and space dimension of proposition variable, the 

scope of uncertainty is fraction dimension space [0, 1] n , 

n>0, which can include integer dimension space [0, 1] n , 

n=2, 3, …, and which can also include 1-dimension 

continuous value space [0, 1]. This gives the possible to 

break the limitations of truth value domain of 1- 

dimaention two-valued logic. 

The classical logic is a single granularity from the view 

of individual variable domain, that is, the logical 

properties of whole domain are identical. The future 

development trend of modern logic is introduced the 

concept of granularity computing into the logic. The 

domain is divided into different sub-domains according to 

some kind of equivalence relations, and the logical 

properties of different sub-domain may be different to 

express the uncertainty of domain. This gives the possible 

to break the limitations of single granularity of 1- 

dimension two-valued logic. 

From the model domain, the classical logic is the 

single-mode. There are many different modes in the 

current modal logic. In the future continuous variable 

mode may be build, which can accurately describe the 

effect of modal area in uncertainty. This gives the 

possible to break the limitations of single mode of 1- 

dimension two-valued logic. 

2) The definition of integrity cluster of operation 

model 

The effect of all kinds of uncertainties on logic 

operations results can be expressed by all kinds of 

continuous-valued proposition conjunction integrity 

cluster of operation model. For example, in the 

propositional universal logics, Firstly, we narrow the 

logical scope to include fitness subspace of the 

contradictions of enemy/friends, loose/strict, light/heavy 

(include one, two or three) through time and space; 

secondly, we introduce two continuous variable flexible 

parameters k, h∈[0, 1] into the logical operation models, 

and use the corresponding adjustment function to 

describe the full impact of the dialectical contradictions 

(or uncertainty) for the proposition conjunction 

computing model. Finally, we get the various types of 

propositional logics. It is obvious that if we can reduce 

the scope of logic to adapt to accommodate just a 

dialectical contradiction (or uncertainty) of the sub-space 

by time and space, then continuously variable flexible 

parameters and adjustment functions are introduced into 

the logic operation model, which can include effectively 

and deal with the dialectical contradictions (or 

uncertainties) in mathematics dialectical logic. This is 

foundation for continuous-valued logical algebra that will 

discuss below. 

3) Defining a variety of flexible quantifiers to express 

the uncertainty of constraints (ranges). 

The flexible quantifiers are: the universal quantifier ∀; the 

existential quantifier ∃; the threshold quantifier ♂ k 

symbolizing the threshold of propositional truth; the 

hypothesis quantifier $ k symbolizing hypothesis 

proposition; the scope quantifier ∮ k constraining the 

scope of individual variables; the position quantifier ♀ k 

indicating the relative position of an individual variable 

and a specific point; the transition quantifier ∫ k changing 

the distribution transitional feature of the predicate truth. 

k∈[0, 1] is a variable parameter, which express the 

change of constraints. When k=1, the constraints are the 

largest (strong), and when k=0, the constraints are the 

smallest (weak). So in this way the logic not only 

describe the uncertainty of constraints, but also control 

the degree of reasoning rules by adjusting the degree of k 



value. For example, in the scope quantifier ∮ k , k can be 

changed continuously to express the uncertainty of the 

scope of individual variables. In special case, k=1 

indicates the universal quantifier∀; k>0 indicates 

existential quantifier ∃, k=! indicates the only existential 

quantifier ∃!; k=0 indicates the constraints of no scope 

quantifier. 

4) All kinds of continuous-valued reasoning model 

Because the truth value of flexible proposition, 

computing model and quantifiers of proposition 

conjunction are flexible, the reasoning rules based on 

them such as deductive reasoning, inductive reasoning, 

analogical reasoning, assuming reasoning, the evolution 

of reasoning are also flexible. The flexible reasoning 

rules are different from standard logic, which can coexist 

in a reasoning process. They transform each other by 

changing flexible parameters, and in which deductive 

reasoning mode is the most basic mode. Therefore, the 

theoretical framework can describe the unity of opposites 

and transformation process of contradictions, which 

provides the possibility to the symbolization and 

mathematization of dialectical logic. 

The operators of universal logic as following: 

1) Not operation: 

NOT operation model N (x) is unary operation on [0, 

1]→[0, 1], which satisfies the following Not operation 

axiom. 

Boundary condition N1: N (0)=1, N (1)=0. 

Monotonicity N2: N (x) is monotonously decreasing, 

iff ∀x, y∈[0, 1], if x 1 then its value will be 1, if x < 0 , its value 

will be 0. 

1-level universal AND operators are mapping 

1 mn mn 1/ 

mn 

T :[0, 1] × [0, 1] → [0, 1] T( x, y, h, k) =Γ [( x + y −1) ] 

which is usually denoted by 

∧ 

hk , 

. The relation m and h is 

as same as (2), the relation of n and k is the same as (1). 

There are four special cases of T (x, y, h) (see Figure 2) 

as follows: 

Zadeh AND operator T (x, y, 1)=T 3 =min (x, y) 

Probability AND operator T (x, y, 0.75)=T2=xy 

Bounded AND operator T (x, y, 0.5)=T 1 =max (0, 

x+y-1) 

Drastic AND operator T (x, y, 0)=T 0 =ite{min (x, 

y)|max (x, y)=1; 0} 

Figure 2. AND operator model figure for special h 

3) OR operation: 

OR operation model S (x, y) is binary operation in [0, 

1] 2 →[0, 1], which satisfies the following operation 

axioms: x, y, z∈[0, 1]. 

Boundary condition S (1, y)=1, S (0, y)=y. 

Monotonicity S (x, y) increases monotonously along 

with x, y. 

Association law S (S (x, y), z)=S (x, S (y, z)). 

Lower bound S (x, y)≥max (x, y). 

The Dualization law holds between S (x, y, k, h) and T 

(x, y, k, h). 

N (S (x, y, k, h), k)=T (N (x, k), N (y, k), k, h) 

N (T (x, y, k, h), k)=S (N (x, k), N (y, k), k, h) 



There are four special cases of S (x, y, h) (see Figure 3) 

as following: 

Zadeh OR operator S (x, y, 1)=S 3 =max (x, y) 

Probability OR operator S (x, y, 0.75)=S2=x+yxy 

Bounded OR operator S (x, y, 0.5)=S 1 =min (1, x+ 

y) 

Drastic OR operator S (x, y, 0)=S 0 =ite{max (x, 

y)|min (x, y)=0;1} 

Figure 4. IMPLICATION operator model figure for special h 

Figure 3. OR operator model figure for special h 

4) IMPLICATION operation 

IMPLICATION operation model I (x, y) is binary 

operation in [0, 1] 2 →[0, 1], which satisfies the following 

operation axioms: x, y, z∈[0, 1]. 

Boundary conditions I1 I (0, y, h, k)=1, I (1, y, h, k) 

=y, I (x, 1, h, k)=1. 

Monotonicity I2 I (x, y, h, k) is monotone increasing 

along with y, and is monotone decreasing along with x. 

Continuity I3 When h, k∈ (0, 1), I (x, y, h, k) is 

continuous along with x, y. 

Order-preserving property I4 I (x, y, h, k)=1, iff x≤y 

(except for h=0 and k=1). 

Deduction I5 T (x, I (x, y, h, k), h, k)≤y (Hypothetical 

consequence). 

0-level universal IMPLICATION operators are 

mapping 

I :[0, 1] × [0, 1] → [0, 1] , I( x, y, h) = ite{1 | x ≤ y; 0 | m ≤ 0 and 

1 m m 1/ 

m 

y = 0 ;Γ [(1 − x + y ) ]}} 

, which is usually denoted by 

⇒ 

h 

. The relation m and h is the same as (1). 

1-level universal IMPLICATION operators are 

mapping I :[0, 1] × [0, 1] → [0, 1] , I( x, y, h) = ite{1 | x≤ y; 0 | 

m and y x y 

1 mn mn 1/ 

mn 

≤ 0 = 0 ;Γ [(1 − + ) ]}, which is usually 

denoted by ⇒ 

h 

. The relation m and h is the same as (1), 

the relation of n and k is the same as (2). 

There are four special cases of I (x, y, h) (see Figure 4) 

as following: 

Zadeh IMPLICATION operator I (x, y, 1)=I 3 = 

ite{1|x≤y; y} 

Probability IMPLICATION operator (Goguen 

Implication) I (x, y, 0.75)=I2=min (1, y/x) 

Bounded IMPLICATION operator (Lukasiewicz 

Implication) I (x, y, 0.5)=I 1 =min (1, 1-x+y) 

Drastic Implication operator I (x, y, 0)=I 0 =ite{y|x 

=1; 1} 

C. Universal Logic System ULh∈ (0, 

1] 

The languages of 0-level UL system ULh∈ (0, 1] are based on 

two basic connectives → and & and one truth constant 0 , 

which semantics are 0-level universal AND, 0-level 

universal IMPLICATION and 0 respectively (see [15]). 

Axioms of the system ULh∈ (0, 1] are as following: 

(i) ( φ →ψ) →(( ψ → χ)( φ → χ)) 

(ii) ( φ & ψ) 

→ φ 

(iii) ( φ & ψ) → ( ψ & φ) 

(iv) φ &( φ →ψ) →( ψ &( ψ → φ)) 

(v) ( φ →( ψ → χ)) →(( φ& 

ψ) → χ) 

(vi) (( φ & ψ) → χ) →( φ →( ψ → χ)) 

(vii) (( φ →ψ) → χ) →((( ψ →φ) → χ) → χ) 

(viii) 0 → φ 

(ix) ( φ →φ& ψ) →(( φ →0) ∨ψ ∨(( φ →φ& φ) ∧( ψ → ψ & ψ))) 

. 

The deduction rule of ULh∈ (0, 1] is modus ponens. 

Definition 2 [15] A ŁΠG 

algebra is a BL-algebra in 

which the identity 

( x⇒ x∗y) ⇒(( x⇒0) ∪ y∪(( x⇒ x∗x) ∩( y⇒ y∗ y))) = 1 

is valid. 

For each h ∈ (0, 1] , ([0, 1] , min, max,∧ h,⇒ h, 0, 1) which is 

called ŁΠ G unit interval is a linear ordering ŁΠ G algebra 

with its standard linear ordering. 

Theorem 1 [16] (Soundness) All axioms of ULh∈ (0, 1] are 

1-tautology in each PC (h). If φ and ϕ → ψ are 1-tautology 

of PC (h) then ψ is also a 1-tautology of PC (h). 

Consequently, each formula provable in ULh∈ (0, 1] is a 1- 

tautology of each PC (h), i.e. Γ φ , then Γ φ . 

Theorem 2 [16] (Completeness) The system ULh∈ (0, 1] is 

complete, i.e. If φ , then φ . In more detail, for each 

formula φ ϕ , the following are equivalent: 

(i) φ is provable in ULh∈ (0, 1] , i.e. φ ; 

(ii) φ is an L-tautology for each ŁΠG 

-algebra L ; 

(iii) φ is an L-tautology for each linearly ordered ŁΠG 

- 

algebra L ; 

(iv) φ is a tautology for each ŁΠ G unit interval, i.e. 

φ . 

D. Universal Logic System UL − h∈ (0, 

1] 

Definition 3 [17]Axioms of UL − h∈ (0, 1] are those of ULh∈ (0, 

1] 

plus 

( − −φ) 

≡ φ (Involution) 



Δ( φ →ψ) →Δ( −ψ →− φ) 

(Order Reversing) 

Δφ 

∨¬Δ φ 

Δ( φ ∨ψ) →( Δφ ∨Δ ψ) 

Δφ 

→ φ 

Δφ 

→ΔΔ φ 

Δ( φ →ψ) →( Δφ →Δ ψ) 

where 

¬ φ is φ → 0 . Deduction rules of UL − h∈ (0, 1] are those 

of UL Δ h∈ (0,, 1] that is, modus ponens and generalization: from 

ϕ derive Δ ϕ . 

Definition 4 [17] A ŁΠG Δ 

-algebra is a structure 

L =< L,∗,⇒,∩,∪, 01 , ,Δ > which is a ŁΠG 

algebra 

expanded by an unary operation Δ in which the 

following formulas are true: 

Δx∪( Δx⇒ 0) = 1 

Δ( x ∪ y) 

≤ Δx∪Δ 

y 

Δx 

≤ x 

Δx 

≤ ΔΔ x 

( Δx) ∗( Δ( x⇒ y)) 

≤ Δ y 

Δ 1= 

1 

Definition 5 [17] A ŁΠG − -algebra is a structure L 

=< L,∗,⇒,∩,∪, 01 , ,Δ,− > which is a ŁΠG Δ 

-algebra 

expanded by an unary operation -, and satisfying the 

following conditions: 

(1) −− x = x 

(2) Δ( x ⇒ y) =Δ( −y⇒ − x) 

(3) Δx 

∨¬Δ x = 1 

(4) Δ( x ∨ y) ≤( Δx∨Δ 

y) 

(5) Δx ≤ x 

(6) Δx ≤ ΔΔ x 

(7) ( Δx) ∗( Δ( x⇒ y)) 

≤ Δ y 

(8) Δ 1= 

1 

Theorem 3 [17] (Soundness) Each formula provable in 

UL − h∈ (0, 1] is a L-tautology for each ŁΠG − -algebra. 

Theorem 4 [17] (Completeness) The system UL − h∈ (0, 1] is 

complete, i.e. If φ , then φ . In more detail, for each 

formula φ , the following are equivalent: 

(i) φ is provable in UL − h∈ (0,, 1] i.e. ϕ , 

(ii) φ is an L-tautology for each ŁΠG − -algebra L, 

(iii)φ is an L-tautology for each linearly ordered ŁΠG − - 

algebra L. 

III. PREDICATE FORMAL SYSTEM ∀ h (0 1] 

UL − ∈ , 

In order to build first-order predicate formal deductive 

system based on 1-level universal AND operator, we give 

the first-order predicate language as following: 

First-order language J consists of symbols set and 

generation rules: 

The symbols set of J consist of as following: 

(1) Object variables: x, yzx , , 

1, y1, z1, x2, y2, z2,; 

(2) Object constants: abca , , , 

1, b1, c1,, Truth constants: 

01 , ; 

(3) Predicate symbols: PQRP , , , 

1, Q1, R1,; 

(4) Connectives: &,→, Δ,− ; 

(5) Quantifiers: ∀ (universal quantifier), ∃ 

(existential quantifier); 

(6) Auxiliary symbols: (, ), , . 

The symbols in (1)- (3) are called non-logical symbols 

of language J. The object variables and object constants 

of J are called terms. The set of all object constants is 

denoted by Var (J), The set of all object variables is 

denoted by Const (J), The set of all terms is denoted by 

Term (J). If P is n-ary predicate symbol, t 1 

, t 2 

,, t n 

are 

terms, then Pt ( 

1, t2,, t n 

) is called atomic formula. 

The formula set of J is generated by the following 

three rules in finite times: 

(i) If P is atomic formula, then P∈ J ; 

(ii) If PQ , ∈ J, then P&Q, P→ Q,ΔP∈ J,−P∈ J ; 

(iii) If P∈ J , and x ∈ Var( J ) , then 

( ∀ x) P,∃ ( x) 

P∈ J . 

The formulas of J can be denoted by φ, ϕψ , , φ1, ϕ1, ψ1,. 

Further connectives are defined as following: 

φ ∧ ψ is φ & ( φ → ψ) 

, 

φ ∨ ψ is (( φ →ψ) →ψ) ∧( ψ →φ) → φ) 

, 

¬ φ is φ → 0 , 

φ ≡ ψ is ( φ →ψ) & ( ψ → φ) 

. 

Definition 6The axioms and deduction rules of predicate 

formal system ∀ UL − h∈ (0, 

1] as following: 

(i)The following formulas are axioms of ∀ UL − h∈ (0, 

1] : 

(U1) ( φ →ψ) →(( ψ → χ) →( φ → χ)) 

(U2) ( φ & ψ) 

→ φ 

(U3) ( φ & ψ) → ( ψ & φ) 

(U4) φ &( φ →ψ) →( ψ &( ψ → φ)) 

(U5) ( φ →( ψ → χ)) →(( φ& 

ψ) → χ) 

(U6) (( φ & ψ) → χ) →( φ →( ψ → χ)) 

(U7) (( φ →ψ) → χ) →((( ψ →φ) → χ) → χ) 

(U8) 0 → φ 

(U9) ( φ →φ& 

ψ) →(( φ →0) ∨ψ ∨(( φ →φ& 

φ) 

∧ 

( ψ → ψ & ψ))) 

(U10) ( − −ϕ) 

≡ ϕ 

(U11) Δ( ϕ →ψ) →Δ( −ψ →− ϕ) 

(U12) Δφ ∨¬Δ φ 

(U13) Δ( φ ∨ψ) →( Δφ∨Δ 

ψ) 

(U14) Δφ → φ 

(U15) Δφ →ΔΔ φ 

(U16) Δ( φ →ψ) →( Δφ →Δ ψ) 

(U17) ( ∀x) φ( x) → φ( t) 

(t substitutable for x in φ ( x) 

) 

(U18) φ() t →( ∃ x) φ( x) 

(t substitutable for x in φ ( x) 

) 

(U19) ( ∀x)( χ →φ) →( χ →( ∀ x) φ) 

(x is not free in 

χ ) 



(U20) ( ∀x)( φ → χ) →(( ∃x) φ → χ) 

(x is not free in 

χ ) 

(U21) ( ∀x)( φ ∨χ) →(( ∀x) φ∨ χ) 

(x is not free in χ ) 

Deduction rules of ∀ UL − h∈ (0, 

1] are three rules. They are: 

Modus Ponens (MP): from φ, φ → ψ infer ψ ; 

Necessitation: from φ infer Δ φ ; 

Generalization: from φ infer ( ∀ x) 

φ . 

The meaning of “t substitutable for x in φ ( x) 

” and “x 

is not free in χ ” in the above definition have the same 

meaning in the classical first-order predicate logic, 

moreover, we can define the concepts such as proof, 

theorem, theory, deduction from a theory T, T- 

consequence in the system ∀ UL − h∈ (0, 

1] . T φ denotes that 

φ is provable in the theory T. φ denotes that φ is a 

theorem of system ∀ ULh 

∈ (0 , 1] 

. Let 

− 

Thm( ∀ UL h∈ (0, 

1] ) = { φ ∈ J | φ} , Ded( T) = { φ∈ J | T φ} 

. 

Being the axioms of propositional system UL − h∈ (0, 1] are in 

predicate system ∀ UL − h∈ (0, 

1] , then the theorems in 

UL h∈ (0, 1] are theorems in ∀ UL − h∈ (0, 

1] . According the 

similar proof in [3, 16, 17] we can get the following 

lemmas. 

Lemma 1 The hypothetical syllogism holds in 

∀ , i.e. let Γ= { φ → ψψ , → χ} 

, then Γ φ → χ . 

UL − h∈ (0, 

1] 

Lemma 2 ∀ UL − h∈ (0, 

1] proves: 

(1) φ → φ ; 

(2) φ →( ψ → φ) 

; 

(3) ( φ →ψ) →(( φ →γ) →( ψ → γ)) 

; 

(4) ( φ & ( φ →ψ)) 

→ ψ ; 

(5) Δφ ≡ Δφ& 

Δ φ . 

Lemma 3 If T = { φ → ψ, χ → γ} 

, then 

T ( φ & χ) → ( ψ & γ) 

. 

Let J is first-order predicate language, L is linearly 

ordered ŁΠG − algebra, M = ( M, ( rP ) 

P, ( mc) c) 

is called a 

L-evaluation for first-order predicate language J, which 

M is non-empty domain, according to each n-ary 

predicate P and object constant c, r 

P 

is L-fuzzy n-ary 

n 

relation: rP 

: M → L, m 

c 

is an element of M. 

Definition 7 Let J be predicate language, M is L- 

evaluation of J, x is object variable, P∈ J . 

(i) A mapping v: Term( J ) → M is called M- 

evaluation, if for each c ∈Const (J), vc () = mc 

; 

(ii)Two M-evaluation vv′ , are called equal denoted 

by v ≡ 

x 

v′ if for each y∈ 

Var( J) \ x , there is 

vy ( ) = v′ 

( y) 

. 

(iii) The value of a term given by M, v is defined by: 

x = v( x) 

; c = mc 

. We define the truth value 

M, v 

M, 

v 

L 

M v 

φ , 

of a formula φ as following. Clearly, ∗,⇒,Δ 

denote the operations of L . 

L 

1, 2,, n 

= 

M v P 1 

,, 

, M, v n M, 

v 

L L L 

→ = ⇒ 

M, v M, v M, 

v 

L L L 

& = ∗ 

M, v M, v M, 

v 

L 

L 

Pt ( t t) r( t t ) 

φ ψ φ ψ 

φ ψ φ ψ 

0 = 0; 1 = 1 

M, v 

M, 

v 

L 

L 

φ 

M, v 

M, 

v 

L 

L 

φ 

M, v M, 

v 

L 

L 

φ φ 

M, v 

M, 

v′ 

L 

L 

φ φ 

M, v 

M, 

v′ 

Δ φ = Δ 

− φ =− 

( ∀ x) = inf{ | v ≡ v ′ } 

( ∃ x) = sup{ | v ≡ v ′ } 

In order to the above definitions are reasonable, the 

infimum/supremum should exist in the sense of L. So the 

structure M is L-safe if all the needed infima and suprema 

L 

exist, i.e. φ 

M , 

is defined for all φ, v . 

v 

Definition 8 Let φ ∈ J , M be a safe L-structure for J. 

(i) The truth value of φ in M is 

L 

L 

φ = inf{ φ ,v 

| v M − evaluation} . 

M 

M 

(ii) A formula φ of a language J is an L -tautology if 

φ 

L 

= 1 for each safe L-structure M. i.e. L 

M L 

φ 1 

Mv , 

= for 

each safe L-structure M and each M-valuation of object 

variables. 

Remark For each h∈ (0, 1] , k∈ (0, 1) , 

([0, 1] ,∧ 

hk , 

,⇒ 

hk , 

, min, max, 0, 1 ,Δ,−) 

is a ŁΠG − -algebra. 

So the predicate system ∀ UL − h∈ (0, 

1] can be considered the 

axiomatization for 1-level universal AND operator. 

III. SOUNDNESS OF SYSTEM ∀ h (0 1] 

x 

x 

UL − ∈ , 

Definition 9 A logic system is soundness if for its each 

theorem φ , we can get φ is a tautology. 

Theorem 5 (Soundness of axioms) The axioms of 

∀ are L-tautologies for each linearly ordered 

UL − h∈ (0, 

1] 

G − 

ŁΠ -algebra L. 

Proof. The axioms of (U1)- (U16) are L-tautologies 

can be get as in propositional calculus. We verify (U17)- 

(U21) 

To verify (U17), (U18), let y is substitutable for x to 

φ , when v′′ ≡ 

x 

v and v′′ ( x) = v( y) 

, there is 

L 

L 

L 

L 

φ( y) = φ ( x) 

So, ( ∀ x) φ( x) = inf ( ) 

M, v 

M, 

v′′ 

M v v′≡ v 

φ x 

, M, 

v′ 

≤ 

L L L 

φ( y) ≤ sup ( ) ( ) ( ) 

M v v 

φ x = ∃ ′ 

x φ x , then 

, ′′ M, v′ 

M, 

v 

( ∀ x ) φ( x ) → φ( y ) = ( ∀ x ) φ( x ) → φ( y ) = 1. 

M, v M, v M, 

v 

For (U19), let x not free in χ , then for each M- 

valuation w, when w≡ 

x 

v , we have v = φ( x) 

. 

M, w 

M, 

v 

We have to prove 

L L L L 

inf ( v ⇒ φ ) ≤( v ⇒ inf φ ) . 

w 

M, w M, w M, v w M, 

w 

L 

L 



L 

L 

Let v = v = a , φ 

M, v M, 

w 

M , 

= b 

w w 

, thus we must 

prove inf 

w( a⇒bw) ≤( a⇒ inf 

wbw) 

. On the one hand, 

inf w 

b w 

≤ b w 

, thus a⇒bw ≥( a⇒ inf 

wbw) 

for each w, 

thus inf 

w( a⇒bw) ≥( a⇒ inf 

wbw) 

. On the other hand if 

z ≤( a⇒ b w 

) for each w, then z∗a ≤ bw 

for each w, 

z∗a ≤ inf w 

b w 

, z ≤( a⇒ inf 

wbw) 

. Thus ( a⇒ inf 

wbw) 

is 

the infimum of all ( a⇒ 

b w 

). So (U19) holds. 

For (U20), we need to verify 

inf 

w( aw ⇒ bw) = (sup 

w 

aw 

⇒ b) 

. Indeed, sup w 

≥ a w 

, thus 

(sup 

w 

aw ⇒b) ≤( aw 

⇒ b) 

, hence 

(sup 

w 

aw ⇒b) ≤inf w( aw 

⇒ b) 

, If z ≤ aw 

⇒ b for all w , 

then aw 

≤( z ⇒ b) 

for all w, then sup 

w 

aw 

≤( z ⇒ b) 

, 

z ≤(sup waw 

⇒ b) 

, so sup w 

a w 

⇒ b is the infimum. So 

(U20) holds. 

Finally we verify (U21), we need to verify 


w( a∨ bw) = a∨ infwbw 

. Indeed, a ≤ a∨ bw 

, thus 

a ≤inf w( a∨ bw) 

; similarly, infwbw ≤inf w( a∨ bw) 

, thus 

a∨infwbw ≤inf w( a∨ b) 

. Conversely, let z ≤ a∨ bw 

for 

all w , we prove z ≤ a∨ inf w 

b w 

. 

Case 1: Let a ≤ inf w 

b w 

. Then z ≤ bw 

for each w , 

z ≤ inf w 

b w 

and z ≤ a∨ inf w 

b w 

. 

Case 2: Let a ≥ inf w 

b w 

. Then for some w 0 

, a ≥ b w0 

, 

thus z ≤ a and z ≤ a∨ inf w 

b w 

. 

So we prove the soundness of axioms. 

Theorem 6 (Soundness of deduction rules) (1) For 

arbitrary formulas φ, ψ , safe-structure M and evaluation 

L L L 

v , ψ ≥ φ ∗ φ → ψ . In particular, if 

M, v M, v M, 

v 

L 

L 

L 

= → = 1 

M, v 

M, 

v L 

then ψ 1 

M , 

= 

v L 

. 

L L L 

(2) Consequently, ψ φ φ ψ 

M M M 

φ φ ψ 

≥ ∗ → , thus if 

φ, φ → ψ are then ψ is 1 L 

-true in M. 

(3) If φ is 1 L 

-true in M then Δ φ is 1 L 

-true in M . 

(4) If φ is 1 L 

-true in M then ( ∀ x) 

φ is 1 L 

-true in M. 

Proof. (1) is just as in propositional calculus. 

To prove (2) put φ = aw, ψ = bw, inf 

w 

w 

w 

aw 

= a. We 

have to prove inf 

w( aw ⇒bw) ≤infw aw ⇒ infwbw 

. 

Observe the following: 

inf( aw ⇒bw) ≤( aw ⇒bw) ≤( a⇒ bw) 

, 

thus inf 

w( aw ⇒bw) ≤inf w( a⇒ bw) 

. It remains to prove 


w( a⇒bw) ≤ a⇒ infwbw, this is holds from Theorem 

5. 

L 

(3) If φ is 1 L 

-true in M then φ 

M 

= 1L 

, so 

L 

L 

Δ φ =Δ φ = . Then (3) holds. 

1 

M, v 

M, 

v L 

L 

M 

φ ′ 

′ 

, 

} 

L 

M 

L 

M 

(4) Being φ = inf{ φ ,v 

| v M − evaluation} 

≤ inf{ 

Mv| v ≡ v = ( ∀ x) φ } , So (4) holds. 

So we can get the following soundness theorem. 

L 

Theorem 7 (Soundness) Let L is linearly ordered 

ŁΠG − -algebra and φ is a formula in J, if φ , then φ is 

L 

L-tautology, i.e. φ = 1 . M L 

Similarly, we can get the following strong soundness 

theorem. 

Definition 10 Let T be a theory, L be a linearly ordered 

ŁΠG − -algebra and M a safe L-structure for the language 

of T. M is an L-model of T if all axioms of T are 1 L 

-true 

in M, i.e. φ = 1 L 

in each φ ∈ T . 

Theorem 8 (Strong Soundness) Let T be a theory, L is 

linearly ordered ŁΠG − -algebra and φ is a formula in J, 

L 

if T φ ( φ is provable in T), then φ 

M 

= 1L 

for each 

linearly ordered ŁΠG − -algebra L and each L-model M 

of T. 

Proof. In fact, from the proof of Theorem 5, for each 

L-model M of T, the axioms are true, and the formulas in 

T are true, from the proof of Theorem 6, the deduction 

rules preserve true. So the theorem holds. 

Theorem 9 (Deduction Theorem) Let T be a theory, 

φ, ψ are closed formulas. Then ( T ∪φ) 

ψ iff 

T Δφ →ψ 

. 

Proof. Sufficiency: Let T Δφ →ψ 

, from φ 

( φ∈ ( T ∪ φ) 

), then Δ φ by necessitation, so we can get 

ψ by MP rules. 

Necessity: Let m is the proof length from T ∪ φ} 

to ψ , 

we prove by induction for the length m. 

When m = 1 , ψ ∈T 

∪φ∪Axm(C ∀ ) , if ψ = φ , The 

result holds. If ψ ∈ T or ψ is axiom, from Lemma2 (2), 

we have ψ →( Δφ → ψ) 

, then by ψψ , →( Δφ→ ψ) 

, we 

get Δφ → ψ , thus T Δφ →ψ 

. 

Assume that the result holds when m≤ 

k , i.e. we get 

γ at k step, then T Δφ → γ . Now Let m= k + 1. 

If ψ is obtained from MP rule by the above results 

γγ , → ψ in the proof sequence, then by induction 

hypothesis, we get T Δφ → γ, T Δφ →( γ →ψ) 

. 

From Lemma 3, we can get 

T ( Δφ& Δφ) →( γ &( γ →ψ)) 

. Being 

T ( Δφ) &( Δφ) 

≡ Δφ 

, so T Δφ →( γ &( γ →ψ)) 

. 

From lemma 2 (4) we have ( γ & ( γ →ψ) 

→ ψ , so we 

get T Δφ →ψ 

by the hypothetical syllogism. 

If ψ is obtained from necessitation rule by the above 

step γ in the proof sequence, i.e. Δ γ = ψ , then by 

induction hypothesis, we get T Δφ →γ 

. 

T Δ( Δφ →γ) 

, from (U16) we can get T ΔΔφ → Δγ 

, 

from (U15) we can get Δφ 

→ΔΔ φ , thus by the 

hypothetical syllogism we can get T Δφ →Δγ 

, i.e. 

T Δφ →ψ 

. 

If ψ is obtained from generalization rule by the above 

step γ in the proof sequence, i.e. ( ∀ x) 

γ = ψ , then by 



induction hypothesis, we get T Δφ →γ 

, From 

generalization rule we can get T ( ∀x)( Δφ →γ) 

, being 

Δ φ, γ are closed formula and from (U19), we can get 

T Δφ 

→( ∀x) 

γ , i.e. T Δφ →ψ 

. 

So the theorem holds. 


In this paper a predicate calculus formal deductive 

system ∀ h (0 1] based on the propositional system 

UL − ∈ , 

UL − h∈ (0, 1] for 1-level universal AND operator is built up. 

We prove the system ∀ UL − h∈ (0, 

1] is sound. The deduction 

theorem is also given. Next we will discuss the 

completeness of system ∀ h (0 1] . 

UL − ∈ , 


This work is partially supported Scientific Research 

Program Funded by Shaanxi Provincial Education 

Department (Program No. 12JK0878) and Doctor 

Scientific Research Foundation Program of Xi'an 

Polytechnic University. 

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Yingcang Ma, is a professor in school 

of science, Xi'an Polytechnic University. 

He received the PhD. degree from 

School of Computer Science, 

Northwestern Polytechnical University, 

in July 2006. His main researchinterests 

are in the areas of fuzzy set, rough set 

and non-classical mathematical logic. 

Hucan He, male, Professor and Ph.D. 

tutor from the Department of Computer 

Science and Engineering of 

Northwestern Polytechnical University, 

interested in the foundation and 

application of AI, universal logic and 

uncertainties reasoning. 



Analysis of Boolean Networks using An 

Optimized Algorithm of Structure Matrix based 

on Semi-Tensor Product 

Jinyu Zhan 

University of Electronic Science and Technology of China, Chengdu, China 

Email: zhanjy@uestc.edu.cn 

Shan Lu and Guowu Yang 

University of Electronic Science and Technology of China, Chengdu, China 

Email: 617999242@qq.com, guowu@uestc.edu.cn 

Abstract—The structure matrix based on semi-tensor 

product can provide formulas for analyzing the 

characteristics of a Boolean network, such as the number of 

fixed points, the number of circles of different lengths, 

transient period for all points to enter the set of attractors 

and basin of each attractor. However, the conventional 

method of semi-tensor product gains the structure matrix 

through complex matrix operations with high computation 

complexity. This paper proposes an optimized algorithm 

which gains the structure matrix through the truth table 

reflecting the state transformation of Boolean networks. The 

effectiveness and feasibility of our optimized approach are 

demonstrated through the analysis of a practical Boolean 

network of the mammalian cell. 

Index Terms—semi-tensor product, Boolean network, 

structure matrix, truth table 


The Boolean network, introduced firstly by Kauffman 

[1], and then developed by [2][3][4][5][6][7][8] and 

many others, becomes a powerful tool in describing, 

analyzing, and simulating the cell network. It was shown 

that the Boolean network plays an important role in 

modeling cell regulation, because they can represent 

important features of living organisms [9][10]. It has 

received the most attention, not only from the biology 

community, but also physics, system science, etc. 

The structure of a Boolean network is described in 

terms of its cycles and the transient states that lead to 

them. Several useful Boolean networks have been 

analyzed and their circles have been revealed [11][12]. It 

was pointed in [13] that finding fixed points and circles 

of a Boolean network is an NP hard problem. Semi-tensor 

Manuscript received May 24, 2012; revised June 1, 2012; accepted 

July 1, 2012. 

This work was supported by the Fundamental Research Funds for 

the Central Universities of China under Grant No. ZYGX2009J062 and 

the National Natural Science Foundation of China under Grant No. 

60973016. 

Corresponding author: Jinyu Zhan, email: zhanjy@uestc.edu.cn 

product of matrix (STP), presented by Cheng [14]. Using 

STP, a Boolean network equation can be expressed as a 

conventional discrete time linear system which contains 

complete information of the dynamics of a Boolean 

network. Analyzing the structure matrix of a Boolean 

network, precise formulas are obtained to determine the 

number of fixed points and numbers of all possible 

circles of different lengths. 

But the conventional method to calculate the structure 

matrix of a Boolean network, presented in 

[15][18][19][21], is very complex. In this paper, a 

optimized algorithm is proposed to calculate the structure 

matrix. Unlike existing methods, our approach gets the 

structure matrix of a Boolean network not through the 

complex matrix operations but through the truth table 

which reflects the state transformation of the Boolean 

network. Compared with the conventional method, our 

approach can greatly reduce the calculation complexity. 

The methods for analyzing the characteristics of a 

Boolean network are given. The analysis of a practical 

Boolean network of the mammalian cell shows that our 

approach is effective and efficient. 

The rest of the paper is organized as follows. Section II 

gives a brief introduction to semi-tensor product of 

matrices, matrix expression of logic and dynamics of 

Boolean network. The conventional method to calculate 

the structure Matrix of a Boolean Network is given in 

Section III and our approach is proposed in Section IV. 

Section V gives the methods to analyze the characteristics 

of Boolean networks through the structure matrix. 

Section VI gives a practical Boolean network of the 

mammalian cell to show the effectiveness and feasibility 

of our approach. Finally, some conclusions are drawn in 

Section VII. 

II. EXPRESSION OF BOOLEAN NETWORKS IN SEMI-TENSOR 

PRODUCT 

A. Semi-tensor Product 

This section is a brief introduction to semi-tensor 

product (STP) of matrices. STP of matrices is a 


doi:10.4304/jcp.8.6.1441-1448


generalization of conventional matrix product, which 

extends the conventional matrix product to any two 

matrices. It plays a fundamental rule in the following 

discussion. We restrict it to some concepts and basic 

properties used in this paper. In addition, only left semitensor 

product for multiplying dimension case is involved 

in the paper. We refer to [14][15][16][17] for right semitensor 

product, arbitrary dimensional case and much 

more details. Throughout this paper “semi-tensor 

product” means the left semi-tensor product for 

multiplying dimensional case. 

Definition 1: 1. Let X be a row vector of dimension 

np , and Y be a column vector with dimension p . Then 

we split X into p equal-size blocks as 1 , 2 p 

X X , , X , 

which are 1× n rows. Define the STP, denoted by × , as 


p 

⎧ 

⎪X 

× Y = ∑ X 

i= 

1 

⎨ 

p 

⎪ 

T T 

Y × X = 

⎪⎩ 

i= 

i 

∑ 

1 

y ∈ R 

i 

y ( X 

i 

i 

n 

) 

T 

∈ R 

2. Let A ∈ M m × n 

and B∈ 

M 

p × q 

. If either n is a 

factor of p , say nt = p and denote it as A ≺ 

t 

B , or 

p is a factor of n , say n = pt and denote is as 

A t 

B , then we define the STP of A and B , denoted 

by C = A× B , as the following: C consists of m × q 

ij 

blocks as C = ( C ) and each block is in (2). 

where 

ij i 

C A B j 

n 

(1) 

= × , i = 1, , m, j = 1, , q . (2) 

i 

A is the i-th row of A and 

B 

j 

is the j-th column 

of B . 

We use some simple numerical examples to describe it. 

Example 1. Let X = [1 2 3 − 1] and 

Then 

Example 2. Let 

X × Y = [1 2] ⋅ 1 + [3 −1] ⋅ 2 = [7 0] 

⎡1 2 1 1⎤ 

A = 

⎢ 

2 3 1 2 

⎥ 

⎢ ⎥ 

⎢⎣3 2 1 0⎥⎦ 

⎡1 

− 2⎤ 

, B = ⎢ ⎥ . Then 

⎣2 

−1 

⎦ 

⎡1⎤ 

Y = ⎢ 

2 ⎥ 

⎣ ⎦ . 

⎡ ⎛1⎞ ⎛−2⎞ 

⎤ 

⎢ ( 1 2 1 1 ) ⎜ ⎟ (1 2 1 1) ⎜ ⎟ ⎥ 

⎢ 

⎝2⎠ ⎝−1⎠ 

⎥ 

⎢ 

⎛1⎞ ⎛−2⎞⎥ 

A× B = ⎢( 2 3 1 2) ⎜ ⎟ ( 2 3 1 2) 

⎜ ⎟⎥ 

⎢ 

⎝2⎠ ⎝−1⎠⎥ 

⎢ 

⎥ 

⎢ 

⎛1⎞ ⎛−2⎞ 

( 3 2 1 0) ( 3 2 1 0) 

⎥ 

⎢ 

⎜ ⎟ ⎜ ⎟ 

⎝2⎠ ⎝−1⎠ 

⎥ 

⎣ 

⎦ 

⎡3 4 −3 −5⎤ 

= 

⎢ 

4 7 5 8 

⎥ 

⎢ 

− − 

⎥ 

⎢⎣ 

5 2 −7 −4⎥⎦ 

B. Matrix Expression of Logic 

In this section, the matrix expression of logic will be 

given. In a logical domain, we usually set "true" as "1" 

and "false" as "0". Then a logical variable is defined as 

x∈ D = {0,1} . There are several fundamental binary 

functions such as ¬ , ∧ , ∨ , ↔ , → , ∨ , ↑ and ↓ . 

Their truth table is as TABLE I. 

To use matrix expression each element can be 

2 

0 ~ δ , 

1 

identified in D with a vector as 1~δ 

2 

and 

2 

i 

where δ = Col( I ) . Therefore, That a n-ary logical 

n 

n 

n 

operator (or function) is a mapping: f : D → D can be 

formed as f : Δ n →Δ. 

2 

Theorem 1: Let f ( x1 

, , x n 

) be a logical function in 

vector form as f : Δ n →Δ. Then there exists a unique 

2 

, called the structure matrix of f , such that 

∈L 

M 

f 2× 

2 n 


n 

f ( x1 

, , xn) 

= M 

f 

× x, where x =× 

i= 

1 

xi 

(3) 

Therefore, the structure matrix of Negation, 

Conjunction, Disjunction, Equivalence and Implication 

are as in (4) - (11). 

¬ 

= δ 2 

[ 2 1] 

[ 1 2 2 2] 

M (4) 

M 

∧ 

= δ 2 

(5) 

M = δ 2 [ 1 1 1 2 

∨ ] 

(6) 

M = δ 2 [ 1 2 2 1 

↔ ] 

(7) 

M = δ 2 [ 1 2 1 1 

→ ] 

(8) 

p q ¬ p p∧ q p ∨ q 

TABLE I. 

TRUTH TABLE OF ¬ , ∧ , ∨ , ↔ , → , ∨ , ↑ AND ↓ 

p ↔ q p → q 

p ∨ q p↑ q p ↓ q 

0 0 1 0 0 1 1 0 1 1 

0 1 1 0 1 0 1 1 1 0 

1 0 0 0 1 0 0 1 1 0 

1 1 0 1 1 1 1 0 0 0 



M = δ 2 [ 2 1 1 2 

∨ ] 

(9) 

M = δ 2 [ 2 1 1 1 

↑ 

] 

(10) 

M = δ 2 [ 2 2 2 1 

↓ 

] 

(11) 

n k 

Theorem 2: Let F( x1 

, , xn 

): D → D be a logical 

mapping: F : Δ n →Δ k .Then there exists a unique 

2 2 

k n called the structure matrix of F , such in 

∈L 

M 

F 2 × 2 

(12). 

F( x , , x ) = M × x 

(12) 

1 

C. Dynamics of Boolean Networks 

The Boolean networks play an important role in 

modeling cell regulation, because they can represent 

important features of living organisms. The dynamics of 

the Boolean networks will be given in this section. 

Definition 2[15][18][20]: A Boolean network is a set 

of nodes A , A , 1 2 

, An 

, which interact with each other 

in a synchronous manner. At each given time t=0, 1, 2, …, 

a node has only one of two different values: 1 or 0. Thus 

the network can be described by a set of equations as in 

(13). 

⎧ A1( t+ 1) = f1( A1( t), A2( t), , An 

( t)) 

⎪A2( t+ 1) = f2( A1( t), A2( t), , An 

( t)) 

⎨ 

(13) 

⎪ 

 

⎪ 

⎩An( t+ 1) = fn( A1( t), A2( t), , An( t)) 

Where 

i 

n 

f , ( i = 1,2, , n) 

, are n-ary logic functions. 

Note that in Boolean networks each function f i 

has 

only constant, linear, or product terms [12]. 

F 

Example 3: Consider a Boolean network which 

dynamics is described as in (15). 

⎧ A1( t + 1) = A2( t) ∧ A3( t) ∧ A1( t) 

⎪ 

⎨A2( t + 1) = ( A1() t ∧ A2()) t ∨( A1() t ∧ A3() t ∧ A2()) 

t 

⎪ 

⎪⎩ 

A3( t + 1) = ( A1() t ∧ A2() t ∧ A3()) t ∨( A2() t ∧ A3()) 

t 

(15) 

In algebraic form (the notation " × " is omitted), we can 

have as in (16). 

⎧A1( t+ 1) = M∧( M A2() t A3()) t A1() 

t 

↑ 

⎪ 

⎪A2( t+ 1) = M∨(( M∧ A1( t)( M¬ 

A2( t)) 

⎪ ( M 

∧( M A1() t A3()) t A2())) 

t 

↓ 

⎨ 

⎪A3( t+ 1) = M∨(( M∧( M∧A1() t A2()) 

t 

⎪ ( M 

¬ 

A3( t)))( M∧ ( M¬ 

A2( t)) 

⎪ 

⎪⎩ A3 

()) t 

(16) 

There are some propositions in [15][18] to calculate the 

structure matrix L. 

t 

Proposition 1: Let Z ∈ R be a column. Then there exists in 

(17). 

ZA= ( I ⊗ A) 

Z 

(17) 

Proposition 2: There exists an unique matrix 

W ∈ M × 

, called the swap matrix, such that for any 

[ mn , ] 

mn mn 

two column vectors . X ∈ R 

m 

t 

n 

. and Y ∈ R . 

W[ mn , ] 

XY = YX 

(18) 

We refer to [15][18] for constructing swap matrix. 

Proposition 3: Let X . Then we have (19). 

X 

2 

∈ Δ 

= M X , 

r 

M r 

⎡1 0⎤ 

⎢ 

0 0 

⎥ 

= ⎢ ⎥ 

⎢ 0 0 ⎥ 

⎢ ⎥ 

⎣0 1⎦ 

(19) 

III. CONVENTIONAL CALCULATION OF STRUCTURE 

MATRIX 

Using Theorem 1 and 2, the dynamics of Boolean 

networks can be expressed as in (14). 

A( t+ 1) = LA( t) 

(14) 

l 

l 

where At ( + 1) =× 

i= 

1 

Ai( t+ 1) , A( t) 

= × i= 1 

Ai 

( t) 

, L is the 

structure matrix of F , L l l ∈L . 2 × 2 

By means of the STP, the dynamics of Boolean 

networks can be converted into the equivalent algebraic 

forms. Through the analysis of the structure matrix L , 

we can get the characteristics of the Boolean networks 

such as: (1) fixed points; (2) circles of different lengths; 

(3) transient period; (4) basin of each attractor[15][18]. 

Therefore, how to get the structure matrix L easily is 

very important. The conventional method to get the 

structure matrix L is as follows. 

Firstly, a simple example is given to show the structure 

of a Boolean network. 

Where 

M 

r 

is the power-reducing matrix. 

L = M∨M∧M∧ ( I2 ⊗( I2 ⊗M¬ 

( I2 

⊗ 

M∧ M¬ ( I2 ⊗( I2 ⊗M∨M∧ ( I2 

⊗M¬ 

( I2 ⊗M∧M ( I2 ⊗( I2 ⊗( 

I2 

⊗M 

↓ ↓ 

M∧)))))))))) W[2] ( I2 ⊗W[2] )( I4 ⊗W[2] 

) 

( I8 ⊗W[2] )( I32 ⊗W[2] )( I128 ⊗W[2] 

) 

( I256 ⊗W[2] )( I512 ⊗W[2] )( I1024 ⊗W[2] 

) 

W[2] ( I4 ⊗W[2] )( I16 ⊗W[2] )( I64 ⊗W[2] 

) 

( I1 

28 

⊗W[2] )( I256 ⊗W[2] )( I512 ⊗W[2] 

) 

( I2 ⊗W[2] )( I32 ⊗W[2] )( I64 ⊗W[2] 

) 

( I128 ⊗W[2] )( I256 ⊗W[2] )( I16 ⊗W[2] 

) 

( I128 ⊗W[2] )( I8 ⊗W[2] )( I64 ⊗W[2] 

) 

( I4 ⊗W[2] )( I32 ⊗W[2] )( I16 ⊗W[2] 

) 

( I8 ⊗W[2] ) MMM 

r r r( I2 

⊗( 

MM 

r r 

MM( I ⊗ MMM)) 

r r 2 r r r 

(20) 



⎡0 0 0 0 0 0 0 0⎤ 

1 0 1 [0 0 1 0 0 0 0 0] T 

⎢ 

0 0 1 0 0 0 0 0 

⎥ 

1 1 0 [0 1 0 0 0 0 0 0] T 

⎢ 

⎥ 

1 1 1 [1 0 0 0 0 0 0 0] T 

⎢0 0 0 1 0 0 0 0⎥ 

⎢ 

⎥ 

⎢0 0 0 0 1 0 0 0 

= 

⎥ 

Then, we can get the present-state matrix and nextstate 

matrix as in (21) and (22). 

⎢ 0 0 0 0 0 1 0 0 ⎥ 

⎢ 

⎥ 

⎢0 0 0 0 0 0 1 0⎥ 

⎡1 0 0 0 0 0 0 0⎤ 

⎢ 

0 0 0 0 0 0 0 1 

⎥ 

⎢ 

⎢ 

⎥ 

0 1 0 0 0 0 0 0 

⎥ 

⎢ 

⎥ 

⎢⎣1 1 0 0 0 0 0 0⎥⎦ 

⎢0 0 1 0 0 0 0 0⎥ 

⎢ 

⎥ 

0 0 0 1 0 0 0 0 

Using some theorems in [15][18][23][24] and 

Qt () = 

⎢ 

⎥ 

⎢ 

A( t + 1) = LA( t) 

, the structure matrix L is as in (20). 

0 0 0 0 1 0 0 0 ⎥ 

(21) 

⎢ 

⎥ 

We can get the structure matrix by the conventional 

⎢0 0 0 0 0 1 0 0⎥ 

⎢ 

method. But the process is very complex and the biggest 

0 0 0 0 0 0 1 0 

⎥ 

⎢ 

⎥ 

order of the matrices in the equation (20) is more than 

⎢⎣ 

0 0 0 0 0 0 0 1⎥⎦ 

1024. 

⎡0 0 0 0 0 0 0 0⎤ 

IV. NEW METHOD FOR CALCULATION OF STRUTURE 

⎢ 

0 0 1 0 0 0 0 0 

⎥ 

⎢ 

⎥ 

MATRIX 

⎢0 0 0 1 0 0 0 0⎥ 

The conventional method to calculate the structure 

⎢ 

⎥ 

0 0 0 0 1 0 0 0 

matrix L is very complex. A new method will be 

Qt ( + 1) = 

⎢ 

⎥ 

(22) 

⎢ 0 0 0 0 0 1 0 0 ⎥ 

proposed in this section. 

⎢ 

⎥ 

Definition 3: Form a square matrix by all the presentstate 

vectors A() t =× 

⎢0 0 0 0 0 0 1 0⎥ 

l 

i= 

1 

Ai() 

t , the matrix is called presentstate 

matrix, denoted by Qt ().There is another matrix 

⎢⎣ 

1 1 0 0 0 0 0 0⎥⎦ 

correspond to Qt (), called next-state matrix, denoted by 

⎢0 0 0 0 0 0 0 1⎥ 

⎢ 

⎥ 

Therefore, we can get the structure matrix L = Q( t+ 

1) 

Qt+ ( 1) . 


As A ( t + 1) = LA ( t) 

, we can derive 

⎡0 0 0 0 0 0 0 0⎤ 

Q ( t + 1) = LQ ( t) 

. It is easy to know that 

⎢ 

0 0 1 0 0 0 0 0 

⎥ 

Qt () l l ∈L , and Qt () is a invertible matrix. Then the 

⎢ 

⎥ 

2 × 2 

⎢0 0 0 1 0 0 0 0⎥ 

−1 

structure matrix L = Q( t+ 1)[ Q( t)] 

. Further simplify the 

⎢ 

⎥ 

0 0 0 0 1 0 0 0 

calculation, Qt () can be arrayed to 2 l -order identity 

L = Q( t+ 1) = 

⎢ 

⎥ 

(23) 

⎢ 0 0 0 0 0 1 0 0 ⎥ 

matrix. Therefore, L = Q( t+ 1) . 

⎢ 

⎥ 

⎢0 0 0 0 0 0 1 0⎥ 

For the example 3, we have the truth table as TABLE 

⎢0 0 0 0 0 0 0 1⎥ 

II. 

⎢ 

⎥ 

⎢⎣ 

1 1 0 0 0 0 0 0⎥⎦ 

TABLE II. 

TRUTH TABLE OF EXAMPLE 3 

We can compare the two structure matrix L gained in 

Section 3 and our method. And the structure matrix 

A 3 (t) A 2 (t) A 1 (t) A 3 (t+1) A 2 (t+1) A 1 (t+1) 

which is gained by our approach is correct. 

0 0 0 0 0 1 

0 0 1 0 1 0 By our method, it is easy to get the structure matrix 

0 1 0 0 1 1 through the truth table which reflects the transformation 

0 1 1 1 0 0 of the states. Our method to get the structure matrix is 

1 0 0 1 0 1 

simpler than the conventional method. 

1 0 1 1 1 0 

1 1 0 0 0 0 

1 1 1 0 0 0 V. APPLICATION OF STUCTURE MATRIX ON ANALYSIS OF 

BOOLEAN NETWORKS 

The state vectors’ table is as TABLE III. 

Since a Boolean network has only finite states, a 

trajectory will eventually enter into a fixed point or a 

TABLE III. 

STATE VECTORS’ TABLE 

cycle. The fixed points and cycles form the most 

important topological structure of a Boolean network. 

A 3 (t) A 2 (t) A 1 (t) A (t) 

Therefore, there are many methods to analyze the fixed 

0 0 0 [0 0 0 0 0 0 0 1] T 

0 0 1 [0 0 0 0 0 0 1 0] T points and cycles of Boolean networks. 

0 1 0 [0 0 0 0 0 1 0 0] T 

Analyzing the structure matrix of the system, easily 

0 1 1 [0 0 0 0 1 0 0 0] T 

computable formulas are obtained to show the number of 

1 0 0 [0 0 0 1 0 0 0 0] T fixed points, the numbers of circles of different lengths 



and the states in the circles. The following is a general 

result based on the algebraic form. 

Consider the Boolean network equation 

A( t+ 1) = LA( t) 

, and denote by L 

i 

, 1, 2, …, 2 n the i-th 

column of the network matrix L . Then there are 

L ∈Δ [15][18]. 

i 

2 n 

Definition 4: 1. A state x 0 

∈ Δ is called a fixed point 

2 n 

of Boolean network A( t+ 1) = LA( t) 

, if Lx0 = x0. 

k −1 

2. { x , Lx , , L x } is called a circle of Boolean 

0 0 0 

k 

network A( t+ 1) = LA( t) 

with length k , if, Lx0 = x0 

, 

k −1 

and the elements in set { x0, Lx0, , L x0} 

are distinct. 

L can be used for the matrix and its linear mapping. 

So x 

0 

may be in an L-invariant subspace. In this way, a 

circle (or a fixed point) can be defined on an L-invariant 

subspace. 

The next two theorems [15][18] show how many fixed 

points and circles of different lengths a Boolean network 

has. 

Theorem 3: Consider the Boolean network system (13). 

i 

δ is its fixed point, iff in its algebraic form (14) the 

2 n 

diagonal element l ii 

of network matrix L equals 1. It 

follows that the number of equilibriums of system (13), 

denoted by N 

e 

, equals the number of i , for which l ii 

= 1. 

Equivalently, in (24). 

Ne 

= Trace( L) 

(24) 

Theorem 4: The number of length s circles, 

inductively determined by (25). 

N s 

, is 

⎧N1 

= Ne, 

⎪ 

s 

⎨ Trace( L ) − ∑ kNk 

(25) 

k∈P( s) 

⎪ 

n 

Ns 

= , 2≤ s ≤ 2 . 

⎪⎩ 

s 

where Ps () is the set of proper factors of s , s ∈ Z + . For 

instance, P (6) = {1, 2, 3} . 

i 

s 

Let x0 

= δ . Then { x 

2 n 

0 

, Lx 0 

, , L x 0 

} is a circle with 

length s , iff i∈ Ds 

. 

Consider the Boolean network of the example 3, 

N1 = N2 = N3 = N4 = N5 = N6 = N8 = 0 , N 

7 

= 1 . 

Therefore, there is no fixed point in this network, and 

there is only one circle which length is 7. Moreover, note 


⎡0 0 0 0 0 0 0 0⎤ 

⎢ 

1 1 0 0 0 0 0 0 

⎥ 

⎢ 

⎥ 

⎢0 0 1 0 0 0 0 0⎥ 

⎢ 

⎥ 

7 

0 0 0 1 0 0 0 0 

L = 

⎢ 

⎥ 

⎢ 0 0 0 0 1 0 0 0 ⎥ 

⎢ 

⎥ 

⎢0 0 0 0 0 1 0 0⎥ 

⎢0 0 0 0 0 0 1 0⎥ 

⎢ 

⎥ 

⎢⎣0 0 0 0 0 0 0 1⎥⎦ 

(26) 

Then each diagonal nonzero column can generate the 

circle. Choosed Z = [0 0 0 0 0 0 0 1] T , then 

2 

LZ 

LZ = [0 0 0 0 0 0 1 0] T 

2 

LZ= 

3 

LZ= 

4 

LZ= 

5 

LZ= 

6 

LZ= 

[0 0 0 0 0 1 0 0] T 

[0 0 0 0 1 0 0 0] T 

[0 0 0 1 0 0 0 0] T 

[0 0 1 0 0 0 0 0] T 

[0 1 0 0 0 0 0 0] T 

= [0 0 0 0 0 0 0 1] T = Z 

The vector forms in the circle can be got in TABLE IV. 

TABLE IV. 

VECTOR FORMS IN THE CIRCLE 

A (t) A 3 (t) A 2 (t) A 1 (t) 

[0 0 0 0 0 0 0 1] T 0 0 0 

[0 0 0 0 0 0 1 0] T 0 0 1 

[0 0 0 0 0 1 0 0] T 0 1 0 

[0 0 0 0 1 0 0 0] T 0 1 1 

[0 0 0 1 0 0 0 0] T 1 0 0 

[0 0 1 0 0 0 0 0] T 1 0 1 

[0 1 0 0 0 0 0 0] T 1 1 0 

The vector forms can be converted back to the scalar 

form of A 1 

() t , A () t , and A () t 

2 3 

. The circle is as 

000 → 001 → 010 → 011 → 100 → 101 → 110 → 000. 

Finally, the state space graph of the network in Example 

3 can be gained as in Figure 1. 

Figure 1. The state space graph 

VI. CASE STUDY: MAMMALIAN CELL 

In this section, a useful example of mammalian cell[22] 

is given to show that our new approach is effective and 

feasible. 

A proper understanding of the structure and temporal 

behaviors of biological regulatory networks requires the 

integration of regulatory data into a formal dynamical 

model. A logical framework enables a more systematic 

and extensive characterization of all the behaviors 

compatible with a given regulatory graph. Furthermore, 

this framework offers enumerative or analytical means to 

identify relevant asymptotical behaviors (stable states, 

state transition cycles). 

The cell cycle involves a succession of molecular 

events leading to the reproduction of the genome of a cell. 

Here, the logical regulatory graph for a mammalian cell 



cycle network and logical rules associated with the 

regulatory graph (in Figure 2) are given. 

Each node represents the activity of a key regulatory 

element, whereas the edges represent cross-regulations. 

Blunt arrows stand for inhibitory effects, normal arrows 

for activations. 

Rb 

E2F 

UbcH10 

CycD 

CycE 

CycA 

Cdc20 

CycB 

Cdh1 


The logical equations, which are called dynamics of 

Boolean network in STP, are as in (27). 

⎧CycD 

= CycD 

⎪ 

⎪Rb = ( CycD ∧CycE ∧CycA ∧CycB) 

⎪ 

⎪ 

∨( p27 ∧( CycE ∧CycA) 

∧CycB 

⎪ ∧ CycD) 

⎪ 

⎪E2 F = ( Rb ∧CycA ∧CycB) ∨( p27∧ 

⎪ 

⎪ Rb ∧ CycB) 

⎪ 

⎪CycE = ( E2 F ∧Rb) 

⎪ 

⎪CycA = ( E2F ∧Rb ∧Cdc20∧ 

⎪ 

( Cdh1 ∧UbcH10)) ∨( 

CycA ∧ 

⎪ 

⎨ Rb ∧Cdc20 ∧( Cdh1 ∧UbcH10)) 

⎪ 

⎪ p27 = ( CycD ∧CycE ∧CycA ∧CycB) 

⎪ 

∨( p27∧( CycE ∧CycA) 

∧ 

⎪ 

⎪ CycB ∧ CycD) 

⎪ 

⎪Cdc20 

= CycB 

⎪ 

⎪Cdh1 = ( CycA ∧CycB) ∨( Cdc20) 

∨ 

⎪ 

⎪ 

( p27 ∧ CycB) 

⎪ UbcH10 = ( Cdh1) ∨( Cdch1 ∧UbcH10 

⎪ 

⎪ ∧( Cdc20 ∨CycA ∨CycB)) 

⎪ 

(27) 

⎪CycB = ( Cdc20∧Cdh1) 

⎩ 

Then we use the methods mentioned above to get 

stable states and state transition cycles. 

There are 10 nodes, so the complete state transition 

graph contains 1024 vertices. The structure matrix L can 

be gained by algorithm1. 

p27 

Algorithm1 Algorithm for computing structure matrix L 

L=zeros[1024][1024] 

A=zeros[10] 


for k=0 to 1023 do 

A=int_to_binary (k, 10) 

/*convert k to binary number of 10 bit, */ 

CycD=A[1]; 

Rb=A[2]; 

E2F=A[3]; 

CycE=A[4]; 

CycA=A[5]; 

p27=A[6]; 

Cdc20=A[7]; 

Cdh1=A[8]; 

UbcH10=A[9]; 

CycB=A[10]; 

/*assignment each bit to the variables, 

from high bit to low bit, A[1] is the highest bit*/ 

CycD=CycD; 

Rb= ( (!CycD) && (!CycE) && (!CycA) && (!CycB)) 

|| (p27&& (!CycD) && (!CycB)) ; 

E2F= ( (!Rb) && (!CycA) && (!CycB)) || (p27&& (!Rb) 

&& (!CycB)) ; 

CycE= (E2F&& (!Rb)) ; 

CycA= (E2F&& (!Rb) && (!Cdc20) && (! (Cdh1 

&&UbcH10))) || (CycA&& (!Rb) && (!Cdc20) 

&& (! (Cdh1&&UbcH10))) ; 

p27= ( (!CycD) && (!CycE) && (!CycA) && (!CycB)) || (p27 

&& (! (CycE&&CycA)) && (!CycD) && (!CycB)) ; 

Cdc20=CycB; 

Cdh1= ( (!CycA) && (!CycB)) || (Cdc20) || (p27&& (!CycB)) ; 

UbcH10= (!Cdh1) || ( (Cdh1) && (UbcH10) && ( (Cdc20) || 

(CycA) 

|| (CycB))) ; 

CycB= ( (!Cdc20) && (!Cdh1)) ; 

/* substitute into the logical equations */ 

i=1024- (CycD*512 + Rb*256 + E2F*128 + CycE*64 + 

CycA*32 

+ p27*16 + Cdc20*8+Cdh1*4 + UbcH10*2 + CycB*1) ; 

j=1024-k; 

L[i][j]=1; 

return L 

end 

According to Theorem 3, the characteristics of the 

mammalian cell example, such as the number of fixed 

points, the numbers of circles of different lengths and the 

states in the circles, can be analyzed by algorithms2. 

Through Algorithm1 and Algorithm2, the number of 

stable states or fixed point in the example of mammalian 

cell is 1. The state or fixed point is 0100010100, which 

means only Rb, p27 and Cdh1 active, in the absence of 

CycD. And there is 1 circle with the length of 7 in the 

example of mammalian cell. The states on the circle 

include 1011100100, 1001100000, 1000100011, 

1000101011, 1000001110, 1010000110, and 1011000100. 

Algorithm2 Algorithm for computing the number of stable states; 

the numbers of circles of different lengths; 

Input: structure matrix L 

N=zeros[1024] 


N[1]=trace (L) 

if N[1]≠0 then 

report the number of stable states is N[1] 

for i=2 to 1024 do 

T=0 

for j=1 to i/2 do 

if mod (i, j) =0 then 

T=T+j*N[j]; 



return T 

N[i]= (trace (L^i) -T) /i; 

if N[i]>0 then 

report the number of circle length of i is N[i] 

end 

The fixed point and the circle of the mammalian cell 

example are as in Figure 3. 

0100010100 

1 fix point 

1011100100 1001100000 1000100011 1000101011 

1011000100 1010000110 1000001110 

1 circle with the length of 7 


The algorithms in the mammalian cell example in this 

section seem difficult. In fact, it can be easily done in 

computer. We have created a program to handle them. 

VII. CONCLUSION 

Semi-tensor product is an efficient tool for analyzing 

the characteristics of Boolean networks which are 

determined by the structure matrix. Unlike existing 

methods which calculates the structure matrix through 

matrix operations with high computation complexity, an 

optimized approach is proposed in this paper. The 

approach gets the structure matrix of Boolean network 

through the truth table which reflects the state 

transformation of the Boolean network. Compared with 

the conventional methods, our method can greatly reduce 

the calculation complexity. A practical Boolean network 

of mammalian cell shows our approach is effective and 

efficient. 

The structure matrix which is gained in semi-tensor 

product is a sparse matrix. On the other hand, with the 

number of variables in a Boolean network increasing, the 

size of the structure matrix will become larger and larger. 

These cause higher computation complexity. To optimize 

the algorithms in section VI, we need to solve the 

following problems: How to express the structure matrix 

in sparse matrix How to analyze the fixed points and 

circles in the sparse matrix They are our future work. 


This work was supported by the Fundamental 

Research Funds for the Central Universities of China 

under Grant No. ZYGX2009J062 and the National 

Natural Science Foundation of China under Grant No. 

60973016. 

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Jinyu Zhan was born in Heilongjiang Province of China in 

1978. She received the Ph.D. degree in computer applications 

from the University of Electronic Science and Technology of 

China in 2006. 

Currently, she is an associate professor at the University of 

Electronic Science and Technology of China. Her research 

interests include formal co-verification of SoC, model checking, 

real time embedded systems, and VLSI design and verification. 

Shan Lu was born in Hunan Province of China in 1989. He 

received the Bachelor degree in information and computation 

science from Chongqing Three Gorges University in 2011. 

Currently, he is a graduate student at the University of 

Electronic Science and Technology of China. His research 

interests include formal verification and model checking. 

Guowu Yang was born in Hubei Province of China in 1966. He 

received the Ph.D. degree at Electrical and Computer 

Engineering department of Portland State University in USA in 

2005. He was a research associate at Computer Science 

department of Portland State University from 2005 to 2006. 

Currently, he is a professor of College of Computer Science 

and Engineering at University of Electronic Science and 

Technololgy of China. His research interests include formal 

verification and developing corresponding program package, 

theoretical study of synthesis algorithms in quantum computing, 

and non-linear control theory. 



Adaptive Chaotic Prediction Algorithm of RBF 

Neural Network Filtering Model based on Phase 

Space Reconstruction 

Lisheng Yin, Yigang He, Xueping Dong, Zhaoquan Lu 

School of Electrical and Automation Engineering, Hefei University of Technology, Hefei, China 

E-mail: yls20000@163.com, hyghnu@yahoo.com.cn, hfdxp@126.com, luzhquan@126.com 

Abstract—With the analysis of the technology of phase space 

reconstruction, a modeling and forecasting technique based 

on the Radial Basis Function (RBF) neural network for 

chaotic time series is presented in this paper. The predictive 

model of chaotic time series is established with the adaptive 

RBF neural networks and the steps of the chaotic learning 

algorithm with adaptive RBF neural networks are expressed. 

The network system can enhance the stabilization and 

associative memory of chaotic dynamics and generalization 

ability of predictive model even by imperfect and variation 

inputs during the learning and prediction process by 

selecting the suitable nonlinear feedback term. The 

dynamics of network become chaotic one in the weight space. 

Simulation experiments of chaotic time series produced by 

Lorenz equation are proceeded by a RBF neural 

network.The experimental and simulating results indicated 

that the forecast method of the adaptive RBF neutral 

network compared with the forecast method of back 

propagation (BP) neutral network based on the chaotic 

learning algorithm has faster learning capacity and higher 

accuracy of forecast.The method provides a new way for 

the chaotic time series prediction. 

Index Terms—Chaos Theory, Phase Space Reconstruction, 

Time Series Prediction, RBF Neural network, Algorithm 


Since the phase space reconstruction theory proposed 

by Packard et al. in 1980, many scholars at home and 

abroad to set off a climax of chaotic time series 

prediction. Prediction for chaotic time series is to 

approximate the unknown nonlinear functional mapping 

of a chaotic signal. The laws underlying the chaotic time 

series can be expressed as a deterministic dynamical 

system. Farmer and Sidorowich suggest reconstructing 

the dynamics in phase space by choosing a suitable 

embedding dimension and time delay [1]. Takens’ 

theorem ensures that the method is reliable, based on the 

fact that the interaction between the variables is such that 

every component contains information on the complex 

dynamics of the system [2]. 

The neural network [3-6]. not only has the selfadaptive, 

parallelism and fault tolerance characteristics, 

but also has the ability to approximate any nonlinear 

function. Based on these advantages, the neural network 

model of the nonlinear system has a very wide range of 

applications [7-10]. In recent years, particular interest has 

been put into predicting chaotic time series using neural 

networks because of their universal approximation 

capabilities. Most applications in this field are based on 

feed-forward neural networks, such as the Back 

Propagation (BP) network [11-13], Radial Basis Function 

(RBF) network [14-15], Recurrent neural networks 

(RNNs) [16-18], FIR neural networks [19-20] and so on. 

It is widely used tool for the prediction of time series [21- 

23]. 

The RBF neural network model structure is easy to 

understand, training process stability, training speed is 

fast, training result is high accuracy and generalization 

ability is strong. In this paper, the chaotic algorithm is 

proposed to a RBF neural network filtering predictive 

model and the model is proposed to make prediction of 

chaotic time series. The network system can enhance the 

stabilization and associative memory of chaotic dynamics 

and generalization ability of predictive model even by 

imperfect and variation inputs by selecting the suitable 

nonlinear feedback term. The dynamics of network 

become chaotic one in the weight space. The model is 

tested for the chaotic time series which venerated with 

Lorentz system by on-line method. The experimental and 

simulation results indicated that the adaptive filtering has 

a good self-suitable prediction performance and can be 

successfully used to predict chaotic time series. 

II. ESTABLISHMENT OF ADAPTIVE RBF NEURAL 

NETWORK FILTERING PREDICTIVE MODEL BASED ON 

CHAOTIC ALGORITHM 

A. Model of Chaotic Time Series Prediction 

Takens theorem considers evolution of any component 

of the system is decided by other components interacting 

with this component, therefore, the information of 

relevant component imply in the development process of 

this component, so the original rules of the system can be 

extracted and restored from a group of time-series data of 

a certain component. The one-dimensional time series is 

embedded to multi-dimensional phase space through 

reconstruction and the new system with same dynamic 

characteristics as original system can be obtained through 

the selection of a suitable embedding dimension m and 

time delayτ . The usual method of selecting time delay 


doi:10.4304/jcp.8.6.1449-1455


τ includes autocorrelation function method, multiple 

correlation function method, mutual information method. 

Embedding dimension m is calculated by the methods of 

GP algorithm, pseudo-nearest-point method, correlation 

integral method and Cao method. 

The chaotic time series prediction is based on the 

Takens' delay-coordinate phase reconstruct theory. If the 

time series of one of the variables is available, based on 

the fact that the interaction between the variables is such 

that every component contains information on the 

complex dynamics of the system, a smooth function can 

be found to model the portraits of time series. If the 

chaotic time series are{ x() 

t }, then the reconstruct state 

vector is 

x( t) = ( x( t), x( t+ τ ), , x( t+ ( m−1) τ )) 

where m ( m = 2,3, ) is called the embedding 

dimension ( m= 2d 

+ 1 , d is called the freedom of 

dynamics of the system), and τ is the delay time. The 

predictive reconstruct of chaotic series is a inverse 

problem to the dynamics of the system essentially. There 

exists a smooth function defined on the reconstructed 

m 

manifold in R to interpret the 

dynamics x( t+ T) = F( x( t)) 

, where T ( T > 0) is forward 

predictive step length, and F() 

⋅ is the reconstructed 

predictive model. 

B. RBF Neural Network Function Approximation Theory 

Takens embedding theorem states that there is a 

smooth mapping F of the F makes: 

x( t+ τ ) = F( x( t)) 

(1) 

that is, 

xt ( + τ), xt (), , xt ( −( m− 2) τ) = F{[ xt (), xt ( −τ), , xt ( −( m−1) τ]} 

For purposes of calculation, equation (1) can be rewritten 

as: 

xt ( + τ ) = Fxt [ ( ), xt ( −τ), , xt ( −( m−1) τ] 

(2) 

where, f is the mapping from R M to R L . Chaos theory 

suggests that the chaotic time series is short-term forecast, 

and the essence of prediction is how to get a good 

approximation f on the function f . Chaotic time series 

determined by the internal regularity, this regularity 

comes from the non-linear, it exhibits the time series in 

the time delay state, this feature makes the system seem 

to have some kind of memory capacity. The same time, it 

is difficult to demonstrate such a regularity by using the 

analytic methods; this type of information processing 

happens to be the neural network, and the Kolmogorov 

continuity theorem in the neural networks theory 

provides a theoretical guarantee for the neural network 

nonlinear function approximation. 

Theorem (Kolmogorov continuity theorem) Let ϕ ( x) 

be a non-constant and bounded monotonically increasing 

a continuous function; M is a compact sub-set of R n , 

and f( x) = f( x1, x2, , x n 

) is the continuous real value 

function on M , then for ∀ ε > 0 , exists a positive integer 

N and real numbers C , makes: 

 

N n 

f( x , x , , x ) = Cϕ( ϖ x −θ 

) (3) 

1 2 

∑ 

∑ 

n i ij j j 

i= 1 j= 

1 

meet: 

 

max f( x , x , , x ) − f( x , x , , x ) < ε (4) 

M 

1 2 n 1 2 

By the above theorem, the nonlinear time series 

prediction process using neural network can be 

considered as dynamic reconfiguration, which is an 

inverse process. Namely, the existence of a three-layer 

network, the hidden unit output function, the network 

input and output function is linear, three-layer network 

input and output relation f can approximate p. 

Therefore, the theorem from mathematics is to ensure 

the feasibility of chaotic time series prediction by neural 

network. 

C. Realized Architecture of Adaptive RBF Neural 

Network Filtering Predictive Model 

After reconstructing the phase space, the RBF neural 

networks adopt three layers networks of Figure 1. Where 

the input layer has m nerve cells, the first layer feed to 

the second layer directly and it do not need the power 

processing. r i 

( i = 1, 2, , L ) is the reference vector and 

ϖ 

k 

( i = 1, 2, , L ) is the adjustable parameters in the 

adaptive RBF neural network filtering. Thus, the adaptive 

RBF neural network filtering is more flexible in studying 

the nonlinear functions. The differentiation between the 

networks and the traditional neural networks is that the 

activation function is a RBF function but not the Sigmoid 

function. The activation function usually choose the 

Gauss function, the spline function f ( di 

( k )) , 

where d ( k) = x( k) − r( k) 

. In the adaptive RBF neural 

i 

network filtering, yk ( ) is expressed as 

i 

2 

L−1 

yˆ( k) = f ( ∑ ϖ ( k) f( d ( k))) 

, 

i= 

0 

i = 0, 2, , L−1, 

where f () 2 

⋅ is the activation function of output signal. 

i 

x(k) 

−1 

z 

−1 

z 

−1 

z 

r 0 

r 1 

r 2 

r L 

i 

ϖ 0 

( k) 

ϖ 1 

( k) 

ϖ 2 

( k) 

(k) ϖ L 

n 

∑ 

yˆ ( k) 

input hidden layer output 

Figure 1. Structure of adaptive RBF neural network filtering 

Generally, the learning of the RBF neural network 

filtering has three steps. If the gradient method and the 

Gauss activation function are adopted, the regulate 

formulas of RBF are shown as: 



⎧ϖi( k+ 1) = ϖi( k) + 2 μϖ 

e( k) f( di( k)) 

⎪ 

2 

⎪ di 

( k) 

σi( k+ 1) = σi( k) + 2 μϖ 

e( k) f( di( k)) ϖi( k) 

⎪ 

3 

σ 

i 

( k) 

⎪ 

⎨ 

x( k) − ri 

( k) 

(5) 

⎪ri( k + 1) = ri( k) + 2 μre( k) f( di( k)) ϖi( k) 

2 

σ 

i 

( k) 

⎪ 

⎪ 

x( k) − ri 

( k) 

⎪ri( k + 1) = ri( k) + 2 μre( k) f( di( k)) ϖi( k) 

2 

⎩ 

σ 

i 

( k) 

i = 0, 2, , L−1. 

The RBF neural network system can enhance the 

stabilization and associative memory of chaotic dynamics 

and generalization ability of predictive model even by 

imperfect and variation inputs by selecting the suitable 

nonlinear feedback term. The dynamics of network 

become chaotic one in the weight space. Thus, the 

regulate formula ϖ ( k) 

is shown as 

ϖ 

i( k + 1) = ϖi( k) + 2 μϖ 

e( k) f( di( k)) + g( ϖi( k) −ϖI( k−1)) 

(6) 

2 

where g( x) = tanh( ax)exp( − bx ), x = ϖ ( k) −ϖ 

( k− 1) . 

That the feedback function g( x ) is chose is because 

that g( x) 

can get the difference feedback function 

corresponding to the dissimilar parameter, such as the 

staircase function, δ function and so on. If the feedback 

function is seen as the motion-promoting force, the 

different feedback parameters a and b corresponding to 

the amplitude and width of the motion-promoting force. 

The paper [18] was detailed to discuss the influences by 

selecting the suitable learning and predictive process. The 

simulation results indicated that the network system can 

enhance the stabilization and associative memory of 

chaotic dynamics and generalization ability of predictive 

model even by imperfect and variation inputs during the 

learning and prediction process by selecting the suitable 

nonlinear feedback term. 

III. DETERMINATION METHOD OF THE OPTIMAL DELAY 

TIME AND MINIMUM EMBEDDING DIMENSION 

A. Determination Method of the Optimal Delay Time τ 

During Phase Space Reconstruction in the Takens 

embedding theorem does not make limited to the delay 

time τ .In theory, when the observational data point is an 

infinitely long, the effect of embedded not too large. 

However, in actual operation, τ is caused a great impact. 

If τ is too small, the chaotic attractor cannot be fully 

expanded, redundant error is larger; if τ is too large, the 

no related error is larger. Therefore, in order for complex 

nonlinear systems, using the mutual information method 

to determine the optimal delay time τ , the mutual 

information method using a minimal value of the mutual 

information function to determine the optimal delay time 

τ , its expression is as follows: 

P, 

() r 

M( x , ) 

, 

( )ln i j 

t 

xt− τ 

= ∑ Pi j 

r 

(7) 

PP 

i, 

j i j 

i 

i 

where, P 

i 

is the probability of point x t 

in the i time 

interval; Pi, j() 

r is the joint probability of the point x t 

in 

t moment fall into the i time interval and the t + τ 

moment fall into the j time intervals. 

B. Determination Method of the Minimum Embedding m 

In this paper, the commonly used pseudo-near-point 

method to calculate the minimum embedding dimension 

m , set the number of attractor dimension d , then m is 

just the minimum embedding dimension when the 

attractor is fully open. When m< d , the attractor in the 

phase space cannot be completely open, the attractor will 

produce some projection point in the embedded space, 

the projection point and the other points in the phase 

space will form the closest point. In the original system, 

the 2 points are not true nearest neighbors, so called 

pseudo adjacent points. Assume that any point yt () in the 

phase space, the criterion of false neighboring points are 

as follows: 

1 

2 2 

D () () 2 

m+ 1 

t − Dm 

t xt ( + mτ) − xt ( ′ + mτ) 

= > ρm 

(8) 

D () t D () t 

m 

Where D () t is the Euclidean distance between the 

m 

N 

points of yt () with its nearest neighbor y () t in the 

phase space when the embedding dimension is m . 

According to this criterion, the calculation pseudo-nearest 

neighbor number N when m from small to large, and 

then calculate the change amount Δ N when the 

embedding dimension from m to m + 1. Draw the curve 

ΔN 

Δ 

from to m ; when Δ N = 0 , just N dropped to 0, 

N 

N 

the value m * of m is seeking the minimum embedding 

dimension. 

IV. ADAPTIVE RBF NEURAL NETWORK RAPID LEARNING 

ALGORITHM 

On the establishment of chaotic time series RBF, 

Network input the number of neurons, hidden layers and 

the number of neurons in the hidden layer are to be 

considered.The following chaotic time series used are 

from Lorenz chaotic sampling time series. The Lorenz 

chaotic sampling time series RBF neural network can be 

constructed: RBF neural network is designed to be three 

layers: input layer, single hidden layer and output layer; 

the number of hidden layer wavelet neural taken as 9 by 

Kolmogorov Theorem, the number of input layer neurons 

equal to the minimum embedding dimension, the number 

of output layer is 1, so that the 4-9-1 structure of Lorenz 

chaotic sampling time series RBF was obtained, 

specifically shown in Figure 1. 

Algorithm The steps of the chaotic time series learning 

and prediction of the adaptive RBF neural network 

filtering predictive model are showed: 

Step1) Based on the Takens' delay-coordinate phase 

reconstruct theory, the number of the input nerve cells 

m 



M of the adaptive RBF neural network filtering is 

determined. 

The dimension m of chaotic time series is 

calculated by the way of G- P algorithms, and 

the delay time τ is calculated by the selfcorrelation 

method. For the overall description 

of the dynamics characteristic of the original 

system by the Takens' delay-coordinate phase 

reconstruct theory, a chaotic series demand 

m≥ 2d 

+ 1 variances at least, so the number of 

the input nerve cells of the adaptive RBF neural 

network filtering is M = m ; The reconstruction 

phase space vector number is 200, Then, the 

200 phase space vectors to make a simple 

normalized, the normalized as 

[ x() t −mean( x())]/[max( t x()) t − min( x())] 

t 

, 

t = 1, 2, 200 , and making the value is owned by a range 

of -1 / 2 to 1/2. 

Step2) The adaptive filtering is initialized and the 

weights are vested the initial values. RBF neural network 

vector weighting parameters w is initialized, where the 

weight vector w in each component take random function 

between 0 and 1; and the learning rate η is initialized at 

the same time, where η = 0.0002 . β and γ are the 

learning rate adjustment factors, 0< β < 1, γ > 1 , for 

example, β = 0.75, γ = 1.05 . 

Step3) Using the above the initialization network and 

the pretreatment traffic flow time series, the first training 

network is carried out. 

Step4) The error is calculated. If the error is in the 

scope of the permission, the error is calculated and it 

turns into Step4), otherwise it continues; the error 

function formula: 

200 

1 2 

E( θ ) = ( y( t) − y( t)) 

(9) 

∑ 

2 t = 1 

Set the maximum error is E max 

= 0.035 , if E < Emax 

, 

the storage RBF neural network parameter use w ; 

otherwise, then a second training network will be 

required. 

Step5) Adjust the adaptive learning rate If A previous 

training error is recorded as En 

− 1 

, the current error is 

recorded as E n 

, then Calculate the ratio of E 

n 

to En 

− 1 

, 

En 

Setting constants k = 1.04 , if > k = 1.04 , then 

En 

− 1 

substitute βη for η to reduce learning rate; otherwise, 

replace η with γη to increase learning rate. 

Step6) In the adaptive RBF neural network filtering for 

the chaotic time series prediction in Figure 1, 

x( k) = x( t) 

t = 1, 2, , N is the input, yk ˆ( ) = xt ˆ( ) is the 

output. 

Introduce nonlinear feedback into the weighting 

formal to adopt Chaos Mechanisms, due to the nonlinear 

feedback is vector form of weighting variables. In order 

to facilitate understanding, respectively, gives the vector 

w and its weighting formal, as follows. 

Note 

Δ w l ( t+ 1) = w l ( t+ 1) −w l ( t) 

, 

ji ji ji 

which represents the current value of weighting variables, 

then 

1 

Δ w l ( t+ 1) = w l ( t+ 1) − w l () t = −ηδ l+ 

() t x 

l () t 

ji ji ji j i 

In order to speed up the learning process, in the right to 

l 

join a momentum term αΔw () t , then 

l 1 

( 1) l + 

( ) l ( ) l 

ji 

t ηδ 

j 

t 

i 

t α 

ji 

( t) 

ji 

Δ w + = − x + Δw (10) 

where α is inertia factor. As a constant, the weight of 

amendments is linear, not introduce chaos mechanism. 

then we Introduce a nonlinear feedback (chaos 

mechanism on the right): 

1 

Δ w l ( t+ 1) = − ηδ l+ 

( t) x l ( t) + g( Δ w l ( t+ 

1)) (11) 

ji j i ji 

Expand this equation into scalar form as follow: 

l l+ 

1 l l 

⎧Δ wji ( t+ 1) = − ηδ 

j 

( t) xi ( t) + g( Δwji 

( t)) 

⎪ 

l l+ 

1 

l l 

⎪Δ wji ( t+ 1 + τ) =− ηδ 

j 

( t+ τ) xi ( t+ τ) + g( Δ wji 

( t+ 

τ)) 

⎪ 

l l+ 

1 

l l 

⎪Δ wji ( t+ 1+ 2 τ ) = − ηδ 

j 

( t+ 2) xi ( t+ 2 τ ) + g( Δ wji 

( t+ 

2 τ )) 

⎨ 

⎪ 

⎪ l l+ 

1 

l 

⎪ 

Δ wji ( t+ 1 + ( m− 1) τ ) =− ηδ 

j 

( t+ ( m− 1) τ ) xi 

( t+ ( m−1) τ ) 

⎪ l 

⎩ 

+ g( 

Δwji 

( t+ ( m−1) τ )) 

(12) 

where, feedback can take a variety of vector functions, 

for example: 

2 

g( x) = tanh( px)exp( − qx ) 

or 

g( x) = pxexp( − q x) 

, 

in the study, p = 0.7 , q = 0.1. 

Step7) Using the new learning rate in Step5) and RBF 

network parameters with nonlinear feedback in Step6) to 

calculate the new value, and train network again, then get 

the error and enter into Step4), repeated training until the 

relative error in traffic meet E < Emax 

. 

Step8) Output of each stored network parameters and 

training error curve. 

V. EXAMPLE ANALYSIS AND CONCLUSIONS 

A. Model and Data 

In this paper, the chaotic time series is the object of 

study of the numerical simulation in Lorenz dynamic 

system. In 1963, the meteorologist Lorenz describe the 

evolution of the weather by three-dimensional 

autonomous equations; when the parameter σ = 10 , 

8 

r = 28 , b = , the long-term changes in the weather 

3 

unpredictable, that is, the system presents a chaotic state, 

and for the first time given a strange attractor. The 

attractors are shown in Figure 2 (a), Figure 2 (b), Figure 2 

(c) and Figure 2 (d): 



z(t) 

30 

20 

10 

0 

-10 

-20 

-30 

20 

10 

0 

y(t) 

-10 

attractor of Lorenz 

-20 -20 

(a) three-dimensional map of Lorenz attractor 

y(t) 

20 

15 

10 

5 

0 

-5 

-10 

-15 


-20 

-10 0 10 20 30 40 50 

x(t) 

(b) two-dimensional map of Lorenz attractor in the x-y-plan 

z(t) 

30 

20 

10 

0 

-10 

-20 


-30 

-10 0 10 20 30 40 50 

x(t) 

(c) two-dimensional map of Lorenz attractor in the x-z-plan 

y(t) 

30 

20 

10 

0 

-10 

-20 


-30 

-20 -15 -10 -5 0 5 10 15 20 

z(t) 

(d) two-dimensional map of Lorenz attractor in the z-y-plan 

0 

x(t) 

20 

40 

60 

Lorenz map: 

• 

⎧ 

⎪ 

x = σ ( y − x) 

⎪ • 

⎨ y = rx − y − xz 

(13) 

⎪ • 

⎪ z =− bz+ 

xy 

⎩ 

8 

Where σ = 10 , r = 28 , b = .The initial value is 

3 

x (0) = 0 , y (0) = 5 , z (0) = − 5 ; and the fixing step length 

of initial value is 0.05s . Time series to the branch x with 

70s is produced by the Runge-Kutta algorithms and the 

total data is 1200. The embedded dimension of the 

sampling chaotic time series m is 8 by the G- P 

algorithms. The delay time is τ= 1 by the self-correlation 

function algorithms and the input dimension of the 

adaptive RBF neural network filtering is 8.The former 

1200 data is trained and other 200 data is predicted by the 

adaptive RBF neural network filtering predictive model. 

B. Evaluation of the Predictive Ability 

The model's predictive ability is generally measure the 

following three indicators: of MAPE (mean absolute 

percentage error), RMSE (root mean square error) and 

RMSPE (root mean square percentage error), they are 

calculated as follows: 

n 

1 yi 

− yi 

MAPE = 100 

n 

∑ × , (14) 

y 

i= 

1 

i 

n 

1 ⎛ yi 

− y ⎞ 

i 

RMSPE = 100× ∑ ⎜ ⎟ 

n I = 1 ⎝ y 

, (15) 

i ⎠ 

n I = 1 

i i 

1 n 

RMSE = y − y 

∑( ) 2 

(16) 

where, y i 

is predictive value of the model; y i 

is the real 

value; n is prediction phases, and MAPE assess the 

predictive capability are as follows: less than or equal to 

10%, then predictive ability is excellent; 10% -20%, then 

the predictive ability is excellent; 20% -50%, more than 

50%, then the prediction is inaccurate. For RMSPE, the 

prediction square vulnerable to the impact of outliers, for 

the larger error given greater weight, but still can be 

modeled on the MAPE to determine the model of the pros 

and cons. RMSPE values range from zero to infinity. 

MAPE and RMSPE are the relative indicator, RMSE is 

the absolute indicator. The RMSE is the smaller, the 

model predictive ability is the stronger. 

C. The Simulation Results 

That the experimental outcome of Lorenz chaotic 

sampling time series, the true value (real line) and the 

predictive value (star line) and the predictive error curve 

are showed in Figure 3., Figure 4. and Figure 5. 

2 

Figure 2. Lorenz attractor in the phase space reconstruction 

Considering Lorenz chaotic system 



50 

40 

30 

20 

10 

0 

-10 

0 200 400 600 

n 

800 1000 1200 1400 

40 

35 

30 

25 

20 

15 

Figure 3. Lorenz chaotic sampling time series 

10 

1200 1220 1240 1260 1280 1300 1320 1340 1360 1380 1400 

n 

Figure 4. True value (real line) and predictive value (star line) 

error 

square 

0.5 

x 10 -3 

1 

0 

1200 1220 1240 1260 1280 1300 1320 1340 136013801400 

Figure 5. Predictive error curve 

In Figure 3 the sampling chaotic time series number is 

1200 by the Runge-Kutta algorithms. 

The former 1200 datum is used to learn and train the 

adaptive wavelet neural networks every 8 datum. After 

the learned and trained stage, the true value (real line) and 

predictive value (star line) are shown in Figure 4. 

The predictive error curve of the true value and the 

predictive value is very small in Figure 5. 

The true value and the predictive value in the adaptive 

RBF neural network filtering is to find a inner law in the 

series itself, which can avoid the disturbance of some 

subjective factors and enjoys higher reliability. In this 

study, the fusion of chaotic theory with the adaptive RBF 

neural network filtering based on chaotic algorithm 

provides a new method for chaotic time series prediction. 

The experimental indicated that the network system can 

enhance the stabilization and associative memory of 

chaotic dynamics and generalization ability of predictive 

model even by imperfect and variation inputs during the 

learning and prediction process by selecting the suitable 

nonlinear feedback term. Simulation results for the 

modeling and prediction of chaotic time series show 

better predictive effectiveness and reliability. 

TABLE 1 

PREDICTIVE PERFORMANCE COMPARISON TABLE 

comparative 

indicators 

BP neural network 

prediction 

RBF neural network 

prediction 

MAPE 5.01% 3.71% 

RMSPE 6.13% 4.55% 

RMSE 62.50 46.37 

From Table 1, the mean absolute percentage error of 

Lorenz chaotic sampling time series prediction and actual 

values, BP neural network based on the learning rate 

variable training algorithm, RBF network based on fast 

learning algorithm, are 5.1% and 3.71%, respectively. 

Similarly, for the RMSPE, the results were 6.13% and 

4.55%; For RMSE, the results were 62.50 and 46.37. Can 

be seen from the data on Lorenz chaotic sampling time 

series RBF network prediction is better than BP neural 

network. 

VI. CONCLUSIONS 

In the paper the chaotic time series RBF neural 

network model was designed. A RBF neural network 

Adaptive learning algorithm based on Chaos mechanism 

was proposed. The method of model selection and 

algorithm design, are considered the chaos of Lorenz 

chaotic sampling time series, which is a theoretical value. 

Simulation results show that the method can reduce 

MAPE, RMSPE, RMSE, and improve the forecast 

accuracy, and show better predictive effectiveness and 

reliability. 


This research is financially supported by the National 

Natural Science Funds of China for Distinguished Young 

Scholar under Grant (50925727), and the Fundamental 

Research Funds for the Central Universities, Hefei 

University of Technology for Professor He Yigang, the 

National Natural Science Foundation of China (NSFC) 

for Professor Xue-ping Dong (No. 60974022) and the 

Universities Natural Science Foundation of Anhui 

Province (No. KJ2012A219) for Professor Yin Lisheng. 

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Lisheng Yin (yls20000@163.com) received his doctor’s degree 

in Control Theory and Control Engineering from School of 

Automation, Chongqing University, Chongqing China. He is an 

associate professor in the School of Electrical and Automation 

Engineering, Hefei University of Technology.He conducts 

research in Modern intelligent algorithm, Chaos Theory, Neural 

network theory and Fuzzy Theory. 

Yigang He (hyghnu@yahoo.com.cn) received his doctor’s 

degree in Electrical Engineering from Electrical Engineering, 

Xi'an Jiaotong University, Xian China. He is a professor in the 

School of Electrical and Automation Engineering, Hefei 

University of Technology. He conducts research in Electrical 

science and engineering, automatic test and diagnostic 

equipment, High-speed low-voltage low-power integrated 

circuits, systems, intelligent and real-time information 

processing, Smart grid, electrical measurement techniques and 

Circuit theory of massive proportions and Mixed-signal system 

testing and diagnosis 

Xueping Dong (hfdxp@126.com) received his doctor’s degree 


Automation, Nanjing University Of Science and Technology, 

Nangjing China. He is an associate professor in the School of 

Electrical and Automation Engineering, Hefei University of 

Technology.He conducts research in Modeling and control of 

complex systems, Modern control theory and its application. 

Zhaoquan Lu (luzhquan@126.com) received his doctor’s 

degree from University of Science and Technology of China, 

Hefei China. He is a professor in the School of Electrical and 

Automation Engineering, Hefei University of Technology.He 

conducts research in Large time delay uncertain process and 

control, complex systems and controls, intelligent control, 

wireless communication network and automation systems, 

automotive electronics technology research and development, 

energy-saving control system research and development. 



Intrusion Detection Based on Improved SOM 

with Optimized GA 

ZHAO Jian-Hua 1, 2 

1 College of computer, Northwestern Polytechnical University, Xi’an 710072, China 

2 Department of Computer Science, ShangLuo University, ShangLuo 726000, China 

E-mail: zhaojh2009@yahoo.com.cn 

LI Wei-Hua 

College of computer, Northwestern Polytechnical University, Xi’an 710072, China 

Abstract—In order to improve the effectiveness of 

supervised self-organizing map (SSOM) neural network, a 

kind of genetic algorithm is designed to optimize it. To 

improve its classification rate, a real number encoding 

genetic algorithm is provided and used to optimize the 

learning rate and neighbor radius of SSOM. To speed up 

the modeling speed, a binary encoding genetic algorithm is 

provided to optimize input variables of SSOM and reduce 

its dimension of input sample. Finally, intrusion detection 

data set KDD Cup 1999 is used to carry out experiment 

based on the proposed model. The results show that the 

optimized model has shorter modeling time and higher 

intrusion detection rate. 

Index Terms—SOM, intrusion detection, classification, 

dimension reduction, genetic algorithm 


Nowadays, network communications become more 

and more important to the information society [1, 2]. 

Business, e-commerce, online shopping, Internet bank 

and other network transactions require more secured 

networks. As these operations increases, computer crimes 

and attacks become more frequents and dangerous, 

compromising the security and the trust of a computer 

system and causing costly financial losses [3, 4]. 

While a number of effective techniques exist for the 

prevention of attacks, it has been approved over and over 

again that attacks and intrusions will persist and always 

be there [5, 6]. Although intrusion prevention is still 

important, another aspect of network security, intrusion 

detection, is just as important [7, 8]. With trenchant 

intrusion detection techniques, network systems can 

make themselves less vulnerable by detecting the attacks 

and intrusions effectively so the damages can be 

minimized while keeping normal network activities 

unaffected [2, 9, 10]. 

The intrusion detection system (IDS) is used to detect 

intrusion action. Collecting and analyzing the information 

This work was sponsored by Scientific Research Program Funded by 

Shaanxi Provincial Education Department (No.12JK0748) and National 

ministries foundation in China. 

of a network or system [11, 12], IDS can find the actions 

of violating security policy and detect the traces of being 

attacked from the network or system. According to the 

network information, it classifies the network behavior 

normal behavior or abnormal behavior [13, 14]. 

The neural network has the function of pattern 

recognition, it may be used in the field of the 

classification of intrusion detection and get very good 

results [15, 16]. At the same time, neural network has 

self-learning and adaptive capacity. As long as the system 

audit data and the network data packet are provided, 

neural network can extract normal user or system feature 

model from it and detect the attack mode from the 

abnormal activity [25]. 

The self-organizing map (SOM) neural network 

constitutes an excellent tool for knowledge discovery in a 

data base, extraction of relevant information, detection of 

inherent structures in high-dimensional data and mapping 

these data into a two-dimensional representation space. It 

has been applied successfully in multiple areas. Many 

researcher has apply it in the field of intrusion detection 

and got the good test result. 

However, the network architecture of SOM has to be 

established in advance and it requires knowledge about 

the problem domain. Moreover, the hierarchical relations 

among input data are difficult to represent and it is an 

unsupervised network and not easy to determine the 

classification type. Some researcher has improved SOM 

and they improved unsupervised SOM to supervised 

SOM (name SSOM) and obtain good results. However, 

there are still some problem exiting for SOM and SSOM. 

For example, it is difficult to determine the parameters of 

SOM and SSOM [17, 18]. 

In light of the disadvantage of SOM and SSOM, this 

paper uses genetic algorithm to optimize their parameters 

(including learning rate and neighborhood radius). New 

neural network model (GA-SOM and New-GA-SSOM) 

are proposed and applied in the field of intrusion 

detection. 

The rest of the paper is organized as follows: In 

Section II we describe the basic definitions and 

characteristics of SOM neural network, SSOM neural 

network and genetic algorithm. Section III designs a 


doi:10.4304/jcp.8.6.1456-1463


genetic algorithm based on real number encoding, which 

is to optimize the learning rate and neighbor radius of 

SSOM and solve the random initialization problem of 

learning rate and neighbor radius. Section IV designs a 

genetic algorithm based on binary encoding to optimize 

the input variables and reduce the dimension for SSOM. 

In Section V, intrusion detection experiment is carried 

out based on KDD Cup 1999 data sets to verify the 

effectiveness of the provided model. 

II. PROPOSED SCHEME 

A. SOM Neural Network 

Self-organizing feature map network (SOM) is also 

known as Kohonen network, which is proposed by 

Holland scholar Teuvo Kohonen in 1981. The network is 

a no-teachers, self-organization and self-learning network 

consisting of fully connected neurons array. 

Adjust the weights of the winning neuron and its 

adjacent neurons, so that the weights can reflect the 

relationship between the input samples. Through the 

repeated training and learning, the neurons are divided 

into different regions which have different response 

characteristics to input model and implement the 

clustering of input model. And it can realize the 

classification of the input samples and can be applied in 

various areas of the classification. 

The steps of SOM neural network algorithm are as 

follow: 

(1) Initialization. Initialize the weights and the 

neighbor radius etc. 

(2) Distance calculation. Distance can reflect the 

similarity degree and closeness degree between samples. 

We calculate the distance d between input vector 

x 

i 

= ( x 1 

, x 2 

,..., xn 

) and competitive layer neuron j , which 

is shown in equation (1). 

j 

m 

2 

j 

= ( 

i 

− ωij) = 1,2... 

i= 

1 

d ∑ x j n (1) 

Figure 1. 

The structure diagram of SOM 

SOM is an artificial neural network model and it is 

proved to be exceptionally successful for data 

visualization applications mapping from a usually very 

high-dimensional data space into a two-dimensional 

representation space. The remarkable benefit of SOM is 

that the similarity between the input data as measured in 

the input data space is preserved as faithfully as possible 

within the representation space. Thus, the similarity of 

the input data is mirrored to a very large extends in terms 

of geographical vicinity within the representation space 

[19, 20]. 

The structure of SOM neural network is shown in 

Figure 1, including two layers feed forward neural 

network structure which is an input layer and a 

competitive layer. The first layer is the input layer and its 

dimension is equal with the input vector dimension which 

is set to m. The second layer is a competitive layer and it 

generally shows a two-dimensional array distribution. A 

competitive layer node represents a neuron and the 

number of competitive layer node is set to n. The 

association between input layer and competitive layer is 

in the form of a full connection; its weight is indicated 

byω . 

ij 

The basic working principle of SOM neural network is 

as follow: during the network train and learning the 

neurons on competitive layer get the response to the input 

model by competing with each other, the neuron having 

the minimum distance from input sample becomes the 

winning neuron. 

(3) The winning neuron selection on competitive 

layer. 

Find out neuron c with the minimal distance from the 

winning neuron and calculate the neighborhood N c (t) of 

c in accordance with equation (2). 

N() t = ( t find( norm( pos , pos ) < r) t = 1,2,.., n (2) 

c t c 

where posc 

represents the position of neuron c 

and post 

represents the position of neuron t; norm 

represents the calculation of Euclidean distance between 

two neurons; r represents the neighborhood radius. 

(4) Weight adjustment. Adjust the neuron weights of 

neuron c and others in its neighborhood N c (t) according 

to equation (3). 

ω = ω + η( x − ω ) 

(3) 

ij ij i ij 

where ω represents the weight between input layer and 

competitive layer, η represents learning rate, η 

decreases with the increase of evolution number 

(5) Judge whether the algorithm ends. If not end, 

return to (2). 

B. SSOM Neural Network 

SOM is an unsupervised neural network and it can 

effectively classify unlabeled data. However It cannot 

determine the classification types of labeled data more 

effectively in the help of data labels.. To facilitate the 

processing of classification problem and quickly get the 

classification type, some researchers improve the 

unsupervised SOM to supervised SOM which is named 

SSOM. 

As shown in Figure 2, there are three-layer structures 

in SSOM instead of two layer structure in SOM. They are 

input layer, competitive layer and output layer. In this 

network, the number of output layer is equal with data 

classification category. Each output node represents a 



data category, and connection between the output layer 

node and the competitive layer node is also full 

connection way. 

According to different prediction category of input 

samples, SSOM selects different weight adjustment 

formula to adjust weights and train network. SSOM not 

only adjusts the weight ω ij 

between input layer and 

competitive layer, but also adjust the weight ω 

jk 

between 

competitive layer and output layer. Finally, the 

classification results are generated by the combination of 

the two weights 

Figure 2. 

The structure diagram of SSOM 

The learning and train step of SSOM is as follow: 

(1) Initialization. Initialize the weight ω ij 

between 

input layer and competitive layer, the weight 

ω 

jk 

between competitive layer and output layer, and the 

neighbor radius r etc. 

(2) The winning neuron selection on competitive layer. 

Compute the distance between input sample x i 

and 

competitive layer neural j to get the neuron c with the 

minimal distance from the winning neuron. Assume d is 

the minimal distance, use c i 

to marker output categories 

connected to it. 

(3) Weight adjustment. Adjust the neuron weights 

ω and ω according to the predictive value of input 

ij 

jk 

sample x i 

. Here we assume the actual output value of x 

i 

is c 

x 

. If c i 

= c x 

, adjust the weights in the neighbor area 

of Nc (t) according to equation (4) and (5). 

ω new old ( old ) 

ij 

= ωij + η1 x − ωij 

(4) 


jk 

= ωjk + η2 x − ωjk 

(5) 

If ci 

≠ c x 

, adjust the weights according to equations 

(6) and (7). 


ij 

= ωij −η1 x − ωij 

(6) 


jk 

= ωjk −η2 x − ωjk 

(7) 

i 

where η 

1 

and η2 

represent the learning rate, they 

decrease with the evolution number increasing. 

(5) Judge whether the algorithm ends. If not end, 

return it to step (2). 

During the train process of SSOM neural network, The 

initial parameters such as weight ω ij 

, ω 

jk 

, learning rate 

η 

1 

, η2 

and neighbor radius r have much influence on 

testing result. These parameters randomly selected will 

have a negative effect on test result. In this paper, we use 

genetic algorithm to optimize the parameters ( η 

1 

, η2 

and 

neighbor radius r ) of SSOM.. 

Genetic algorithm (GA) is a kind of parallel search 

optimization method, which simulates the natural genetic 

mechanisms of biological evolution and Darwinian 

natural selection. Genetic algorithm simulates the 

phenomenon of duplication, crossover and mutation that 

occur in natural selection and genetic replication. 

Starting at a group which is a potential solution set of 

problem, it performs selection, crossover and mutation 

operation to generate a group of individuals better 

adapted to the environment. Then, group evolves into 

better and better areas in the search space and continues 

to evolve through the generations. Eventually they 

converge to a group of individuals best adapted to the 

environment and obtain the optimal solution. 

In recent years, genetic algorithm has been 

successfully used in the fields of economic management, 

traffic transportation, and industrial design and resolved 

many technical problems successfully. For example, 

reliability optimization, flow shop scheduling, job shop 

scheduling, machine scheduling, equipment layout design, 

image processing and data mining etc. 

The basic operation of optimization using genetic 

algorithm includes population initialization, fitness 

function calculation, selection, crossover and mutation 

operation. 

III. OPTIMIZATION OF WEIGHTS AND THRESHOLDS 

After train and learning SSOM network can quickly 

and easily achieves the classification of testing data. It 

can be used in a variety of classification field for labeled 

data such as text classification, intrusion detection, fault 

detection, etc. However during the train and learning 

process of SSOM neural network, the initialization of 

three parameters (learning rate η 1 

andη 2 

, neighborhood 

radius r ) have much influence on the experiment result. 

If the choice of these parameters is not very good or not 

very correct, it will have much negative effect on the test 

results and lead to lower correct classification rate. 

The real number encoding method is an important 

encoding method of genetic algorithm, in which each 

individual gene value is real number. The real number 

encoding method has following advantages: 

• Suitable for the scope of the larger number. 

• Easy to expand the space of the genetic search. 

• It can improve the accuracy requirements of the 

genetic algorithm. 



• It can improve the computational complexity and 

efficiency of operations. 

• Easy to use together with other classical optimization 

method. 

Here, we design a real encoding genetic algorithm to 

optimize the parameters η 1 

, η 

2 

and r of SSOM to 

obtain the optimal parameters. Using these optimal 

parameters we create a new SSOM network model named 

GA-SSOM and perform intrusion classification based on 

KDD Cup 1999 data set. 

To complete the optimization using GA, we firstly 

should initialize the individual population composed of 

parameters η 

1 

, η 

2 

and r in real coding, then design a 

proper fitness function to perform selection operation, 

crossover operation and mutation operation. After many 

times repeated iteration, the optimal individual including 

the optimal parameters is obtained. It is what we needed 

to create the GA-SSOM model. 

The implementation step is shown in Figure 3 and the 

detailed process is as follows: 

Figure 3. The optimization of parameter 

(1) Data normalization 

Data normalization is a data preprocessing procedure 

before training network; it is accomplished by data 

normalized function. Data normalization function is used 

to cancel the orders of magnitude difference between the 

dimensions of data and avoid large prediction error 

caused by differences in input and output. In this paper, 

the input feature value is normalized to [0, 1] by data 

normalization function in equation (8). 

x = ( x −x )/( x − x ) (8) 

k k min max min 

where x k represents the data sequence, x min and x max 

represents the minimum value and maximum value in 

data sequence. 

(2) The initialization of population 

A population is formed by N individuals generated 

randomly and genetic algorithm starts the iteration from 

this population as the initial point. 

In this part, individual coding adopts real coding and 

each individual is a real number series, which consists of 

3 components: learning rate η 1 

, learning rate η 2 

and 

neighborhood radius r . And N is set to 20 in our work. 

(3) Fitness function calculation 

Fitness value is to measure the excellent degree that 

each individual approach or reach in optimization 

calculation. The higher fitness value the individual has, 

the larger probability it is genetic to next generation than 

others. Fitness value is usually calculated through a 

fitness function. 

Here, we choose the reciprocal of the square of the 

absolute error between forecast output and the desired 

output data as the fitness function to judge the quality 

level of individual. The individual with greater fitness 

value will have more opportunity to be selected and 

inherited to the next generation. The fitness function is 

shown in equation (9). 

F = 

1 

m 

2 

∑(ci-c x) 

i= 

1 

Where F represents the fitness value, c i represents the 

forecast output and c x represent the desired output of the 

first i node, m is the number of output node. 

(4) Selection operation 

The task of select operation is to select body from the 

parent group to inherit to the next group. The genetic 

algorithm uses selection operator (or copy operation) to 

achieve the group individual survival of the fittest 

operation. The probability that high fitness individual is 

inherited to the next generation of group is great, and the 

probability that small fitness individual is inherited to the 

next generation of group is small. 

During the process of selection operation, proportional 

selection method is used. The basic idea of proportional 

selection method is as follow: the probability that 

individuals are selected is proportional to the size of its 

fitness. 

The selection probability p i which represents the first i 

individual is shown in equation (10). 

p 

i 

= 

N 

F 

∑ 

j = 1 

i 

F 

j 

(9) 

(10) 

where Fi is fitness value of the first i individual, N is the 

population size. 

(5) The crossover operation 

The crossover operation is a process in which the two 

paired chromosomes exchange some of its genes in a 

certain way to form two new individuals. The crossover 

operation is an important feature that the genetic 

algorithm is different from other evolutionary algorithms. 

It plays a key role in the genetic algorithm and is the 

main method to generate new individual. 



Because we use real number encoding GA, the 

crossover operation uses arithmetic crossover which is a 

linear combination of the two individuals to produce a 

new individual. The process is shown in equation (11). 

In this equation, it shows that the first k chromosome 

named a k performs crossover operation with the first l 

chromosome named a l , and the crossover bit is at first j 

bit. After crossover operation, a new pair of individual 

with good genes is generated. 

In this part we use binary encoding genetic algorithm 

to optimize input variable and reduce its dimensionality. 

To complete it, first encode the individual components, 

initialize the number of populations and the evolution, 

and design the fitness function. Then perform selection 

operation, crossover operation and mutation operation to 

generate the best individual which is the optimal 

combination of independent variables. The workflow is 

shown in Figure 4, each part functions as follows: 

⎧⎪ akj = akjb+ alj 

(1 −b) 

⎨ 

⎪⎩ alj = aljb+ akj 

(1 −b) 

(11) 

where b represents a random number between 0 and 1. 

(6) Mutation operation 

The so-called mutation operation is a process in which 

the value of certain genes in the individual encoded string 

is replaced by other genetic value to form a new 

individual. The mutation operation is a helper method to 

generate new individual, but it is essential to a computing 

step. Mutation operation determines the local search 

ability of genetic algorithms. 

Equation (12) shows the process of mutation operation 

in this part. Select a ij , which is the first j gene of the first i 

individual to perform mutation operation. The mutation 

operation is as follows: 

a 

ij 

⎧⎪ aij 

+ ( aij 

− amax 

) × r r > 0.5 

= ⎨ 

⎪⎩ aij 

+ ( amin 

− aij 

) × r r < 0.5 

(12) 

where a max is the upper bound of a ij , a min is the lower 

bound of a ij , r is the random value between 0 and 1. 

Through the above steps, we get the optimal 

chromosome which is composed of the optimal learning 

rate η 

1 

and η 

2 

, the optimal neighborhood radius r . Use 

these optimal variables to create SSOM neural network 

model named GA-BP. Then we use this model to carry 

out intrusion detection experiment based on KDD Cup 

1999 data set. 

IV. OPTIMIZATION OF INPUT VARIABLE FOR 

DIMENSIONALITY REDUCTION 

Using SSOM neural network to establish the model, 

the excessive input variable is easy to over fitting, which 

leads to the low precision, low rates of detection and 

excessive time. So it is necessary to optimize the 

selection of input variables, remove the redundancy 

variables and retain the variables which can most reflect 

the relationship between input and output variables in the 

model [21]. 

Binary encoding is one of the most commonly coding 

of genetic algorithm. It has the following advantages: 

• Encoding, decoding operation is simple. 

• The cross and mutation operation is easy to realize. 

• Meeting the minimum character set encoding 

principle. 

• Easy to use schema theorem theoretical to analyze the 

algorithm. 

Figure 4. The optimization of input variables 

(1) Data normalization 

Data normalization is a data preprocessing procedure 

before the experiment, it is also important for variable 

dimension reduction. Here, the input feature value is also 

normalized to [0, 1]. Data normalization function also 

uses equation (8). 

(2) The initialization of population 

In this optimization process, the individual coding 

adopts the binary coding mode. As the intrusion detection 

data has 41 features, the length of coding is designed to 

41 and every individual is a binary string composed of 41 

binary bits. Every chromosome corresponds to an input 

feature and every gene can only be 1 and 0. If the value 

of a particular chromosome is 1, it means that the input 

variable corresponding to this bit takes part in the final 

model, otherwise not. 

A population is formed by N individuals generated 

randomly and genetic algorithm starts the iteration from 

this population as the initial point. 

(3) Fitness function calculation 

Here, the reciprocal of the absolute error between 

forecast output and the desired output data is chose as the 

fitness function and it is shown in equation (13). 

In the process of calculating the fitness function, the 

learning rate η 1 

and η 2 

, neighborhood radius r of 

every individual is optimized by the genetic algorithm in 

Section III, avoiding the impact of its random on fitness 

function calculation. 

F= 

1 

m 

∑(Ci 

-C 

x 

) 

i=1 

(13) 



where F represents the fitness function, m is the number 

of output node, c i and c x represent respectively forecast 

output and the desired output of the first i node. 

(4) Selection operation 

During this process, we adapt proportion selection 

operator and calculate the probability of each individual's 

fitness in accordance with the equation (10). The 

individuals with larger probability is selected as the best 

individual to the next generation of genetic population, 

the one with smaller probability not. 

(5) The crossover operation 

During crossover operation, two individual are selected 

randomly from population to generate a new and 

outstanding individual. 

As the optimization of this part adopts binary coding, 

one-point crossover operator is used during the crossover 

operation. For a matched pair of individual, select 

randomly the cross-point and swap the other bit from 

cross-point. The operating diagram is shown in Figure 5. 

The binary string 1001 in individual A exchanges data 

information with binary string 0011 in individual B. After 

crossover operation, it generates two new individual and 

increases the diversity of individual. 

Figure 5. 

Crossover operation 

(6) Mutation operation 

Mutation operation can also increase the diversity of 

individual. Here, select a single point mutation operator 

and random mutation point, then 0 and 1 is exchanged. 

The principle is shown in Figure 6. Two new individual 

generate after this operation. 

Figure 6. Mutation operation 

(7) The establishment of New-GA-SSOM network 

model 

After many times evolution, when meeting the 

iteration condition, the output of the population is the 

optimal solution of the problem. They are the handsome 

and the most representative input variable combination. 

Through the above steps, we get the optimal 

chromosome which is composed of the optimal feature. 

Extract a set of variables from the best chromosome gene 

as the final input variables to achieve the dimension 

reduction of independent variables. That is the new neural 

network model, named New-GA-SSOM. Then we use 

this model to train network, and carry out intrusion 

detection data based on KDD Cup 1999 data set. 

V. EXPERIMENT 

KDD Cup 1999 data set is a standard data set for 

intrusion detection, including the training data set and test 

data set. The training data set includes 494 021 records 

and testing data set includes 311 029 records. In the 

KDD99 data set, each data example represents attribute 

values of a class in the network data flow, and each class 

is labeled either as normal or as an attack with exactly 

one specific attack type. There are 22 types of attacks in 

the training data set and an increase of new 14 kinds of 

attacks in the testing data set. All the attack types can be 

divided into four major categories: Probing, Denial of 

Service (DoS), User-to-Root (U2R) and Remote-to-Local 

(R2L). Each complete TCP (transmission control 

protocol) connection is considered as a record, including 

four types of attributes collection: time-based traffic 

features, host-based traffic features, content features and 

basic features [22, 23, 24]. 

Our experiment is based on the KDD Cup 1999 

intrusion detection data set. Training data set is composed 

of 3 000 data of normal type and 3 000 data of attack type, 

selected randomly from KDD Cup99 of "10% KDD" 

dataset. Testing data set is composed of 2 000 data of 

normal type and 2 000 data of attack type, selected 

randomly from KDD Cup99 of the "Corrected KDD" 

dataset. The selected data set is shown in Table I. 

Each data has 41 different attributes (32 continuous 

attributes and 9 discrete attributes) used as SSOM input 

value and 1 attack type label used as output value of 

SSOM. Some of them are the numerical types, and some 

are character types, but SSOM can only deal with 

numerical data. Therefore, before training we must make 

the input data numerical and normalized. This study used 

simple substitution symbols with numerical data types. 

The protocol-type, service and flag are replaced by digital 

attributes. For example, three kinds of protocol-type (tcp, 

udp and icmp) will be expressed with 1, 2, 3. Also, 70 

kinds of services are substituted with 1, 2… 70. The 

attack types are also numbered with 1, 2, 3 and so on. 

Experimental platform is the PC with Intel Core2 Duo 

CPU 2.0GHz, memory 2.0GB, Windows XP operating 

system and MATLAB 7.8.0 (R2009.0a) programming 

environment. 

Based on the experiment data in Table I, training and 

test are carried out respectively using SSOM (its 

parameters are selected randomly), GA-SSOM and New- 

GA-SSOM neural network. According to the different 

classification number of attack type, experiment is carried 

out as following two cases. 

TABLE I. 

TRAINING SET AND TEST SETS 

Attack class Attack type Training set Test set 

Normal normal 6000 3000 

back 700 400 

DOS 

neptune 2700 1200 

smurf 1600 800 

R2L guess_passwd 53 40 

U2R buffer_overflow 30 22 

ipsweep 350 180 

Probe portsweep 350 200 

satan 217 158 



TABLE II. 

DETECTION RATE AND MODEL TIME (TWO CLASSIFICATION) 

Type 

Detection rate (%) 

Time 

Model 

normal abnormal 

SSOM 

93.2 90.2 

38.1s 

GA-SSOM 98.5 95.3 

New-GA-SSOM 13.5s 97.5 95.5 

TABLE III. 

DETECTION RATE AND MODEL TIME (FIVE CLASSIFICATION) 

Model 

Model 

GA- New-GA- 

Type 

SSOM 

SSOM SSOM 

Normal 92.1% 98.4% 96.5% 

DOS 89.8% 94.4% 94% 

R2L 6.7% 7.7% 7.1% 

detection U2R 19.2% 23.4% 22.4% 

rate (%) Probe 89.3% 95.1% 96.1% 

time (s) 45.4.s 16.5s 

Experiment 1: the attack types of selected experiment 

data are divided into normal data and attack data, the 

normal data is numbered with 1 and the attack data is 

numbered with 2. It is a two classification problem and 

the experiment result is shown in Table II. 

Experiment 2: The attack types are classified into 

Normal data, DOS, R2L, U2L, Probe. The Normal label 

data is numbered with 1, the other four types are 

numbered with 2, 3, 4 and 5. It is a multiple classification 

problem and the experiment result is shown in Table III. 

From Table II and Table III, we can know that the 

proposed GA-SSOM and New-GA-SSOM have higher 

detection than SSOM whose parameters are selected 

randomly. Although there is little difference in detection 

rate between GA-SSOM and New-GA-SSOM, New-GA- 

SSOM spends less time than SSOM and GA-SOM in 

modeling. So it shows that GA-SSOM has rather higher 

intrusion detection rate than SSOM, and New-GA-SSOM 

has higher intrusion detection rate and much shorter 

modeling time than SSOM. 

VI. CONCLUSION 

In this paper, we use genetic algorithm to optimize the 

SSOM which is an improved and a supervised SOM 

neural network. A real encoding genetic algorithm is 

applied to optimize the learning rate η1 

and η 

2 

, 

neighborhood radius r of SSOM neural network to 

improve detection rate. And a binary encoding genetic 

algorithm is used to reduce the dimension of input 

variable of SSOM neural network to improve the 

efficiency of modeling. 

Through optimization, it can quickly and effectively 

establish SSOM network model and improve speed of 

training and learning. Classification experiments based 

on KDD Cup 1999 data set was carried out and results 

showed that the optimized model has shorter modeling 

time and higher intrusion detection rate. 

In the future, we plan to propose a semi-supervised 

intrusion detection classifier based SOM, and use genetic 

algorithm to optimize the input parameters of this semisupervised 

classifier. 


The authors wish to thank the support of ShangLuo 

University and Northwestern Polytechnical University. 

This work was sponsored by Scientific Research Program 

Funded by Shaanxi Provincial Education Department 

(No.12JK0748) and National ministries foundation in 

China. 

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“Intrusion Detection Using BP Optimized by PSO”, IJACT: 

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“An Intrusion Detection System Based on Hierarchical 

Self-Organization, “ Advances in Soft Computing, vol. 53, 

pp. 139-146, 2009. 

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[25] Hettich S, Bay S D.The UCI KDD Archive [EB/OL]. http: 

//kdd.ics.uci.edu/ databases/kddcup99.] 

Zhao Jianhua was born in 1982. He is currently a lecturer and 

seeking for his doctor’s degree. His research interests include 

machine learning, network security. 

Li Weihua was born in 1951. He is currently a professor. His 

research interests include network security and intelligent 

decision. 



Fault Diagnosis System for NPC Inverter based 

on Multi-Layer Principal Component Neural 

Network 

Danjiang Chen 

Shanghai Maritime University, Shanghai, China 

Zhejiang Wanli University, Ningbo Zhejiang, China 

Email: cdj02@163.com 

Yinzhong Ye and Rong Hua 

Shanghai Institute of Technology, Shanghai, China 

Email: yzye@sit.edu.cn, huarong@sit.edu.cn 

Abstract—This paper presents a fault diagnosis method for 

a neutral point clamped (NPC) inverter using a multi-layer 

artificial neural network (MANN). The considered possible 

faults of NPC inverter include the open-circuit fault 

occurring in one single device or more devices. The upper, 

middle and down bridge voltages are adopted the test 

signals because of the difficulties in isolating some fault 

modes. A novel multi-layer neural network is proposed to 

diagnose all possible open-circuit faults. Furthermore, the 

principal component analysis (PCA) is utilized to reduce the 

input size of neural network. The comparison between 

neural network with and without PCA is performed. The 

simulation and experimental results prove the feasibility of 

the diagnostic method and show that the proposed method 

has the advantages of good classification performance and 

high reliability. 

Index Terms—three level inverter, fault diagnosis, MANN, 

PCA 


The multilevel inverter could achieve more levels, 

lower harmonic distortion in the voltage output in 

addition to lowering the voltage stress of the power 

devices, as compared with the conventional two-level 

inverters [1-5] . Due to these advantages, NPC inverter has 

been widely used in high-power industrial applications. 

However, the NPC inverter system is composed of many 

switching devices which would reduce the reliability of a 

multilevel inverter, as a break in any one of these devices 

will inevitably make the entire inverter fail to work and 

produce the economic losses [6]. Therefore the fault 

diagnosis methods would be necessary to ensure the 

reliability of the multilevel inverter. 

Some efforts have been made in the problem 

mentioned above. For example, the voltage output in 

faulty situation could be analyzed in real time mode and 

compared with the voltage output in normal situation in 

order to find out the faulty device, see [7]-[10]. 

Furthermore, it has been shown that the diagnostic 

performance could be enhanced if the intelligent methods 

like neural network, support vector machine etc. are 

introduced in recognizing different fault modes, see [11]- 

[14], though only simple applications of the neural 

network in NPC inverter have been proposed [15] . 

Investigating the current research works reveals that 

only the simplest fault mode, i.e. the open-circuit 

occurring in a single device has been taken into account. 

In order to improve the reliability of NPC inverter, this 

paper will focus on a more complicated fault mode, i.e. 

the open-circuit fault occurring in two devices 

simultaneously, in addition to diagnosing the open-circuit 

fault mode. Fault features will be extracted from three 

bridge voltages by the discrete Fourier transform (DFT) 

and a multi-layer artificial neural network (ANN) will be 

proposed to accomplish diagnosing all fault modes under 

consideration. In additional, the PCA is performed in this 

paper to reduce the input neural size [16-17]. Figure 1 

shows a three level NPC inverter. 

1 

U 

2 d 

o 

1 

U 

2 d 

D a5 

D a6 

S a1 

S a2 

S a3 

S a4 

a 

D a1 

D a2 

D a3 

D a4 

D b1 

D S D 

b5 b2 

b 2 

D b6 

S b1 

S b3 

b 

D b3 

D c5 

D c6 

S c1 

S c2 

S c3 

S D b4 

S c 4 

b4 

Figure 1. Main circuit of a three level NPC inverter 

II. ANALYSIS OF POSSIBLE FAULT MODE 

One single bridge leg of NPC inverter could be derived 

from Figure 1, e.g., as shown in Figure 2 for phase a. 

There are three bridge voltages in Figure 2. The 

voltage between points a 

u 

and o V 

ao 

is named as ‘middle 

bridge voltage’, or ‘bridge voltage’ for simplicity. The 

voltage between points a 

u 

and o V auo 

is named as ‘upper 

c 

D c1 

D c2 

D c3 

D c4 

R a 

R b 

R c 

L a 

L b 

L c 

n 


doi:10.4304/jcp.8.6.1464-1471


bridge voltage’, while V ado 

between points a 

d 

and o is 

‘down bridge voltage’. 

1 

U 

2 d 

D a5 

S a1 

S a2 

D a1 

a u 

D a2 

o 

1 

U 

2 d 

D a6 

S a3 

S a4 

a 

i a 

D a3 

a d 

D a4 

Ra 

L a 

b 

n 

Rb 

L b 

c 

Rc 

L c 

(c) S 

a2 

open-circuit 

Figure 2. Single bridge leg of NPC inverter 

A. Open-circuit Fault of Single Device 

Consider the circuit shown in Figure 2 which consists 

of six devices, namely S 

a1 

, S 

a2 

, S 

a3 

, S 

a4 

, D 

a5 

and D 

a6 

. 

Correspondingly, there are six possible fault modes for 

the open-circuit fault of single device, with each mode 

being denoted by the same symbol of each device. As the 

circuit is symmetric in configuration, those fault modes 

of S 

a1 

, S 

a2 

and D 

a5 

need to be analyzed in detail, and 

the results apply for the other three fault modes. 

Performing simulation for the NPC inverter by the 

software PSIM, with the input DC voltage U being 

100V, the load of each phase being resistance 8Ω and 

inductance 20mH in series, under the normal (fault free) 

condition and each single device open-circuit fault mode, 

the simulation waveforms of bridge voltage could be 

obtained as shown in Figure 3. 

(a) Fault free mode 

(b) S 

a1 

open-circuit 

d 

(d) D 

a5 

open-circuit 

Figure 3. Simulation waveforms of bridge voltage for open-circuit 

fault of single device 

It could be seen obviously from Figure 3 that the 

waveform of the bridge voltage is different from one 

another and has specific features. By theory of spectrum 

analysis [18], each waveform of bridge voltage in Figure 

3 consists of specific harmonics differing from the other’s. 

Therefore the ‘fault features’ could be extracted from the 

bridge voltages. Based on such fault features, it is 

possible to isolate the open-circuit fault of single device 

in some proper ways. 

B. Open-circuit Fault of Two Devices 

Two different situations arise while the case that two 

devices malfunction by open-circuit during certain period 

is taken into account. The first situation arises when two 

faulty devices lie in the same phase, e.g. S 

a1 

and S 

a3 

, and 

the second one arises when two faulty devices lie in 

different phases, e.g. S 

a1 

in phase a and S 

b1 

in phase b. 

Only the first situation needs to be investigated because 

the second situation could be reduced to the open-circuit 

fault of single device in two phases and then be treated by 

the way mentioned above. 

Considering the phase a without loss of generality, 

possibly there are six different fault modes as { S 

a1 

, S 

a2 

}, 

{ S 

a1 

, S 

a3 

}, { S 

a1 

, S 

a4 

}, { S 

a2 

, S 

a3 

}, { S 

a2 

, S 

a4 

} and 

{ S 

a3 

, S 

a4 

}. Due to the symmetry in the configuration of 

NPC inverter, for the fault modes { S 

a2 

, S 

a4 

} and { S 

a3 

, 

S 

a4 

}, the bridge voltage would be the same as one for 

{ S 

a1 

, S 

a3 

} and { S 

a1 

, S 

a2 

} respectively, while the phase 

is just opposite. Therefore only the other four fault modes 

should be analyzed. The bridge voltages’ simulation for 

these four faulty modes is given out in Figure 4. 



(a) { S 

a1 

, S 

a2 

} 

only one path through D 

a1 

and D 

a2 

as shown in Figure 5 

(c). When the fault { S 

a2 

} occurs, current flow (3) is 

possible while current flow (1) or (2) is impossible. When 

the fault { S 

a1 

, S 

a2 

} occurs, only current flow (3) is 

possible. Hence, no difference exists in current flow and 

the bridge voltages for the cases { S 

a2 

} and { S 

a1 

, S 

a2 

}. 

This reveals that the fault modes { S 

a2 

} and { S 

a1 

, S 

a2 

} 

cannot be isolated if only the bridge voltage is used. 

1 

U 

2 d 

D a5 

S a1 

S a2 

D a1 

a u 

D a2 

o 

a 

i a 

Ra 

b 

Rb 

c 

Rc 

(b) { S 

a1 

, S 

a3 

} 

1 

U 

2 d 

D a6 

S a3 

S a4 

D a3 

a d 

D a4 

L a 

n 

L b 

L c 

(a) Current flow (1) 

1 

U 

2 d 

D a5 

S a1 

S a2 

D a1 

a u 

D a2 

o 

a 

i a 

R a 

b 

Rb 

c 

Rc 

(c) { S 

a1 

, S 

a4 

} 

1 

U 

2 d 

D a6 

S a3 

S a4 

D a3 

a d 

D a4 

L a 

n 

L b 

L c 

(b) Current flow (2) 

1 

U 

2 d 

D a5 

S a1 

S a2 

D a1 

a u 

D a2 

(d) { S 

a2 

, S 

a3 

} 

Figure 4. Bridge voltage when two devices malfunction 

From Figure 3 and Figure 4 it could be found that the 

circuit would have the same bridge voltage for the fault 

modes { S 

a2 

} (see Figure 3 (c)) and { S 

a1 

, S 

a2 

} (see 

Figure 4 (a)). This will be also the case for the fault 

modes { S 

a3 

} and { S 

a3 

, S 

a4 

}. 

Consider the current path in Figure 2 from a to o 

through the upper half bridge where S 

a1 

, S 

a2 

, D 

a5 

, 

Da1 

and D 

a2 

are involved, and denote the current of phase 

a as i a 

. If i 

a 

> 0 , the current has two possible paths as 

shown in Figure 5 (a-b), but if i 

a 

< 0 , the current has 

o 

1 

U 

2 d 

D a6 

S a3 

S a4 

a 

i a 

D a3 

a d 

D a4 

Ra 

(c) Current flow (3) 

L a 

b 

n 

Rb 

L b 

c 

Rc 

Figure 5. Diagram of NPC inverter work states 

In order to isolate all possible fault modes, the voltages 

of both the upper bridge and the down bridge as defined 

before are introduced. Figure 6 shows the waveform of 

the upper bridge voltage for { S 

a2 

} and { S 

a1 

, S 

a2 

}. 

Obviously the waveform is different from each other. 

L c 



Fault free 

x 104 

4 

Sa1 open-circuit 

x 104 

4 

Amp 

2 

Amp 

2 

0 

0 1 2 3 4 

Freq:kHz 

Sa2 open-circuit 

x 104 

4 

0 

0 1 2 3 4 

Freq:kHz 

Da5 open-circuit 

x 104 

4 

Amp 

2 

Amp 

2 

(a) { S 

a2 

} 

0 

0 1 2 3 4 

Freq:kHz 

{Sa1,Sa2} 

x 104 

4 

Figure 8. DFT result of figure 3 

0 

0 1 2 3 4 

Freq:kHz 

{Sa1,Sa3} 

x 104 

4 

Amp 

2 

Amp 

2 

0 

0 1 2 3 4 

Freq:kHz 

{Sa1,Sa4} 

x 104 

4 

0 

0 1 2 3 4 

Freq:kHz 

{Sa2,Sa3} 

x 104 

4 

Amp 

2 

Amp 

2 

0 

0 1 2 3 4 

Freq:kHz 

Figure 9. DFT result of figure 4 

0 

0 1 2 3 4 

Freq:kHz 

(b) { S 

a1 

, S 

a2 

} 

Figure 6. Waveform of the upper bridge voltage 

III. FAULT DIAGNOSIS 

A. Structure of Fault Diagnosis System 

The structure for a fault diagnosis system is shown in 

Figure 7. The system is composed of three major states: 

feature extraction, principal component analysis and 

multi-layer neural network. The output of the MNN is 

nearly 0 and 1 as binary code which can be related to 

different fault mode. 

NPC 

Inverter 

Bridge Voltage 

Feature 

Extraction 

System 

MNN 

PCA 

Figure 7. Structure of Fault Diagnosis System 

B. Feature Extraction 

An appropriate selection of the feature extractor is to 

provide the MNN with adequate significant details in 

original data so that the highest accuracy in the MNN 

performance can be obtained. In this paper the DFT 

technique is adopted to extract feature from the middle, 

upper and down bridge voltages. The transformed signals 

of Figure 3 and Figure 4, whose fundamental frequency is 

50Hz and carrier frequency is 1.5kHz, are represented in 

Figure 8 and Figure 9 respectively. 

According to the spectrum characteristics of PWM 

inverters [19], and also could be seen from Figure 8 and 

Figure 9, obviously, main harmonics of the bridge 

voltage are distributed in the fundamental frequency, 

carrier frequency and their multiples. Hence, some 

components of these main harmonics are selected as the 

fault feature by feature extraction system in Figure 7. 

The selection of input data for the main neural network 

include amplitude of DC component, fundamental, 

double fundamental, three times of fundamental, carrier 

frequency (1.5kHz), side frequency of carrier (1.4kHz 

and 1.6kHz) and double carrier frequency. The phase of 

DC component, fundamental and double fundamental are 

also selected as input data for the main neural network. It 

could be counted that the dimension of the input data for 

the main neural network is 11. 

For both auxiliary neural networks, the amplitude of 

DC component, fundamental and double fundamental are 

selected as the input data with the dimension of three. 

C. Principal Component Analysis 

It could be seen that the input data of the main neural 

network has high dimension and we don’t know whether 

these 11 dimension data are correlated or uncorrelated. 

PCA is a statistical technique used to transform a set of 

correlated variables to a new lower dimensional set of 

variables, which are uncorrelated or orthogonal with each 

other. The fundamental PCA used in a linear 

transformation is shown as follows: 

T = X ⋅ P 

(1) 

Where T is the m× k score matrix (transformed data), 

m is number of observations, k is dimensionality of the 

PC space; X is the m× n data matrix, m is number of 

observations, n is dimensionality of original space; and 

P is the n× k loadings matrix (PC coordinates), n is 

dimensionality of original space, k is number of the PCs 

kept in the model. The detail equation of Equation (1) is 

shown in the follow expression: 



⎡t11 t12 t1 k ⎤ ⎡x11 x12 x1 n ⎤ ⎡p11 p12 p1k 

⎤ 

⎢ 

t21 t22 t 

⎥ ⎢ 

2k x21 x22 x 

⎥ ⎢ 

2n p21 p22 p 

⎥ 

⎢ 

 

⎥ ⎢ 

 

⎥ ⎢ 

 

2k 

= ⋅ 

⎥ 

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 

t t t x x x p p p 

⎣ m1 m2 mk⎦ ⎣ m1 m2 mn⎦ ⎣ n1 n2 

nk⎦ 

Selecting a reduced subset of PC space results in a 

reduced dimension structure with respect to the important 

information available as shown in the following 

expression: 

[ t t t ] [ x x x ] 

⎡ p11 p12 p1 

k ⎤ 

⎢ 

p p p 

⎥ 

⎢ 

 

⎥ 

 

⎢ 

⎥ 

⎣ pn 1 

pn2 

pnk⎦ 

21 22 2k 

1 2 k 

= 

1 2 

n 

⋅ ⎢ ⎥ 

D. Artificial Neural Network 

ANN is a computer model whose architecture 

essentially mimics the knowledge acquisition and 

organizational skills of the human brain. Although there 

are a variety of ways to construct these models, Back- 

Propagated (BP) neural network has become one of the 

most widely used ANNs in practice. BP neural network 

with a single hidden layer is selected in this paper, which 

has been demonstrated to be sufficient to approximate 

any continuous function within the desired accuracy [20]. 

Figure 10 shows a diagram of neural network with a 

single hidden layer. 

x 1 

(2) 

(3) 

The goal of the training of ANN is to minimize the 

error between predicted and target values by adjusting the 

connection weights and biased. The error is given by 

Equation (6): 

p q 

2 

E = ∑∑ ( apq 

−opq 

) 

(6) 

p= 1 q= 

1 

Where q is the number of logic units in output layer, and 

p is the number of training samples, a pq 

and o 

pq 

are 

the predicted and target values, respectively. 

E. Multi-layer Neural Network 

A new method named as multi-layer neural network is 

proposed to diagnose all open-circuit fault modes under 

consideration for the NPC inverter, as shown in Figure 11. 

Feature A 

Main 

Feature 

Feature B 

Main 

ANN 

Output 

Auxiliary 

ANN A 

S or { S , S } 

a a a 

2 1 2 

S or { S , S } 

a a a 

3 3 4 

Auxiliary 

ANN B 

Figure 11. Multi-layer neural network 

Output 

Output 

y 1 

x 2 

x 3 

 

x n 

 

n h q 

 

 

y 2 

 

y q 

Figure 10. Neural network with a single hidden layer 

The three layers are called the input layer, hidden layer 

and output layer, respectively. Each layer consists of 

logic units or neurons, as the basic information 

processing units in ANN. The relationship of the input 

value of the unit i in input layer and that of unit j in 

hidden layer is: 

n 

uj = ∑ ω 

ji 

xi + bj 

(4) 

i= 

1 

Where x 

i 

is an input value of the logic unit i in the input 

layer, u 

j 

an initial output value of the logic unit j in the 

hidden layer, ω 

ji 

connection weights between unit j and 

i , b 

j 

input bias of the unit j , n the number of logic 

units in the input layer. 

The initial output value u 

j 

is further transformed with 

the common transfer function in a sigmoid form: 

1 

= (5) 

+ 

O j u j 

1 e − 

Where O is the final output value of the logic unit j . 

j 

TABLE I. 

FAULT MODES AND OUTPUT OF MAIN ANN 

Fault modes (open-circuit) 

Target output 

Fault free 000000 

S 

a1 

100000 

S 

a2 

or { S 

a1 

, S 

a2 

} 010000 

S 

a3 

or { S 

a3 

, S 

a4 

} 001000 

S 

a4 

000100 

D 

a5 

000010 

D 

a6 

000001 

{ S 

a1 

, S 

a3 

} 101000 

{ S 

a1 

, S 

a4 

} 100100 

{ S 

a2 

, S 

a3 

} 011000 

{ S 

a2 

, S 

a4 

} 010100 

TABLE II. 

FAULT MODES AND OUTPUT OF AUXILIARY ANN A 


Target output 

S 

a2 

0 

{ S 

a1 

, S 

a2 

} 1 

Main Feature extracted from the bridge voltage V ao 

is 

used as input data for main ANN, which is used to 

diagnose eleven fault modes represented in Table I 

(including fault free mode). While Feature A and Feature 

B extracted from upper bridge voltage V auo 

and down 

bridge voltage V ado 

are used as the input data for 

auxiliary ANN A and B respectively. Table II and Table 



III represent the fault modes diagnosed by two auxiliary 

ANNs and their target output. 

TABLE III. 

FAULT MODES AND OUTPUT OF AUXILIARY ANN B 


Target output 

S 0 

{ 

a3 

a3 

S , S 

a4 

} 1 

IV. DIAGNOSIS RESULT 

To verify the proposed method, an NPC inverter using 

MOSFET IRF640 as the switching device is used to carry 

out the three bridge voltages. A DSP chip TMS320F2812 

is utilized to generate gate drive signals. The input DC 

voltage is 90V to 110V and the three phase wyeconnected 

load is 8Ω resistance series with 20mH 

inductance. Fault occurrence is created by physically 

removing switching signal in the desired position. 

Figure 12 shows the experimental bridge voltage 

waveforms for open-circuit fault of single device. Figure 

13 shows the experimental bridge voltage waveforms 

when open-circuit fault occurring in two devices 

simultaneously. 

Figure 12. Experimental bridge voltage waveforms for open-circuit of 

single device 

Each fault mode from Tab.1 to Tab.3 must cover the 

operating region. Thus, there are three degrees of input 

DC voltage in the experiment include 90V, 100V and 

110V. Under each DC voltage, the modulation index is 

changed from 0.2 to 1 with step of 0.1. Therefore, 27 sets 

original data can be obtained for each fault mode. The 

data whose modulation index is 0.5, 0.7 and 0.9 are 

utilized as test sample and the rest data are utilized as 

train sample. 

Volt:20/div 

Time:5ms/div 

(a) { S 

a1 

, S 

a2 

} 

Volt:20/div 

Time:5ms/div 

(a) S 

a1 

open-circuit 

Volt:20/div 

Time:5ms/div 

(b) S 

a2 

open-circuit 

Volt:20/div 

Volt:20/div 

Time:5ms/div 

(b) { S 

a1 

, S 

a3 

} 

Volt:20/div 

Time:5ms/div 

(c) { S 

a1 

, S 

a4 

} 

Volt:20/div 

Time:5ms/div 

(c) D 

a5 

open-circuit 

Time:5ms/div 

(d) { S 

a2 

, S 

a3 

} 

Figure 13. Experimental bridge voltage waveforms when two devices 

malfunction 



TABLE IV. 

DIAGNOSIS RESULT OF MULTI-LAYER ANN (WITHOUT PCA) 

Main SVM 

Auxiliary 

SVM A 

Auxiliary 

SVM B 

No noise 98.84% 100% 100% 

10% white 

nosie 96.31% 100% 100% 

Table IV shows diagnosis result of the multi-layer 

ANN without PCA and the dimension of the input data of 

the main ANN is 11. 

Table V shows diagnosis result of the multi-layer ANN 

with PCA. Here, only the input data of the main ANN is 

transformed by the technique of PCA and the dimension 

of the new input data of the main ANN is 8. 

TABLE V. 

DIAGNOSIS RESULT OF MAIN ANN (WITH PCA) 

Main SVM 

No noise 99.24% 

10% white nosie 98.43% 

It could be seen from Table IV and Table V that the 

diagnosis precision of the main ANN with PCA is higher 

than that without PCA. It could be deduced that the ANN 

with PCA must be trained better than the ANN without 

PCA and has better generalization ability. 


Additional signals are required in order to isolate more 

complicated faults of open-circuit occurring in two 

devices in NPC inverter during certain period. Note that 

this is not just a theoretical problem but a practical one 

because some failures have been reported recently, see 

[21]-[22]. In this paper, the voltages in all the upper, 

middle and down bridge are suggested to extract fault 

features. A scheme of multi-layer ANN is proposed to 

implement fault diagnosis of NPC inverter, involving the 

simple open-circuit of one device or more devices. Better 

precision could be achieved when the input data is 

transformed by PCA. 


The project is supported by Innovation Project of 

Shanghai Municipal Education Commission numbered 

12zz191, Graduates’ Innovation Fund of Shanghai 

Maritime University numbered YC2011061. 

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[9] Ho-In Son, Tae-Jin Kim, Dae-Wook Kang, Dong-Seok 

Hyun, “Fault Diagnosis and Neutral Point Voltage Control 

When the 3-level Inverter Faults Occur”, Power 

Electronics Specialists Conference, 2004, pp.4558- 4563. 

[10] Jae-Chul Lee, Tae-Jin Kim, Dae-Wook Kang, Dong-Seok 

Hyun, “A Control Method for Improvement of Reliability 

in Fault Tolerant NPC Inverter System”, 37th IEEE Power 

Electronics Specialists Conference, 2006, pp.1-5. 

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Circuit Fault Diagnosis Based on BP Neural Network and 

D-S Evidence Theory”, 8th World Congress on Intelligent 

Control and Automation, 2010, pp.2249-2253. 

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“The Studies of Single-phase Inverter Fault Diagnosis 

Based on D-S Evidential Theory and Fuzzy Logical 

Theory”, CES/IEEE 5th International on Power 

Electronics and Motion Control Conference, 2006, pp.1-4. 

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Three-phase PWM Inverters Using Wavelet and SVM”, 

IEEE International Symposium on Industrial Electronics, 

2008, pp.329-334. 

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Three-phase Sine-PWM Inverter Based on Rough Setneural 

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Technology, 2005, 25 (6), pp.351-353. 

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“Fault Diagnosis in Multi-level Inverter System Using 

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Conference, INDICON 2008, pp.494-498. 

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Eigenvalue/Eigenvector 3D Current Reference Method for 

Detection and Fault Diagnosis in a Voltage Source 

Inverter”, 35th Annual Conference of IEEE on Industrial 

Electronics, 2009, pp.190-194. 

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Reconfiguration for Multilevel Inverter Drive Using AI- 

Based Techniques”, IEEE Transactions on Industrial 

Electronics, vol.54, no.6, 2007, pp.2954-2968. 

[18] Hu Guang-shu, “Digital Signal Processing-theory, 

Algorithms and Implementation”, Beijing, Tsinghua 

University Press, 2003. 

[19] Lin Wei-xun, “Modern Power Electronics Technology”, 

Beijing, Machinery Industry Press, 2006. 

[20] U.Ahmad, A.Gavrilov, S.Lee, “Modular Multilayer 

Perceptron for WLAN Based Localization”, Proc. of 

International Joint Conference on Neural Networks, 2006, 

pp. 3465-3471. 



[21] Sun Jing, “Fault Recovery Processing for CRH2 Multipleunit 

Traction Converter”, Railway Locomotive & Car, vol. 

29, no. 6, pp. 64-66, 2009,. 

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Processing for CRH2 M ultiple-unit Traction Converter”, 

Railway Locomotive & Car, vol. 28, no. 4, pp. 69-70, 2008. 

Danjiang Chen was born in Ningbo, China, on Feb 15, 1979. 

He received the B.S. and M.S. degrees in electrical engineering 

from Zhejiang University, Hangzhou, China, in 2002 and 2005, 

respectively. He is currently working toward the Ph.D. degree in 

Shanghai Maritime University, Shanghai, China. 

After received the M.S. degree, he joined Zhejiang Wanli 

University, where he is a lecturer in the faculty of electronic and 

information engineering. His current area of research includes 

power electronics and their fault diagnosis system. 

Yinzhong Ye was born in Zhejiang, China, in 1964. He 

received the B.Sc., M.Sc. and Ph.D. degrees in industrial 

automation and electronic engineering from East China 

University of Science and Technology, Shanghai, China in 1982, 

1985 and 1989, respectively. 

After receiving the M.Sc. degree, he joined the Research 

Institute of Automation, East China University of Science and 

Technology, Shanghai, China, where he had worked as a 

Teaching Assistant, Lecturer and Associate Professor. In 1994 

he joined Shanghai Maritime University, Shanghai, China, as a 

Professor of electrical and automatic control engineering. Since 

2009 he has joined Shanghai Institute of Technology, Shanghai, 

China as Vice President and Professor in electrical engineering 

and automation. His main research interests and experience 

include fault diagnosis, fault-tolerant control, system simulation, 

power electronics, measurement and control of industrial 

processes. 

Dr. Ye is a Vice Chairperson of SAFEPROCESS CHINA, 

Chinese Association of Automation. 

Rong Hua was born in Shanghai, China, on March 26, 1960. 

He received the B.S. degrees in motor control engineering from 

Shanghai University, Shanghai, China, in July 1982, and the 

M.S. degrees in control engineering from East China University 

of Science and Technology, Shanghai, China, in March 2008. 

At present, he joined the Shanghai Institute of Technology, 

Shanghai, China, as a Professor and a Master's Supervisor of 

electronics Information engineering. His main research interests 

and experience include control engineering, signal processing 

and power electronics and fault diagnosis system. 



Pulse Wave K Value Averaging Computation and 

Pathological Diagnosis 

Li Yang 1, 2 , Jinxue Sui 

1 Shandong Institute of Business and Technology / School of Information and Electronic Engineering, Yantai, China 

Email: suijinxue@163.com 

Yunan Hu 

2 Department of Control Engineering / Naval Aeronautical Engineering University, Yantai, China 

Email: yangl-2005@163.com 

Abstract—Many cardiovascular diseases will lead to changes 

in pulse wave. Pulse wave’s transmission will play a 

significant role in promoting the clinical detection and 

diagnosis, one kind pulse wave computational method based 

on averaging method is proposed, and computing 

cardiovascular function parameter K according to the 

waveform area, the K value is associated with pathological 

analysis and diagnosis. A large number of clinical 

simulation and experiments proved that the relationship 

between the form factor K value and the human 

cardiovascular health, the pulse wave of the cerebral 

infarction matches with the actual clinical detection, it can 

provide theoretical support for the non-invasive detection 

and parametric analysis of the cardiovascular function. 

Index Terms—pulse wave, averaging computation, cerebral 

circulation, pathological diagnosis 


As the cycle of contraction and relaxation of the heart, 

blood pressure, blood flow velocity and blood flow’s 

pulsation and vessel wall changes’ expansion spread in 

the vascular network, are known as pulse wave. 

Pulse wave transmitting characteristics are closely 

linked with the hemodynamic parameters of the blood 

circulation system. Changes in pulse waveform 

characteristics are an important basis to evaluate the 

physiological and pathological state of the human 

cardiovascular system. When the pulse wave spreads 

from the heart to the arterial system, it is not only 

affected by the heart itself, but also by various 

physiological factors that flow through all artery and its 

branches, such as vascular resistance, vessel wall 

elasticity, the pulse wave contains very rich physiological 

and pathological information in cardiovascular system, so 

that whether Chinese pulse-taking or Western 

cardiovascular tests is tried to extract a variety of 

physiological and pathological information from the 

pulse waveform and pressure’s changes. Therefore, the 

pulse wave transmitting studies are combined with the 

clinical testing and the pathological diagnosis in order to 

use non-invasive detection to analyze and diagnose the 

cardiovascular disease, will play a very important 

practical effect [1-12]. 

This paper proposed a solving method that 

cardiovascular function parameters K-value will be 

calculated based on the averaging method, according to 

changes of the area and waveform of the pulse in 

different physiological and pathological conditions, 

combined the K value with the pathological and 

diagnostic analysis. 

II. WAVE DIAGNOSTIC PRINCIPLES BASED ON BLOOD 

FLOW 

A. The Formation of Arterial Pulse Wave 

The driving force of the blood circulatory system is the 

heart of the ejection, which the ventricle play a major role, 

it is usually called the cardiac cycle, in fact, refers to the 

movement cycle of the ventricle. Arterial blood pressure 

is the driving force that promotes blood to flow; it must 

reach a certain height in order to ensure the blood supply 

for all over organ. The process formed the arterial pulse 

wave that the arterial pressure transmits from the aorta to 

the small blood vessels and capillaries, which changes 

periodically into the cardiac cycle [11]. 

Figure 1. Pulse waveform coefficient K. 

The typical pulse wave is shown in figure 1, it can be a 

good reflection of cardiovascular information system, if 

the body abnormal occurs (such as atherosclerosis, etc.), 

the arteries’ nature will change, so pulse waveform 

changes must also occur. 


doi:10.4304/jcp.8.6.1472-1479


B. Cardiovascular Function Parameters K Computing 

Based on Pulse Wave 

Needless to say, the characteristic information of pulse 

wave is closely related with the physiological factors. To 

study the relationship each other, many researchers get 

information from the time domain or frequency domain 

characteristics based on pulse wave in clinical trials or 

model. In the time domain, usually the pulse extracts 

some point with a clear physical meaning (such as the 

main wave peak, heavy pump wave height, etc.). The 

combination with the characteristic points and the 

corresponding physiological factors may get much 

clinical value. Some researchers have used simulation 

models to measure pulse wave different model 

parameters, to determine the person's physical condition 

according to different parameters. Facts have proved that 

this method is more effective, but the simulation models 

and the extracted characteristic parameters must be 

proper, can effectively distinguish the pathological state. 

In many studies, because the extracted parameters are 

too complicated to make the distinction between pulse 

waves, it often occurs the misjudging phenomenon. 

Therefore, the extraction of the pulse wave parameter is 

the critical research. Professor Luo Zhichang used the 

existing two-chamber model of elastic wave pulse to 

extract the characteristics of K (called form factor) which 

represents changes of the pulse wave’s area [11]. 

Through the model theoretical analysis, thousands of 

animal experiments and clinical testing with different 

age’s healthy people and patients with cardiovascular 

disease, confirmed that caused the pulse wave map 

features and the corresponding changes in the area by 

physiological and pathological cardiovascular changes, 

and then reflect on the changes in K value. Determine the 

body's physical condition with the K value, although it 

can not achieve accurate quantitative analysis, but a 

simple calculation, differentiation, and the advantages of 

high sensitivity, which is important in the clinical 

reference value, is an important physiological indicators 

of the cardiovascular clinical examination. 

The K value reflects the characteristic quantities which 

changes in the amount of area of the pulse wave [11], 

which is defined as the average of the relative position of 

the pulse wave, which is defined by type (1) and figure 1. 

Pm 

− Pd 

K = . (1) 

P − P 

where K is the form factor; P 

m 

is mean arterial pressure, 

P 

d 

is the diastolic blood pressure; P s 

is the systolic 

blood pressure. 

Thus, the form factor K value have nothing to do with 

the absolute value of systolic and diastolic blood pressure, 

it only depends on wave map area of the pulse wave, is a 

dimensionless parameter. Pulse waveform and area will 

have a great change in different physiological and 

pathological conditions, these changes can be expressed 

as K value. 

Because the pulse wave is difficult to accurately 

measure and solve, this paper propose a solution based on 

s 

d 

the averaging method that K value of the pulse wave can 

be computed, and then through the specific network 

simulation of the cerebral circulation, the results is 

coincided with clinical measurement. 

Ⅲ. CARDIOVASCULAR NETWORK HEMODYNAMIC 

ANALYSIS AND AVERAGING COMPUTATION 

According to the aforementioned study, in order to 

solve the pulse wave of blood circulation network 

diagram, first, analyze its network model [12-18]. In 

order to build blood circulation network's model, at first 

establishes the dynamic equation of one blood vessel 

branch. For simplicity, we make the following 

assumptions: Al. the blood is incompressible; A2.the 

temperatures in all branches are identical. Under 

assumptions Al and A2, one branch of the blood network 

is described with the following equations [12-18]: 

dQ 

j 

T 

j 

= −R 

j 

Q 

j 

Q 

dt 

TQ 

2 

= −Q 

R + H 

D 

j 

+ H 

j 

. (2) 

where Q 

j 

is flow through a branch j , R 

j 

are 

hemodynamic resistances, H 

j 

are pressure drops of the 

branches, Tj = ρl j 

/ S are inertia coefficients, j = 1, 

, 

n 

j 

and n is the number of network branches (excluding the 

generator branch). T = diag T } , R = col R } and 

{ j 

{ j 

2 

Q = diag{ 

Q Q } . (3) 

D 

Let nc 

denote the number of nodes. Then l = n − nc 

+ 1 

is the number of links (excluding the generator branch) 

and n − l is the number of tree branches. 

Like an electrical network, a fluid network must satisfy 

Kirchhoff's current law, i.e., the flow out of any node is 

equal to the flow into that node. Mathematically, 

Kirchhoff's current law for fluid flow networks can be 

expressed as: 

n 

∑ 

j= 

1 

E 

Qij 

E 

⎡Qin 

⎤ 

⎢ ⎥ = 0 

⎣ Q ⎦ 

Qin 

or 

Q + e 

j 

Qini 

Q 


j 

j 

= 0, 

i = 1, , n − l . (4) 

where n − l + 1 is the number of nodes (of which one is a 

“reference” node), Q is a vector of flows, 

E = [ e E ] Q 

, and E = E ] is a full rank matrix of 



Q 

[ 

Qij 

order ( n − l) 

× n where E = 1 if branch j is connected 

Qij 

to node i and the flow goes away from node i , 

E = −1 if it goes into node i , E = 0 if branch j is 

Qij 

not connected to node i ; e 


is an (n-l)×1 vector such 

that, if the generator is connected to node i and the flow 

goes away from node i then e = 1 , if the flow goes 


Qij 



into node i then e = −1 

, and e = 0 if the generator 


is not connected to node i . 

Similarly, the network satisfies Kirchhoff's voltage law, 

i.e., the sum of the pressure drops around any loop in the 

network must be equal to zero, or mathematically 

E H 

H = 0 or 

n 

∑ 

j = 1 

E 

Hij 

H 

j 


= 0, 

i = 1, , l, 

(5) 

where H 

j 

is the pressure drop of the branch j , H is a 

vector of pressure drops, E 

H 

= [ EHij 

] is an l × n mesh 

matrix, in which each mesh (loop) is formed by a link and 

a unique chain in the tree connecting the two nodes of the 

link. The elements of E Hij 

are defined as follows: 

E 

Hij 

= 1 if branch j is contained in mesh i and has the 

same direction, E 

Hij 

= −1 

if branch j is contained in 

mesh i and has the opposite direction, E 

Hij 

= 0 if branch 

j is not contained in mesh i . 

In order to establish a dynamic model of minimal order, 

one has to find independent variables as states of the 

system. We take the flows of link (co-tree) branches as 

state variables. If regards one time heartbeat as one 

period T , decomposes the blood pressure wave f (t) 

into each kind of simple harmonic wave combination, 

that is: 

n 

⎛ 2πk 

⎞ 

Qin( 

t) 

= Q0 

+ ⎜∑ak 

sin( t + φk 

) ⎟ 

⎝ k= 

1 T ⎠ 

(6) 

n 

= Q + a sin( kωt 

+ φ ) 

0 

∑ 

k= 

1 

k 

For convenience of analysis, we label the link branches 

(except the generator branch) from 1 to l. Define 

⎡Qc 

⎤ ⎡H 

c ⎤ 

Q = ⎢ ⎥ , H = ⎢ ⎥ (7) 

⎣Qa 

⎦ ⎣H 

a ⎦ 

so that Q c 

and H 

c 

vectors describe flow and pressure 

drop, respectively, in the links, excluding the generator 

branch, and Q and H vectors describe them in the tree 

branches. 

The matrices 

where [18-19] 

E 

a 

Qa 

a 

E 

H 

and EQ 

in can be split into blocks 

H 

[ E E ] 

E = (8) 


Hc 

Ha 

[ eQin 

EQc 

EQa] 

E = (9) 

= I , E 

Hc 

= I l × l 

, E 

( n−l 

) × ( n−l 

) 

k 

= − (10) 

T 

Ha 

E Qc 

Hence, the structure of the network can be expressed in 

the matrix form as 

⎡ 0 

E = ⎢ 

⎢⎣ 

e 


E 

I 

Qc 

− E 

I 

T 

Qc 

⎤ 

⎥ 

⎥⎦ 

(11) 

Furthermore, 

⎡T 

c 

T = ⎢ 

⎣0 

0 , [ ] T 

⎤ 

T T 

T 

⎥ R = R c 

Ra 

(12) 

a⎦ 

Fluid circulation through the network of network 

modeling, according to the aforementioned study, using 

the average method can solve the flow waveform, and 

then find its pulse wave flow waveform[15-20], that is: 

n 2 

⎛ a ⎞ 

k −1 

Q 

⎜ 

⎟ 

c 

( t) 

= Qc0 

− ∑ V U 

⎝ k= 

1 4 ⎠ 

(13) 

n 

⎛ 

⎞ 

+ Bc 

⎜∑ 

ak 

sin( kωt 

+ φk 

) ⎟ 

⎝ k= 

1 

⎠ 

where 

Q ( t) 

= ( −E 

a 

Qc 

⎛ 

+ Bc 

⎜ 

⎝ 

Q 

c0 

n 

∑ 

k= 

1 

− e 


⎛ 

Q + 

⎜ 

0) 

⎝ 

n 

∑ 

k= 

1 

⎞ 

ak 

sin( kωt 

+ φk 

) ⎟ 

⎠ 

T ( T) 

= T + E T E 

2 

a ⎞ 

k 

⎟E 

4 ⎠ 

Qc 

V 

−1 

U 

(14) 

T 

0 c Qc a Qc 

(15) 

2 

T 2 

{ B R } E col{ B R } 

U ( R, 

T, 

E) 

= col − 

(16) 

ci 

ci 

Qc 

ai 

ai 

T 

{ Q R } − E W 

V ( R, 

E, 

Q0) 

= diag 

c0i 

ci Qc 

(17) 

= E ( −E 

Q − e Q R (18) 

{ 

Qcij Qci c0 Qin 0) 

ci} n l l 

W 

i ( − ) × 

0 

( R, 

E, 

Q0 

and Q c 

) denotes l-dimensional solution of 

quadratic equation, that is: 

2 

T 

2 

Q R − E diag ( E Q + e Q ) R (19) 

i 

{ } 0 

c0 D c Qc 

Qci c0 

Qin 0 a 

= 

− 

such that V is nonsingular and − T 1 V is Hurwitz. Then 

for a given Q 

0 

> 0 , for sufficiently small a and 

sufficiently large ω the solutions of the system (1) ~ (6) 

4 

locally exponentially converge to a O ( 1 ω + a ) 

neighborhood. 

IV. PULSE WAVE K VALUE SIMULATION AND CLINICAL 

PATHOLOGICAL DIAGNOSIS 

A. Healthy Middle-aged Clinical Detection and Pulse 

Wave Simulation Analysis 

To observe the relationship between the clinical value 

of K changes and the major physiological factors (such as 

the hardening degree of the blood vessel wall, peripheral 

resistance, etc.). First we measured the pulse waveform to 

a thousand patients with different age groups, including 

healthy people and people with varying degrees of high 

blood pressure or vascular sclerosis. The instrument is 

used with cardiovascular blood flow parameters TP-CBS 

detector. After statistical analysis, the typical waveform 

and the corresponding coefficient K are shown in Figure 

2. 

After measurement and clinical trials, the results 

showed that: 

(1) Young and healthy people, pregnant women, 

athletes are low vascular resistance, arterial elasticity, the 

K value is about 0.33 (Figure 2 (a)); 

0 



(2) Healthy young people in the vascular resistance 

and arterial elastic are medium, the K value between 

about 0.34 to 0.39 (Figure 2 (b), (c), (d), (e)); 

(3) Middle aged and elderly people are higher vascular 

resistance, poor arterial elasticity, the K value is about 0.4 

or so (Figure 2 (f)); 

(4) Patients with severe hypertension and 

atherosclerosis are high vascular resistance, poor arterial 

elasticity, the K value is about 0.45 to 0.5 (Figure 2 (g), 

(h) ). 

Generally we measured radial artery pulse wave, 

because of its high flow, it is easy to measure, but 

considering that the circulatory system is large and 

complex, its model is difficult to solve, because the 

arterial pulse wave is constant in the transmission cycle, 

Therefore, we use the above method to solve cerebral 

circulation network. 

Cerebral circulation refers to the movement of blood 

through the network of blood vessels supplying the brain. 

The arteries deliver oxygenated blood, glucose and other 

nutrients to the brain and the veins carry deoxygenated 

blood back to the heart, removing carbon dioxide, lactic 

acid, and other metabolic products. Since the brain is very 

vulnerable to compromises in its blood supply, the 

cerebral circulatory system has many safeguards. Failure 

of these safeguards results in cerebrovascular accidents, 

commonly known as strokes. The amount of blood that 

the cerebral circulation carries is known as cerebral blood 

flow. 

Cerebral arteries describe three main pairs of arteries 

and their branches, which irrigate the cerebrum of the 

brain. The three main arteries consist of the: Anterior 

cerebral artery (ACA), Middle cerebral artery (MCA), 

Posterior cerebral artery (PCA). Both the ACA and MCA 

originate from the cerebral portion of internal carotid 

artery, while PCA branches from the intersection of the 

posterior communicating artery and the anterior portion 

of the basilar artery. The three pairs of arteries are linked 

via the anterior communicating artery and the posterior 

communicating arteries. All three arteries send out 

arteries that perforate brain in the medial central portions 

prior to branching and bifurcating further. Anatomy of 

the cerebral circulation is shown in figure 4, the cerebral 

circulation equivalent plane structure (18 branches) is 

shown in figure 5. 

Figure 2. Pulse waves and K of people in different ages and healthy 

conditions. 

Thus, increased with age or the development of 

hypertension, atherosclerosis, vascular resistance, pulse 

wave waveform develops bread-type waveform by the 

steep progressive, the waveform coefficient K increases 

correspondingly (in general changes between 0.35 ~ 0.5). 

It is shown in figure 3, maps of K values in the different 

age groups 

Figure 4. Anatomy of the cerebral circulation. 

Figure 3. Maps of K values in the different age groups 



Loop 7: H 

7 

− H9 

− H10 

+ H11 

= 0 , 

Loop 8: H 

8 

− H10 

+ H11 

− H12 

− H13 

+ H14 

− H15 

= 0 . 

We knew l , d 

1 

, ρ of the cerebral circulation network 

from paper [1], it is shown in table I. 

TABLE I. 

THE ARTERIAL GEOMETRY PARAMETERS OF THE CIRCLE OF WILLIS 

artery number length(cm) diameter(cm) 

internal carotid a. 7,1 25 0.4 

basilar a. 9 3 0.4 

Posterior communicating 11,15 2 0.12 

a. 

posterior cerebral a.Ⅰ 10,8 2 0.3 

anterior cerebral a.Ⅰ 12,14 2 0.25 

anterior communicating a. 13 0.5 0.15 

middle cerebral a. 5,2 7 0.35 

posterior cerebral a.Ⅱ 6,16 7 0.3 

Figure 5. The network equivalent plane diagram of cerebral circulation 

(16 branches). 

The network of the cerebral circulation has 16 

branches, 8 nodes and 1 generator branch. Choose 

branches 9 to 16 and generator as the tree of the network. 

The node equations can be expressed as: 

Node 1: Q in 

− Q1 − Q7 

− Q9 

= 0 ; 

Node 2: Q 

8 

+ Q10 

− Q9 

= 0 ; 

Node 3: Q 

6 

− Q10 

− Q11 

= 0 ; 

Node 4: Q 

5 

− Q7 

+ Q11 

+ Q12 

= 0 ; 

Node 5: Q 

4 

− Q12 

+ Q13 

= 0 ; 

Node 6: Q 

3 

− Q13 

− Q14 

= 0 ; 

Node 7: Q 

2 

+ Q14 

+ Q15 

− Q1 

= 0 ; 

Node 8: Q 

16 

− Q8 

− Q15 

= 0 ; 

After transformation: 

Q in 

= Q1 + Q7 

+ Q9 


= Q1 + Q7 

+ Q8 

+ Q10 


= Q1 + Q6 

+ Q7 

+ Q8 

− Q11 


= Q1 + Q5 

+ Q6 

+ Q8 

+ Q12 


= Q1 + Q4 

+ Q5 

+ Q6 

+ Q8 

+ Q13 


= Q1 + Q3 

+ Q4 

+ Q5 

+ Q6 

+ Q8 

− Q14 


= Q2 + Q3 

+ Q4 

+ Q5 

+ Q6 

+ Q8 

+ Q15 


= Q2 + Q3 

+ Q4 

+ Q5 

+ Q6 

+ Q16 

The loop equations can be expressed as: 

Loop 1: H 

1 

− H 

9 

− H10 

− H11 

+ H12 

− H13 

− H14 

= 0 ; 

Loop 2: H 

2 

− H15 

− H16 

= 0 ; 

Loop 3: H 

3 

+ H14 

− H15 

− H16 

= 0 ; 

Loop 4: H 

4 

− H13 

+ H14 

− H15 

− H16 

= 0 , 

Loop 5: H 

5 

− H12 

− H13 

+ H14 

− H15 

− H16 

= 0 , 

Loop 6: H + H − H − H + H − H − H 0 , 

6 11 12 13 14 15 16 

= 

anterior cerebral a.Ⅱ 4,3 5 0.25 

ρl 

1.63l 

We can obtain T from T = and R from R = . 

4 

S 

D 

We may obtain Q c0 equation set from type (19), this 

equation only has numerical solution, but does not have 

the exact solution, uses the genetic algorithm to get the 

iterative solution. We can get H from Q , H is equal to 

P . 

First, we solve the cerebral circulation blood flow Q 

with the normal person, and we can get H from (2), that 

is P in (1), its computing simulation result is shown in 

figure 6. 

` 



It is shown in figure 6, the normal cerebral circulation 

network 10 times harmonic waveform are basically the 

same with healthy middle-aged in figure 2 and figure 3 , 

the K value is 0.356 by calculating, and K is clinically 

consistent with 0.34 ~ 0.39. 

B. Cerebral Infarction Clinical Detection and Pulse 

Wave Pathological Analysis 

Cerebral infarction causes brain tissue partial arterial 

blood flows poorly or completely stop due to insufficient 

blood supply, and blood viscosity is an important factor 

in causing vascular resistance, and its dynamic changes 

are related with the cerebral lesions closely. From paper 

[11], in order to clarify the correlation between the 

waveform characteristic K value and the blood viscosity, 

in clinical test, the observed 100 cerebral infarction 

patients with CT or NMR diagnosis (mean age 54 years, 

male 63 cases, females 37 cases) are varying degrees of 

hyperviscosity and microcirculation. Before and after 

treatment, use blood flow parameters TP.CBS 

nondestructive detector to detect the patient's pulse wave 

pressure and K-value. At the same time, use LS30 to test 

blood viscosity, and compared with the K value, the 

results is shown in Table II. 

TABLE II. 

CLINICAL EXAMINING RESULTS 

Parameter 

Before treatment After treatment 

K 0.55±0.12 0.31±0.1 

Blood viscosity 6.27±1.9 3.6±1.2 

Setting the terminal resistance value of R 2 that is 3 

times higher than normal to simulate the side of the 

middle cerebral artery area infarction lesions, choose to 

simulate the case of compensatory cerebral calculation, 

select the compensatory situation in which the normal 

circle of Willis before and after the traffic artery open. 

Taking the terminal resistance value of R 2 which is 3 

times higher than normal to simulate the side of the 

middle cerebral artery area infarction lesions, choose the 

compensatory situation to simulate cerebral calculation, 

which the traffic arteries of the circle of Willis are open. 

Taking the diameter of the anterior communicating artery 

to calculate parameters, D13=0.2cm, the diameter of the 

posterior communicating artery D 11 =D 15 =0.15cm, R 13 , 

R 11 , R 15 are 590, 6439 and 6439 dyn·s/cm, T 13 =119.4908, 

we can get Ten harmonics from (13) and (14), The circle 

of Willis pulse wave with the cerebral infarction is shown 

in figure 7. 

Figure 6. The circle of Willis pulse wave with the normal human. 



Figure 7. The circle of Willis pulse wave with the cerebral infarction. 

We can see the pulse wave of the cerebral infarction 

from the simulation figure 6, the K value is 0.495, and is 

close to the clinical test of cerebral infarction in Table II, 

K = 0.55 ± 0.12, from the changing trend of the K 

value, this result matches with the actual clinical 

detection basically. 

V. CONCLUSION 

In summary, the pulse waveforms extracted the K 

value by averaging computation and the wave area, 

although it does not fully reflect subtle changes in the 

pulse curve that contains all the local physiological and 

pathological significance, but it represents some 

important physiological parameters in the human blood 

circulatory system, such as peripheral vascular resistance, 

blood viscosity and so on. Considering the characteristic 

information to reduce only one characteristic quantity K, 

it is easy to remember, a clear physiological significance, 

and changes very regular, can be easily accepted by 

clinicians, so it can be used as important cardiovascular 

physiological parameters of the clinical examination. 

In the averaging computing pulse wave process, the 

network only needs to know the relevant basic 

physiological parameters of blood vessel branch, and 

calculating the pulse wave and the K value is more high 

precision than pulse wave detector. The stability testing 

results do not affect with the emotional fluctuates in the 

waveform, the different K values corresponds to different 

pathological conditions, so that it can provide an nondestructive 

testing mathematical calculation and analysis 

methods for the clinical parameters of blood circulation. 


This work is supported by NSF 60970105; education 

department S&T plan J08LJ70 and NSF of Shandong 

Province ZR2010FL015 and ZR2010FL021; MOHURD 

and Shandong Development science and technology 

project 2010-K9-26 and 2011YK05. 

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Shandong Institute of Business and 

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Jinxue Sui, associate professor, he 

received the M.S. degree in the control 

theory and control engineering from 

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in 2005 and the Ph.D.~degree in the 

navigation, guidance and control from 

Naval Aeronautical Engineering 

University, Yantai, China in 2009. 

Currently, he is a instructor with 

Shandong Institute of Business and 

Technology, China. His research interests are intelligent sensor, 

fluid network control and biological control now. 



Multi-Step Prediction Algorithm of Traffic Flow 

Chaotic Time Series based on Volterra Neural 

Network 

Lisheng Yin 


E-mail: yls20000@163.com 

Yigang He, Xueping Dong, Zhaoquan Lu 


E-mail: hyghnu@yahoo.com.cn, hfdxp@126.com, luzhquan@126.com 

Abstract—The accurate traffic flow time series prediction is 

the prerequisite for achieving traffic flow inducible system. 

Aiming at the issue about multi-step prediction traffic flow 

chaotic time series, the traffic flow Volterra Neural Network 

(VNN) rapid learning algorithm is proposed. Combing with 

the chaos theory and the Volterra functional analysis, 

method of the truncation order and the truncation items is 

given and the VNN model of traffic flow time series is built. 

Then the mechanism of the chaotic learning algorithm is 

described, and the adaptive learning algorithm of VNN for 

traffic flow time series is designed. Last, a multi-step 

prediction of traffic flow chaotic time series is researched by 

traffic flow VNN network model, Volterra prediction filter 

and the BP neural network based on chaotic algorithm. The 

simulations show that the VNNTF network model predictive 

performance is better than the Volterra prediction filter and 

the BP neural network by the simulation results and rootmean-square 

value. 

Index Terms—Chaos Theory, Phase Space Reconstruction, 

Time Series Prediction, VNN Neural Networks, Algorithm 


The Volterra series is a model for non-linear behavior 

similar to the Taylor series. It differs from the Taylor 

series in its ability to capture 'memory' effects. It has the 

advantages of high precision and clear physical meaning, 

has become one of the very effective non-parametric 

model of nonlinear system [1-4]. Traffic flow chaotic 

time series with the nonlinear behavior of the response 

and memory function, the Volterra series to become one 

of the primary means of traffic flow in nonlinear system 

identification [5-6]. Many scholars and technology 

developers have proposed a lot of Volterra identification 

algorithm, but the establishment of nonlinear systems on 

Volterra Series model is very difficult [7-9]. Volterra 

series has an obvious drawback is that if you want to 

achieve a satisfactory accuracy may require a 

considerable number of estimated parameters. The highlevel 

nuclear estimates are facing the greatest difficulties. 

Therefore, the Volterra functional model of the 

application is to be greatly restricted, and sometimes in 

order to avoid solving the higher-order kernel function 

and Volterra functional model artificially simplified, 

resulting in the modeling inaccuracy. 

With the rapid development of computer technology, 

the neural network is more deeply and widely used in 

nonlinear systems [11-13]. The neural network not only 

has the self-adaptive, parallelism and fault tolerance 

characteristics, but also has the ability to approximate any 

nonlinear function. Based on these advantages, the neural 

network model of the nonlinear system has a very wide 

range of applications [14-16]. Due to the consistency of 

the Volterra model and the three-layer ANN model, 

combined with the traffic flow chaotic time series chaotic 

characteristics, how to make use the Volterra accurate 

modeling of the advantages to overcome the 

shortcomings of Solutions of Higher Order kernel 

function; and how to use the advantages of ANN neural 

network model for learning and training network to 

overcome the blindness of the ANN neural network 

modeling is worth exploring. 

Based on the above considerations, the physical 

significance of the truncation order of the Volterra series 

model and the truncated number and the mathematical 

properties of the minimum embedding dimension and 

delay time in traffic flow chaotic time series 

reconstructed phase space, thus, traffic flow chaotic time 

series VNNTF network model and the corresponding 

algorithm has been established [17-20]. VNNIF neural 

network model to learn the advantages of the Volterra 

series to establish an accurate traffic prediction model 

and the ANN network training is easy to solve the 

Volterra model kernel function; thus, to overcome the 

difficulties on Volterra series model for solving the 

higher order kernel function and the blindness of the 

ANN network model, in the traffic flow chaotic time 

series prediction, obtained good results. 

II. TRAFFIC FLOW CHAOTIC TIME SERIES VOLTERRA 

MODEL 


doi:10.4304/jcp.8.6.1480-1487


For nonlinear systems, discretization of the Volterra 

model is as follows: 

Where, 

∞ 

∑∑ 

yn ( ) = h( l, , l) xn ( −l) xn ( −l) 

(1) 

nl , i 

i l1 

, , li 

= 0 

i 1 i 1 

i 

∈ R, yn ( ) is the output of the nonlinear 

system; x( n− l i 

) is the input of the nonlinear system and 

hi( l1, l2, , li) 

( i = 1, 2, , n ) is Volterra kernel function 

of order i . 

A. Model of Chaotic Time Series Prediction 

The chaotic time series prediction is based on the 

Takens' delay-coordinate phase reconstruct theory. If the 

time series of one of the variables is available, based on 

the fact that the interaction between the variables is such 

that every component contains information on the 

complex dynamics of the system, a smooth function can 

be found to model the portraits of time series. If the 

chaotic time series are{ x() 

t }, then the reconstruct state 

vector is x( t) = ( x( t), x( t+ τ ), , x( t+ ( m−1) τ )) , Where 

m ( m = 2,3, ) is called the embedding dimension 

( m = 2d 

+ 1, d is called the freedom of dynamics of the 

system), and τ is the delay time. The predictive 

reconstruct of chaotic series is a inverse problem to the 

dynamics of the system essentially. There exists a smooth 

m 

function defined on the reconstructed manifold in R to 

interpret the dynamics x( t+ T) = F( x( t)) 

, 

where T ( T > 0) 

is forward predictive step length, and 

F() 

⋅ is the reconstructed predictive model. 

B. The Determination of the Truncation Order on Traffic 

Flow Chaotic Time Series Volterra Model 

Assume that the measured traffic flow chaotic time 

series is { xt ()( t= 1,2,3, )}, the traffic flow chaotic time 

series phase space reconstruction based on Takens 

Theorem, you can get the input of the nonlinear system is 

xt ( ), xt ( + τ ), xt ( + 2 τ), , xt ( + ( m−1) τ) 

, where, m is the 

embedding dimension, namely the reconstruction of 

phase space dimension, τ is the delay time. Here, m 

corresponds to the number of finite order in the 

discretization of the Volterra model, and to predict the 

traffic flow is predicted on the basis of the m item, then 

the traffic flow chaotic time series phase space 

reconstruction model with m-order truncation Volterra 

series model can be characterized as follows: 

x( t′ + T) = F( X( t)) = h + h ( l ) x( t−lτ 

) 

∞ ∞ ∞ 

∑∑ 

∞ 

l1= 0l2= 0 lp 

= 0 

∞ 

∑∑ 

∞ 

∑ 

0 1 0 0 

l0 

= 0 

+ h ( l , l ) x( t−lτ) x( t− lτ) 

+ 

2 1 2 1 2 

l1= 0l2= 

0 

∑ 

+ h ( l, l, , l ) xt ( −lτ ) xt ( −lτ) xt ( −lτ) 

m 1 2 m 1 2 

m 

(2) 

where, hm( l1, l2, , lm) 

is the m order Volterra kernel 

function, t′ = t+ ( m− 1) τ , T ( T > 0 ) is the forward 

prediction step. This infinite series, theoretically, can be 

very accurately predicting traffic flow chaotic time series, 

but difficult to achieve in practical applications, it must 

be a finite order truncation and the finite sum in the form. 

Your goal is to simulate the usual appearance of papers 

in a Journal of the Academy Publisher. We are requesting 

that you follow these guidelines as closely as possible. 

For traffic flow chaotic time series prediction from 

equation (2), it is the m-order truncated infinite item 

summation form. For example, when m = 3, it is a finite 

sum of the third order intercept Volterra series model: 

N1 

−1 

∑ 


) 

N2−1N2−1 

∑∑ 

l1= 0 l2= 

0 

0 1 0 0 

l0 

= 0 

+ h ( l , l ) x( t−lτ 

) x( t−lτ 

) 

2 1 2 1 2 

N3−1N3−1N3−1 

∑∑∑ h2( l1, l2, l3) x( t l1τ ) x( t l2τ) x( t l3τ) 

(3) 

l1= 0 l2= 0 l3= 

0 

+ − − − 

so, actually want to calculate the total number of 

2 2 

coefficients is 1+ N1+ N2 + N3 

. Be seen with the 

increase of m in the Volterra series, the number of items 

of Volterra Series will power rapid increase; the 

corresponding required number of calculations also 

showed exponential growth, which makes the actual 

traffic flow chaotic time series predicted to achieve more 

and more difficult. The total number of items of Volterra 

series number decreases exponentially growth. In practice, 

the truncation order is generally the second-order 

truncation or third order intercept. 

C. The Determination of the Truncation Items on 

Traffic Flow Chaotic Time Series Volterra Model 

In the form of the flow chaotic time series Volterra 

series model is (2), assume that the truncated form of 

limited items are as follows: 

N1 

−1 

∑ 


) 

N2−1N2−1 

∑∑ 

l1= 0 l2= 

0 

Nm−1Nm−1 Nm−1 

∑∑ 

l1= 0 l2= 0 lp 

= 0 

0 1 0 0 

l0 

= 0 

+ h ( l , l ) x( t−lτ) x( t− lτ) 

+ 

∑ 

2 1 2 1 2 

+ h ( l , l , , l ) x( t−lτ ) x( t−lτ) x( t−l 

τ) 

m 1 2 m 1 2 

m 

For traffic flow chaotic time series, it is assumed that 

x() 

t and yt () are the input and output signals of the 

functional system f (, txt (′), t′ ≤ t) 

in the traffic flow, the 

input signal of the functional system in the traffic flow to 

meet: 

1 Traffic flow input signal is a causal relationship is 

met when t < 0 , then xt () = 0. 

2 Traffic flow functional system f (, txt (′), t′ ≤ t) 

is 

the limited memory, that is, for the t time in the system, 

(4) 



t 

0 

time very far from the t time, t 0 

→∞, x( t− t0 

) has 

no effect on yt (); means that the predicted value of yt () 

is irrelevant to x( t− t0 

). 

In the prediction of chaos traffic flow chaotic time 

series, t′ = t+ ( m− 1) τ , T ( T > 0 ) is forward prediction 

step, x( t′ + T) 

represents the output associated with the 

input signal x() 

t and the delay time τ , then 

N l −1 

1 

l1 l 

 

2 N li 0 ∑ 1 1 1 

l1 

= 0 

x( t′ + T) = f( x , x , x ) = h + h ( l ) x( t−lτ 

) 

Nl 

−1N 

1 

2 l − 

2 

∑∑ 

+ h ( l , l ) x( t−lτ 

) x( t−l 

τ ) 

l1= 0 l2= 

0 

2 1 2 1 2 

Nl −1N 3 l −1N 

1 

3 l − 

3 

∑∑∑ h3( l1, l2, l3) xt ( l1τ) xt ( l2τ) xt ( l3τ) 

(5) 

l1= 0 l2= 0 l3= 

0 

+ − − − + 

note 

Nmax = max( N , N , N , N ) , ( i = 1, 2, 3, ), 

when n≥ 

N 

li 

max 

l1 l2 l3 

l i 

, the same to meet the input traffic flow 

signal x = xt ( − lτ ) is irrelevant to yt () , then the 

formula (4) can be written as: 

i 

Nmax 

−1 

l1 l 

 

2 N li 0 ∑ 1 1 1 

l1 

= 0 


) 

Nmax 

−1Nmax 

−1 

∑ ∑ 

+ h ( l , l ) x( t−lτ 

) x( t−lτ 

) 

l1= 0 l2= 

0 

Nmax −1Nmax −1Nmax 

−1 

∑ ∑ ∑ 

l1= 0 l2= 0 l3= 

0 

2 1 2 1 2 

+ h ( l , l , l ) x( t−lτ) x( t−lτ) x( t− lτ) 

+ 

3 1 2 3 1 2 3 

Know from the above analysis of the traffic flow 

functional systems, the power series expansion item of 

prediction results are in fact only related to Know from 

the above analysis of the traffic flow functional systems, 

the power series expansion item of prediction results are 

in fact only related to summation form all the products of 

the Input signal and the first power delay time signal. 

This means that the value of 

Nmax = max( Nl , N , , ) 

1 l 

N 

2 l 

N 

3 l i 

, ( i = 1, 2, 3, ) is only 

related with the number of input signal and the delay time 

signal, which is the minimum embedding dimension m 

of phase space, so Nmax = max( Nl , N , , ) 

1 l 

N 

2 l 

N 

3 l i 

= m. 

Such traffic flow chaotic time series Volterra series 

model is finalized by the formula (5) as follows: 

m−1 

l1 l 

 

2 N li 0 ∑ 1 1 1 

l1 

= 0 


) 

m−1 m−1 m−1 

∑∑∑ 

m−1 m−1 

∑∑ 

+ h ( l , l ) x( t−lτ 

) x( t−lτ 

) 

2 1 2 1 2 

l1= 0l2= 

0 

+ h( l, l, l) xt ( −lτ) xt ( −lτ) xt ( − lτ) 

+ 

3 1 2 3 1 2 3 

l1= 0l2= 0l3= 

0 

m−1m−1m−1 m−1 

∑∑∑ ∑ 

+ h (, l l, l, , l xt−lτ)( xt−lτ)( xt−lτ) xt ( −lτ) 

(7) 

m 1 2 3 m 1 2 3 

m 

l1= 0l2= 0l3= 0 lm= 

0 

(6) 

III. TRAFFIC FLOW TIME SERIES VOLTERRA NEURAL 

NETWORK MODEL (VNNTF) 

A. Representation of Nonlinear Systems Using Artificial 

Neural Network 

Has proven that the BP neural network with one 

hidden layer can approximate any continuous bounded 

non-linear system, therefore, generally selected to contain 

a three-layer back propagation BP network with one 

hidden layer to approximate nonlinear systems. A single 

output three-layer back propagation neural network is 

shown in Figure 1. In the figure, the input vector 

T 

x = [ x , x , x ] at moment n can obtain by the 

k k,0 k,1 k, 

M 

delay of x( k ), where x 

, 

= xk ( − m) 

, the input of the l 

km 

hidden unit ( l = 1, 2, , L) is 

Z 

= S ( u ); ulk , 

= ∑ wlm , 

xkm 

, 

(8) 

lk , l lk , 

M 

m= 

0 

A single output three-layer back propagation neural 

network is shown in Figure 1. 

x k,0 

x km , 

x kM , 

w L , m 

w 1,0 

w 

,0 

w l 

L,0 

w 1,m 

w lm , 

w 1,M 

w lM , 

w L , M 

U 1,k 

U lk , 

U L , k 

S() 

⋅ 

S() 

⋅ 

S() 

⋅ 

Z 1,k 

Z lk , 

Z L , k 

input hidden layer output 

Figure 1. Three layer neural networks in response to M+1 input and 

single output system 

If the implicit function selected the sigmoid function, 

then 

1 

Sl( u 

, 

) = l k 

1 + exp[ − λ( u − θ )] 

(9) 

Where, θ 

l 

is the threshold of the unit n, If the output unit 

is linear summation unit, the output at moment n is 

y 

L 

r l 

lk , 

r 1 

r L 

k l l, 

k 

l = 1 

l 

Z 

= ∑ rZ 

(10) 

The output of each hidden unit to expand into a Taylor 

series at the threshold θ 

l 

: 

Z = ϕ ( u ) =∑ d ( θ ) u 

i 

(11) 

l, k l l, k i l l, 

k 

i= 

0 

where, d ( θ ) is the commencement of the coefficient, 

i 

l 

the value associated with 

M 

lk , lm , km , 

m= 

0 

∞ 

θ 

l 

y k 

, and because of 

u = ∑ w x , then the output of the neural network 

is 

L ∞ 

M M 

∑∑ ∑ ∑ 

y = r d ( θ ) ⋅ w w x x (12) 

k l i l l, m1 l, mi 

k, m1 

k, 

mi 

l= 1 i= 0 m1 

= 0 mi 

= 0 



B. Traffic Flow Volterra Neural Network Model 

Analysis and comparison of traffic flow Volterra series 

model in equation (6) and three-layer BP neural network 

in equation (12), if the input vector in equation (12) in 

VNNTF to take the traffic flow chaotic time series, then 

between them in the function, structure and method for 

solving are inherently close contact and similarity. 

1) From a functional point of view, the traffic flow 

chaotic time series, Volterra series model and ANN 

model can be measured traffic flow chaotic time series, to 

simulate and predict the traffic flow process. Traffic flow 

chaotic time series Volterra model can determine the 

model truncation order of the truncation by the 

characteristics analysis of the traffic flow time series. 

Then, it can use the system identification to strike a 

nuclear function of the Volterra series model, or proper 

orthogonal decomposition method, stepwise multiple 

regression method, iterative decline in the gradient 

method, Volterra filter and constraints orthogonal 

approximation method to solve the nuclear function or 

Volterra series, which reflect the chaotic nonlinear law of 

the traffic flow. 

2) From a structural point of view, the traffic flow 

chaotic time series Volterra model and ANN model is 

also isomorphic. Length of the storage memory of past 

traffic flow relative to chaotic time series in the traffic 

flow Volterra model, that is, the minimum embedding 

dimension in phase space reconstruction of is equivalent 

to the number of neurons of the ANN model input layer. 

3) From a method for solving point of view, Traffic 

flow chaotic time series Volterra model is based on 

orthogonal polynomials for the numerical approximation 

to find the approximate solution.the Meixner function 

systems and network weights have the same effect. 

x() 

t 

xt ( + τ ) 

xt ( + ( m−1) τ ) 

w N ,1 

w 1,m 

w 1,0 

w2,0 

wN ,0 

w 1,1 

w 2,1 

w 2,m 

w N , m 

V () t 1 

V () t yt 

g () 

2 2 

V () N 

t 

Input Hidden layer Output 

Figure 2. The chaotic time series Volterra neural network traffic flow 

model (VNNTF) 

Through consistency of traffic flow chaotic time series 

Volterra model and ANN model, in this paper, the traffic 

flow chaotic time series Volterra neural network model 

(VNNTF) has been proposed in Figure 2. In the figure, 

X() t = ( xt (), xt ( + τ ), , xt ( + ( m−1) τ ) T ( t = 1, 2, ) is the 

traffic flow chaotic time series reconstructed phase space 

vector; w 

i, 

j 

( i = 1, 2, ; j = 1, 2, ), r n 

is the traffic flow 

chaotic time series Volterra neural network weights 

parameters; g , ( s = 1, 2, , N ) is the activation function 

s 

and Vs 

( k ) is the traffic flow of the convolution of the 

input signal: 

g 1 

g N 

r 2 

r 1 

r N 

m 

V () t = w x( t+ ( i−1) τ ) 

N 

∑ Ni 

(13) 

i= 

0 

Thus, the traffic flow chaotic time series Volterra 

neural network expression is 

N 

 

 

y( t) = f( X( t)) = f( x( t)) =∑ rsgs( VN( t)) 

N 

m 

s s si 

s= 1 i= 

0 

s= 

1 

∑ ∑ (14) 

= rg ( w xt ( + ( i−1) τ )) 

IV. TRAFFIC FLOW VOLTERRA NEURAL NETWORK RAPID 

LEARNING ALGORITHM 

A. Activation Function Analysis of Traffic Tlow Volterra 

Neural Network 

Activation function of hidden layer to the VNNTF 

model designed for the following polynomial function: 

g = a + a x+ a x + + a x + (15) 

2 

i 

s 0, s 1, s 2, s i, 

s 

where ais 

, 

∈ R is the polynomial coefficients, and then 

So, to get: 

N 

N +∞ 

 

i 

y( t) = r g ( V ( t)) = ra ( V ( t)) 

∑ 

∑∑ 

s s N s i, 

s N 

s= 1 s= 1 i= 

1 

N 

+∞ 

m 

∑∑ ∑ 

i 

= ra ( w xt ( + ( i−1) τ )) 

s i, 

s si 

s= 1 i= 1 i= 

0 

N 

h ( l , l , l ) = ∑ ra w w w 

j 1 2 j s js , sl , 1 sl , 2 sl , j 

s= 

1 

( j = 1, 2, , m) (16) 

In the VNNTF model, the sigmoid function or other 

functions as the activation function gs( Vs( t )) training 

VNNTF network, the weights and thresholds are obtained, 

the activation function gs( Vs( t )) is expanded into a 

Taylor series, you can obtain the polynomial coefficients: 

a 

js . 

( j) 

gs 

( θs 

) 

= (17) 

j! 

Among them, ( j 

g ) ( θ ) is the j -order derivative of 

s 

s 

function gs( Vs( t ) in θ s 

; that is a different activation 

function, you can get a 

js . 

. VNNTF network learning and 

training, according to the connection weights of the 

network of neurons and the coefficients of a 

js . 

, you can 

solve any order kernel function, which would address the 

difficulties of solving high-level nuclear function in the 

Volterra model. In general, if directly using the 

polynomial function for the activation function, the 

polynomial order is taken as m , the same Taylor 

expansion of the Taylor series, the order is taken to the 

m , so VNNTF model by setting different order of the 

activation functions to reflect the effect equivalent to the 

Volterra model higher order kernel function. 



B. Traffic Flow Volterra Neural Network Rapid Learning 

Algorithm 

On the establishment of traffic flow chaotic time series 

WNN, Network input the number of neurons, hidden 

layers and the number of neurons in the hidden layer are 

to be considered. The following traffic flow data used are 

from "Chongqing Road Traffic Management Data Sheet 

I" and "Chongqing Road Traffic Management Data Sheet 

II" in 2006. There is the study of traffic volume time 

series of two-lane road 28 hours and 5 minutes every 5 

minutes, including mini-vehicles, passenger cars, light 

trucks, midsize, large cars, trailer, micro van, not 

stereotypes, such as vehicles, and its sequence length 

n = 337 .First, Pretreatment of the traffic flow time series, 

the minimum embedding dimension m = 4 and delay 

time τ = 3 are obtained by calculation. Then, the traffic 

flow Volterra neural network can be constructed: traffic 

flow Volterra neural network is designed to be three 

layers: input layer, single hidden layer and output layer; 

the number of hidden layer wavelet neural taken as 9 by 

Kolmogorov Theorem, the number of input layer neurons 

equal to the minimum embedding dimension ( m = 4 ), 

the number of output layer is 1, so that the 4-9-1 structure 

of traffic flow Volterra neural network was obtained, 

specifically shown in Figure 2. The hidden layer 

activation function can be used sigmoid function or other 

commonly used functions, and here it be used with 

polynomial activation functions 

2 

i 

gs = a0, s 

+ a1, sx+ a2, sx + + ai, 

sx 

+ , ais 

, 

∈ R is 

polynomial coefficients. Optimal network parameter w 

s, 

j 

and r 

s 

( s = 1, 2, N , j = 1, 2, m ) can be obtained by 

learning and training the network for reducing the 

error E , and further hj( l1, l2, lj) 

( j = 1, 2, m) can be 

calculated by combining the polynomial coefficients. 

The steps of traffic flow chaotic time series Volterra 

Neural Network fast learning algorithm is showed and the 

specific steps are as follows: 

Algorithm VNNTF model fast learning algorithm 

Step1) The hidden neurons number is 9 by 

Kolmogorov Theorem, so that the 4-9-1 structure of 

traffic flow VNNTF neural networks was obtained. The 

traffic flow time series input signal is 

( xt ( ), xt ( + τ ), , xt ( + ( m−1) τ ) T , ( t = 1, 2, ) ; the 

 

output signal is yt (); the weight coefficient matrix of the 

hidden layer is w = ( ws, l 

) 

N× m 

= ( ws, 

i) 

N× 

m 

, ( s = 1, 2, 9 , 

j 

i , j = 1, 2, , 4 ) and the parameter is r s 

( s = 1, 2, 9 ). 

Step2) The traffic flow chaotic time series Volterra 

Neural Network parameters w = ( w 

s, 

i) 

N× 

m 

and r 

s 

( s = 1, 2, 9 , i = 1, 2, 4 ) are initialized, where the 

parameters w = ( w 

s, 

i) 

N× 

min each component take random 

function between 0 and 1; and r s 

are initialized to take 9 

number between 0 and 1 by the random function. 

Step3) Using phase space reconstruction theory to 

preprocess the traffic flow chaotic time series, and 

perform normalization for the reconstructed network 

input signal. Based on Takens theorem, the minimum 

embedding dimension m = 4 , and the delay time τ = 3 . 

The reconstruction phase space vector number is 

N −1 −( m− 1) τ = 327, which the top 250 vector are used 

as network input signals. the form is 

( xt ( ), xt ( + τ ), , xx ( + ( m−1) τ )) T , where t = 1, 2, 250 , 

m = 4 and τ = 3. 

Then, the 250 phase space vectors to make a simple 

normalized, the normalized as 

[ x() t − mean( x())]/[max( t x()) t − min( x())] 

t 

, 

t = 1, 2, 250 and, making the value is owned by a range 

of -1 / 2 to 1/2. 

Step4) Using the initialized network and the 

preprocessed traffic flow time series, the first VNNTF 

neural network training begin with the function 

N +∞ m 

 

i 

yt () = ra ( wxt ( + ( i−1) τ )) , 

∑∑ 

∑ 

s i, 

s si 

s= 1 i= 1 i= 

0 

and the assumed activation function is a polynomial 

activation function g s 

, here a is , 

∈ R are polynomial 

coefficients. 

Step5) Calculate error function, the function formula: 

250 

1 2 

E( θ ) = ( y( t) − y( t)) 

∑ 

2 t = 1 

Set the maximum error is E max 

= 0.035 , if E < Emax 

, 

the storage VNNTF neural network parameter use 

w = ( w 

s, 

i) 

N× 

m 

and r 

s 

( s = 1, 2, 9 , i = 1, 2, 4 ) ; and 

further hj 

( l1, l2, lj 

) ( j = 1, 2, m) can be calculated by 

combining the polynomial coefficients, otherwise, 

transferred to step6). 

Step6) Calculate local gradient of the traffic flow 

chaotic time series Volterra neural network. Specifically, 

according to the formula δ ( t) = ( y( t) − y ( t)) g ′( V ( t)) 

( j is the output layer) and the formula 

j j s j 

∂Et 

() 

δ 

j() t =− g ′ 

s 

( Vj()) 

t 

(18) 

∂ y () t 

j 

where, the local gradients are calculated in the hidden 

layer. 

Step7) By introducing the momentum term, to adjust 

the learning weights of the traffic flow chaotic time series 

Volterra neural network. Introduce nonlinear feedback 

into the weighting formal to adopt Chaos Mechanisms, 

due to the nonlinear feedback is vector form of weighting 

variables. In order to facilitate understanding, 

respectively, gives the vector w and its weighting formal, 

as follows. Note Δ w l ( t+ 1) = w l ( t+ 1) −w l ( t) 

, which 

ji ji ji 

represents the current value of weighting variables, then 

1 

Δ w l ( t+ 1) = w l ( t+ 1) − w l () t = −ηδ l+ 

() t x l () t . 

ji ji ji j i 

In order to speed up the learning process, in the right to 

l 

join a momentum term αΔw () t , then 

Δ w + = − x + Δw 

ji 

l 1 

( 1) l + 

( ) l ( ) l 

ji 

t ηδ 

j 

t 

i 

t α 

ji 

( t) 



where α is inertia factor; η is learning step; 

αΔ wji 

, 

( t+ 1) is the introduction of the momentum and 

δ () t is calculated with the formula (9). 

j 

Expand this equation into scalar form as follow: 

l l+ 

1 l l 

⎧Δ wji( t+ 1) =− ηδ 

j 

() t xi () t + g( Δwji()) 

t 

⎪ 

l l+ 

1 l l 

⎪Δ wji( t+ 1 + τ) =− ηδj ( t+ τ) xi ( t+ τ) + g( Δ wji( t+ 

τ)) 

⎪ 

l l+ 

1 l l 

⎨Δ wji( t+ 1+ 2) τ =− ηδj ( t+ 2) xi ( t+ 2) τ + g( Δ wji 

( t+ 

2)) τ 

⎪ 

⎪ 

 

⎪ l l+ 

1 

l l 

Δ wji( t+ 1 + ( m− 1) τ) =− ηδj ( t+ ( m− 1) τ) xi ( t+ ( m− 1) τ) + g( 

Δwji( t+ ( m−1) τ)) 

⎩ 

(19) 

where, feedback can take a variety of vector functions, 

for example: 

2 

g( x) = tanh( px) exp( − qx ) or 

g( x) = pxexp( − q x) 

, 

in the study, p = 0.7 , q = 0.1. 

Step8) Calculating the modified weights in the traffic 

flow chaotic time series Volterra neural network in Step8) 

and transferred to step4), and train network again, then 

 

calculate the network output yt () and the error E , 

repeated training until the relative error in traffic meet 

E < E max 

= 0.035 . 

Step9) Output of every training storage of network 

parameters w = ( w 

s, 

i) 

N× 

m 

and r 

s 

( s = 1,2, 9 , 

i = 1, 2, 4 ) in the traffic flow chaotic time series 

Volterra neural network. The activation function 

g ( V ( t )) is expanded into a Taylor series at the 

s 

s 

threshold θ 

s 

and the expansion coefficient di( θ 

s) 

is 

obtained. If the activation function is a polynomial, then 

d ( θ ) = a ( s = 1, 2, 9 , i = 1, 2, 4 ). 

i s i, 

s 

Step10) According to the formula 

N 

h ( l , l , l ) = ∑ rd ( θ ) w w w (20) 

j 1 2 j s i s sl , 1 sl , 2 sl , j 

s= 

1 

the kernel function ( s = 1, 2, 9 , i = 1, 2, 4 ) of the 

output system is calculated. 

N + 3 values... N + T values ( T > 0 ). That is, for the 

known sample set can be extrapolated to predict T step. 

The following multi-step prediction of the traffic flow 

VNNTF network, and the results compare with the multistep 

prediction of the BP neural network and filter 

Voltrra, further, analyzing the causes of the different 

predictions. In fact, the multi-step prediction results can 

also be compared with the prediction results of wavelet 

neural network Algorithm and Wavelet Neural Network 

Based on Chaotic Algorithm. Can also be an attempt of 

the analysis for the prediction of the different results. 

Where, the minimum embedding dimension in phase 

space is m = 4 , the delay time is τ = 3 , and the vector 

number of phase space reconstruction which can be used 

to train and predict is N − ( m− 1) τ = 327. 

Figure 4. The 2-step forecast result and real result 

Figure 5. The 2-step forecast error curve 

V. EXPERIMENTAL RESULTS AND ANALYSIS 

Experimental objective is study how much extent does 

the prediction performance in VNNTF neural network 

improve from the aspects of model construction and 

algorithm application. 

In order to study the prediction performance of traffic 

flow time series in traffic flow VNNTF network, 

respectively the VNNTF network model, Volterra 

prediction filter and ANN to predict the network traffic 

flow chaotic time series, and analyze and compare their 

predictions. 

Multi-step prediction is a major aspect to reflect the 

performance of predictive model. Traffic flow time series 

Multi-step prediction is as follows: If the sample size is 

N , in the new data point cannot be used or only the 

sample points N , It can be predicted beyond N + 1 

values, can also predict the N + 2 values, 


In the network training of the multi-step prediction, 

such as Step 2 to Step 4, the training objectives of the 250 

reconstructed vector among the 327 reconstructed phase 

space vector are the traffic flow signals from t′ to 

t′ + 249 ( t′ = 12,13,14 ).Network training, in order to 

compare with the measured traffic flow signal, the 

TT= ( 2,3,4) step forecast traffic flow signal 



corresponding 260 + T ( T = 2,3, 4 ) to 337 traffic flow 

signal, that is, if the forecast number of steps each one 

more, then its projection is reduced by one. If not to make 

a prediction comparison with the measured signal, it does 

not have this restriction. 


which corresponds to 2-step, 3-step and 4-step absolute 

error curve. Figure 4 to Figure 9 shows the effect of 3- 

step prediction results is worse than the 2-step prediction, 

the effect of 4-step prediction results is worse than the 3- 

step prediction; and the general trend is to predict the 

longer the step, the prediction performance has become 

getting worse. 

Analysis of multi-step prediction results to VNNTF 

network, the 2-step, 3-step and 4-step predictable 

performance overall is better than the BP neural network 

prediction and the Volterra filter prediction; this is 

because the network VNNTF combines the Volterra 

series and ANN network advantages, to overcome the 

difficulties of solving the Volterra kernel function and the 

blindness of ANN network modeling. In fact, the 

prediction results to VNNTF network is better than the 

wavelet neural network prediction based on chaotic 

algorithm, and this may be the establishment of a good 

traffic flow time series prediction model is relatively 

more important than to choose a good algorithm, from 

this sense, the establishment of traffic flow prediction 

model is the most critical. 

TABLE I. 

NORMALIZATION OF RMSE COMPARISON 


prediction 

step 

BP 

network 

Volterra 

filter 

VNNTF 

network 

1 step 0.7014 0.3567 0.1368 

2 step 0.8074 0.3941 0.1507 

3 step 0.8653 0.4225 0.2322 

4 step 0.9799 0.4782 0.2417 

VI. CONCLUSIONS 

In the paper traffic flow chaotic time series VNNTF 

model was designed. A traffic flow VNNTF fast learning 

algorithm based on chaos theory was proposed. The 

method of model selection and algorithm design, are 

considered the chaotic characteristics of traffic flow time 

series, which is a theoretical value. Simulation results 

show that the method can reduce network training time 

and improve the forecast accuracy, and show better 

predictive effectiveness and reliability. 


Were calculated the error root mean square in Figure 5, 

7 and 9, and these results are compared with the error 

root mean square of the BP network and the wavelet 

neural network based on the non-chaotic algorithm, and 

the compare results are shown in Table 1. From Table 1, 

with the increasing number of prediction steps, in which 

the same prediction step, the root mean square of the 

wavelet neural network based on chaotic algorithm is 

significantly less than the root mean square of BP neural 

network and the wavelet neural network based on nonchaotic 

algorithm. 

Figure 4, 6 and 8, respectively, which corresponds to 

2-step, 3-step and 4-step predicted and actual comparison 

curves of VNNTF network based VNNTF network rapid 

learning algorithm; and “+” shows the true value, “o” 

shows the forecasted value Figure 3, 7, and 9 respectively, 


This research is financially supported by the National 

Natural Science Funds of China for Distinguished Young 

Scholar under Grant (50925727), and the Fundamental 

Research Funds for the Central Universities, Hefei 

University of Technology for Professor He Yigang, the 

National Natural Science Foundation of China (NSFC) 

for Professor Xue-ping Dong (No. 60974022) and the 

Universities Natural Science Foundation of Anhui 

Province (No.KJ2012A219) for Professor Yin Lisheng. 

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convolution type”, Differential Equations, 45, no. 9, pp. 

1326-1336, 2009. 

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model of Volterra neural network and its application”, 

Journal of Hydroelectric Engineering.25, no. 5, pp. 22-26, 

2006. 

[12] Haiying Yuan, Guangju Chen, “Fault Diagnosis in 

Nonlinear Circuit Based on Volterra Series and Recurrent 

Neural Network”, Lecture Notes in Computer Science, 

vol.4234, pp.518-525, 2006. 

[13] Wei Si, Zhe-Min Duan, Hai-Tao Wang, “Novel Method 

Based on Projection of Vectors in Linear Space to Identify 

Volterra Kernels of Arbitrary Orders”, Application 

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Systems with Applications, vol. 36: pp.6244-6255.2009. 

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Systems with Applications, vol. 36: pp. 6244-6255, 2009. 

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convolution type”, Differential Equations, 2009, 45, no. 9), 

pp.1326-1336. 

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robust stability of positive linear Volterra equations in 

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3972, pp. 759-764, 2006. 

Lisheng Yin (yls20000@163.com) received his doctor’s degree 


Automation, Chongqing University, Chongqing China. He is an 

associate professor in the School of Electrical and Automation 

Engineering, Hefei University of Technology.He conducts 

research in Modern intelligent algorithm, Chaos Theory, Neural 

network theory and Fuzzy Theory. 

Yigang He (hyghnu@yahoo.com.cn) received his doctor’s 

degree in Electrical Engineering from Electrical Engineering, 

Xi'an Jiaotong University, Xian China. He is a professor in the 

School of Electrical and Automation Engineering, Hefei 

University of Technology. He conducts research in Electrical 

science and engineering, automatic test and diagnostic 

equipment, High-speed low-voltage low-power integrated 

circuits, systems, intelligent and real-time information 

processing, Smart grid, electrical measurement techniques and 

Circuit theory of massive proportions and Mixed-signal system 

testing and diagnosis 

Xueping Dong (hfdxp@126.com) received his doctor’s degree 


Automation, Nanjing University Of Science and Technology, 

Nangjing China. He is an associate professor in the School of 

Electrical and Automation Engineering, Hefei University of 

Technology.He conducts research in Modeling and control of 

complex systems, Modern control theory and its application. 

Zhaoquan Lu (luzhquan@126.com) received his doctor’s 

degree from University of Science and Technology of China, 

Hefei China. He is a professor in the School of Electrical and 

Automation Engineering, Hefei University of Technology. He 

conducts research in Large time delay uncertain process and 

control, complex systems and controls, intelligent control, 

wireless communication network and automation systems, 

automotive electronics technology research and development, 

energy-saving control system research and development. 



Adaptive Tracking Control for Nonaffine 

Nonlinear Systems with Zero Dynamics 

Hui Hu 

Dept of Electrical and Information Engineering, Hunan Institute of Engineering, Hunan Xiangtan, China 

Email: onlymyhui@126.com 

Peng Guo 

Dept of Computer Science, Hunan Institute of Engineering, Hunan Xiangtan, China 

Email: da_peng219@126.com 

Abstract—A direct adaptive neural network tracking 

control scheme is presented for a class of nonaffine 

nonlinear systems with zero dynamics. The method does not 

assume boundedness on the time derivative of a control 

effectiveness term. Parameters in neural networks are 

updated using a gradient descent method which designed in 

order to minimize a quadratic cost function of the error 

between the unknown ideal implicit controller and the used 

neural networks controller. The final updated law is a 

nonlinear function of output error. No robust control term 

is used in controller. The convergence of parameters and the 

uniformly ultimately bounded of tracking error and all 

states of the corresponding closed-loop system are 

demonstrated by Lyapunov stability theorem.Simulation 

results illustrate the availability of this method. 

Index Terms—nonaffine nonlinear, neural network, 

tracking control, gradient descent method, zero dynamic 


Modern mechanical or electrical systems that are to be 

controlled become more and more complicated and, thus, 

their mathematical models are often hard to be 

established. In recent years, adaptive neural network [1, 2, 

3, 4, 7, 8, 9, 10, 12, 15] that model the functional 

mechanism of the human brain and fuzzy logic control [5, 

6, 11, 13, 14, 16, 17, 18] that can cooperate with human 

expert knowledge have been successfully applied to many 

control problems because they need no accurate 

mathematical models of the system under control. These 

methodologies become especially more helpful if control 

of highly uncertain, nonlinear and complex systems is the 

design issue. The main philosophy that is exploited 

heavily in system theory applications is the universal 

function approximation property of neural networks or 

fuzzy logic. Benefits of using neural networks or fuzzy 

logic for control applications include its ability to 

effectively control nonlinear plants while adapting to 

unmodeled dynamics. 

In fact, most of the works [1-4, 6, 9, 11, 12, 13, 15-18, 

22-25]are devoted to the control problem of the affine-incontrol 

nonlinear systems, i.e., systems characterized by 

inputs appearing linearly in the system state equation. 

Few results are available for nonaffine nonlinear systems 

where the control input appears in a nonlinear fashion [5, 

7, 8, 10, 14, 19, 21]. In general, a two-step procedure is 

taken in nonaffine nonlinear system. First, based on 

implicit function theorem an ideal controller is developed 

to stabilize the underlying system and makes the tracking 

approach a neighborhood of zero. Then, a neural network 

or fuzzy logic to approximate this ideal controller is 

designed. Based on the Lyapunov stability analysis, an 

adaptation law is devised to update the adjustable 

parameters. However a bounding controller may also be 

added for more performance robustness. 

In the above most methods the parameter adaptation 

laws are designed based on a Lyapunov approach, where 

an error signal between the desired output and the actual 

output is used to update the adjustable parameters and the 

control laws are composed of three control terms: a linear 

control term, an adaptive neural network control term and 

a robust control term used to compensate for disturbances 

and approximation errors. On the other hand, almost all 

of the above works don’t consider the zero dynamics, 

though it plays an important role in nonlinear system 

control. Considering that zero dynamics exist in many 

practical systems, including isothermal continuous stirred 

tank reactors, aircraft trajectory tracking control systems 

and others, it is necessary to investigate their influence on 

nonlinear system. 

In the paper, according to [5], we introduce a direct 

adaptive neural network control approach for a class of 

nonaffine nonlinear systems with zero dynamics. The 

basic idea is to use neural network to adaptively construct 

an unknown ideal controller and the parameter adaptive 

laws is designed, based on the gradient descent method, 

to directly minimizing the error between the unknown 

ideal controller and the neural network controller And no 

robust control term is used in controller. This paper 

proves the availability of the method in both theory and 

simulation experiment. 

The paper is organized as follows. First, the problem is 

formulated in Section II. Zero dynamics is given in III. 

Designing a control law with on-line tuning of neural 

network weighting factors is given in Section IV. In 

Section V, convergence and stability analysis of control 


doi:10.4304/jcp.8.6.1488-1495


system is given. In Section VI, simulation results are 

presented to confirm the effectiveness and applicability of 

the proposed method. Finally, conclusions are included. 

A. Notations and Preliminaries 

The following notations and definitions will 

extensively be used throughout the paper. Let be the 

real number, n 

n× 

m 

and represent the real n-vectors 

and the real n× m matrices, respectively. i denotes the 

usual Euclidean norm of a vector. In the case where y is 

a scalar, y denotes its absolute value and if Y is a 

matrix, Y means Frobenious norm defined as 

Y 

T 

{ } 

= tr Y Y .where tr{ i} 

stands for trace operator. 

Implicit Function Theorem: Assume that 

n m n 

h : × → is continuously differentiable at each 

n m 

ab of an open set S ⊂ × a , b be a 

point ( , ) 

. Let ( 0 0) 

point in S for which ( , ) 

h a b and for which the 

0 0 

Jacobian matrix ⎡∂h 

⎤( a , b ) 

⎣ 

∂a⎦ 

0 0 

is nonsingular. Then 

n 

m 

there exist neighborhoods U ⊂ of a0 

and V ⊂ of 

b0 

such that for each b∈V 

the equation h( a, b ) = 0has a 

unique solution a∈ 

U . Moreover, the solution can be 

given as a = g( b) 

where g is continuously differentiable 

at b= b0 

. 

II. PROBLEM FORMALATION 

Consider the following SISO nonaffine nonlinear 

system [8]: 

where [ ] 

⎧ dξi 

⎪ = ξi+ 

1 

i =1, , r−1 

dt 

⎪ 

dξr 

⎪ = h( ξη , , u) 

⎨ dt 

⎪ dη 

⎪ = q(, ξη, u) 

⎪ dt 

⎪ ⎩ y = ξ1 

, , 

T r 

ξ = ξ1 ξ r 

∈ Rξ 

⊂ , 

(1) 

n−r 

η∈R η 

⊂ are 

system states and u ∈Ωu 

⊂ , y ∈ are system input 

and output respectively. h(, ξη, u) 

is a smooth partially 

known function, and q(, ξη , u) 

is a smooth partially 

known vector field. 

The control objective is to design an adaptive neural 

network controller for a class of SISO nonaffine 

nonlinear systems (1) such that the system output follows 

a desired trajectory while all signals in the closed-loop 

system remain bounded. 

∂h(, ξη, u) 

Assumption 1: The function hu 

(, ξη , u) 

= 

∂u 

is nonzero and bounded for all (, ξη, u) ∈ × × 

R 

R 

. 

This implies that h (, ξη , u) 

is strictly either positive or 

u 

ξ 

η 

negative for all ( ξη , , u) ∈ × × 

R 

R 

.Without loss of 

generality, it is assumed that it exists a constant c such 

that hu 

(, ξη , u) ≥ c > 0. 

Define the reference vector 

( r−1) 

T r 

y = ( y y y ) ∈R 

ξ 

d d d d 

The reference signal y d 

and its time derivative are 

assumed to be smooth and bounded. We also define the 

tracking error as 

e= yd 

− y 

and corresponding error vector as 

( r−1) 

T r 

e = (,, e e e ) ∈ R . 

Assumption 2: When the desired output y d 

and its r- 

order derivative are of known bound, there exists a 

positive constant bd 

to satisfy 

(1) ( r−1) 

T 

( yd yd yd ) ≤ bd 

Then the error equation is as follows: 

η 

(2) 

( r) 

e = A0 e + b⎡ 

⎣yd 

−h(, ξη, u) 

⎤ 

⎦ (3) 

⎡ 0 1 0 0⎤ 

⎡0⎤ 

⎢ 

0 0 1 0 

⎥ 

⎢ 

 

⎢ 

⎥ 

0 

⎥ 

⎢ ⎥ 

where A0 

= ⎢ ⎥ 

, b = ⎢0⎥ 

. 

⎢ ⎥ 

⎢ ⎥ 

⎢ 0 0 0 1⎥ 

⎢ 

⎥ 

⎢ 

⎣ 0 0 0 0 0⎥ 

⎦ 

⎢ 

r × r ⎣1⎥ 

⎦ r × 1 

A b is controllable, then there will exist a 

Obviously, ( , 0 ) 

constant matrix [ , , ] 

T 

0 1 r 1 

T 

c 

K = k k k − 

which makes 

eigenvalues of matrix A = A0 

− bK all have negative 

real part. Thus, for any given positive definite symmetric 

matrix Q , there exists a unique positive definite 

symmetric solution P to the following Lyapunov 

algebraic equation: 

A P+ PA = − Q 

(4) 

T 

c 

Define a signal 

T 

( r) 

T 

⎛b Pe ⎞ 

ν= yd 

+ K e + λtanh⎜ ⎟ 

⎝ Ξ ⎠ 

where tanh( •) ∈− ( 1,1) is the hyperbolic tangent function, 

Ξ,λ 

are the positive design parameters, when error 

T 

⎛bPe⎞ e →+ 

∞ , the value of tanh ⎜ ⎟ → + ∞ , and when 

⎝ Ξ ⎠ 

T 

⎛b Pe ⎞ 

error e →-∞ the value of tanh ⎜ ⎟ → - ∞ . 

⎝ Ξ ⎠ 

T 

⎛b Pe ⎞ 

When e → 0 , tanh ⎜ ⎟ → 0 .The term 

⎝ Ξ ⎠ 

T 

⎛b Pe ⎞ 

λ tanh ⎜ ⎟ is a smooth approximation of the 

⎝ Ξ ⎠ 

T 

discontinuous term sign( b Pe ) 

c 

λ usually used in robust 



control. So, λ is selected larger than the magnitude of the 

uncertainty and it will affect the convergence rate of the 

tracking error, and Ξ is chosen very small to best 

approximate the sign function and it will affect the size 

of the residual set to which the tracking error will 

converge. The sign function is not used here to avoid 

problems associated with it as chattering and solutions 

existence. 

By adding and subtracting ν in (3), we obtain 

T 

T 

bPe 

e ⎛ ⎞ 

= ( A0 −bK ) e −bλ 

tanh ⎜ ⎟−b[ h( ξη , , u) 

−v] 

(5) 

⎝ Ξ ⎠ 

From the fact that the signal v does not explicitly 

depend upon the control input u and Assumption 1, the 

partial derivative of h(, ξη , u) 

− v with respect to the 

input u satisfies 

( ξη ) 

∂ h(, , u) −v ∂h(, ξη, u) 

= > 0 

∂u 

∂u 

Thus according to the implicit function theorem, there 

exists some ideal controller u * ( ξην , , ) satisfying the 

following equality for all (, ξη,) v ∈ × × 

R 

R 

: 

ξ 

η 

(6) 

* 

h(, ξη, u (, ξη ,)) v − v = 0 

(7) 

Therefore, if the control input u is chosen as the ideal 

controller u 

* (, ξη ,) v , the closed-loop error dynamic (5) is 

reduced to 

T 

T 

b Pe 

e ⎛ ⎞ 

= ( A0 −bK ) e −bλ 

tanh ⎜ ⎟ (8) 

⎝ Ξ ⎠ 

Considering the following positive function to the 

error dynamic: 

V 

T 

= e Pe 

(9) 

Using (4) and (8), the time derivative of (9) becomes 

T 

T T b Pe 

V ⎛ ⎞ 

=−e Qe −2λb Pe tanh⎜ ⎟ (10) 

⎝ Ξ ⎠ 

T 

⎛b Pe ⎞ 

Because the term b T Pe and tanh ⎜ ⎟ always 

⎝ Ξ ⎠ 

have same sign, we conclude that V 

≤ 0 , and only 

when e = 0 , V = 0 , which means lim | e | = 0 . 

t→∞ 

III. ZERO DYNAMICS 

If system (1) is controlled by the input u, the state 

vector η is completely unobservable from the output, 

then the subsystem 

dη 

q(0, , u(0, , v(0, ))) 

dt = η η η (11) 

is addressed as the zero dynamic. 

Assumption 3: Zero dynamics (11) is exponentially 

stable, and the function q( ξη , , u) 

is Lipschitz inξ . There 

exists Lipschitz constants L ξ 

and L 

q 

such that 

q(, ξη, u) − q(0, η, u ≤ L ξ + Lq 

(12) 

where u = u(0, η η 

, v(0, η ))) . 

By Lyapunov converse theorem, there is a Lyapunov 

function V ( ) 0 

η which satisfies 

η 

2 2 

1 

V0( ) 

2 

ξ 

σ η ≤ η ≤ σ η (13) 

∂V0 

( η) 

q(0, η) 

≤−σ3 

η 

∂η 

∂V ( η) 

0 

∂η 

≤ σ 

Where σ , i = 1,2,3,4 are positive constant. 

i 

4 

η 

IV. DESIGN OF CONTROLLER 

2 

(14) 

(15) 

In control engineering, radial basis function (RBF) 

NNs are usually used as a tool for modeling nonlinear 

functions because of their good capabilities in function 

approximation. RBFNN represents a class of linearly 

parameterized approximations and can be replaced by any 

other linearly parameterized approximations such as 

spline functions or fuzzy systems. Moreover, nonlinearly 

parameterized approximations, such as multilayer neural 

network (MNN), can be linearized as linearly 

parameterized approximations, with the higher order 

terms of Taylor series expansions being taken as part of 

the modeling error. 

In this paper, the following RBF NN based on GGAP- 

RBF [20] algorithm which can avoid to select initial 

neural network parameters and nodes number of hidden 

T 

layer artificially uz ( ) = φ ( z) 

θ is used to approximate 

the ideal controller 

1 

* T T 

u ( z ) , where z = ⎡ ⎣ ξ , η , v⎤ 

⎦ , 

φ( z) = ( φ ( z), , φ ( z)) T is the basic function vector, and 

M 

θ = ( θ1, , θ ) T 

M 

is the adjustable parameter. It has been 

proven that neural network can approximate any smooth 

q 

function over a compact set ΩZ 

⊂ R to arbitrarily any 

accuracy as 

( ) = φ ( ) θ + δ( ) (16) 

* T * 

u z z z 

with bounded function approximation error δ ( z) 

satisfying δ ( z) 

≤ δ .Where 

vector which minimizes the function δ ( z) 

* 

θ is an ideal parameter 

T 

. In this paper, 

we assume that the used neural network does not violate 

the universal approximation property on the compact set 

Ω 

Z 

, which is assumed large enough so that the variable 

z remains inside it under closed-loop control. 

Let us define the control error between the controllers 

uz ( ) and u 

* ( z ) as 



* T 

e = u ( z) − u( z) = φ ( z) θ + δ( z) 

(17) 

u 

* 

where θ = θ −θ 

is the parameter estimation error vector. 

According to the mean value theorem, there exist 

constant 0< α < 1, h(, ξη , u) 

can be described as 

( ) 

h ξηu h ξη u h u z u z (18) 

* * 

(, , ) = (, , ) + 

u 

() − () 

λ 

where 

h =∂h(, ξη , u) ∂u| 

uλ 

u= 

uλ 

uλ = αu z + − α u z 

* 

( ) (1 ) ( ) 

By substituting (5) into the equation (18) and considering 

(7), we get 

T 

bPe 

* 

e 

⎛ ⎞ 

= Ac 

e −bλtanh ⎜ ⎟−b⎡ 

⎣h( ξη , , u ) −ν⎤ 

⎦− 

⎝ Ξ ⎠ 

* 

−bhu 

( u( z) −u ( z) 

) 

(19) 

λ 

T 

⎛bPe⎞ 

* 

= Ae c −bλ 

tanh ⎜ ⎟−bhu 

( u( z) −u ( z) 

) 

λ 

⎝ Ξ ⎠ 

T 

Considering Ac 

= A0 

− bK , then (19) can be rewritten as 

T 

( r) T ⎛bPe⎞ 

* 

e + K e + λ tanh ⎜ ⎟ = h ( u ( z) − u( z) 

u ) = h e (20) 

λ 

uλ 

u 

⎝ Ξ ⎠ 

We notice here that u 

* ( z) 

is an unknown quantity, so 

the signal e u 

defined in (17) is not available. Eq. (20) will 

be used to overcome the difficulty. Indeed, from (20), we 

see that even if the signal e is not available for 

measurement, the quantity h uλ 

e u 

is measureable. This fact 

will be exploited in the design of the parameters adaptive 

law. 

In order to obtain the update law ofθ , we consider a 

quadratic cost function defined as 

u 

1 2 1 * T 

J ( ( ) ( ) ) 2 

θ 

= eu 

= u z − φ z θ (21) 

2 2 

By applying the gradient descent method, we obtain as an 

adaptive law for the parameters θ 

θ = - γ∇ θ 

J ( θ) = γφ( ze ) u 

(22) 

From (22), we know e u is not available, the adaptive 

law (22) cannot be implemented. In order to render (22) 

computable, from Eq. (20), we select the design 

parameter γ = γ θ 

hu 

λ 

, where γ 

θ 

is a positive constant. We 

have 

θ = γ φ( zh ) e 

θ 

γφ 

⎧⎪ 

uλ 

u 

λ 

( r) 

T 

= 

θ 

( z) ⎨e + K e + tanh 

⎪⎩ 

⎛ 

⎜ 

⎝ 

T 

bPe 

Ξ 

⎞⎫⎪ 

⎟⎬ 

⎠⎪⎭ 

(23) 

At the same time, in order to improve the robustness of 

adaptive law in the presence of the approximation error, 

we modify it by introducing a σ -modification term as 

follows: 

T 

 

⎧⎪ 

( r) 

T 

⎛b Pe ⎞⎫⎪ 

θ = γθφ( z) ⎨e + K e + λ tanh⎜ 

⎟⎬−γ θσθ 

(24) 

⎪⎩ 

⎝ Ξ ⎠⎪⎭ 

whereσ is a small positive constant 

Since the function of the σ -modification adaptive law 

is to avoid parameter drift, it does not need to be active 

when the estimated parameters are within some 

acceptable bound. The system stability relies entirely on 

the neural network because the proposed adaptive 

controller in the paper is only composed of a neural 

network part without additional control terms. The term 

T 

⎛b Pe ⎞ 

λ tanh ⎜ ⎟in the parameter adaptive law (24) plays, 

⎝ Ξ ⎠ 

in some way, the role of a robustifying control term. Thus 

by selecting a large positive value for the design 

parameter λ and a small positive value for the 

parameter Ξ , the robustness of the controller can be 

improved. 

V. STABILITY AND CONVERGENCE ANALYSIS OF 

CONTROL SYSTEM 

In order to analysis the convergence of neural network 

weights, we firstly consider the following positive 

function: 

V θ 

1 

= T 

θ θ 

(25) 

2 γ 

Using (17), (20) and (24), the time derivative of (25) 

can be written as 

Considering the inequalities 

θ 

( z hu 

eu 

) 

T 

V 

θ 

= - θ φ( ) -σθ 

λ 

T 

T 

= - φ ( z) 

θhu 

e 

λ u 

+ σθ 

θ 

T 

=− h e + h δ ( z) 

e + σθ 

θ 

2 

uλ 

u uλ 

u 

T σ σ σ 

σθ θ =− θ − θ + θ + θ 

2 2 2 

σ 2 σ * 

2 

≤− θ + θ 

2 2 

2 2 

2 

(26) 

(27) 

2 1 2 1 2 1 

− e ( ) ( ) ( ( )) 2 

u 

+ δ z eu = − eu + δ z − eu 

−δ 

z 

2 2 2 

(28) 

1 2 1 2 

≤− eu 

+ δ ( z)) 

2 2 

Considering (27) and (28), Eq. (26) can be bounded as 

1 2 

2 1 2 * 

2 

V σ σ 

θ 

≤− hu eu + hu 

δ ( z) 

− θ + θ (29) 

λ 

λ 

2 2 2 2 

Because the functions δ ( z) 

and hu 

λ 

are bounded in this 

paper, and the parameters θ * are constants, so we can 

define a positive constant bound ψ as 

⎛1 

2 ⎞ σ * 

2 

ψ = sup ⎜ hu 

δ ( z) 

θ 

λ ⎟+ 

(30) 

t ⎝2 ⎠ 2 

Then 



V 1 1 

2 V 2 h e 

θ 

≤− ρ 

θ 

+ ψ − 

u λ u 

≤− ρV 

+ ψ 

θ 

2 

(31) 

where ρ = σγ 

θ 

Eq. (31) implies that for V 

ψ 

θ 

> , V 

0 ρ θ 

< 

and, therefore, θ is bounded. By integrating (31), we can 

establish that: 

From (32), we have 

ψ 

θ θ γ 

ρ 

2 2 

− t 

≤ (0) e ρ + 2 

θ 

(32) 

(33) 

−0.5ρt 

θ ≤ θ(0) e + 2γθψ ρ 

Using (33) and the fact that δ ( z) 

and hu 

λ 

are bounded, 

we can write 

T 

( 

+ ) 

βξη ( , ) hu 

φ ( z) θ δ( z) 

λ 

T 

≤ βξη ( , ) hu 

φ ( z) θ+ βξη ( , ) hu 

δ( z) 

λ 

λ 

T 

≤ βξη ( , ) h φ ( z) θ + 

uλ 

+ βξη ( , ) h δ( z) 

uλ 

−0. 

5ρt 

T 

≤ βξη ( , ) h φ ( z) θ(0) 

e 

uλ 

T 

+ βξη ( , ) h φ ( z) 2 γψ ρ+ 

 

uλ 

+ βξη ( , ) h δ( z) 

uλ 

≤ ψ e + ψ 

−0.5ρt 

0 1 

θ 

(34) 

+ 

Where ψ 

0, 

ψ 

1 

are some finite positive constants. 

Lemma 1: The following inequality holds for all 

Ξ> 0 and ς ∈ R with K = 0.2785 . 

c 

⎛ς 

⎞ 

0≤ ς −ς 

⋅tanh⎜ 

⎟≤ KcΞ 

⎝Ξ 

⎠ 

(35) 

Theorem 1: Suppose that Assumption1-3 are satisfied 

for the system (1), then the neural network controller and 

adaptation law given by (24) guarantees the convergence 

of the neural network parameters and to be uniformly 

ultimately bounded of all the signal in the closed-loop 

system. 

Proof: Consider the Lyapunov function candidate: 

V( e, η) = e T Pe +μV 

( η ) (36) 

Where μ > 0 is the design parameter. Considering (4), 

(19), (20), (34) and lemma 1, differentiating V( e, η ) with 

respect to time, we obtain 

0 

T 

T T T bPe 

Ve 

⎛ ⎞ 

(,) η = e ( Ac 

P+ PAc) 

e− 2bPeλ 

tanh⎜ 

⎟+ 

 

⎝ Ξ ⎠ 

T * dV0 

() η 

+2 bPehu 

( u− u) 

+ μ 

λ 

dt 

T 

T T 

⎛bPe⎞ 

dV0 

() η 

=−eQe− 2bPeλtanh 

⎜ ⎟+ μ + 

⎝ Ξ ⎠ dt 

T 

( φ θ+ 

δ ) 

T 

+2 bPeh ( z) ( z) 

uλ 

T 

T T 

⎛bPe⎞ dV0 

() η 

≤−eQe−2 bPeλ 

tan h⎜ 

⎟ ++ μ + 

⎝ Ξ ⎠ dt 

T 

−0.5 

t 

+ 2 bPe ψ e ρ + ψ 

( 0 1) 

(37) 

If the design parameter λ is large enough to make 

λ ≥ ψ 1 

and considering assumption 4, we have 

 

T T −0.5ρt 

Ve ( , η) eQe 2 bPeψ 

e +2ψ 

K 

0 1 c 

≤− + Ξ+ 

 

∂V 

( η) 

[ q(0, η, u ) q( ξ, η, u) q(0, η, u ) 

η 

η 

] 

0 

+ μ 

+ − 

∂η 

T 

2 

e Qe μσ 

3 

μσ 

4Lξ 

μσ 

4Lq 

≤ − − η + ξ η + η + 

(38) 

T 

+ 2 b Pe ψ e + 2ψ 

K Ξ 

Then 

−0.5ρt 

0 1 

Considering assumption 2 and 

c 

T −0.5ρt 2 T 

2 

2 −ρt 

ψ0 ≤ + ψ0 

2 b Pe e 0.5 e 2 b P e 

ξ ≤ e + y y y ≤ e + b 

(1) ( r−1) 

T 

( 

d d 

 

d 

) 

d 

( λ ) 

Ve ( , η) ≤- ( Q) −0.5 

e − + 

Using the inequality 

2 2 

min 

μσ3 

η 

+ μσ L e η + μσ L b η + 

4 ξ 

4 

ξ d 

T 

2 

2 −ρt 

4 q 

η 

0 1 c 

+ μσ L + 2 b P ψ e + 2ψ 

K Ξ 

4 ξ 4 ξ 1 4 ξ 

2 2ε1 

(39) 

1 2 1 

2 

μσ L e η ≤ μσ L ε η + μσ L e (40) 

μσ 

( ) ( ( )) 2 2 

Lb 

ξ d 

Lq μσ ε Lb 

ξ d 

Lq 

1 

+ η ≤ + η + (41) 

4 4 2 2 

4ε 

2 

Then (39) satisfies 

V 

( e, η) 

⎛ 

1 ⎞ 2 

≤- ⎜λmin ( Q) −0.5− μσ4Lξ 

⎟ e + 

⎝ 

2 ε1 

⎠ 

⎡ 1 

2 

⎤ 2 

−μ⎢σ3 − σ4Lξε1 − μ( σ4ε2( Lξbd 

+ Lq) 

) 

2 

⎥ η + 

⎣ 

⎦ 

T 

2 

1 

+ 2 bP ψ e + 2ψ 

KΞ+ 

2 −ρt 

0 1 c 2 

4ε 

2 

(42) 

where ε1, 

ε 

2 

are suitable positive constants. We 

adjust ε1, 

ε 

2 

to 

1 

make σ ( ( )) 2 

3 

σ4Lξε1 μ σ4ε2 

Lξbd 

Lq 

− − + > 0 . 

2 



Supposing 

selecting μ = 

1 

T 

2 

2 −ρt 

ε = + 2 bP ψ0e + 2ψ1K c 

Ξ , and 

4ε 

2 

2 

1⎛ 

1 ⎞ 

⎜σ 3 

− σ4Lξ 

ε1⎟ 

2⎝ 

2 ⎠ 

, then 

( σε 

4 2( Lb 

ξ d 

+ Lq) 

) 

1 

2 

V 

⎛ 

⎞ 

( e, η) ≤−⎜λmin ( Q) −0.5− μσ4Lξ 

⎟ e + 

⎝ 

2 ε1 

⎠ 

Adjusting Q to make 

⎛ 1 ⎞ 

3 4 1 

1 

⎜σ − σ Lξ 

ε ⎟ 

2 

2 

− 

⎝ 

⎠ 

η + ε 

2 

4 

( σε 

4 2( Lb 

ξ d 

+ Lq) 

) 

1 

λ ( ) −0.5− μσ > 0. 


Q 

4L ξ 

2ε1 

2 

2 

(43) 

From the above equation, we can know that tracking 

error and internal states η are all uniformly ultimately 

bounded. 

Besides, 

since ξ ≤ e + y y y ≤ e + b , then 

(1) ( r−1) 

T 

( 

d d 

 

d 

) 

d 

the state ξ is uniformly ultimately bounded too. This 

completes the proof. 

VI. SIMULATION RESULTS 

In this part, the following SISO nonaffine nonlinear 

system with zero dynamics is simulated to illustrate the 

effectiveness of the proposed adaptive neural network 

tracking controller. The nonaffine nonlinear system is 

described as follows: 

ξ = ξ 

1 2 

2 

(( ) )( ) 

ξ =−2 ξ −η −1 ξ −η −η − 0.2η 

+ 

2 1 1 2 2 1 2 

⎡ 1 3 ⎤ 

+ ( 2 + sin ([ ξ1−η1][ ξ2 − η2] 

)) 

⎢u+ u + sin( u) 

3 ⎥ (44) 

⎣ 

⎦ 

η1 = η2 

η =−2η − 0.2η + ξ 

2 1 2 1 

y = ξ 

1 

The control objective is to force the system output y 

to track the desired trajectory yd 

= 2sint+ cos ( 0.5t).The 

simulation parameters are selected as follows: 

15 5 

Q = diag[10,10] , P = ⎡ ⎤ 

⎢ 

5 5 ⎥ , K = [ 1, 2] 

T 

, Ξ = 0.01 , 

⎣ ⎦ 

λ = 10 , γ = 11 , σ = 0.02 . 

θ 

T 

The output of RBFNN controller is uz ( ) = φ ( z) 

θ . The 

basis function vector is φ( z) = ( φ1 

( z) φ ( )) T 

M 

z , where 

T 

( z μ ) ( z μ ) 

⎡− − 

i 

− ⎤ 

i 

φi 

( z) = exp ⎢ 

⎥, i = 1, , M . M is the 

2 

⎢⎣ 

σ 

i ⎥⎦ 

number of hidden layer nodes which is stable at the 33 

nodes by training on-line using the GGAP-RBF 

algorithm. 

According to (23), the control law is 

T 

uz ( ) = φ ( z) 

θ 

θ =− 11 φ( z) e + e+ 2e + 10 tanh 100 × (5e+ 

5 e 

) 

− 11× 

0.02θ 

{ ( )} 

The system initial conditions are ξ = [ ] 

(0) 1 2 T 

.The 

simulation results using MATLAB are shown in Fig1, 2, 

3, 4. 

Figure 1. Plots of output tracking of system 

Figure 1 shows the result of output tracking, and the 

control input signal is shown in Figure 2. The growing 

and pruning automatically of hidden layer nodes are 

shown in Figure 3. 

Figure 2. Plots of Control input 

Figure 3. Node Number of Hidden Layer 



Figure 4. Norm of the weight vector θ 

Figure 4 shows the weights is always bounded in 

whole control process though the structure and 

parameters of neural network is adjusted on line. It can be 

seen that the actual trajectories converge rapidly to the 

desired ones. The computer simulation results show that 

the adaptive neural network controller can perform 

successful control and achieve desired performance. 

VII. CONCLUSIONS 

A new adaptive neural network tracking control 

algorithm is presented for a class of SISO nonaffine 

nonlinear systems with zero dynamics in this paper. The 

method does not assume boundedness on the time 

derivative of a control effectiveness term, and only need 

sign known and boundedness of the control effectiveness 

term. The update law of neural network adjustable 

parameters is obtained by the gradient descent algorithm. 

The overall adaptive scheme guarantees that all signals 

involved are uniformly ultimately bounded and the output 

of the closed-loop system tracks the desired output 

trajectory. Simulation results demonstrate the feasibility 

of the proposed control scheme. 


It is a project supported by Provincial Natural Science 

Foundation of Hunan, China (Grant No.09JJ3094), the 

Research Foundation of Education Bureau of Hunan 

Province, China (Grant No.09B022), the Great Item of 

United Provinces Natural Science Foundation of Hunan, 

China (Grant No.09JJ8006), the Planned Science and 

Technology Project of Hunan Province, China (Grant 

No.2011FJ3126). Supported by the Construct Program of 

the Key Discipline in Hunan Province: Control Science 

and Engineering Science and Technology Innovation 

Team of Hunan Province: Complex Network Control. 

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2009. 

Hui HU is a lecturer of Department of electrical and 

information engineering, Hunan institute of engineering. Dr.Hu 

received the B.S. degree in electronics and information 

engineering from Hunan University of Science and Technology 

in 2001.And received the M.S. degree in power electronics and 

drives from Xiangtan University in 2004.And received the Ph. 

D degree in control theory and control engineering from Hunan 

University in 2010. Her research interests include nonlinear 

systems tracking control, MIMO systems control, uncertain 

nonlinear system control and intelligent control. 

Peng GUO is a lecturer of Department of Computer and 

Science, Hunan institute of engineering. He received the B.S. 

degree in electronics and information engineering from Hunan 

University of Science and Technology in 2000, and received the 

M.S. degree in computer science from Hunan University in 

2006. His research interests include intelligent control and 

computing theory, multimedia computing and networking and 

agent technology. 



Improved Feasible SQP Algorithm for Nonlinear 

Programs with Equality Constrained Sub- 

Problems 

Zhijun Luo 1 , Guohua Chen 3 and Simei Luo 4 

Department of Mathematics & Applied Mathematics, Hunan University of Humanities, Science and Technology, Loudi, 

China 

Email: ldlzj123@163.com 

Zhibin Zhu 2 

School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China 

Email: zhu_zhibin@163.com 

Abstract—This paper proposed an improved feasible 

sequential quadratic programming (FSQP) method for 

nonlinear programs. As compared with the existing SQP 

methods which required solving the QP sub-problem with 

inequality constraints in single iteration, in order to obtain 

the feasible direction, the method of this paper is only 

necessary to solve an equality constrained quadratic 

programming sub-problems. Combined the generalized 

projection technique, a height-order correction direction is 

yielded by explicit formulas, which can avoids Maratos 

effect. Furthermore, under some mild assumptions, the 

algorithm is globally convergent and its rate of convergence 

is one-step superlinearly. Numerical results reported show 

that the algorithm in this paper is effective. 

Index Terms—Nonlinear programs, FSQP method, Equality 

constrained quadratic programming, Global convergence, 

Superlinear convergence rate 


Consider the following nonlinear programs 

min f( x) 

s.. t g ( x) ≤0, j∈ I = {1,2, , m}, 

j 

Where f ( x), g ( ): n 

j 

x R → R( j∈I) 

are continuously 

differentiable functions. Denote the feasible set for (1) by 

n 

X = { x∈R | g 

j 

( x) ≤0, j∈ I} 

. 

The Lagrangian function associated with (1) is defined 

as follows: 

Lx ( , λ) f( x) λ g( x) 

m 

= +∑ 

j= 

1 

A point x ∈ X is said to be a KKT point of (1), if it is 

satisfies the equalities 

This work was supported in part by the National Natural Science 

Foundation (11061011) of China, and the Educational Reform Research 

Fund of Hunan University of Humanities, Science and Technology 

(NO.RKJGY1030), corresponding author, E-mail: ldlzj123@163.com . 

j 

j 

(1) 

m 

∇ f( x) + λ ∇ g ( x) = 0, 

j= 

1 

λ g ( x) = 0, j∈I, 

j 

j 

∑ 

where λ = ( λ1 

, , λ ) T 

m 

is nonnegative, and λ is said to 

be the corresponding KKT multiplier vector. 

Method of Sequential Quadratic Programming (SQP) 

is an important method for solving nonlinearly 

constrained optimization [1, 2, 18]. It generates 

iteratively the main search direction d 0 

by solving the 

following quadratic programming (QP) sub-problem: 

j 

T 1 T 

min ∇ f( x) 

d + d Hd 

2 

T 

s.. t g ( x) + ∇g ( x) d ≤0, j∈I, 

j 

n n 

where H ∈ R × is a symmetric positive definite matrix. 

However, such type SQP algorithms have two serious 

shortcomings: 

1) SQP algorithms require that the relate QP subproblems 

(2) must be consistency; 

2) There exists Matatos effect. 

Many efforts have been made to overcome the 

shortcomings through modifying the quadratic subproblem 

(2) and the direction d [4, 5, 7, 8]. Some 

algorithms solve the problem (1) by using the idea of 

filter method or trust-region [13, 16, 17]. 

For the problem (2), it is also a hot topic to solve the 

QP problem like (2) in the field of optimization. By using 

the idea of active constraints set, some algorithms solve 

step by step a series of corresponding QP problems with 

only equality constraints to obtain the optimum solution 

to the QP sub-problem (2). P. Spellucci [6] proposed a 

new method, the d 0 

is obtained by solving QP subproblem 

with only equality constraints: 

j 

j 

(2) 


doi:10.4304/jcp.8.6.1496-1503


T 1 T 


d + d Hd 

2 

T 

s.. t g ( x) +∇ g ( x) d = 0, j∈A⊆ 

I, 

j 

j 

where the so-called working set A ⊆ I is suitably 

determined. If d 0 

= 0 and λ ≥ 0 ( λ is said to be the 

corresponding KKT multiplier vector.), the algorithm 

stops. The most advantage of these algorithms is merely 

necessary to solve QP sub-problems with only equality 

constraints. However, if d 

0 

= 0 , but λ < 0 , the algorithm 

will not implement successfully. In [10], proposed an 

SQP method for general constrained optimization. Firstly, 

make use of the technique which handle the general 

constrained optimization as an inequality parametric 

programming, then, consider a new quadratic 

programming with only equality constraints as follow: 

T 1 T 


d + d Hd 

2 

T 

s.. t g ( x) +∇ g ( x) d =−min{0, π ( x)}, j∈J( x). 

j 

j 

Where π ( x) 

is a suitable vector, J ( x ) is a suitable 

approximate active set. But the QP problems may no 

solution under some conditions. Recently, Zhu [14] 

Consider the following QP sub-problem: 

T 1 T 


d + d Hd 

2 

T 

s.. t p ( x) +∇ g ( x) d = 0, j∈L. 

j 

j 

where p ( x ) is a suitable vector, L is a suitable 

j 

approximate active, which guarantees to hold that if 

d 

0 

= 0 , then x is a KKT point of (1), i.e., if d 

0 

= 0 , then 

it holds that λ ≥ 0 . Depended strictly on the strict 

complementarity, which is rather strong and difficult for 

testing, the superlinear convergence properties of the 

SQP algorithm are obtained. For avoiding the superlinear 

convergence depend strictly on the strict complementarity, 

Another some SQP algorithms (see [15]) have been 

proposed, however it is regretful that these algorithms are 

infeasible SQP type and nonmonotone. In [16], a feasible 

SQP algorithm is proposed. Using generalized projection 

technique, the superlinear convergence properties are still 

obtained under weaker conditions without the strict 

complementarity. 

We will develop an improved feasible SQP method for 

solving optimization problems based on the one in [14]. 

The traditional FSQP algorithms, in order to prevent 

iterates from leaving the feasible set, and avoid Maratos 

effect, it needs to solve two or three QP sub-problems 

like (2). In our algorithm, per single iteration, it is only 


programming, which is very similar to (4). Obviously, it 

is simpler to solve the equality constrained QP problem 

than to solve the QP problem with inequality constraints. 

In order to void the Maratos effect, combined the 

generalized projection technique, a height-order 

correction direction is computed by an explicit formula, 

and it plays an important role in avoiding the strict 

(3) 

(4) 

complementarity. Furthermore, its global and superlinear 

convergence rate is obtained under some suitable 

conditions. 

This paper is organized as follows: In Section II, we 

state the algorithm; the well-defined of our approach is 

also discussed, the accountability of which allows us to 

present global convergence guarantees under common 

conditions in Section III, while in Section IV we deal 

with superlinear convergence. Finally, in Section V, 

numerical experiments are implemented. 

II. DESCRIPTION OF ALGORITHM 

The active constraints set of (1) is denoted as follows: 

I( x) = { j∈ I | g ( x) = 0, j∈ I}. 

(5) 

Now, the following algorithm is proposed for solving 

the problem (1). 

Algorithm A: 

Step 0 Initialization: 

Given a starting point 

0 

x ∈ X , and an initial 

n n 

symmetric positive definite matrix H 0 

∈ R × . Choose 

1 

parameters ε0 

∈(0,1), α∈(0, ), τ ∈ (2,3) . Set k = 0 ; 

2 

Step 1. Computation of an approximate active set J 

k 

. 

Step 1.1. For the current point 

0 

j 

k 

x 

k 

ε ( x ) = ε ∈ (0,1). 

i 

∈ X , set i = 0, 

Step 1.2. If det( A ( x k ) T A( x k )) ≥ ε ( x 

k ) , let 

i i i 

k k k 

Jk 

= J( x ), Ak 

= A( x ), i( x ) = i , and go to Step 2. 

Otherwise go to Step 1.3, where 

k k k 

J ( x ) = { j∈I | −ε 

( x ) ≤ g ( x ) ≤0}, 

i i j 

k k k 

A( x ) = ( ∇g ( x ), j∈J ( x )). 

i i i 

k 1 k 

Step 1.3. Let i = i+ 1, εi( x ) = εi 

− 1( x ) , and go to 

2 

Step1. 2. 

k 

Step 2. Computation of the vector d 

0 

. 

Step 2.1 

B A A A v v j J B f x 

T −1 

T k k k 

k 

= ( 

k k) k 

, = ( 

j, ∈ 

k) = − 

k∇ 

( ), 

k k 

⎧ , 0 

k ⎪ − vj 

vj 

< 

k k 

pj = ⎨ 

p = ( pj, j∈Jk). 

k k 

⎪⎩ g 

j( x ), vj 

≥ 0 

Step 2.2 Solve the following equality constrained QP 

k 

Sub problem at x : 

k T 1 T 

min ∇ f( x ) d + d Hkd 

2 

k k T 

s. t. p +∇ g ( x ) d = 0, j∈J 

. 

j j k 

k 

Let d0 

be the KKT point of (8), and 

k k 

b = ( b , j∈J 

) be the corresponding multiplier vector. 

j 

k 

k 

If d 

0 

= 0 , STOP. Otherwise, CONTINUE; 

(6) 

(7) 

(8) 



Step 3 

Computation of the feasible direction with descent 

Where 

δ 

ek 

k 

d : 

k k T −1 

d = d0 − δ 

kAk( Ak Ak) 

ek 

(9) 

T | Jk 

| 

= (1, ,1) ∈R 

, and 

|| d || ( d ) H d 

k k T k 

0 0 k 0 k T −1 

T k 

k 

= , μ =−( Ak Ak) Ak∇f( x ) 

kT k 

2 | μ ek 

||| d0 

|| + 1 

Step 4. Computation of the high-order revised direction 

k 

d : 

where 

d A A A d e g x d (10) 

k T −1 

k k k 

=− ( ) (|| 

0 

|| τ 

k k k k 

+ 

J 

( + )), 

k 

k k k k k k T k 

g 

( x + d ) = g ( x + d ) −g ( x ) −∇g ( x ) d . 

J J J 

k k k J k 

Step 5. Line search: 

Compute t k 

, the first number t in the sequence 

1 1 1 

{1, , , ,...} 

satisfying 

2 4 8 

2 

f ( x k + td k + t d k ) ≤ f( x k ) + αt∇f( x k ) T d 

k , (11) 

g x td t d j I 

(12) 

k k 2 k 

j 

( + + ) ≤0, ∈ . 

Step 6. Update: 

Obtain H 

k + 

by updating the positive definite matrix 

1 

H k 

using some quasi-Newton formulas. Set 

k 1 k k 2 k 

x + = x + t d + t d , and k = k+ 1 . Go back to step 1. 

k 

Throughout this paper, following basic assumptions 

are assumed. 

H2.1 The feasible set X ≠Φ, and functions f ( x ), 

g 

j 

( x), 

j∈ I are twice continuously differentiable. 

H2.2 ∀ x ∈ X , the vectors { ∇g ( x), j∈I( x)} 

are 

linearly independent. 

Lemma 2.1 Suppose that H2.1and H2.2 hold, then 

1) For any iteration, there is no infinite cycle in step 1. 

2) If a sequence { x k } of points has an accumulation 

point, then there exists a constant _ ε > 0 

ε 

kik , 

_ 

> ε for k large enough. 

j 

such that 

Proof. 

1) Suppose that the desired conclusion is false, that is 

to say, there exists some k, such that there is an infinite 

cycle in Step 1, then we obtain, ∀ i = 1, 2, , that Aki 

, 

is 

not of full rank, i.e., it holds that 

det( A A ) = 0, i = 1,2, , (13) 

T 

ki , ki , 

And by (6), we can know that Jki 

, + 1 

⊆ Jki 

, 

. Since there 

are only finitely many choices for J 

ki , 

⊆ I , it is sure that 

~ 

J ≡ J L for i large enough. From (6) and (13), 

ki , + 1 ki , k 

with i →∞, we obtain 

~ 

L k 

k = I ( x ), det( A A ) = 0. 

T 

k k 

I( x ) I( x ) 

This is a contradiction to H 2.2, which shows that the 

statement is true. 

2) Suppose K is an infinite index set such that 

* 

{ x } → x . We suppose that the conclusion is false, 

k k∈K 

i.e., there exists 

for 

~ 

L 

k 

Let 

~ 

' 

' 

K ⊆ K K 

(| | =∞ ) , such that 

ε 

ki 

→ k∈K k →∞ 

' 

, 

0, , . 

k 

Lk = Jk, i k −1. From the definition of ε 

ki , k 

, it holds, 

k∈ 

K ' , 

k large enough, that 

~ 

T T k 

~ ~ ε 

ki , k j k 

Lk 

Lk 

det( A A ) = 0, −2 ≤ g ( x ) ≤0, j∈ L . (14) 

Since there are only finitely many choices for sets 

⊆ I , it is sure that there exists 

such that 

~ ~ 

'' 

k 

, ( ) 

'' ' '' 

K ⊆ K (| K | =∞ ) , 

L ≡ L k∈ K , for k large enough. 

Denote ~ * 

A = { ∇g ( x )| j∈ L 

~ 

} , then, let 

from (14), it holds that 

j 

~ T ~ ~ 

* * 

= 

j 

= ∈ ⊆ 

k∈K '' , k →∞ , 

det( A A) 0, g ( x ) 0, j L I( x ). 

This is a contradiction to H 2.2, too, which shows that 

the statement is true. 

Lemma 2.2 For the QP sub-problem (8) at x 

k , if 

k 

d 

0 

= 0 , then x k 

k 

is a KKT point of (1). If d0 ≠ 0 , then 

k 

x computed in step 4 is a feasible direction with descent 

k 

of (1) at x . 

Proof. 

By the KKT conditions of QP sub-problem (8), we 

have 

k k k 

∇ f( x ) + Hkd0 

+ Akb 

= 0, 

k k T k 

p +∇ g ( x ) d = 0, j∈J 

, 

j j 0 

k 

k 

If d 

0 

= 0 , we obtain 

k k k 

∇ f ( x ) + A b = 0, p = 0, j∈ 

J , 

k j k 

k 

Thereby, from (7) and x ∈ X, 

∀ k implies that 

k 

k 

g ( x ) = 0, v ≥0, j∈ 

J . 

j j k 

b k B k k 

k 

f x v 

In addition, we have =− ∇ ( ) = , in a word, 

we obtain 

k k 

∇ f ( x ) + A b 

k k 

= 0, g ( x ) = 0, b ≥0, j∈ 

J , 

k j j k 

k 

Let bj 

= 0, j∈ I \ Jk 

, which shows that x k is a KKT 

point of (1). 

k 

If d0 ≠ 0 , we have 

k T k T k k 

g ( x ) d = A d = −p − δ e , 

So, 

Jk 

k k k 

k T k k T k kT k 

∇ f ( x ) d = − ( d ) H d + b p , 

0 0 k 0 



∇ f ( x ) d =∇f( x ) d −δ 

∇f( x ) A ( A A ) e 

k T k k T k k T T −1 

0 k k k k k 

1 k T k kT k 1 k T k 

≤− ( d0 ) Hkd0 + b p ≤− ( d0) 

Hkd0 < 0. 

2 2 

Thereby, we know that d 

k is a feasible descent 

k 

direction of (1) at x . 

III. GLOBAL CONVERGENCE OF ALGORITHM 

In this section, firstly, it is shown that Algorithm A 

given in section 2 is well-defined, that is to say, for every 

k, that the line search at Step 5 is always successful 

Lemma 3.1 The line search in step 5 yields a stepsize 

1 i 

t 

k 

= ( ) for some finite i = i( k) 

. 

2 

Proof. 

It is a well-known result according to Lemma 2.2. For 

(11), 

k k 2 k k k T k 

s f( x + td + t d 

) − f( x ) −αt∇f( x ) d 

k T k 2 k k T k 

=∇ f ( x ) ( td + t d 

) + o( t) −αt∇f( x ) d 

k T k 

= (1 −α) t∇ f( x ) d + o( t). 

For (12), if 

k k 

j∉ I( x ), gj 

( x ) < 0; 

k k k T k 

j∈ I( x ), gj( x ) = 0, ∇ gj( x ) d < 0, 

so we have 

k k 2 k k T k 2 k 

g 

j 

( x + td + t d 

) =∇ f( x ) ( td + t d 

) + o( t) 

k T k 

= αt∇ g 

j 

( x ) d + O( t). 

In the sequel, the global convergence of Algorithm A 

is shown. For this reason, we make the following 

additional assumption. 

H3.1 { x k } is bounded, which is the sequence 

generated by the algorithm, and there exist constants 

2 T 

2 

b≥ a > 0 , such that a|| y|| ≤ y Hk 

y ≤ b|| y|| 

, for all k 

n 

and all y∈ R . 

Since there are only finitely many choices for sets 

k k k k k 

Jk 

⊆ I , and the sequence { d0, d1 

, d , v , b } is bounded, 

we can assume without loss of generality that there exists 

a subsequence K, such that 

x → x , H → H , d →d , d →d , d 

→d 

, 

b b v v J J k K 

k * k * k * k * 

k * 0 0 

k * k * 

→ , → , 

k 

≡ ≠ Φ, ∈ , 

where J is a constant set. 

(15) 

Theorem 3.2 The algorithm either stops at the KKT 

k 

point x of the problem (1) in finite number of steps, or 

generates an infinite sequence { x k } any accumulation 

* 

point x of which is a KKT point of the problem (1). 

Proof. 

The first statement is easy to show, since the only 

stopping point is in step 3. Thus, assume that the 

algorithm generates an infinite sequence { x k }, and (15) 

holds. According to Lemma 2.2, it is only necessary to 

* 

prove that d = 

0 

0 

. Suppose by contradiction that 

* 

d0 ≠ 0 . 

Then, from Lemma 2.2, it is obvious that d * is welldefined, 

and it holds that 

* T * * T * * 

∇ f ( x ) d < 0, ∇ g 

j 

( x ) d < 0, j∈I( x ) ⊆ J (16) 

Thus, from (16), it is easy to see that the step-size t k 

obtained in step 5 are bounded away from zero on 

K , i. 

e. 

t ≥ t* = inf{ t , k∈ K} > 0, k∈ K. 

(17) 

k 

k 

In addition, from (11) and Lemma 2.2, it is obvious 

k 

that { f ( x )} is monotonous decreasing. So, according to 

* 

assumption H 2.1, the fact that { x 

k } → x implies that 

k 

* 

f( x ) → f( x ), k →∞ . 

(18) 

So, from (11), (16), (17), it holds that 

k * 

k T k 

0= lim( f ( x ) − f( x )) ≤lim( αt ∇f( x ) d ) 

x∈K 

x∈K 

1 

* T * 

≤ αt* 

∇ f( x ) d < 0, 

2 

k 

which is a contradiction thus lim d0 

= 0 . Thus, x * is a 

x→∞ 

KKT point of (1). 

IV. THE RATE OF CONVERGENCE 

Now we discuss the convergent rate of the algorithm, 

and prove that the sequence { x 

k } generated by the 

algorithm is one-step super-linearly convergent under 

some mild conditions without the strict complementarily. 

For this purpose, we add some regularity hypothesis. 

H 4.1 The sequence { x 

k } generated by Algorithm A is 

bounded, and possess an accumulation point x * , such 

* * 

that the KKT pair ( x , u ) satisfies the strong secondorder 

sufficiency conditions, i.e., 

T 2 * * 

d ∇ 

xxL( x , u ) d > 0, 

n 

* T 

∀d∈Ω 

{ d∈R : d ≠ 0, ∇ gI 

+ 

( x ) d = 0}, 

+ 

* 

Lxu ( , ) = f( x) + ug( x), I = { j∈ I: u > 0}. 

∑ 

j∈I 

j j j 

Lemma 4.1 Suppose that assumptions H 2.1-H 3.1 hold, 

then, 

1) There exists a constant ζ > 0 , such that 

T −1 

|| ( Ak 

Ak) || ≤ ζ ; 

2) lim d k 0 

= 0; lim d k = 0; lim d 

k = 0; 

k→∞ k→∞ k→∞ 

3) 

k k k k 2 

|| d || ∼|| d0 

||, || d 

|| = O(|| d || ), 

. 

k k k 3 k k 2 

|| d − d0||= O(|| d0 

|| ), || d 

|| = O(|| d || ). 

Proof. 

1) By contradiction, suppose that sequence 

T 1 

{|| ( Ak 

Ak) − ||} is unbounded, then there exists an infinite 

subset K, such that 

T −1 

|| ( A A ) || →∞, ( k∈ 

K). 

k 

k 

K 

k 



In view of the boundedness of { x k } and J 

k 

being a 

subset of the finite set I = {1, 2, , m} 

as well as 

Lemma 2.1, we know that there exists an infinite index 

' 

set K ⊆ K such that 

' ' 

T 

k k k k 

k 

x → x, J ≡ J , ∀k∈K , det( A A ) ≥ε, ε ≥ ε. 

As a result, 

T 

lim( ) ( T 

A A =∇g x) ∇g ( x), 

' 

k∈K 

k k ' 

' 

J J 

T 

det( ∇g 

'( x) ∇g '( x)) ≥ ε > 0. 

J 

J 

T −1 

Hence, we obtain T 

|| ( A ) || || 

k 

Ak → ∇g '( x) ∇ g '( x) ||, 

J J 

T −1 

this contradict || ( Ak 

Ak) || →∞, ( k∈ K). 

So the first 

conclusion 1) follows. 

k 

2) We firstly show that lim d0 

= 0 . 

k →∞ 

k 

We suppose by contradiction that lim d0 

≠ 0, then 

k →∞ 

there exist an infinite index set K and a constant σ > 0 

k 

such that || d0 

|| > σ holds for all k∈ 

K. 

Taking notice 

of the boundedness of { x 

k } , by taking a subsequence if 

necessary, we may suppose that 

k 

' 

x → x, Jk 

≡ J , ∀k∈ 

K. 

Using Taylor expansion, we analyze the first search 

inequality of Step 5, combining the proof of Theorem 3.2, 

k 

the fact that x → x * ,( k →∞ ) implies that it is true. 

k 

k 

The proof of limd 

= 0; limd = 0 are elementary 

k→∞ 

k→∞ 

from the result of 1) as well as formulas (9) and (10). 

3) The proof of 3) is elementary from the formulas (9), 

(10) and assumption H2.1. 

Lemma 4.2. Let H2.1 to H4.1 holds, 

k+ 

1 k 

lim || x − x || = 0 . Thereby, the entire sequence { x 

k } 

k →∞ 

* k 

converges to x i.e. x → x * , k →∞ . 

Proof. 

From the Lemma 4.1, it is easy to see that 

k+ 

1 k k 2 k 

lim || x − x || = lim(|| tkd + tkd 

||) 

k→∞ 

k→∞ 

k 

k 

≤ lim(|| d || + || d 

||) = 0 

k →∞ 

Moreover, together with Theorem 1.1.5 in [4], it shows 

k 

that x → x * , k →∞ 

Lemma 4.3 It holds, for k large enough, that 

* k 

* k * 

1) J 

k 

≡ I( x ) I* , b → uI = ( u , 

* j 

j∈I* ), v →( uj, j∈I* 

) 

k k T k 

2) I + ⊆ Lk = { j∈ Jk : g 

j( x ) +∇ g 

j( x ) d0 

= 0} ⊆ Jk. 

Proof. 

1) Prove J 

k 

≡ I* 

. 

On one hand, from Lemma 2.1, we know, for k large 

enough, that I * 

⊆ J k 

. On the other hand, if it doesn’t 

hold that J 

k 

⊆ I* 

, then there exist constants j 0 

and 

β > 0 , such that 

* 

g 

j 

( x ) ≤− β < 0, j 

0 

0 

∈ Jk. 

k 

So, according to d 0 

→ 0 and the functions g ( x ), 

j 

( j∈ 

I ) are continuously differentiable, for k large 

k 

enough, if v < 0 , we have 

j0 

k * T k k * T k 

+∇ 

j0 0 

=− 

j 

+∇ 

0 j0 

0 

p ( x ) g ( x ) d v g ( x ) d 

j0 

1 k 

≥− v 

j 

> 0. 

0 

2 

Otherwise, 

k * T k 

p ( x ) +∇g ( ) 

j 

j 

x d 

0 

0 

0 

k * T k 1 

k 

= g 

j 

( x ) +∇g ( ) 

0 j 

x d 

0 0 

≤− β < 0, ( vj 

≥0) 

0 

2 

which is contradictory with (8) and the fact j 0 

∈ J k 

. So, 

J 

k 

≡ I* 

(for k large enough). 

k 

* k * 

Prove that b → uI = ( u , 

* j 

j∈I* ), v →( uj, j∈ I* 

). 

k * 

For the v →( uj 

, j∈I* 

) statement, we have the 

k 

following results from the definition of v , 

k * T −1 T * 

v →−−B∇ f( x ) =−( A A ) A ∇ f( x ) 

* * * * 

In addition, since x * is a KKT point of (1), it is 

evident that 

* * 

∇ f( x ) + Au . 

* I 

= 0, u 

* I 

= −B * * 

∇ f( x ) 

T −1 T * 

i.e. uI 

=−( A 

* * 

A* ) A* 

∇ f( x ). 

k 

Otherwise, from (8), the fact that d0 → 0 implies that 

k k k k 

* 

∇ f ( x ) + Hkd0 + Akb = 0, b →−B* 

∇ f( x ) = uI 

. 

* 

The claim holds. 

2) For 

Furthermore, it has 

* 

lim( k k 

x , d ) ( x , 0) 

0 

k →∞ 

k * 

uI+ uI+ 

x→∞ 

= , we have 

Lk 

* 

⊆ I( x ) . 

lim = > 0 , so the proof is 

finished. 

In order to obtain super-linear convergence, a crucial 

requirement is that a unit step size is used in a 

neighborhood of the solution. This can be achieved if the 

following assumption is satisfied. 

H4.2 Let 

2 k k k k 

|| ( 

xxLx ( , uJ ) H) || (|| ||) 

k k 

d o d 

∇ − = , where 

= +∑ . 

k 

k 

Lxu ( , ) f( x) u g( x) 

Jk 

Jk 

j 

j∈Jk 

Lemma 4.4 Suppose that Assumption H 2.1 to H 4.2 

are all satisfied. Then, the step size in Algorithm A 

always one, i.e. tk 

≡ 1, if k is large enough. 

Proof. 

It is only necessary to prove that 

f ( x k + d k + d k ) ≤ f( x k ) + α∇f( x k ) T d 

k , (19) 

k k k 

g ( x + d + d ) ≤0, j∈I. 

(20) 

j 

* 

For (12) if j ∈ I \ I we have g ( ) 0 

* 

j 

x < , 

k k 

k 

* 

( x , d , d ) →( x , 0, 0)( k →∞ ), then, it is easy to 

obtain g ( k k k 

j 

x + d + d ) ≤0 

holds. 

If j ∈ I* 

we have 



g ( x + d + d ) = g ( x + d ) +∇ g ( x + d ) d + O(|| d 

|| ) 

k k k k k k k T k k 2 

j j j 

k k k T k k 

gj 

x + d +∇ gj 

x d + O d 

k 

d k 

+ O d 

2 

k k k T k k 

gj 

x + d +∇ gj 

x d 

+ O d 

k 

d 

= ( ) ( ) (|| |||| ||) (|| || ) 

= ( ) ( ) (|| |||| ||). 

In addition, from (9) and (10), 

k T k k T k 

∇ g 

j 

( x ) d =∇g j( x ) d0 

− δ 

k, 

k T 

k 

( ) 

k τ 

k k 

∇ g 

j 

x d = −|| d0 

|| − g 

j( x + d ) 

k k T k 

+ g 

j( x ) +∇g j( x ) d , 

so, for τ ∈ (2,3) we have 

k k k 

gj 

( x + d + d 

) 

= − || d || + g ( x ) +∇g ( x ) d − δ + O(|| d |||| d 

||) 

k τ k k T k k k 

0 j j 0 k 

k τ 

k k 

0 

(21) 

≤− || d || + O(|| d |||| d ||) ≤0. 

Hence, the second inequalities of (20) hold for t = 1 

and k is sufficiently large. 

The next objective is to show the first inequality of (19) 

holds. From Taylor expansion and taking into account 

Lemma 4.1 and Lemma 4.3, we have 

k k k k k T k 

s f( x + d + d 

) − f( x ) + α∇f( x ) d 

k T k k 1 k T 2 k T k 

= ∇ f ( x ) ( d + d ) + ( d ) ∇ f( x ) d (22) 

2 

k T k k 2 

−α∇ f( x ) d + o(|| d || ). 

On the other hand, from the KKT condition of (8) and 

the active set L 

k 

defined by Lemma 4.3 one has 

∑ 

∇ f( x ) =−H d − u ∇g ( x ) 

k k k k 

k 0 

j j 

j∈Lk 

k k k k 2 

=−Hd k 

−∑ 

uj∇ g 

j( x) + o(|| d || ), 

j∈Lk 

So, from (23) and Lemma 4.3, we have 

∇f( x ) d 

k T k 

∑ 

k T k k k T k 

( d ) Hkd uj g 

j( x ) d 

k 2 

o(|| d || ) 

j∈Lk 

k 

d 

T k k k T k 

Hkd ∑ uj g 

j 

x d0 

o 

k 

d 

2 

j∈Lk 

=− − ∇ + 

= −( ) − ∇ ( ) + (|| || ) 

k T k 

k 

∇ f( x ) ( d + d 

) 

∑ 

k T k k k T k 

k 

k 2 

k j j 

j∈Lk 

=−( d ) H d − u ∇ g ( x ) ( d + d ) + o(|| d || ), 

Again, from (21) and Taylor expansion, it is clear that 

k 2 

k k k 

o(|| d || ) = gj( x + d + d 

) 

1 

g x +∇ g x d + d 

+ d ∇ g x d + o d 

2 

where j∈ 

L , then, we obtain 

(23) 

(24) 

(25) 

k k T k k k T 2 k T k k 2 

= 

j( ) 

j( ) ( ) ( ) 

j( ) (|| || ) 

k 

∑ 

k k T k 

k 

− u ∇ g ( x ) ( d + d 

) 

j j 

j∈Lk 

k k T 

∑ uj 

g 

j( x ) 

j∈Lk 

1 ⎛ ( ) 

2 T ⎞ 

k T k ( 

k ) 

k (|| 

k || 

2 

+ d uj 

g 

j 

x d o d ), 

2 ⎜∑ 

∇ ⎟ 

+ 

j∈Lk 

= ∇ 

From (25) and (26), we have 

⎝ 

k T k 

k 

∇ f( x ) ( d + d 

) 

k T k k k 

=−( d ) H d − u ∇g ( x ) 

1 

k j j 

j∈Lk 

⎛ 

k T k 2 k T k k 2 

+ ( d ) j j( ) (|| || ) 

2 ⎜ 

u ∇ g x ⎟ 

d + o d 

j∈Lk 

⎝ 

∑ 

∑ 

Substituting (27) and (24) into (22), it holds that 

1 k T k k k 

s ( α − )( d ) Hkd + (1 −α) ∑ ujg j( x ) 

2 

1 ⎛ 

⎞ 

2 

⎜ ∑ 

⎟ 

⎝ 

j∈Lk 

⎠ 

1 k T k k k 

=( α − )( d ) Hkd + (1 −α) ∑ ujg j( x ) 

2 

⎠ 

⎞ 

⎠ 

j∈Lk 

(26) 

(27) 

+ 

k T 

( d ) 

T 

2 k k 2 k 

k k 2 

∇ f ( x ) + u ∇ g ( x ) − H d + o(|| d || ) 

j j k 

j∈Lk 

1 k T 2 k k k k 2 

+ ( d ) ( ∇ L( x , uJ 

) − H ) (|| || ). 

k k 

d + o d 

2 

Then, together assumption H 3.1 and H 4.2 as well as 

k k 

ug( x) ≤ 0, shows that 

j 

j 

1 1 

s ≤ α − a d + o d ≤ α∈ 

2 2 

Hence, the inequality of (19) holds. 

k 2 k 2 

( ) || || (|| || ) 0. ( (0, )). 

Furthermore, in a way similar to the proof of Theorem 

5.2 in [5] and in [19, Theorem 2.3], we may obtain the 

following theorem: 

Theorem 4.5 Under all above-mentioned assumptions, 

the algorithm is superlinearly convergent, i.e., the 

sequence { x k } generated by the algorithm satisfies that 

1 * * 

|| k 

k 

x + − x || = o(|| x − x ||). 

Proof. 

From Lemma 4.1 and Lemma 4.4, we can know that 

the sequence { x 

k } yielded by Algorithm A has the form 

of 

k 1 k k 

k 

x + = x + d + d 

k k k 

k 

k 

= x + d0 + ( d + d −d0) 

k 

k k 

x + d + d 

. 

0 

k 

where k 

k 

( k 

d = d + d − d ) (for k large enough) and 

k 

k 3 

d O d0 

0 

|| || = (|| || ) . Consequently, we can obtain the 

result together with Ref. [5] and [19]. 

V. NUMERICAL RESULTS 



In this section, we carry out numerical experiments 

based on the Algorithm A. The code of the proposed 

algorithm is written by using MATLAB 7.0 and utilized 

the optimization toolbox. The results show that the 

algorithm is effective. During the numerical experiments, 

it is chosen at random some parameters as follows: 

ε = 0.5, α = 0.25, τ = 2.25, H = I, 

0 0 

where I is the n× n unit matrix. H 

k 

is updated by the 

BFGS formula [2]. 

k k 

H = k+ 1 

BFGS( H 

k, s , y ), 

Where, 

^ 

k k+ 

1 k k k k 

= − = θ + −θ 

k 

s x x , y y (1 ) H s , 

^ 

m 

k k+ 1 k k k+ 

1 

k 

=∇ −∇ + ∑ j 

∇ 

j 

−∇ 

j 

j = 1 

y f( x ) f( x ) u ( g ( x ) g ( x )), 

kT 

⎧1, if y s k 

≥ 0.2( s k 

) T 

H k 

k 

s , 

⎪ 

θ = 

k T k 

⎨ 0.8( s ) Hk 

s 

⎪ , otherwise. 

kT 

k T k 

( ) k 

⎪⎩ s Hk 

s − y s 

In the implementation, the stopping criterion of Step 2 

k −8 

is changed to “If || d || ≤ 10 , STOP.” 

0 

TABLE I. 

THE DETAIL INFORMATION OF NUMERICAL EXPERIMENTS 

NO. n, m NT CPU 

HS12 2, 1 10 0 

HS43 4, 3 17 10 

HS66 3, 8 14 0 

HS100 7, 4 18 62 

HS113 10, 8 45 50 

NO. 

HS12 

HS43 

HS66 

HS100 

HS113 

TABLE II. 

THE APPROXIMATE OPTIMAL SOLUTION 

* 

x FOR TABLE I 

* 

x 

the approximate optimal solution 

(1.999999999995731, 3.000000000011285) T 

(0.000000000000000, 1.000000000000000, 

2.000000000000000, −1.000000000000000) T 

(0.184126482757009, 1.202167866986839, 

3.327322301935746) T 

(2.330499372903103, 1.951372372923884, 

-0.477541392886392, 4.365726233574537, 

-0.624486970384889, 1.038131018506466, 

1.594226711671913) T 

(2.171996371254668, 2.363682973701174, 

8.773925738481299, 5.095984487967813, 

0.990654764957730, 1.430573978920189, 

1.321644208159091, 9.828725807883636, 

8.280091670090108, 8.375926663907775) T 

This algorithm has been tested on some problems from 

Ref.[20], a feasible initial point is either provided or 

obtained easily for each problem. The results are 

summarized in Table 1 to Tabe 4. The columns of this 

table have the following meanings: 

No.: the number of the test problem in [20]; 

n: the number of variables; 

m: the number of inequality constraints; 

NT: the number of iterations; 

CPU: the total time taken by the process (unit: 

millisecond) ; 

FV: the final value of the objective function. 

TABLE III. 

THE APPROXIMATE VALUE OF THE DIRECTION 

k 

d 

0 

FOR TABLE I 

k 

|| d || 

NO. n, m 

0 

HS12 2, 1 7.329773437334 E-09 

HS43 4, 3 5.473511535838 E-09 

HS66 3, 8 8.327832675386 E-09 

HS100 7, 4 8.595133692328 E-09 

HS113 10, 8 6.056765632745 E-09 

TABLE IV. 

THE FINAL VALUE OF THE OBJECTIVE FUNCTION FOR TABLE I 

NO. 

FV 

HS12 -29.999999999999705 

HS43 -44.000000000000000 

HS66 0.518163274181542 

HS100 

6.806300573744022e+002 

HS113 24.306209068179822 


This paper proposed an improved feasible sequential 

quadratic programming (FSQP) method for nonlinear 

programs. As compared with the existing SQP methods 

which required solving the QP sub-problem with 

inequality constraints in single iteration, in order to obtain 

the feasible direction, the method of this paper is only 


programming sub-problems. Combined the generalized 

projection technique, a height-order correction direction 

is yielded by explicit formulas, which can avoids Maratos 

effect. Furthermore, under some mild assumptions, the 

algorithm is globally convergent and its rate of 

convergence is one-step super-linearly. Numerical results 

reported show that the algorithm in this paper is effective. 


The author would like to thank the editors, whose 

constructive comments led to a considerable revision of 

the original paper. 

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Finite Element Analysis Based Design of Mobile 

Robot for Removing Plug Oil Well 

Xiaojie Tian 

College of Mechanical and Electronic Engineering, China University of Petroleum, Dongying, China 

Email: tianxj20050101@163.com 

Yonghong Liu, Rongju Lin, Baoping Cai, Zengkai Liu, Rui Zhang 

College of Mechanical and Electronic Engineering, China University of Petroleum, Dongying, China 

Email: liuyh@upc.edu.cn, 1440644797@qq.com, caibaoping987@163.com, liuzengk@163.com, flyrockgod@163.com 

Abstract—In order to develop the mobile robot for removing 

the plug oil well, the robot was designed based on the wheeltype 

and leg-type robot mechanism. A well functioning 

prototype has been manufactured. To demonstrate the 

validity and the benefit of the mobile robot, supporting 

mechanism and guiding rod were chosen to design based on 

the FEM. The mathematical model of the supporting 

mechanism is established and the mechanical property is 

analyzed using the FEM. The deformation and stress of 

some components of the supporting mechanism and the 

guiding rod is investigated. The results show that the 

supporting mechanism and the guiding rod have excellent 

performance with little displacement and small stress under 

working condition. The strength and rigidity of supporting 

mechanism and the guiding rod are good enough to ensure 

the reliability of the whole robot mechanism. 

Index Terms—Mobile robot; Oil well; FEM; Supporting 

mechanism 


Mobile robots have been widely used to carry out 

manifold tasks such as industrial applications, planetary 

exploration, rescue operation and medical services in 

recent years. In the oil and gas field, there are a lot of 

pipes that need to be detected and rescued, which 

promote the development of the mobile robots. 

Most reservoirs in the oil field are low permeability 

because of oil reservoirs pollution, scale formation, 

paraffin deposit and so on. The low permeability usually 

causes the reduction of oil production [1, 2]. Accordingly 

the technology of removing plug oil well has become a 

important guarantee to protect oil reservoirs, improve oil 

production and oil recovery ratio [3]. The technology of 

removing plug oil well manly includes the chemical 

removing plug oil well and physical removing plug oil 

well. The plug removal technology with electrical pulse 

for oil reservoir is a new method developed to solve the 

problem of oil well plugging. It uses a mobile robot 

Corresponding author. Tel.: +86 546 8392303; Fax: +86 546 

8393620. Email addresses: liuyhupc@126.com, liuyh@upc.edu.cn 

(Y.H. Liu) 

putting positive and negative electrodes into the 

perforation and loads discharge pulse on them generated 

by pulse power. Owing to the special work condition of 

the mobile robot, the design of the robot is very important. 

According to a locomotive mechanism to achieve the 

desired mobility, mobile robots may be split into 

following categories: leg-type, track-type and wheel-type 

mobile robots. While the leg-type mobile robot ensures 

the most superior adaptability to all kinds of 

environments, its mechanism is quite complicated 

because active control algorithms equipped with 

additional actuators and sensors are required to steadily 

maintain its balance, which inevitably leads to slow 

movement and poor energy efficiency [4, 5]. The tracktype 

mobile robot provides acceptable mobility on an offroad 

environment by virtue of its inherently stable 

mechanism. However, the excessive friction is lost during 

changing a direction, which also results in poor energy 

efficiency [6]. Compared to other alternatives, the wheeltype 

mobile robot can be developed in the simplest 

configuration. Therefore the fast movement as well as 

good energy efficiency is guaranteed without any 

complicated control strategy. However, its adaptability to 

an environment does not seem to be sufficiently good and 

its mobility is restricted depending on both the type and 

the size of encountered obstacle [7]. 

Therefore, it is not surprising that high mobility on 

various environments have been a primary factor among 

others when evaluation the performance of the mobile 

robot. Li Peng et al. [8] proposed an adaptive mobile 

robot which had the adaptability to the change of pipe 

diameters. When the robot encounters a step, the adaptive 

mobile mechanism of the robot will change its working 

mode to surmount the obstacle. Compared to classical 

screw-driven robots, this robot does not employ the linktype 

configuration, but only uses one actuator to solve the 

low capability of surmounting obstacle. The observed 

rotation problem of the supporting parts is solved by the 

kinematical analysis of the robot. Joshi et al. [9] designed 

a spherical mobile robot, rolling on a plane with the help 

of two internal rotors and working on the principle of 

conservation of angular momentum. The robot is a classic 

nonholonomic system. The kinematic model of the 


doi:10.4304/jcp.8.6.1504-1511


system is developed using quaternion for the description 

of the orientation of the robot. The model is fully 

controllable and can be taken from any arbitrary 

configuration to any arbitrary configuration within the 

unit 3-sphere in the quaternion space. Kim et al. [10] 

presented an optimal design of a wheel-type mobile robot 

having high mobile stability as well as excellent 

adaptability while climbing stairs. The Taguchi method 

is adopted as an optimization tool and the sensitivity 

analysis with respect to design parameters is carried out 

to provide an insight to their effects on the performance 

criterion under kinematic constrains which are imposed to 

avoid undesired interference between a mobile robot and 

stairs. Aracil et al. [11] proposed the parallel robots for 

autonomous climbing along tubular structures and studied 

the dynamics of some different configurations. The 

parallel robot is based on the application of the Gough- 

Stewart (G-S) platform. Technical specifications of the 

system are presented and the control scheme is analyzed. 

Several experiments have been carried out and the 

analysis of the results has checked the high capacity of 

the parallel robot to climb on tubular structures with 

unknown trajectories. 

Based on the wheel-type mobile mechanism, an 

optimal design of the mobile robot for removing the plug 

oil well is presented. A well functioning prototype has 

been manufactured. Section 2 describes the structure of 

the mobile robot including micro-step walking 

mechanism, revolving measuring mechanism, and EDM 

removing plug mechanism. Section 3 presents the 

mathematical and FEM models for the supporting 

mechanism. Section 4 gives the analysis results. And 

Section 5 summarized the paper. 

II. STRUCTURE PRINCIPLE OF THE ROBOT 

A. The Whole Mobile Robot System 

To remove the plug oil well, the technology of EDM 

(electrical discharge machining) removing plug well is 

proposed in this paper. And the mobile robot is developed 

for this technology. The wheel-type robot has the 

simplest configuration and the fast movement. The legtype 

mobile robot has the most superior adaptability to all 

kinds of environments. Based on the merits of the wheeltype 

and leg-type robot, the mobile robot mechanism is 

designed to use in the oil pipe. Considering the rigors 

environments of the oil pipe, the configuration of the 

mechanism should be simple, small sizes, flexibility and 

reliability. Therefore the prototype of mobile robot has 

been manufactured in the laboratory. The whole mobile 

robot system for removing the plug oil well is shown in 

Fig.1 (a). 

As shown in Fig.1 (b), the mobile mechanism is mainly 

composed of micro-step walking mechanism, revolving 

measuring mechanism, and EDM removing plug 

mechanism. When the oil pipe is plugged, the moving 

robot is tripped into the oil pipe under several kilometers 

by the drawworks. Once the robot arrives at the 

designated position, the drawwoks will stop working. 

Then the micro-step walking mechanism will start 

moving to search for the perforating position because the 

designed position is not the perforating position exactly. 

The robot crawls along the inner surface of the oil pipe by 

the micro-step walking mechanism; and the revolving 

measuring mechanism rotates to detect the perforating 

position according to the sensors at the same time. Once 

the perforating position is detected, the robot will stop 

moving and halted in the oil pipe. And then the EDM 

removing plug mechanism will remove the plugged 

objects under the enormous discharge energy. Moreover 

the movement of robot is controlled by the remote control 

system and the whole working process can be monitored 

on the ground. 

Figure 1. Schematic diagram of the mobile robot. 

B. Micro-step Walking Mechanism 

The micro-step walking mechanism is one of the main 

members of the mobile robot. It can enable the mobile 

robot walk and stop in any position of the vertical oil pipe. 

It also can guide and centralize the robot in the pipe. 

Moreover it can be adaptive to different diameters of the 

pipe. 

Figure 2. Micro-step walking mechanism 

As shown in Fig 2, the micro-step walking mechanism 

contains two sets of adaptive guiding mechanism, 

supporting mechanism and electric telescopic rod. Based 

on the principle of slider-crank mechanism, the adaptive 

guiding mechanism has four cranks distributed for 90° 

that are opened by the slider pushing at the effect of the 

pretightening force of spring. It can be self-adaptive to 

different diameters of pipe. The tension wheels are 



installed on the adaptive guiding mechanism to reduce 

the friction force and help the robot tripped into the oil 

pipe smoothly. The supporting mechanism is composed 

of four supporting legs distributed for 90° and controlled 

by the electric telescopic rod. The electric telescopic rod 

can push the supporting legs of the supporting 

mechanism on to the inner surface of the pipe. And the 

friction force between supporting legs and pipe is large 

enough to ensure the robot hovering steadily for a long 

time. The electric telescopic rod also can control the 

distance per step while the robot walking, which is 

changed by controlling its telescopic direction and turnon 

time. 

C. Revolving Measuring Mechanism 

The revolving measuring mechanism is responsible for 

detecting the perforating location in the oil well and can 

revolve 360° in the pipe, which makes the measuring 

sensor detect the circumferential surface of the pipe. The 

revolving mechanism is manly composed of step motor, 

supporting bearing, shaft coupling and conducting slip 

ring, as shown in Fig 3(a). It can be revolved by the step 

motor and transmitted motion by the shaft coupling. The 

conducting slip ring is an important part to transmit the 

signals among the revolving parts with the non-revolving 

parts. There are four connecting rods between the step 

motor and the conducting slip ring. This can ensure the 

steady and centralization of the revolving measuring 

mechanism. 

current. The EDM removing plug mechanism feeds on 

the tool electrode wire used for removing plug 

continuously. This can compensate the removed tool 

electrode during the plug removing process. In one word 

the revolving measuring mechanism should have higher 

positioning accuracy to ascertain the detection of the 

perforating location. 

III. MECHANICAL MODEL FOR THE SUPPORTING 

MECHANISM 

A. Mathematical Modeling 

It is worthwhile to consider the static analysis on the 

robot mechanism so as to meet the requirement of the 

strength and rigidity of the whole mechanism. The 

supporting mechanism is composed of four pairs of 

supporting legs distributed for 90°, the upper supporting 

plate, and the lower supporting plate. The upper 

supporting plate is fixed with the electric telescopic rod 

by nut, whose position could not be moved. However the 

lower supporting plate is mobile, which is fixed with the 

central pole of the electric telescopic rod by nut. Through 

adjusting the nut of the lower supporting plate, the mobile 

robot can be adaptive to various diameters of pipe. The 

central pole of electric telescopic rod moves up and down 

by controlling the power on and off of the electric 

telescopic rod. Therefore the supporting mechanism can 

be opened to the pipe wall and enable the whole mobile 

robot stop in the vertical oil pipe. 

Figure 3. 

(a) Removing measuring mechanism; (b) EDM removing 

plug mechanism. 

Moreover the lower part of the revolving measuring 

mechanism is attached with the measuring sensor and the 

EDM removing plug mechanism distributed 

symmetrically, as shown in Fig 3(b). When the 

perforating location is detected, the revolving measuring 

mechanism will rotate 180° and the EDM removing plug 

mechanism is in alignment with the perforating location 

exactly. The measuring work is mainly depending on the 

electric eddy current sensor which is a non-contacting 

sensor and produces the output signals according to the 

eddy current. So the removing plug work can be carried 

out. The removing plug work is mainly completed by the 

electric discharge between the electrodes. And the power 

supply on the ground provides the discharge voltage and 

Figure 4. Mathematical modeling of the supporting mechanism (a) 

simplified model of the supporting mechanism; (b) mechanical analysis 

of connecting pin A. 

The supporting mechanism is the most important 

component in the whole robot mechanism and ensures the 

stability of the whole mechanism. It endures the gravity 

of the whole mechanism, the supporting force of the pipe 

wall and the friction force. In order to analyze the 

interaction forces between the supporting mechanism and 

the pipe wall during the EDM removing plug mechanism 

working condition, we established the mathematical 



model. Considering the symmetry of the mechanism, the 

mathematical model is simplified as shown in Fig. 4(a). 

The supporting leg could be simplified to the two-force 

bar [12-14]. The force on the pin A that is contacted with 

the pipe wall is analyzed in Fig. 4(b). According to the 

principle of force balance, the force can be expressed as 

∑ F ( 0) = F x + Fy 

= 0 

(1) 

( ) − F × ( θ + θ ) L 

F x = F2 × L × sin θ 1 1 sin 1 2 × (2) 

( ) 

F y = f × F2 × cos θ 2 

(3) 

F = F sin( ) 

(4) 

1 0 2 θ2 

Where F is the resultant force; F 0 is the force produced 

by the spring on the lower supporting plate; F 1 is the 

supporting force of the supporting leg; F 2 is the force on 

the supporting mechanism by the pipe wall, L is the 

length of the upper supporting leg, f is the friction 

coefficient between pipe wall and supporting mechanism; 

θ 1 is the angle of the upper supporting leg to the 

horizontal line; θ 2 is the angle of the lower supporting leg 

to the horizontal line. 

The force on the supporting mechanism by the pipe 

wall F 2 can be achieved by Equation (1), (2), (3) and (4) 

and expressed as 

F0 

sin( θ1 

+ θ2) 

F2 

= (5) 

2(sinθ 

− f cosθ 

) 

From Equation (5), the force on the supporting 

mechanism by the pipe wall F 2 is related to the force 

produced by the spring on the lower supporting plate F 0 

and the angle of the upper supporting leg to the horizontal 

line θ 1 , the angle of the lower supporting leg to the 

horizontal line θ 2 . And it has the maximum value only 

when the sum of θ 1 and θ 2 is the largest and sinθ 1 is 

almost equal to cosθ 2 . 

B. FEM Modelling 

FEM software is used to simulate and analyze stress 

and deformation of the supporting mechanism to ensure 

the strength and rigidity of the whole robot mechanism. 

When the mobile robot arrives at the perforation position, 

the electric telescopic rod is power on and the supporting 

legs are supported onto the pipe wall. The whole robot 

mechanism is hovered in the oil pipe steadily and the 

EDM plug mechanism starts to work. Therefore the 

supporting mechanism should have enough supporting 

force to support the whole mechanism. The forces on the 

supporting mechanism are mainly the electromagnetic 

force, the gravity and the acting force with the pipe wall. 

Therefore the electromagnetic force and the gravity can 

be simplified to the force acted on the upper and lower 

supporting plates only. 

The finite element model of the supporting mechanism 

is established using the 3-D modeling element SOLID98 

as shown in Fig. 5. The high precision element SOLID98 

is adopted to analyze the stress and deformation. It is 

1 

2 

because that the SOLID98 element is a ten nodes 

Tetrahedral element and more suitable for producing the 

irregular shape grid [15, 16]. In addition, the guiding rod 

is introduced to be analyzed the stress and deformation 

based on FEM. The guiding rod is throughout the 

supporting mechanism (shown in Fig. 1 (b)) and places 

an important role at the aspect of guiding and supporting 

the whole robot mechanism. Its strength and rigidity can 

ensure the stability of the whole robot mechanism. 

Stainless steel and aluminium alloy are considered for 

simulation in the FEM models because the supporting 

mechanism is manufactured with stainless steel and the 

guiding rod is manufactured with aluminium alloy. The 

stainless steel has the merit of high strength and the 

aluminium alloy has the merit of light weight [17, 18]. 

The boundary conditions are fixed on the models and 

static analyses are performed in sequence in order to 

obtain the analysis results of the stress and deformation of 

the components. 

Figure 5. FEM model of the supporting mechanism 

IV. RESULTS AND DISCUSSION 

A. Displacement and Stress of the Upper Supporting 

Plate 

The upper supporting plate is round and has four 

connecting pins with the upper supporting legs. And it is 

stationary fixed with the electric telescopic rod. So it 

manly bears the forces of the upper supporting legs when 

the supporting mechanism is supported on to the pipe 

wall. Under the effect of the electromagnetic force and 

gravity, the displacement of the upper supporting plate is 

shown in Fig. 6 (a). The maximal deformation emerges at 

the connecting points with the upper supporting legs. This 

is mainly owing to the weight of the whole mechanism 

that ultimately caused the connecting points buckled. 

Therefore the rigidity of the connecting points should be 

improved. And the manufacture of the connecting points 

could adopt the special machining technology or the 

material used could be the high strength materials 

different from the round supporting plate. The stress of 

the upper supporting plate is shown in Fig. 6 (b). It can be 

seen that the stress value of the upper supporting plate is 

very small and the maximum value is only 8.85Mpa, 

which only emerges in minor places. The stress value is 



much smaller than the allowable stress of material. 

Therefore the thickness of the upper plate can be reduced 

properly. 

places with the pipe wall. The stress between upper 

supporting leg and lower supporting leg is also very large. 

Therefore the materials with high strength and light 

weight will be a better chose for the upper supporting 

legs. 

Figure 6. Simulation results of the upper supporting plate (a) 

displacement (b) stress. 

B. Displacement and Stress of the Upper Supporting Leg 

The support and steady effect of the supporting 

mechanism mainly depends on the upper and lower 

supporting legs supporting on to the pipe wall. The upper 

supporting leg is connected to the lower supporting leg by 

pins. So the upper leg moves with the movement of the 

lower leg. Therefore the force of upper supporting leg 

mainly comes from the lower supporting leg. 

In this FEM analysis it is supported that the 

displacement between the upper supporting leg and the 

inner pipe wall is zero. And the maximal displacement of 

the upper supporting leg emerges at the intermediate 

section as shown in Fig. 7 (a). It is concluded that the 

upper supporting leg is liable to produce bending 

deformation and the material of the upper supporting leg 

can be chosen to the better material with high strength. 

Obviously, the upper supporting leg is a mainly forcing 

component and bears the effect of electromagnetic force. 

So the supporting arm could produce larger stress as 

shown in Fig. 7 (b). And the greatest stress value is to 

56Mpa which also meets the strength requirement. The 

greatest stress is mainly distributed in the contacting 

Figure 7. Simulation results of the upper supporting leg (a) 


C. Displacement and Stress of the Lower Supporting Leg 

The lower supporting leg is another important 

supporting component of the supporting mechanism. It is 

connected with the lower supporting plate and moves by 

the pushing of the lower plate. Therefore the force of 

lower supporting leg mainly comes from the lower 

supporting plate. The shape of the lower supporting leg is 

different from the upper one. It is used to support the 

upper leg. 

The lower supporting leg could be regarded as a two 

force bar whose force is in the direction of its application. 

Therefore the deformation of the lower supporting leg is 

in the direction of its application. As shown in Fig. 8 (a), 

the maximal displacement of the lower supporting leg 

emerges at the connecting joint with the lower supporting 

plate. The lower supporting leg is mainly under the effect 

of the compressive force coming from the lower plate 

because it moves with the movement of the lower 

supporting plate. As shown in Fig. 8 (b), the maximum 

stress is produced at the pins connecting place. The stress 

is a little greater due to the effect of the electromagnetic 



force by the lower supporting plate. And the greatest 

value is 48.8Mpa which also meets the strength 

requirement. In general, the size of the lower supporting 

leg is suitable and the displacement and the stress based 

on FEM are in the reasonable scope. 

uniformly at about 0.56Mpa. But the maximal stress 

value of is to 56.1Mpa. This only emerges at the 

connecting place. Also the stress concentration appears at 

the sharp angle. Therefore, the high rigidity material 

should be chosen to machine this part. And the sharp 

angle should be filleted to reduce the stress concentration 

during machining. 

Figure 8. Simulation results of the lower supporting leg (a) 


D. Displacement and Stress of the Lower Supporting 

Plate 

Comparing to the upper supporting plate, the lower 

supporting plate has a smaller size and is moveable. It is 

fixed with the central pole of the electric telescopic rod 

and moves up and down by controlling the power on and 

off of the electric telescopic rod. Under the movement of 

the lower supporting plate, the supporting mechanism can 

be adaptive to many sizes of pipe. So it manly bears the 

electromagnetic force from the electric telescopic rod 

when the supporting mechanism is supported on to the 

pipe wall. 

The maximal deformation of the lower supporting 

plate emerged at the centre as shown in Fig. 9 (a), which 

is differently from the deformation of upper supporting 

plate. This is because that the electromagnetic force and 

gravity is directly put on the centre of the lower 

supporting plate. Therefore the lower supporting plate 

should have sufficient rigidity. As shown in Fig. 9 (b) the 

stress of the lower supporting plate is almost distributed 

Figure 9. Simulation results of the lower supporting plate (a) 


E. Displacement and Stress of the Guiding Rod 

The guiding rod is located at the upper part of the 

whole robot and throughout the supporting mechanism. 

It is a centre rod to hold the stability and the verticality of 

the whole mechanism. It also bears the weight of the 

whole mechanism and belongs to a bearing bar. There are 

two holes on the guiding rod as shown in Fig. 10. The 

upper one is used to fix the cables and the lower one is 

used to install the spring retainer ring. When the robot in 

tripped into the oil pipe, the guiding rod bears the pulling 

force of the cable and the gravity of the whole 

mechanism; when the robot is hovered in the oil pipe, it 

manly bears the gravity. 

Before developing the mathematical optimum model 

of the guiding rod, the following assumption are made 

that the gravity of the whole robot is changed into the 

compressive force that is acted on the outside of the 

guiding rod lower part. So the 10kg force was acted on 



the guiding rod. According to the static analysis, the 

deformation and stress of the guiding rod is shown in Fig. 

10 (a) and Fig. 10 (b). The guiding rod mainly bears a 

tensile force and the deformation increases gradually 

from the up to down. Finally, the deformation is up to the 

maximum value of 0.0021mm at the lower part of the 

guiding rod. The material of the guiding rod should have 

enough tension strength. At the intermediate section of 

the guiding rod, the stress value is almost the same. 

However, at the two ends the stress value is a little 

smaller. And the maximal stress of 8.96Mpa emerges at 

the lower part. The maximum stress value is smaller than 

the allowable stress of aluminum alloy. Therefore it can 

meet the requirements of strength and rigidity. 

value of deformation increases from 0.0015mm to 

0.00526mm as the force increase from 5Kg to 25Kg. 

However, the deformation value is very small, which has 

no influence to the whole mechanism. 

Deformation (mm) 

0.016 

0.014 

0.012 

0.01 

0.008 

0.006 

0.004 

0.002 

0 

ø6 

ø8 

ø10 

ø12 

5 10 15 20 25 

Force(Kg) 

Figure 11. Simulation results of the guiding rod deformation under 

different forces 

Figure 10. Simulation results of the guiding rod (a) displacement (b) 

stress. 

The simulation results of the guiding rod under the 

force of 10Kg have been obtained above. Considering the 

working condition, different forces has been acted on the 

guiding rod to study its deformation. Also the diameter of 

the guiding rod is changed from 6mm to 12mm. The 

deformation of different sizes guiding rod under the force 

of 5Kg to 25Kg is shown in Fig. 11. The deformation 

increases with the increasing of the force linearly at the 

same guiding rod diameter. With the increasing of the 

diameter, the deformation is also increasing. Moreover 

the deformation difference with different sizes is more 

obvious when the force is very large. The maximum 


A mobile robot for removing the plug oil well is 

presented in this work and the prototype has been 

manufactured. The mechanical model and FEM model of 

the supporting mechanism is established. The 

deformation and stress of the upper supporting plate, the 

upper supporting leg, the lower supporting leg, the lower 

supporting plate and the guiding rod are analyzed. 

(1) The mobile robot for moving the plug oil well is 

designed based on the wheel-type and leg-type mobile 

mechanism and adaptive to various pipe sizes. The robot 

has the merits of simple structure, easy operation, good 

adaptability and reliability. 

(2) The Mathematical model of the supporting 

mechanism is established according to the force balance 

under the EDM removing plug mechanism working 

condition. The force of the supporting mechanism with 

the pipe wall can be obtained. 

(3) Based on the FEM, some components of the 

supporting mechanism are analyzed. The results of finite 

element analysis indicate that the maximum deformation 

of upper supporting plate emerges at the pins connecting 

place, the maximum deformation of upper supporting leg 

emerges at the intermittent section, the maximum 

deformation of lower supporting leg emerges at the pins 

connecting place and the maximum deformation of lower 

supporting plate emerges at the centre. And the stress of 

the components is all at the range of the allowable stress 

of materials. 

(4) The guiding rod of the robot is also analyzed 

based on the FEM. And the results prove that the guiding 

rod has a small deformation and allowable stress value. It 

can meet the requirements of strength and rigidity. The 

whole robot mechanism has a good performance. 


The authors wish to acknowledge the financial support 

of National High-Technology Research and Development 

Program of China (No.2007AA09A101), National 

Natural Science Foundation of China (No.50874115), 

Taishan Scholar project of Shandong Province 

(TS20110823), Science and Technology Development 

Project of Shandong Province (2011GHY11520) and 



Fundamental Research Funds for the Central Universities 

(11CX04031A). 

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662. 

Xiaojie Tian was born in Shandong, China, in 1985. She 

received her B. S. and M. S. degree in Mechanical Engineering 

from China University of Petroleum in 2008 and 2010 

respectively. Currently, she is a Ph.D. candidate in 

Electromechanics Engineering in China University of Petroleum, 

China. Her recent research interest is the casing cutting tool 

system. 

Yonghong Liu was born in Anhui, China, in 1965. He received 

his Ph.D. degree in Mechanical Manufacture from Harbin 

Institute of Technology, Harbin, China, in 1996. 

He is currently a professor and doctoral supervisor in College 

of Mechanical and Electronic, China University of Petroleum, 

China. He has published over 120 papers in some international 

or national journals and conferences. His current research 

interests include EDM of ceramics, expansion sand screen for 

sand control and control system of subsea drilling equipments. 

Dr. Liu is a member of China Nontraditional Machining 

Committee and Nontraditional Machining Association of 

Shandong Province. He is Prominent Young and Middle-aged 

Specialist of Shandong Province and selected in New Century 

National Hundred, Thousand and Ten Thousand Talent Project. 

Rongju Lin was born in Fujian, China, in 1988. He 

received his B. S. degree in Machinery Design and 

Manufacturing and its Automation from China University 

of Petroleum in 2010. Currently, he is a postgraduate 

student in Mechanical Engineering in China University of 

Petroleum, China. His recent research interest is 

numerical control system of casing cutting tool. 

Baoping Cai was born in Hebei, P. R. China, in 1982. He 

received his B. S. and M. S. degree in Electromechanics 

Engineering from China University of Petroleum in 2006 and 

2008 respectively. Currently, he is a Ph.D. candidate in 

Electromechanics Engineering in China University of Petroleum, 

China. His recent research interest is control system of subsea 

drilling equipments. 



Contour Error Coupled-Control Strategy based on 

Line Interpolation and Curve Interpolation 

Guoyong Zhao 

Department of Mechanical Engineering, Shandong University of Technology, Zibo, China 

Email: zgy709@126.com 

Hongjing An and Qingzhi Zhao 

Department of Mechanical Engineering, Shandong University of Technology, Zibo, China 

Email: anhongjing2006@163.com, zhaoqingzhi@sdut.edu.cn 

Abstract—In practical machining, the multi-axis actual 

dynamic performances don’t match well, which reduces the 

profile precision greatly. The computer numerical control 

(CNC) machine tools contour error coupled-control strategy 

based on line interpolation and curve interpolation is 

developed in the paper. After analyze the conventional CNC 

contour error control scheme, put forward the contour 

error coupled-control scheme based on line interpolation 

and curve interpolation; Then bring forward the contour 

error computing models based on line interpolation and 

curve interpolation; Furthermore, add the obtained contour 

error to the following error of current sampling period, and 

send the results to CNC PID position controller to calculate 

position controlled quantity in order to compensate contour 

error. The contour error compensation control 

experimentation results show that the developed approach 

can reduce contour error effectively and enhance profile 

precision further. 

Index Terms—machine tools, contour error, complex parts, 

linear interpolation, curve interpolation 


In manufacturing fields many parts have complex 

profile, and the profile includes analytic curve, piecewise 

curve, listing curve and so on [1, 2]. In general, multiaxis 

CNC machine tools are adopted to process these 

complex parts, after approximating complex cutter 

position track instruction curve with straightway [3, 4]. 

To multi-axis CNC machine tools, the profile precision is 

the important factor to determine its machining accuracy 

[5, 6]. But the profile precision relates with the matching 

degree of all the linked axes dynamic performances, and 

is decided by both each-axis position accuracy and the 

multi-axis linked accuracy [7, 8]. Because CNC machine 

tools have complicated servo drive equipments, and the 

CNC system parameters may change in practical 

machining, the multi-axis actual dynamic performances 

This project is supported by the National Natural Science 

Foundation of China (No. 51105236), and the Shandong Province 

Promotive research fund for excellent young and middle-aged scientists 

of China (No. BS2011ZZ014). 

Corresponding author: Guoyong Zhao, zgy709@126.com 

don’t match well, this reduces the profile precision [9, 10, 

11]. In contrast to the advanced single-axis servo 

controller, the cross-coupled-controller is more effective 

to enhance profile precision [12, 13, 14], which computes 

the contour error and compensates each axis servo motor 

on each sampling period [15]. 

Some research results in point have been achieved 

recently. For instance, after introducing contour error 

transfer function, Syh-Shiuh Yeh transforms the multiaxis 

cross-coupled control to a single-input-single-output 

system, and defines the distance of actual cutter position 

to the tangent on reference curve current position as 

contour error [16]. Myung-Hoon LEE puts forward a 

multi-axis contour controller based on a contour error 

vector using parametric curve interpolation, which is a 

vector from the actual tool position to the nearest point on 

the desired path [17]. Peng Chao-Chung introduces a new 

contour index (CI) aimed to arc and line profile, which 

can be looked as an equivalent contour error such that a 

reduction in CI implies a reduction in contour error [18]. 

Aimed to profile curve in plane and space, Gen Lirong 

and Wang Baoren look the distance of actual position to 

the line which links the dots of the current and the last 

sampling period as the current contour error respectively 

[19-20]. Zhao Ximei and Guo Qingding achieve threeaxis 

linked contour error control on basis of calculating 

XY, YZ, XZ axes plane coupling model [21]. Liu Yi and 

Cong Shuang develop a Frenet coordinate frame on a 

desired trajectory as the task coordinate frame, and the 

contour error is computed by the normal component of 

tracking error in the task coordinate frame [22]. Zhao 

Guoyong defines the distance between the actual cutter 

position and the nearest interpolation dot on cutter path 

curve as contour error on each sampling period [23]. 

However, because of inertia and frictional force, the 

hysteresis phenomena exist in truly CNC machine tool 

each axis movement, which is difficult to be foreseen 

accurately. As a result, the calculation error is uneasy to 

control if the hysteresis time is much longer than a 

sampling period. 

Consequently, in the CNC machining on complex parts, 

how to compute contour error with high precision and 

distribute contour error correction quantity to enhance 


doi:10.4304/jcp.8.6.1512-1519


profile accuracy on each sampling period, has been a 

crucial problem for the researchers to settle. The CNC 

machine tools contour error coupled-control strategy 

based on line interpolation and curve interpolation is 

developed in the paper, which is with stable calculation 

error, high computing precision and satisfied real-time 

characteristic. Above all, analyze the conventional CNC 

contour error control scheme; Secondly, put forward the 

contour error coupled-control scheme based on line 

interpolation and curve interpolation; Thirdly, bring 

forward the contour error computing models based on 

line interpolation and curve interpolation; Then add the 

obtained contour error to the following error of current 

sampling period, and send the results to CNC PID 

position controller to calculate position controlled 

quantity in order to compensate contour error; Finally, the 

contour error compensation control experimentations are 

done on the three-axis linked CNC test table. 

II. CONVENTIONAL CNC CONTOUR ERROR CONTROL 

SCHEME 

A. Definition of Contour Error 

The contour error is defined as the distance between 

the actual cutter trajectory and desired trajectory on the 

direction of trajectory normal. Considering a 2D arbitrary 

curve shown in Figure 1, let P* be the desired position 

vector, P be the actual position vector corresponding to 

P* on the desired contour, P 1 be position vector on the 

desired contour along the direction of curve normal that is 

closest to P, L be the tangent through P* on the desired 

contour, and θ be the angle between L and X axis. Then 

E is the following error between actual position and the 

instantaneous desired position of the cutter, i.e., 

* 

E = P − P. (1) 

Let E x be the part along X axis and E y along Y axis of E. 

And the contour error can be expressed as: 

ε = P − P. (2) 

1 

Let vector P plumbs tangent L on point P 1 *, when the 

following error E is small on low federate. The contour 

error ε is approximately equal to ε * , i.e., 

ε ≈ ε = − =− + . (3) 

* P1 

* P ExCx EyCy 

where C x and C y are computed by the following equations: 

c 

c 

y 

x 

= sin θ − E / (2 ρ) 

(4) 

x 

= cos θ + E / (2 ρ) 

(5) 

where ρ is the instantaneous radius of curvature. 

y 

Figure 1. Definition of contour error 

B. The Conventional CNC Contour Machining Scheme 

Contour error is the maximal influence factor in CNC 

machine system. When machining on complex profile 

parts, conventionally, CAD/CAM systems have to 

segment a complex curve into a huge number of small 

linear segments and send them to CNC systems for linear 

interpolation machining. But the linear interpolation 

approach isn’t able to achieve high speed and high 

accuracy at the same time. Conventional CNC contour 

machining scheme usually adopts position feedback 

controller to minimize following error, adopts feed 

forward controller to minimize tracking lag and contour 

deviation. In conventional cross-coupled control, the 

equation (3), which approximately computes contour 

error ε according to E, is adopted to establish the 

contour error model. Then the cross-coupled controller 

computes and distributes the correction signals to 

individual axis through some PID control algorithms. The 

cross-coupled control system is a multivariable, nonlinear 

and time-varying system, so it is very difficult to compute 

ε , θ and ρ . What is more, the approach to compute ε 

is only suited to condition when following error E is 

small in the low feed rate. Especially, this approach is 

difficult to compute contour error on multi-axes motion. 

So there are some difficulties in applying the approach to 

practical NC machining. The conventional two-axis CNC 

contour control scheme is shown in Figure 2. 

III. CONTOUR ERROR COUPLED-CONTROL SCHEME BASED 

ON LINE INTERPOLATION AND CURVE INTERPOLATION 

After analyzing the conventional two-axis CNC 

contour machining scheme, put forward the contour error 

coupled-control scheme based on line interpolation and 

curve interpolation. As shown in Figure 3, firstly, adopt 

the linear interpolation or curve interpolation on the 

complex parts cutter path instruction curve, and measure 

the real worktable position; Secondly, compute the 

contour error based on interpolation dots and actual 

worktable position; Thirdly, compute the contour error 

correction quantity for x, y, z axes, and output the 

correction quantity to the x, y, z axes drivers and 

worktable. 



obtaining RM and RN , the contour error ε is 

calculated according to two kinds of conditions. 

Figure 2. Conventional two-axis NC contour machining scheme 

IV. CONTOUR ERROR COMPUTING MODELS BASED ON 

LINE INTERPOLATION AND CURVE INTERPOLATION 

A. Contour Error Computing Model Based on Line 

Interpolation 

The key idea of the developed contour error computing 

model is as followed: After approximating complex parts 

cutter position track instruction curve with straightway 

according to equi-error method, calculate the current 

actual cutter position coordinates owing to the position 

measure feedback from each axis and worktable on each 

line interpolation sampling period; Compute the 

minimum distance from current actual cutter position to 

cutter position track instruction curve according to the 

actual cutter position dots and the approximate nodes, in 

other words, to calculate the contour error. 

As shown in Figure 4, the contour error computing 

model is explained more detailedly. Suppose to 

approximate part cutter track instruction curve L under 

the precision requirement with straightway AB, BC…, 

and define the actual cutter position as dot R on certain 

sampling period. Above all, obtain the three approximate 

nodes A, B, C nearest to actual cutter position R on the 

cutter position instruction curve L, and then calculate the 

distance RM , RN from actual cutter position R to 

straightway AB, BC. It is noticed that the calculation is 

complicated if transform the distance from dot to line, to 

the maximum distance from dot to plane pencil through 

the line. Consequently, the vector method with the space 

analytic geometry and vector algebra theory is adopted to 

compute the distance RM , RN from dot R to 

straightway AB, BC: 

AB× 

AR 

RM = . (6) 

AB 

BC × BR 

RN = . (7) 

BC 

The coordinates of both approximate nodes A, B, C 

and actual cutter position R are known, so the 

calculations of Equation (6) and (7) are simple. After 

(8): 

Figure 3. Contour error coupled-control scheme based on line 

interpolation and curve interpolation 

If RM 

≤ 

RN 

, obtain the contour error with Equation 

ε ≈ RM . (8) 

As shown in Figure 4, the approximate error ST is 

constant, suppose the intersection point of RM and curve 

L be dot P, then the calculation error of Equation (8) is 

MP. 

Because MP ≤ ST , the calculation error of contour 

error computing model is less than or equal to 

approximate error. 

If RM > RN , obtain the contour error with Equation 

(9): 

ε ≈ RN . (9) 

In like manner, the calculation error of contour error 

computing model is less than or equal to approximate 

error. 

x 

A 

M 

z S 

N 

R 

L 

o 

T 

Figure 4. The contour error computing model based on line 

interpolation 

B. NURBS Curve Interpolation Approach 

NURBS can express free and analytical curve and 

surface unified with the advantages of smoothness and 

local controllability, and has been applied in the 

CAD/CAM fields successfully. So it’s significant to 

investigate the NURBS curve direct interpolator in the 

CNC fields. At present except the FANUC and Siemens 

y 

P 

B 

C 



CNC system with the NURBS curve direct interpolator, 

most of the CNC systems only have linear interpolation 

and arc interpolation function. The NURBS curve 

interpolation CNC machining flow is shown in Figure 5. 

du v 

= 

dt dP( u)/ 

du 

= 

v 

. . . 

2 2 2 

( x) + ( y) + ( z) 

. (13) 

2 

du 

dt 

dv/ 

dt 

= − 

2 . . . 

2 2 2 

( x) + ( y) + ( z) 

. .. . .. . .. 

2 

v xx+ y y+ 

zz 

( ) 

. . . 

2 2 2 2 

(( x) + ( y) + ( z) ) 

(14) 

Figure 5. The NURBS curve interpolation CNC machining flow 

The NURBS curve representation is given by 

Pu ( ) = 

n 

∑ 

i= 

0 

n 

∑ 

i= 

0 

where V 

i 

is the control point, 

Bik , 

( u) 

WV 

i i 

. (10) 

B ( u) 

W 

ik , 

i 

W 

i 

is its weighting factor. 

By manipulating the values of control points and weights 

factor, a wise variety of part shapes can be designed using 

NURBS. Each point on the curve is corresponding to a 

certain knot parameter u . 

In the I th interpolation period, NURBS curve 

interpolator computes the point Pu ( 

i + 1) 

and send 

Pu ( 

i+ 1) − Pu ( 

i) 

as feed increment to servo controller. 

How to determine successive values of u 

i+ 1 

such that 

appropriate feed increment length can be accurately 

generated is important and complicated in NURBS curve 

interpolation. 

Taylor’s second-order expansion is introduced in the 

NURBS curve interpolation algorithm in this paper aimed 

at the demands of high speed, high accuracy and realtime. 

The procedure for determining successive values of 

u is summarized in the following. 

Let the NURBS curve be defined as 

Pu ( ) = ( xu ( ), yu ( ), zu ( ))' , then the knot factor u 

i+ 1 


i +1 interpolation period can be obtained: 

2 2 

du ΔT d u 

i+ 1 i u= ui 

2 u= 

ui 

u ≈ u +Δ T + . (11) 

dt 2 dt 

As shown in Equation (11), the key is to compute du 

dt 

and real-time. Define the feed rate along the NURBS 

curve as: 

Therefore, 

ds dP( 

u) 

dP( 

u) 

v = = = × 

dt dt du 

du 

dt 

. (12) 

Substituting the computed du and 

dt 

Equation (11), u 

i+ 1 

will be obtained. 

2 

du 

dt 

2 

above into 

C. Contour Error Computing Model Based on Curve 

Interpolation 

Conventionally, CAD/CAM systems have to segment a 

complex curve into a huge number of small linear 

segments and send them to CNC systems for linear 

interpolation machining. However, the experimental 

results show this approach can’t achieve high speed and 

high accuracy at the same time. Especially, the 

interpolation dots aren’t on the tracking curve. To 

overcome this problem, curve direct interpolation has to 

be adopted. Furthermore, according to interpolation dots 

in reference profile, a “three dots arc algorithm” contour 

error computing model is developed to calculate the 

minimal distance between actual dot and complex profile 

in each sampling period. 

As shown in Figure 6, suppose the reference curve be 

L and cutter actual position be M (M x , M y , M z ) in some 

sampling period. Firstly, find the nearest interpolation 

point C i from M on the curve, and suppose the two 

adjacent interpolation dots from C i be C i-1 and C i+1 points. 

It is noteworthiness that all of the three dots are on curve 

L. Secondly, suppose the centre of the circle through C i-1 , 

C i and C i+1 be point O (O x , O y , O z ), and the radius be r. 

Compute the contour error with Eq. (15): 

ε = r− OM = r− 

( M − O ) + ( M − O ) + ( M −O 

) 

2 2 2 

x x y y z z 

. (15) 

where, the contour error ε is along the OM 

direction. 

Finally, decompose vector ε along x, y and z 

coordinate axis 

ε 

x 

= ε ∗ 

M 

x 

− O 

( M − O ) + ( M − O ) + ( M −O 

) 

2 2 2 

x x y y z z 

x 

. (16) 



ε 

y 

= ε ∗ 

M 

y 

− O 

( M − O ) + ( M − O ) + ( M −O 

) 

2 2 2 

x x y y z z 

y 

. (17) 

ε 

z 

= ε ∗ 

M 

z 

− O 

( M − O ) + ( M − O ) + ( M −O 

) 

2 2 2 

x x y y z z 

z 

. (18) 

In conclusion, the contour error computing model 

approximates curve L in locality with arc properly, so 

higher precision will be achieved. 

V. CONTOUR ERROR COMPENSATION APPROACH 

Except for the three PID position controller for X axis, 

Y axis and Z axis, Myung-Hoon LEE sets up an 

additional PID contour error controller [17]. The 

calculation approach is rather complicated. In the paper 

the contour error control compensation approach is 

developed, which adds the obtained contour error to the 

following error of current sampling period, and sends the 

result to CNC PID position controller to calculate 

position controlled quantity. The CNC contour error 

calculation and compensation program flow chart is 

shown in Figure 7. 

L 

Ci-1 

M 

O 

Ci 

r 

Ci+1 

Figure 6. The contour error computing model based on curve 

interpolation 

Firstly, after receiving the N th machining program 

segment coding and pretreatment results on the K th 

sampling period, interpolate and obtain following error E x , 

E y , E z ; Secondly, adopt the contour error computing 

model, and calculate contour error ε with Equation (8), 

Equation (9) or Equation (15) ; Thirdly, decompose ε to 

ε 

x 

, ε 

y 

, ε 

z 

along X, Y, Z coordinate axes, and compute 

each axis optimal displacement of current sampling 

period after contour error compensation, which is μ , 

μ , μ ; Finally, input the μ , μ , 

y 

z 

x 

y 

μ 

z 

to X, Y, Z 

coordinate axes PID position controller respectively, and 

compute the correction quantity to control X, Y, Z 

coordinate axes servo motors. 

x 

Figure 7. The CNC contour error calculation and compensation program 

flow chart 

VI. EXPERIMENTATIONS ON CONTOUR ERROR 

COMPENSATION CONTROL 

A. The Three-axis Linked CNC Test Table 

The three-axis linked CNC test table hardware 

structure is shown in Figure 8. The CNC controller is 

made up of PC and programmable DSP movement 

control card. The PC and DSP movement control card 

communicate through USB2.0. 

The PC acts as the man-machine interface, which 

implements instruction control, code compilation, states 

display and other functions; And the interpolation, 

position control and contour error compensation control 

function are carried out on the programmable DSP 

movement control card. The Panasonic servo drivers and 

motors are adopted in the X, Y, Z axes. Both the 

interpolation period and sampling period are 4 ms. 

Figure 8. The three-axis linked CNC test table hardware structure 

B. The Contrast Experimentations on Contour Error 

Compensation 

Interpolate and machine a block of three order 

NURBS curve. The control knots are: 



A (15, 0, 15) 

B (15, 15, 15) 

C (0, 15, 0) 

D (-15, 15, -15) 

E (-15, 0, -15) 

F (-15, -15, -15) 

G (0, -15, 0) 

H (15, -15, 15) 

I (15, 0, 15) ; 

The scale factors are: 

(1, 0.6, 1, 0.5, 1, 0.5, 1, 0.6, 1) ; 

The knot vector is: 

(0, 0, 0, 0, 0.25, 0.375, 0.5, 0.625, 0.75, 1, 1, 1, 1). 

Firstly, interpolate and machine this NURBS profile 

when not adopting the introduced contour error coupledcontrol 

approach. The ideal profile curve and real profile 

are shown in Figure 9, where the contour error is 

magnified 12 times to display. The contour error when 

machining the curve is shown in Figure 10. From Figure 

10 it can be seen, the maximal contour error is near to 

0.104mm. 

Figure 11. The profile when adopting the introduced contour error 

coupled-control approach based on linear interpolation 

Finally, interpolate and machine this NURBS profile 

when adopting the introduced contour error coupledcontrol 

approach based on curve interpolation. The ideal 

profile curve and real profile are shown in Figure 13, 

where the contour error is magnified 12 times to display. 

The contour error when machining the curve is shown in 

Figure 14. From Figure 14 it can be seen, the maximal 

contour error is near to 0.044mm. 

Figure 9. The profile when not adopting the introduced contour error 

coupled-control approach 

Figure 12. The contour error when adopting the introduced contour 

error coupled-control approach based on linear interpolation 

Figure 10. The contour error when not adopting the introduced 

contour error coupled-control approach 

Secondly, interpolate and machine this NURBS 

profile when adopting the introduced contour error 

coupled-control approach based on linear interpolation. 

The ideal profile curve and real profile are shown in 

Figure 11, where the contour error is magnified 12 times 

to display. The contour error when machining the curve is 

shown in Figure 12. From Figure 12 it can be seen, the 

maximal contour error is near to 0.054mm. 

Figure 13. The profile when adopting the introduced contour error 

coupled-control approach based on curve interpolation 



Figure 14. The contour error when adopting the introduced contour 

error coupled-control approach based on curve interpolation 


The CNC machine tools contour error coupled-control 

strategy based on line interpolation and curve 

interpolation is developed in the paper, which is with 

stable calculation error, high computing precision and 

satisfied real-time characteristic. 

For one thing, bring forward the contour error 

computing model based on line interpolation and the 

contour error computing model based on curve 

interpolation; For another thing, add the obtained contour 

error to the following error of current sampling period, 

and send the results to CNC PID position controller to 

calculate position controlled quantity. The contour error 

compensation control experimentation results show that 

the developed approach can reduce contour error 

effectively and enhance profile precision further. 


The authors are grateful to the Project of the National 

Natural Science Foundation of China (No. 51105236), 

and the Shandong Province Promotive research fund for 

excellent young and middle-aged scientists of China 

(No.BS2011ZZ014). 

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240, May 2012. 

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“Performance analysis of cross-coupled controllers for 

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measurement”, International Journal of Machine Tools and 

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2010. 

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Integrated Control for Multi-Axis Motion Systems”, IEEE 

TRANSACTIONS ON CONTROL SYSTEMS 

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“A multi-axis contour error controller for free form 

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April 2004. 

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control with friction dynamics using a contour index 

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curve interpolator”, Journal of Dalian University of 

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Guoyong Zhao was born in Shandong, China in 1976. He has a 

Ph.D. in Mechanical and Electronic Engineering (2008) from 

Dalian University of Technology, Dalian, China. His main 

interest is mechanical manufacturing and automation 

technology. 

Hongjing An was born in Hebei, China in 1987. She is a master 

postgraduate majored in mechanical manufacturing and 

automation in Shandong University of Technology, Zibo, China. 

Her main interest is mechanical manufacturing and automation 

technology. 

Qingzhi Zhao was born in Shandong, China in 1962. He has a 

Ph.D. in mechanical manufacturing and automation (2005) from 

Nanjing University of Aeronautics and Astronautics, Nanjing, 

China. His main interest is mechanical manufacturing and 

automation technology. 



Research of Leaf Quality Based on Snowflake 

Theory 

Lihui Zhou 

College of Sciences, Hebei United University, Tangshan, Hebei, China 

Email: zhoulh324@163.com 

Jiajia Sun, Juanjuan An and Jun Long 

College of Sciences, Hebei United University, Tangshan, Hebei, China 

Email: zhoulh324@163.com 

Abstract—To study the leaves quality, this paper proposed 

two efficient models to analyze leaf quality, which classify 

leaves based on different shapes, leaf shapes were classified 

from the macro and micro perspectives respectively. In the 

two perspectives, influential factors were extracted and 

analyzed by factor analysis and K-means clustering. After 

comparing clustering result with actual classification result, 

misjudgment probability is found to be very low. In the 

second model, snowflake model theory was proposed. The 

theory is high similarity between snow structure and tree 

structure, and the formation of the branch copies the 

exterior characteristics of the backbone. Then the growth 

process of a tree was simulated, after calculating the 

number of smallest branches through programming, the 

total number of leaves could be calculated out. To estimate 

the tree leaf weight, two steps were divided. First step was to 

estimate the number of leaves using the snow theory. Second 

step was to estimate the area of single leaf. Finally, the area 

measurement model to flat leaf was set up to measure the 

area of the curly leaf, which was dividing the whole curly 

leaf into small pieces. 

Index Terms—factor analysis, snowflake theory, 

misjudgment probability, error evaluation 


Leaves are the material basis of photosynthesis, the 

“green factory” producing nutrients, and the medium of 

transpiration [1, 2]. It is not only the important factors of 

the growth of trees, yields of leaves and species 

characteristics, but also the important means for 

reasonable cultivation and management of trees and 

detection of occurrence and development of plant 

diseases and insect pests [3, 4]. So leaf area is the 

constant consideration in the physiological and 

biochemical research, genetic breeding, cultivation, etc., 

of trees [5]. In trees cultivation, leaf area index is 

commonly used to weigh the trees group's growth, which 

is used as the referential index for determining cultivation 

measures [6, 7]. In addition, the determination of leaf 

area ate by pests is the important content of studying pest 

damage loss. And accurate measurement of leaf area is 

the premise of studying leaf area [8]. 

There has been a variety of algorithm for determining 

surface area of a single leaf. Direct measurements have 

been made by many scholars with instrument 

measurement method, paper drawing method, digital 

image processing method [11, 12], experience formula 

and volume method. Leaves are divided into two types, 

i.e., needle-leaved tree and broad-leaved tree, for which 

different methods should be taken to measure surface 

area of their leaves. The measurement of leaf surface area 

with instrument method is simple and quick in operation. 

Structure used in the measurement could be divided into 

two types: one is leaf area structure and another is 

planimeter [13]. In paper drawing method, leaves are 

spread out on flat paper with well-distributed coordinates 

and outline of the leaves are drawn on the paper [14, 15]. 

After that grids occupied by each leaf are counted to 

calculate surface area of respective leaf. A full grid is 

counted as an area unit and less than a full grid is counted 

according to the proportion occupied by the leaf in the 

grid, i.e., 1 2,1 4 etc. 

There is a variety of shapes for leaves [16]. Leaves are 

the largest organ of trees exposed to air, with the largest 

contact area to outside environment. Therefore, 

environmental conditions have a significant impact on 

shape and structure of leaves. In the evolutionary process 

trees adapting to different ecological environment, a 

variety of ecological types of leaves is shaped. In dry 

climate and drought environment with the lack of 

moisture in soil, in order to adapt to drought environment, 

the leaf structure characteristics of trees growing in arid 

regions is working towards two aspects of development, 

i.e., reducing transpiration and saving water [17, 18]. 

Thus leaves of those trees are usually small to reduce 

transpiration of leaf area. 

Stout branches could withstand larger pressure, and 

farther the branches are away from the branch nodes the 

shorter and thinner they are [7]. The thinner the branches 

are, the lighter the weight born by the branches is and the 

smaller the leaves are. The longer the length to branch 

nodes on the same height to the ground is, the bigger the 

shapes of leaves are [8, 9]. Compared with leaves on 

branches from the same class of branch nodes, leaves on 

branches lower to the ground are bigger to enhance 


doi:10.4304/jcp.8.6.1520-1527


photosynthesis for weak sunlight they receive [10, 11]. 

Therefore, the distribution of leaves on trees and branches 

affects the shape of leaves. 

In 1999, experts have made research into branching 

angle of trees with statistical method, founding that 

branching phenotypes of trees is the mutual effect of 

genetics and environment [12, 13]. Tree species using 30 0 

as basic branching system includes: Pinnata, Spend Pear, 

Sapindus , Hong Kong Quebracho, Chung Yeung Wood, 

etc. Tree species using 60 0 as basic branching system 

includes: White Lam , Phoenix Wood , Crabapple Tree , 

Large Leaves Shi Li, etc. Tree species using 90 0 as basic 

branching system includes: Hainan Indus, Homalium 

Hainanense, Gentianales [14, 19, 20]. The bigger the 

branching angles of the trees are, the larger the leaves are. 

According to statistical data analysis, the bigger the 

branching angles are, the larger the crown of the trees are. 

Because the sunlight shining intensity of the lower leaves 

is weak, in order to increase photosynthesis, the shape of 

leaves become larger. So the shape of crown of trees 

affects the shape of leaves. The shape of leaves (general 

characteristics) is correlated to the outline and branching 

structure of trees. 

In recent years, the use of mathematical model to 

predict leaf area has become a very common method [7, 

17, 20]. With linear model, Robert Rogers Thomas M. 

Hinckley has made a research into the relationship 

between leaf weight and area of oak species and sapwood 

produced in the same year by the same tree (expressed 

with CSA). According to the research, the relationship is 

highly correlated in yellow oaks and white oaks. Through 

the research into the relationship between leaf area and 

chest diameter of arbors and shrubs, Kittredge has 

successful completed the fitting of leaf area and chest 

diameter regression equation. With BP artificial neural 

network, related work has effectively predicted the 

cucamultion volume of standing forest in Greater 

Khingan Range in [3, 13]. BP neural network method has 

been used to solve the problem of leaf shape 

classification, resulting in an accuracy of 86.67%. 

However, mathematical model is seldom used to in-depth 

research of leaf shape classification. 

To study the leaves quality, this paper proposed two 

efficient models to analyze leaf quality, which classify 

leaves based on different shapes, leaf shapes were 

classified from the macro and micro perspectives 

respectively. In the two perspectives, influential factors 

were extracted and analyzed by factor analysis and K- 

means clustering. After comparing clustering result with 

actual classification result, misjudgment probability is 

found to be very low. The second model is based on 

snowflake theory, which is high similarity between snow 

structure and tree structure, and the formation of the 

branch copies the exterior characteristics of the backbone. 

Then the growth process of a tree was simulated, after 

calculating the number of smallest branches through 

programming, the total number of leaves could be 

calculated out. To estimate the tree leaf weight, two steps 

were divided. First step was to estimate the number of 

leaves using the snow theory. Second step was to 

estimate the area of single leaf. Finally, the area 

measurement model to flat leaf was set up to measure the 

area of the curly leaf, which was dividing the whole curly 

leaf into small pieces 

II. PROPOSED CLASSIFICATION MODEL 

A. Terms Explained 

• Ground Diameter: Diameter of the trunk about 20cm 

from the ground. 

• Breast Diameter: Diameter of the trunk about 1.3m 

from the ground. 

• Clear length: height of trunk below minimum 

branches of the crown. 

• Crown of a Tree: The part above the trunk of an arbor 

tree bearing branches and leaves, like a crown. 

• Class 1 branch: Class 1 branch is the framework of a 

tree, the length and special arrangement of which plays 

a dominant role in shaping the tree. It has a certain 

growing position and azimuth attributes on the trunk. 

• Node Sections: Sections dividing by nodes on class 1 

branch. 

• Section Spacing: Distance between each layer of class 1 

branches. 

• Azimuth: The horizontal angle between each class 1 

branch and horizontal plane in verticality to the trunk. 

• Branch Angle: Vertical angle between each class 1 

branch and vertical plane parallel to the surface of the 

trunk. 

• Curvature: Curving degree of class 1 branches. 

• Physiological Age: is a concept comparing with growth 

age, representing plant life vitality, and could be 

distinguished according to the change of the structure 

of plant shapes. When the physiological age of the 

lateral branch is the same to that of the trunk, it is 

called “repeated growth” phenomenon, which accord 

with our hypothesis in snowflake theory. 

B. The Classification Model of Leaves 1 

For trees, there are internal and external causes 

affecting their leaves shape, but the internal and external 

causes all have a variety of factors, such as for internal 

causes there are genes, ways of transportation, and 

mutation, etc.; for external causes there are sunshine, 

moisture, temperature, change of worms, and soil etc. 

Therefore, classification for leaves shapes is a complex 

and delicate job. Our analysis is mainly carried out from 

two perspectives, i.e., macro and micro perspectives. 

The theoretical result shows that the shape of leaves is 

not only determined by their growth genes but also 

affected by growth environment, growth shape and 

growth scale of the trees. From this perspective, certain 

influential factors of the shape of tree leaves could be 

chosen as the indexes. According to relevant material, 

factors describing shapes of trees include: ground 

diameter, breast diameter, tree height, clear height, 

average crown diameter, south-north crown length, eastwest 

crown length, layers, internodes spacing, etc. 

According to the nine factors cluster analysis is made on 

trees to classify the similar growth shapes into one 



category. But it just makes a rough analysis on leaves 

shapes, so the next step is refined analysis. 

C. Classification Model of Leaves 2 

Then factor analysis is made on tree leaf shapes within 

one category to calculate factor score, which is used for 

clustering. This kind of clustering analysis method is 

refined. We know that there are several dozens of factors 

describing leaf shapes, such as leaf shape, leaf width, leaf 

length, leaf vein, etc., but we know that the length of 

veins in a certain extent determines leaf length and leaf 

width. And some factors could be completely described 

by other factors, so we use the method of reducing 

dimension firstly and then clustering. We use factor 

analysis to reduce the dimension of influential factors to 

get factor score for clustering. This method not only can 

distinguish well leaf shapes, but also can reduce the 

complexity of the analyzed problem. 

The mathematical model for factor analysis is as 

follows: 

⎧X1 = a11F1 + a12F2 + + a1 mFm 

+ ε1 

⎪X2 = a21F1+ a22F2 + + a2 mFm 

+ ε 

2 

⎨ 

, (1) 

⎪ 

 

⎪ 

⎩XP = aP 1F1 + aP2F2 

+ + aPmFm + ε 

P 

represented with matrix: 

⎡X1 ⎤ ⎡a11 a12 a1 m ⎤ ⎡F1 

⎤ ⎡ε1 

⎤ 

⎢ 

X 

⎥ ⎢ ⎥ 

2 

a21 a22 a 

⎢ 

2m 

F 

⎥ ⎢ 

2 

ε 

⎥ 

⎢ ⎥ ⎢ 

 

2 

= ⎥ ⎢ ⎥+ 

⎢ ⎥ . 

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 

⎥ 

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 

⎣X P⎦ ⎣aP1 aP2 

aPm⎦ 

⎣Fm 

⎦ ⎣ε 

P⎦ 

Simply recorded as: 

And meet: 

1) m≤ P; 

2) cov ( F, ε ) = 0 ; 

X = AF + ε . (2) 

⎡1 0 ⎤ 

3) D( F) 

= 

⎢ ⎥ 

⎢ 

 

⎥ 

= Im 

; 

⎢⎣0 1 ⎥⎦ 

F , , F is unrelated and variance are 1. 

1 m 

2 

⎡σ 

1 

0 ⎤ 

⎢ ⎥ 

4) D ( ε ) = ⎢ ⎥ . 

⎢ 

2 

0 σ ⎥ 

⎣ 

P ⎦ 

ε 

1, 

,ε P 

denote unrelated and different variance. 

Among them is the P dimensional random vector as 

unobservable volume, comprised by P indexes got in 

F = F , F ′ is called common 

actual observation. ( ) 

factor of ( ) 

1 

, 

m 

X = X , , 1 

X ′ 

P 

the above-mentioned 

integrated variable. A is factor loading matrix, on which 

maximum variance rotation is made with variance, so that 

the structure of A simplified. In other words, the square 

value of every column elements of loading matrix is 

made to polarization 0 or 1 or the more dispersed the 

contribution rate of public factor is the better is the result. 

Variables got from factor analysis are represented as 

linear combination of public factors: 

Xi = ai1F1+ ai2F2 + + aimFm 

+ εi 

i = 1,2, ,P 

(3) 

But usually when public factors are used to represent 

the original variables, it is more convenient to describe 

the characteristics of research object. Therefore, public 

factors are represented as linear combination of variables, 

i.e., the factor score function, namely 

F′= β X + β X + + β X 

j j1 1 j2 2 jP P 

j= 1,2, ,m 

(4) 

We calculated m factor score for each left samples. 

Use the score of these m factors as a variable value to 

cluster different leaves with the method of K-means 

Cluster. 

D. Clustering Error Estimation 

We have given the evaluation method for judging 

clustering effect. Usually we use back substitution 

misjudgment probability and cross misjudgment 

probability. If the number of misjudging samples belong 

to G 1 as belong to G2 

is N 

1 

, and the number of 

misjudging samples belong to G 2 as belong to G 1 is N 

2 

, 

the total number of samples of the two general 

classifications is n ,Then misjudgment probability is: 

N1+ 

N2 

p = (5) 

n 

Back substitution misjudgment probability 

Set G 

1 

, G 

2 

as two general classifications, 

X , , 1 

X 

m 

and Y , , 1 

Yn 

are training samples from 

G 

1 

, G 

2 

respectively, with all the training samples used as 

m+ n new samples, which is substituted gradually into 

established criterion for judging the ownership of the new 

samples. The process is called back substitution. If the 

number of misjudging samples belong to G 1 

as belong 

to G 

2 

is N 

1 

, and the number of misjudging samples 

belong to G 2 

as belong to G 1 

is N 

2 

, then misjudgment 

probability is: 

N1+ 

N2 

pˆ 

= 

m+ 

n 

Cross judgment probability 

Back to generation misjudgment probability is to 

eliminate a sample every time, and use the rest 

of m+ n− 1 training samples to establish a criterion for 

judgment, then use established criterion to make 

judgment on deleted samples. The above-mentioned 

analysis is made on each sample of those training samples, 

and uses its misjudgment proportion as the misjudgment 

probability. The specific procedure is as follows: 

1) From training samples in general classification G 1 , 

eliminate one of the samples, and use the rest of the 



samples m − 1 plus all samples in G2 

to establish 

discriminate function; 

2) Use the established discriminate function to make 

judgment on eliminated samples; 

3) Repeat steps 1), 2) until the samples in G 1 in turn 

be deleted and judged. The number of misjudged samples 

is recorded as m 

12 

; 

4) Repeat steps 1), 2), 3) for samples in G 2 , until all of 

the samples in G 2 in turn be deleted and discriminated. 

The number of misjudged samples is recorded as n 

21 

. So 

cross misjudgment probability is estimated: 

m12 + n21 

pˆ 

= 

(6) 

m+ 

n 

If clustering result is bad, the following several aspects 

of optimization could be carried out. 1) Increase sample 

capacity; 2) Increase new index variables; 3) If statistical 

data is wrong, rediscover data. 

III. PROPOSED MODEL BASED ON SNOWFLAKE THEORY 

A. Snowflake Theory 

Each snowflake on the whole is a hexagonal star, in 

which there are six trunks, and then each trunk has small 

branches, and smaller branches growing on small 

branches, and so on, as shown in figure 1 below. The 

process of shaping snowflake is copying part and the 

whole sections of it constantly. The process with the 

above mentioned of growth characteristics is called 

snowflake theory. 

Figure 1. Snowflake 

We already know in the above that each tree species 

has its own particular branching angle. We think of tree 

trunk as straight, and from another perspective, we could 

see it as a lateral branch. We all know that each lateral 

branch has the function of branching, and all of the lateral 

branches have the same status. Each layer of the branches 

will branch in accordance with certain similar rule. 

According to this growth rule, we simulate the outline of 

a tree, as shown in Fig. 2. 

Figure 2. The Tree of Computer Simulation 

According to the ideas of snowflake theory, the growth 

process of trees is established until it reaches the state of 

the tree for observation. The laws of changing between 

the state of a certain level of branching and the state of its 

sub-level of branching should be found out to for the 

recursion relationship of programming. Among a certain 

level of branch the main parameters are the quantity of 

branches, number of sections, interval of sections, 

azimuth, included angle of branching, curvature, length 

of branches, and stem. In [1] three ways of branching 

have been mentioned, i.e., single axis branching, false 

binary branching and merging axis branching. To 

simulate the growth of a tree, which way of branching it 

belongs to should be found .Then after finding out the 

law of its branching, computer could be used to simulate 

out its growth process. 

B. Ways for Branching 

We have known that the growth process of trees has 

the characteristics of self-adaptive, uncertainty, 

emergency, finality and opening. Different kinds of trees 

have different ways of branching, and the law of copying 

is different. So we will analyze ways of branching. 

Roughly there are three ways of branching for trees: 

• Single axis branching: The apical bud of the tree 

constantly grows up vigorously, shaping the stout trunk. 

And lateral buds also grow into the lateral branch, on 

which sub-branches grow again, as shown in figure 3 

below. The trunk of single axis branching is 

comparatively straight, and the growth of other branches 

at all levels is not so vigorous as it. Poplar, metasequoia, 

etc., are all within the group of single axis branching. 

False binary branching: The apical bud of the tree 

stops growing after shaping a branch. Close to the branch 

two opposite auxiliary buds simultaneously grow into a 

pair of opposite lateral branches. Then the apical bud and 

auxiliary buds on the two opposite lateral branches repeat 

the same growing process, as shown in the figure below. 

Clove, carnation and horse chestnut, etc., are all within 

the group of false binary branching. 



Figure 3. Single Axis Branching 

• In the growth process of the trees, the branching 

angle of float from a certain range. 

• In the growth process of the trees, along with the 

increase of the layer of branching, branches become 

tapered, and length of branches gradually becomes short. 

From a macro point of View l, trees have one thing in 

common in the composition of it’s shape and structure, 

namely the basic constructing element of trees are trunks, 

branches and leaves. The structuring of each basic 

element is following a same way: the trunk gives birth to 

the first layer of branches, which in turn gives birth to the 

second layer of branches, and so on. The process of 

giving birth eventually comes to leaves. In the occurrence 

and development process of the shape of the trees, 

organizations similar to the existing organizations are 

constantly copied and added to the existing ones. 

Based on the above-mentioned cloning process, eight 

basic parameters are used to be defined the structure of 

branches, as shown in Table 1. 

TABLE I. 

EIGHT BASIC PARAMETERS 

Figure 4. False Binary Branching 

Merging axis branching: The growth rate of apical bud 

of the tree slows down or the apical is dead or become 

flower bud. The auxiliary bud immediately under the 

apical bud replaces the growth of the apical bud to shape 

a branch. After that the apical bud of the branch stops 

growing and replaced by the auxiliary bud immediately 

under it. The growth process is repeated. The length of 

node section of merging axis branching is comparatively 

short, often with a tortuous shape, as shown in the figure 

below. Apple, pear, peach and apricot trees, etc., are all 

within the group of merging axis branching. 

Layer Layers of tree [2, 8] 

H Height of branches [0.0, 1.0] 

R Bottom radius of branches [0.0, 1.0] 

Alfa Branching angle [0, 90 0 ] 

K Rattion of top and bottom radius [0.0, 1.0] 

P Height of branching point [0.0, 1.0] 

Q 

Attennuation of thickness of 

branches 

[0.0, 1.0] 

M Attennuation of lenght of branches [0.0, 1.0] 

Because of the influence from many kinds of factors 

such as gravity, wind and sunshine, etc., In the process of 

their growth, the growth shape of trees in nature has got 

great uncertainty and randomness. In order to describe 

shapes of trees more vividly, in the process of 

establishing mathematical model stochastic function is 

introduced. Following is a maple tree simulated with a 

computer model, as shown in Fig. 6 and Fig. 7: 

Figure 5. Merging Axis Branching 

C. Establishment of Models 

Model assumptions are as follows: 

• In the growth process of the trees, abundant nutrients 

are supplied for the growth of each auxiliary bud. 

• In the growth process of the trees, no lateral branch 

dies. 

• Environmental factors shouldn’t increase (decrease) 

to the highest (lowest) point so that to block the normal 

growth of the plants. 

Figure 6. Simulation of maple. 

From the simulation rendering with computer, we can 

find out that the similarity degree between the simulated 

image and maple tree in real life is very high. Visibly, the 



reliability of estimating leaves number with the use of 

snowflake theory is very high. 

curvature angle following the vein is very small, and we 

divide leaves with this kind of features as shown in figure 

6(This is divided along the veins on the leaves), with the 

hypothesis that the rectangle divided out by us is in a 

plane. 

Figure 7. simulation of maple tree 

IV. SINGLE LEAF AREA ESTIMATION 

Ideas of model: we have classified leaf shapes in the 

above, so when we want to establish the model for leaf 

area estimation, we can find a representative leaf for 

analysis. In the process of analysis, mainly ideas of 

integration are used, in which, a reasonable division is 

given to leaves in different shapes in order to divided 

them into graphics, of which areas can be calculated for 

analysis; Also considerations are gave to the bending 

problem of edges of leaves when the veins become closer 

to the central line at the middle of the leaves. For the 

calculation of this model each leave is segmented along 

with the veins of the leave. 

A. Flat Leaf 

Take a typical leaf, and draw its shape on a piece of a 

coordinate paper. Take some points from the drawing and 

make a fitting to work out the leaf outline function with 

Least squares method. We can get the function images as 

shown in figure 8.Then we can calculate the leaf area S 

with curvilinear integral: 

x2 x2 

∫ 1( ) ∫ 2( ) 

(7) 

S = f x dx − f x dx 

x1 x1 

Figure 8. The simulation of flat leaf 

B. Curving Leaf 

Through observation we can find out that most of the 

curving of a leaf follows the vein and towards the middle 

line, and the curving is gentle. The appearance of a bigger 

arc of curving is unusual, so we suppose that the 

Figure 9. The division of curving leaf 

This model can only make a rough estimation of the 

area of the curving leaf, and can only have an analysis on 

leaves with specific curving characteristics. 

C. Results of Model 

N is the number of the leaves on the tree; 

S is the area of a single leaf; 

ρ is the surface density ; 

M is the weight of leaves on the maple tree. 

As for the maple used as an example, the number of 

the leaves simulated by computer belongs to 

[ 2187 , 2357 ]. 

According to statistical data: the area of a single leaf is 

about 52cm 2 , and the surface density is about 0.17g/cm 2 . 

Through calculation: 

M = ρ ⋅S⋅ N 

(8) 

The weight of the leaves on the maple tree is 19.3kg to 

20.8kg. 

We have used the method of factor analysis for 

clustering of leaf shapes to reduce the number of 

variables and simplify our research workload. We use a 

few public factors to explain complicated relationships 

existing in more variables in observation. We use 

snowflake model to catch the law tree growth, well 

estimating the leaves quality of a tree. For the calculation 

the area of a single leaf, not only the comparatively flat 

leaves are considered, but also the calculation of the area 

of leaf surface when there is the problem of surface 

curving. 

However because of time constraints, we couldn’t find 

out large amount of data for verifying our theory. 

V. CONCLUSION 

Our main objective is about leaves quality research. 

First, we classify leaves based on different shapes, then 

simulate the processes of leaf growth and calculate total 

leaves per tree. According to the area and density of a 

leaf, we can easily estimate leaves weight of a tree. 

In the process of leaf shape classification, we firstly 

analyze the diversification of leaf shape. From the genetic 



perspective, existing research data shows that long term 

environment impact changes the gene of tree and this is 

the most essential factor affected the shape of leaf. On the 

other hand, the open branch angle, DBH, knot spacing, 

crown diameter, clear length and tree height of tree will 

affect the shape of leaf. During the research, we found 

that the position of leaf also affects leaf shape. E.g., the 

smaller tip Angle will be the smaller leaf shape of the top 

branch. In the classification of leaf shape, if we directly 

classify leaf shapes according to the parameters of the 

leaf structure, it will be complicated. During analysis, we 

found the method that is using some indexes to classify 

leaf shape at first, and then classifying leaf forms again 

based on the structure of leaf. The method will reduce 

work load in the leaf shape classification, meanwhile, get 

a better result. 

In the weight estimate of tree leaf, we divide into two 

steps. First step, we estimate the number of leaves. 

During research, we found and built the snow model 

theory that is high similarity between snow structure and 

tree structure (Therefore we get conclusion). The 

formation of the branch copies the exterior characteristics 

of the backbone. In the experimental simulation, 

simulated maple tree is highly similar with the actual 

sample at the aspects of crown diameter, breast diameter, 

number of branches, length and thickness of branches and 

so on. This suggests that the snow theory can be applied 

in the three growth simulation and it can be used in tree 

growth model in the future. Second step is estimating 

area of single leaf previous methods of the leaf area 

estimation are direct measurement method and 

mathematical model analysis. However, those methods 

cannot measure curvature leaves. We had the 

corresponding improvement. Firstly, we set up area 

measurement model to flat leaf. Then the area of the curly 

leaf was measured, which is dividing the whole curly leaf 

into small pieces. Finally, we calculate total area of all 

small pieces to get result. The measurement of the curly 

leaf has especially meaning because many factors in 

nature can influence of leaf form. 


The funding organizations are Hebei Higher Social 

Science Research 2011 Annual Fund (No. SZ2011518) 

and Tangshan Municipal Bureau of Science and 

Technology research and development guide plan (No. 

111302013b, No. 111102033b). 

REFERENCES 

[1] Xu Guoxiang, Statistical forecasting and decision- making, 

1 st ed., Shanghai: Shanghai Finance University Press, 1998, 

pp.85-89. 

[2] Du Zifang, Sampling Techniques and Practices, 1 st ed., 

Beijing: Qinghua University Press, 2004, pp.123-124. 

[3] Yang Guiyuan, Huang Yili, Mathematical Modeling,Hefei: 

China science and technology university Press, 2008, 

pp.75-79. 

[4] He Shu, “Application of SOM Neural Network on leaves’ 

shape classification,” in Computer development and 

application, vol. 17, pp. 31–33, 2003. 

[5] Xia Shanzhi, Zhu Xujia, “Review of the measuring method 

in leaf area”, in Forestry survey and design, 2009, pp.15- 

17. 

[6] Jiang Youxu, Zang Runguo, “A preliminary analysis on 

elementary architecture of tropical trees in the topical 

arboretum of Jian Feng ling”, in Resource Scienc, vol. 21, 

1997 

[7] Zhang Chunying, Guo Jingfeng, Liu Lu, “P-Graph and Its 

Application,” unpublished. 

[8] Zhou Lihui, Wang Hong, Du Liping, “A Balanced 

Relationship Analysis Between Chinese Economic Growth 

and the Iron and Steel Production Based on Time Series,” 

International Conference on E-Business and E- 

Government, vol.2, pp. 192-196 , August 2010 

[9] Zhang Chunying, Guo Jingfeng, Chen Xiao, “Research on 

random walk rough matching algorithm of attribute subgraph”, 

International Conference on Advanced Materials 

and Computer Science, pp. 297-302, October 2011. 

[10] Liu Fengchun, Zhang Chunying, “λ-Operations on Packet 

Sets and the Significance of Application”, unpublished. 

[11] Thomas G C, John J E, “Algometric equations for four 

valuable trop i.cal tree species”, in Forest Ecology and 

Management, 2006, pp.351 - 360. 

[12] Zhou Lihui, “Analysis about the Effectiveness Evaluation 

of China’s Real Estate Enterprises based on DEA model”, 

International Conference on Engineering and Business 

Management, vol.1, pp. 1384-1387, October, 2011. 

[13] Yibo Tan, Zhonghui Zhao, “The Main Methods for 

Determining Leaf Area Index”, in Forest Inventory And 

Planning, 2008, pp. 33. 

[14] Yan Gao, Chengjun Zhang and Liyan Zhang, 

“Comparative Analysis of Three GARCH Models Based 

on MCMC”, The 2nd International Conference on 

Information Computing and Applications, vol., pp. 284- 

286, September, 2011. 

[15] Gao Yan, Wan Xinghuo, Liu Qiume, “Study of the 

Spillover Effect Based on the Binary GED-GARCH 

Recent Advance in Statistics Application and Related 

Areas”, Conference Proceedings of The 4th International 

Institute of Stastistics & Management Engineering 

Symposium, vol.2, pp. 134-134, July, 2011. 

[16] Yan Gao, Chengjun Zhang and Liyan Zhang, “Comparison 

of GARCH Models based on Different Distributions,” 

unpublished. 

[17] Zhou Lihui, “The Principal Component Analysis about 

Three-dimensional time series data Of Chinese information 

process”, International Conference on E-Business and E- 

Government, vol.2, pp. 4901-4904, July, 2010. 

[18] Zhang Chunying, Guo Jingfeng, Chen Xiao, “Research on 

random walk rough matching algorithm of attribute subgraph”, 

International Conference on Advanced Materials 

and Computer Science, pp. 297-302, May, 2011. 

[19] Aimin Yang, Chunfeng Liu, Jincai Chang and Li Feng, 

“TOPSIS-Based Numerical Computation Methodology for 

Intuitionistic Fuzzy Multiple Attribute Decision Making”, 

in Nformation-an International Interdisciplinary Journal, 

2010, pp. 3169-3174 

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classification algorithm with rough set”, 7th International 

Conference on Fuzzy Systems and Knowledge Discovery, 

pp. 1565-1568, August, 2010. 



Lihui Zhou was born in Tangshan of Hebei province, on 

November 12, 1980. She got Master Degree of Econometrics in 

Southwestern University of Finance and Economics in July, 

2006, which is in Sichun province, in china. Her major field of 

study is multivariate statistical analysis. 

She has been working in School of Science, Hebei United 

University since September, 2006, which located in Xin Hua 

Street 46, Tangshan, Hebei, P. R. China. Now her Current 

interests are the application of the quintile regression model. 

Jiajia Sun was born in Shijiazhuang of Hebei province, on July 

8, 1986. She is a junior student of Hebei United University. Her 

major is mathematical statistics. 

Juanjuan An was born in Xingtai of Hebei province, on May 

20, 1986. She is a junior student of Hebei United University. 

Her major is mathematical statistics. 

Jun Long was born in Zhengzhou of Henan province, on 

August 14, 1985. He is a junior student of Hebei United 

University. His major is information science. 



Oscillation Criteria for Second Order Nonlinear 

Neutral Perturbed Dynamic Equations on Time 

Scales 

Xiuping Yu 

Department of Mathematics and Physics, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou, China 

Email: xiuping66@163.com 

Hua Du 

Information Science and Engineering College, Hebei North University, Zhangjiakou, China 

Email: dhhappy88@126.com 

Hongyu Yang 

Department of Mechanic and Engineering, Zhangjiakou Vocational Technology Institute, Zhangjiakou, China 

Email: yanghy88@sina.com 

Abstract—To investigate the oscillatory and asymptotic 

behavior for a certain class of second order nonlinear 

neutral perturbed dynamic equations on time scales. By 

employing the time scales theory and some necessary 

analytic techniques, and introducing the class of parameter 

functions and generalized Riccati transformation, some new 

sufficient conditions for oscillation of such dynamic 

equations on time scales were established. The results not 

only improve and extend some known results in the 

literature, but also unify the oscillation of second order 

nonlinear neutral perturbed differential equations and 

second order nonlinear neutral perturbed difference 

equations. In particular, the results are essentially new 

under the relaxed conditions for the parameter function. 

Some examples are given to illustrate the main results. 

Dynamic equations on time scales are widely used in many 

fields such as computer, electrical engineering, population 

dynamics, and neural network, etc. 

Index Terms—oscillation, nonlinear neutral perturbed 

dynamic equation, time scales, Riccati transformation. 


The theory of time scales, which has recently received 

a lot of attention, was introduced by Stefan Higher in his 

Ph.D. thesis [1] in 1988 in order to unify continuous and 

discrete analysis. Not only can this theory of so-called 

“dynamic equations” unify the theories of differential 

equations and of difference equations, but also it is able 

to extend these classical cases “in between”, e.g., to socalled 

q-difference equations. Several authors have 

expounded on various aspects of this new theory, see the 

survey paper by Agarwal [2] and references cited therein. 

A book on the subject of time scales by Bohner and 

Peterson [3] summarizes and organizes much of the time 

scale calculus. A time scales T is an arbitrary nonempty 

closed subset of the real numbers . There are many 

interesting time scales and they give rise to plenty of 

applications, the cases when the time scale is equal to 

reals or the integers represent the classical theories of 

differential and of difference equ-ations. Another useful 

+∞ 

time scale a time scale P 

, n 0[( na b), na ( b) a] 

ab∪ 

= 

+ + + is 

wi-dely used to study population in biological 

communities, electric circuit and so on [3]. 

In recent years, there has been much research activity 

concerning the oscillation and nonoscillation of solutions 

of some dynamic equations on time scales, and we refer 

the reader to the papers [4-17] and references cited 

therein. Regarding neutral dynamic equations, Argarwal 

et al [6] considered the second order neutral delay 

dynamic quation 

Δ 

{ ( t)[( xt ( ) ctxt ( ) ( )) ] γ Δ 

α + − τ } + ftxt ( , ( − δ)) = 0. (1) 

where γ > 0 is an odd positive integer, τ andδ are position 

constants, α Δ () t > 0, and proved that the oscillation 

of (1) is equivalent to the oscillation of a first order delay 

dynamic inequality. Saker [7] considered (1) where γ ≥ 1 , 

is an odd positive integer, the condition α Δ () t > 0is 

abolished and established some new sufficient conditions 

for oscillation of (1). However the results established in 

[6-7] are only valid for the time scales , 

, or h 

, q 

, 

 

where q = { t: t = q k 

, k∈ , q > 1} . 

Sahiner et al [8] considered the general equation 

Δ γ Δ 

{ α( t)[( xt ( ) + ctx ( ) ( τ( t)) ] } + ftx ( , ( δ( t))) = 0 . (2) 

on a time scale T , where γ ≥ 1 and τ () t ≤t, δ () t ≤ t, and 

followed the argument in [6-7] by reducing the oscillation 

of (2) to the oscillation of a first order delay dynamic 

inequality and established some sufficient conditions for 

the oscillation. However one can easily see that the two 


doi:10.4304/jcp.8.6.1528-1535


examples presented in [8] to illustrate the main results are 

valid only when T= and cannot be applied when T = . 

Agarwal, O′Regan and Saker [3]considered (2) where γ ≥ 

1 is an odd positive integer and α Δ () t > 0, and established 

some new oscillation criteria by employing the Riccati 

transformation technique which can be applied on any 

time scale T and improved the results in [6, 8]. 

Bohner and Saker [9] considered perturbed nonlinear 

dynadynamic equation 

Δ 

{ ( t)(( x( t)) ) γ Δ 

} F( t, x σ ) G( t, x σ Δ 

α 

+ = , x ). (3) 

on a time scales T . Where γ > 0 is an odd positive 

integer, using Riccati transformation techniques, they 

obtained some sufficient conditions for the solution to be 

oscillatory or converge to zero. 

Following this trend, we shall study the oscillation for 

the second-order neutral nonlinear perturbed dynamic 

equations of the form 

and 

Δ γ 

{ α( t)(( x( t) + c( t) x( τ( t))) ) } 

Δ 

+ F( tx , ( δ( t))) = Gtx ( , ( δ( t)), x), 

Δ γ 

{ α( t)(( x( t) − c( t) x( τ( t))) ) } 

Δ 

+ F( tx , ( δ( t))) = Gtx ( , ( δ( t)), x). 

on an arbitrary time scales T , where γ is a quotient of 

positive odd integer, α, c is a positive real-valued rdcontinuous 

function defined on a time scales T and the 

following conditions are satisfied: 

+∞ 

1 γ 

(H1) 0 ≤ct 

( ) ≤ c < 1, 

t ( α( t)) 

0 ∫ Δ =∞, for all t ∈ T ; 

t 

0 

(H2) τ , δ : T → T satisfies τ () t ≤ t, 

for all t ∈ T , either 

δ () t ≥ t or δ () t ≤ t for all suffici-ently large t , and 

lim τ ( t) 

= lim δ ( t) 

=∞; 

t→∞ 

t→∞ 

(H3) pq , : T → are rd-continuous function, such that 

qt () − pt () > 0, for all t ∈ T ; 

2 

(H4) F : T× → 

and G : T× → 

are functions 

such that uF(, t u ) > 0and uG(, t u, v ) > 0, for all u ∈ − 

{0} , v ∈ , t ∈ T ; 

(H5) F(, tu) u γ 

≥ qt (), and Gtuv (, , ) u γ 

≤ pt () for all 

uv∈ , −{0} 

, t ∈ T . 

We note that in all the above results the conditions 

0 ≤ ct ( ) < 1, γ ≥ 1 and δ () t ≤ t are required. And some 

authors utilized the kernel function ( t− 

s 

) m 

Δ 

Δ 

(4) 

(5) 

or the general 

class of functions H (, ts) 

and obtained some oscillation 

Δs 

criteria, but the condition H ( ts , ) ≤ 0 is required. In this 

paper the study is free of these restrictions and contains 

the cases when 0< γ < 1, δ ( t) ≥t, 

and − 1 < ct ( ) ≤ 0 . In 

particular, by utilizing the general class of functions 

H (, ts ), we shall derive some sufficient conditions for 

the solutions of (4) and (5) to be oscillatory or converge 

Δs 

to zero when the condition H (, t s) ≤ 0is relaxed. Our 

results are different from the existing results for neutral 

equations on time scales that were established in [6-11, 

13-17]. Also, we give some examples to illustrate the 

main results. 

Since we are interested in the oscillatory and asymptotic 

behavior of solutions near infinity, we assume that 

sup T = ∞ , and define the time scale interval [ t 0 

, ∞) 

T 

by 

[ t , ∞ ) : = [ t , ∞) 

∩ T . By a solution of (4), we mean a 

0 T 0 

nontrivial real-valued function x (t) satisfying (4) 

for t ≥ t . A solution x (t) of (4) is said to be oscillatory if 

0 

it is neither eventually positive nor eventually negative, 

otherwise it is called nonoscillatory. Equation (4) is said 

to be oscillatory if all its solutions are oscillatory. Our 

attention is restricted to those solutions of (4) which exist 

on some half line[ t 0 

, ∞) 

and satisfy sup{| xt ( ) |: t≥ t x 

} > 0 , 

for any t ≥ t . 

x 0 

The paper is organized as follows. In next section, we 

present some basic formula and lemma concerning the 

calculus on time scales. In Section 3, we will use Riccati 

transformation techniques and the general class of 

functions H (, ts) 

and give some sufficient conditions for 

the oscillatory behavior of solutions of (4) and (5). In last 

section, we give some examples to illustrate our main 

results. 

Through this paper, we let 

γ 

d () t = max[0, d()], t Q() t = ( q() t − p())(1 t −c( δ ())), t 

+ 

∫ Δs 

α () s 

d () t = max[0, − d()], t ρ(, t u): = 

, 

− 

() s 

and for sufficiently largeT ∗ , 

δ () t 1 γ 

u 

t 1 γ 

∫ Δs 

α 

u 

1, δ ( t) t, 

∗ 

⎧ 

≥ 

β (, tT ) = ⎨ γ ∗ 

⎩ρ 

(, tT ), δ() t ≤ t. 

II. SOME PRELIMINARIES ON TIME SCALES 

A time scales T is an arbitrary nonempty closed subset 

of the real numbers . In this paper, we only consider 

time scales interval of form [ t 0 

, ∞) 

T 

, on T we define the 

forward jump operatorσ and the graininess μ by 

{ } 

σ (): t = inf s∈ T : s > t and μ(): t = σ () t − t. 

A point t ∈ T with σ () t = tis called right-dense, while t 

is referred to as being right-scattered if σ () t > t . A 

function f : T → is said to be rd-continuous if it is 

continu-ous at each right-dense point and if there exists a 

left limit in all left-dense points. The ( Δ derivative) f Δ of 

f is defined by 

Δ f ( σ ( t)) − f( s) 

f () t = lim , where Ut () = T \{ σ ()} t . 

σ () t − s 

s→t 

sU ∈ () t 



The derivative and the forward jump operator are 

related by the useful formula 

σ 

f f μ f 

Δ 

σ 

= + , where f : = f σ. 

We will also make use of the following product and 

quotient rules for the derivative of the product f g and the 

quotient f g( gg σ ≠ 0) of two differentiable functions f 

and g : 

Δ 

⎛ f ⎞ f g− 

f g 

( f g) Δ = f Δ g+ f σ 

g 

Δ 

, and ⎜ ⎟ = 

⎝ g ⎠ gg σ 

Δ 

Δ 

. (6) 

By using the product rule, the derivative of f () t = 

( t − α) m 

for m ∈ andα ∈ T can be calculated as 

m−1 

Δ 

v 

m−v−1 

() = ( σ() −α)( −α) . 

v= 

0 

f t ∑ t t 

(7) 

For a, b∈ T and a differentiable function f , the 

Cauchy integral of f Δ is defined by 

b Δ 

∫a f () t Δ t = f( b) − f( a) 

. 

The integration by parts formula follows from (6) and 

reads 

b Δ 

b b σ Δ 

∫ f () tgt () Δ t= ftgt () ()| −∫ f tg() 

tΔt. 

a 

To prove our main results, we will use the formula 

1 1 

( x γ Δ 

( t)) [ hx σ (1 h) x] γ − Δ 

= γ + − dhx ( t) 

0 

a 

a 

∫ . (8) 

which is a simple consequence of Keller′s chain rule [2]. 

Also, we need the following lemma [5]. 

Lemma 1 Assume A and B are nonnegtive constants, λ 

> 1, then 

λ 

− 

− ≤( − 1) . 

1 

AB λ A λ λ B 

λ 

The reader is referred to [2] for more detailed and 

extensive developments in calculus on time scales. 

III. MAIN RESULTS 

First, we state the oscillation criteria for (4). 

Set 

yt () = xt () + ctx () ( τ ()). t 

(9) 

Theorem 1 Assume that (H1) - (H5) hold, Furthermore, 

suppose that there exists a positive Δ−differentiable 

function g() 

t such that for all sufficiently large T ∗ 

, and 

∗ 

for all δ (T) > T , we have 

t 

∗ 

limsup ∫ ( β (, sT ) gsQs () () − 

t→∞ 

T 

α( s)(( g ( s)) ) 

( γ + 1) g ( s) 

Δ γ + 1 

+ 

γ+ 

1 γ 

) Δ s =∞. 

Then every solution of (4) is oscillatory on [ t , ∞) 

0 T 

. 

(10) 

proof Suppose (4) has a nonoscillatory solution x (t). 

without loss of generality, there exists some t 1 

≥ t 0 

, 

sufficiently large such that xt () > 0, x( τ ( t)) > 0, x( δ ( t)) 

> 0 for all t ≥ t . Hence In the view of (9), by (H1) we 

1 

get yt () > 0. from (4) and by (H2) - (H5), we have that 

Δ 

( y )) γ 

γ 

α 

Δ 

≤ −( q() t − p()) t x ( δ()) t < 0, 

and using the same proof of Theorem 1 [4], there exists 

t ≥ t such that for all t ≥ t , we have 

2 1 

2 

Δ 

⎧yt () > 0, y () t > 0, 

(11) 

⎨ 

Δ 

( ( y ) γ Δ 

γ 

⎩ α ) ≤ −( q( t) − p( t))(1 − c( δ( t))) y ( δ( t)) < 0. 

By the definition of Qt (), we get 

Δ 

( ( y ) γ 

γ 

α ) 

Δ 

≤ − Q( t) y ( δ( t)) < 0. (12) 

Make the generalized Riccati substitution 

Δ γ 

α()( t y ()) t 

wt () = gt () 

. (13) 

γ 

y () t 

By the product and quotient rules, we have for all t ≥ t2 

Δ γ Δ 

Δ gt ()( α()( t y())) t ⎛ gt () ⎞ 

Δ γ 

w () t = ( ()( t y ())) t 

γ 

+⎜ γ ⎟ α 

y () t ⎝ y () t ⎠ 

Δ γ Δ 

gt ()( α()( t y())) 

t 

= + 

γ 

y () t 

Δ 

γ Δ 

g () t g()( t y ()) t 

Δ γ σ 

( − 

)( α( t)( y ( t)) ) . 

γσ γ γσ 

y () t y () t y () t 

From (12) - (14), we obtain 

Δ 

Δ 

⎛ y( δ ( t)) ⎞ g ( t) 

σ 

w () t ≤− g() t Q() t ⎜ ⎟ + w () t 

σ 

⎝ yt () ⎠ g () t 

σ γ Δ 

gtw () ()( t y()) t 

− 

σ 

γ . 

g () t y () t 

γ 

Δ 

σ 

(14) 

(15) 

First consider the case when δ () t ≥ t . For all large t, 

Δ 

from y () t > 0, we have 

which implies that 

y( δ ( t)) 

≥ 1 , 

yt () 

Δ 

σ γ Δ 

Δ 

g () t σ g() t w ()( t y ()) t 

w () t ≤− g() t Q() t + w () t − . (16) 

σ σ γ 

g () t g () t y () t 

Next consider the case when δ () t ≤ t, for all large t. By 

using α( y 

Δ ) 

γ 

is strictly decreasing on [ t 2 

, ∞ ) , we can 

choose t ≥ t such that δ () t ≥ t , for t ≥ t . Then we 

3 2 

2 

3 

obtain 



and hence 

Δ γ 1 γ 

t ( α( sy ) ( s)) ) 

y() t − y( δ ()) t = ∫ 

Δs 

δ () t 

1 γ 

α () s 

≤ 

t y t 

Δs 

α () s 

Δ 

γ 1 γ t 

( αδ ( ( ))( ( δ( ))) ) ∫ , 

δ () t 1 γ 

Δ 

γ 1 γ 

yt () ( αδ ( ())( t y ( δ()))) 

t t Δs 

≤ 1+ ∫ . (17) 

δ () t 1 γ 

y( δ( t)) y( δ( t)) α ( s) 

Also, for t ≥ t , we can see that 

3 

≥ 

1 γ 

Δ γ 

δ () t 

y( δ( t)) > y( δ( t)) − y( t ) = s 

2 ∫ 

Δ 

t2 

1 γ 

Δs 

α () s 

1 γ 

Δ 

γ δ () t 

( αδ ( ( t))( y ( δ( t))) ) ∫ , 

t2 

1 γ 

and therefore 

( αδ ( ( ))( ( δ( ))) ) 

( α( sy ) ( s)) ) 

α () s 

1 γ 

Δ 

γ 

t y t δ () t s 

≤ ⎜∫t2 

1 γ 

y( δ( t)) α ( s) 

From (17) and the above inequality, we have 

⎛ 

⎝ 

Δ 

⎞ 

⎟ 

⎠ 

−1 

yt () t Δs δ () t Δs 

−1 

≤ ∫ ( ) 

t2 1 γ ∫ , (18) 

t2 

1 γ 

y( δ( t)) α ( s) α ( s) 

therefore we get the desired inequality 

y( δ ( t)) 

≥ ρ(, tt), 

for t ≥ t . (19) 

2 

3 

yt () 

Using (19) in (15), when δ () t ≤ t, we get 

Δ 

Δ 

γ 

g () t σ 

w () t ≤− ρ (, t t ) g() t Q() t + w () t 

2 

σ 

g () t 

σ γ Δ 

gtw () ()( t y()) t 

− 

σ 

γ . 

g () t y () t 

From (16), (20) and the definition of β (, tt) 

, we have 

2 

By (8), we obtain 

Δ 

Δ 

g () t σ 

w () t ≤− β (, t t ) g() t Q() t + w () t 

2 

σ 

g () t 

σ γ Δ 

gtw () ()( t y()) t 

− 

σ 

γ . 

g () t y () t 

y t γ hy h y dh y t 

γ Δ 1 σ γ−1 

Δ 

( ( )) = ∫ [ + (1 − ) ] ( ) 

0 

σ γ−1 

Δ 

⎧γ( y ( t)) y ( t),0< γ ≤1, 

≥ ⎨ 

⎩γ 

yt y t γ ≥ 

γ −1 

Δ 

( ( )) ( ), 1. 

Since α( y 

Δ ) 

γ 

is strictly decreasing on[ t 2 

, ∞ ), we get 

γ 

( y ( t)) 

Δ 

⎧γα 

t y t y t 

⎪ α () t 

≥ ⎨ 

⎪ γα t y t y t 

⎪ 

⎩ α () t 

( 

σ 1 γ 

( )) ( 

σ γ−1 

( )) ( 

Δ σ 

( )) 

1 γ 

( 

σ 1 γ γ−1 

( )) ( ( )) ( 

Δ σ 

( )) 

1 γ 

. 

,0< γ ≤1, 

, γ ≥ 1. 

(20) 

(21) 

From the last inequality and (21), if 0< γ ≤ 1, we have 

Δ 

Δ 

g () t σ 

w () t ≤ − β (, t t ) g() t Q() t + w () t − 

2 

σ 

g () t 

σ 11 + γ σ 

γ gt ()( w()) t ⎛ y () t ⎞ 

1 γ σ 1+ 

1 γ ⎜ ⎟ 

α ()( t g ()) t ⎝ y() 

t ⎠ 

whereas if γ > 1 , we find that 

Δ 

Δ 

g () t σ 

w () t ≤− β (, t t ) g() t Q() t + w () t 

2 

σ 

g () t 

γ gt w t y t 

− 

α ()( t g ()) t y() 

t 

σ 11 + γ σ 

()( ()) () 

1 γ σ 1+ 

1 γ . 

Δ 

And by using y () t > 0, we obtain that 

Δ 

Δ 

g () t 

+ σ 

w () t ≤− β (, t t ) g() t Q() t + w () t 

2 

σ 

g () t 

γ gt () 

− 

α ()( t g ()) t 

1 γ σ λ 

γ 

, 

σ λ 

( w ( t)) , 

where λ : = ( γ + 1) γ . Define A ≥ 0 and B ≥ 0 

by 

σ λ 

1( γ +1) Δ 

λ γ gt ()( w()) 

t 

λ− 1 

α ()( t g ()) t 

+ 

A : = , B : = , 

1 γ σ λ 1 λ 

α ( t)( g ( t)) λ( γg( t)) 

then using Lemma 1, we obtain 

(22) 

g 

Δ 1 

() t () 

()(( ())) 

() ( ()) t g Δ t 

γ + 

σ gt 

σ λ α 

+ 

γ 

+ 

w t − 

w t ≤ 

. 

σ 1γ σ λ γ+ 

1 γ 

g () t α ()( t g ()) t ( γ + 1) g () t 

From the last inequality and (22), we have 

Δ γ + 1 

Δ 

α()(( t g ())) t 

+ 

w () t ≤ 

−β 

(, t t ) g() t Q() 

t . 

γ+ 

1 γ 

2 

( γ + 1) g ( t) 

Integrating both sides from t 3 

to t, we get 

Δ γ + 1 

t 

α( s)(( g ( s)) ) 

+ 

∫ [ β ( s, t ) g( s) Q( s) − 

] Δs 

t3 

2 γ+ 

1 γ 

( γ + 1) g ( s) 

≤ wt ( ) −wt ( ) ≤ wt ( ), 

3 3 

which leads to a contradiction to (10). This completes the 

proof. 

Corollary 1 Assume that (H1) - (H5) hold, Furthermore, 

suppose that for all sufficiently large T ∗ , and for δ ( T ) > 

T ∗ 

, 

we have 

t 

∗ α() 

s 

limsup ∫ ( sβ 

( s, T ) Q( s) − ) Δ s =∞. 

t→∞ 

T 

γ+ 

1 γ 

( γ + 1) s 


0 T 

. 



T ∗ 

, 

we have 

t 

∗ 

limsup ∫ β ( sT , ) Qs ( ) Δ s=∞. 

t→∞ 

T 




0 T 

. 

We next study a Philos-type oscillation criteria for (4). 

First, Let us introduce the class of functions R which 

will be extensively used in the sequel. 

2 

Let D= {( ts , ) ∈T : t≥ s≥t} 

.The function H ∈ Crd 

( D, ) 

is said to belong to the class R by H ∈R, if 

H (,) tt 0, t t 

0 

= ≥ ; H (, ts) 0, t s t 

0 

0 

> > ≥ , (23) 

Δs 

and H has a continuous Δ− partial derivative H (, ts) 

with respect to the second variable. 

Theorem 2 Assume that (H1) - (H5) hold. Let g (t) be 

as defined in Theorem 1, and Hh , ∈C rd 

( D, ) 

such that 

H ∈R. Furthermore, suppose that there exists a positive 

rd-continuous function ϕ() 

t satisfies 

Hts (, ) 

≤ ϕ() 

s , (24) 

Htt (, ) 

0 

Δ 

Δ g () s h(,) 

t s 

s γ ( γ+ 

1) 

−H (, t s) − H(, t s) = ( H(, t s)) 

, (25) 

σ 

σ 

g () s g () s 

and for all sufficiently largeT ∗ , we have 

1 t 

∗ 

limsup ∫ [ β (, s T ) g() s Q() s H(,) 

t s 

t→∞ 

t0 

Htt (, ) 

0 

α()( s h (,)) t s 

− ] Δ s =∞. 

γ + 1 

− 

γ+ 

1 γ 

( γ + 1) g ( s) 

(26) 


0 T 

. 

Proof Suppose (4) has a nonoscillatory solution x (t), 

without loss of generality, say xt () > 0, x( τ ( t)) > 0, 

x( δ ( t)) > 0, for all t ≥ t , for some t 

1 

1 

≥ t 0 

. By (H2) - (H5), 

proceed as in the proof of Theorem 1, we get that (11) 

holds for all t ≥ t . Again we define wt () as in the proof of 

1 

Theorem 1, then there exists t 2 

≥ t 1 

, sufficiently large such 

that for all t 

∗ 

≥ t and for t t ∗ 

Δ 

≥ , (22) holds and let g () t 

2 

+ 

Δ 

be replaced by g () t in (22), thus 

Δ 

Δ g () t σ 

β (, tt) gtQt () () ≤− w() t + w() 

t 

2 

σ 

g () t 

γ gt () 

− 

α ()( t g ()) t 

1 γ σ λ 

σ λ 

( w ( t)) . 

(27) 

Multiplying both the sides of (27), with t replaced by s, 

by H (t, s) and integrating with respect to s from t ∗ to t, 

we obtain 

t 

∫ ∗ Hts (,) β (, st) gsQs () () Δs≤ 

2 

t 

Δ 

t 

Δ 

t g () s σ 

−∫ 

∗H (, tsw ) ( s) Δ s+ ∗Hts (, ) w( s) 

s 

t 

∫ 

Δ 

t 

σ 

g () s 

t 

γ gs () 

σ λ 

−∫ 

∗ Hts (, ) ( w( s)) Δs. 

t 

1 γ σ λ 

α ()( s g ()) s 

Integrating by parts formula and using (23) and (25), 

we get 

t 

∗ ∗ 

∫ ∗ Hts ( , ) β( st , ) gsQs ( ) ( ) Δs≤ Htt ( , ) wt ( ) + 

t 

2 

1 λ 

t hts (, )( Hts (, )) σ γ Htsgs (, ) ( ) 

(28) 

− 

σ λ 

∫ ∗[ w ( s) − 

( w ( s)) ] Δs. 

t 

σ 1 γ σ λ 

g () s α ()( s g ()) s 

And applying Lemma 1, we obtain 

1 λ 

(, )( (, )) 

− 

σ γ (, ) ( ) σ λ 

w () s − 

( w ()) s 

σ 1 γ σ λ 

h t s H t s Htsgs 

g () s α ()( s g ()) s 

α 

≤ 

( γ + 1) g ( s) 

γ + 1 

( h ( t, s)) ( s) − 

γ+ 

1 γ . 

From the last inequality and (24), (28), we have 

1 

( h ( t, s)) α( s) 

[ (, s t ) g() s Q() s H(,) t s ] Δs 

Htt g s 

γ + 1 

t 

− 

∫ β 

− 

t0 

2 γ+ 

1 γ 

(, ) ( γ + 1) ( ) 

0 

∗ 

∗ ∗ t 

≤ ϕ( t ) w( t ) + ∫ ϕ( s) β( s, t ) g( s) Q( s) Δ s T , we have 



t 

∗ 

limsup ∫ [ β ( s, T ) g( s)( q( s) − p( s)) 

t→∞ 

T 

Δ γ + 1 

α()(( s g ())) s 

+ 

− ] Δ s =∞. 

γ+ 

1 γ 

( γ + 1) g ( s) 

(29) 

Then every solution of (5) is either oscillatory on [ t , ∞) 

0 T 

or tends to zero. 

proof Suppose that x is an eventually positive solution 

of (5), say xt () > 0, x( τ ( t)) > 0, x( δ ( t)) > 0for all t ≥ t for 

1 

some t ≥ t . We consider only this case, because the 

1 0 

proof for the case that x is eventually negative is similar. 

In the view of (5), by (H2) - (H5), and there exists 

t ≥ t such that for all t ≥ t , we have 

2 1 

2 

Δ 

( ( z ) γ 

γ 

α ) 

Δ 

≤−( q( t) − p( t)) x ( δ( t)) < 0 , (30) 

γ 

then α( z 

Δ ) is strictly decreasing on [ t 2 

, ∞ ). Hence z (t) 

Δ 

and z () t are of constant sign eventually. We claim that 

x() 

t is bounded. If not, there exists { t k 

} ⊆ [ t 2 

, ∞ ), such 

that lim t =∞ ,lim x( t ) =∞, 

and 

k→∞ 

k 

k→∞ 

k 

x( t ) = max{ x( s): t ≤ s≤ 

t }. 

k 

Since lim τ ( t ) =∞, we can choose a large k such that 

k→∞ 

0 

k 

τ ( t ) > t , and by (H2), we obtain that 

k 

x( τ( t )) = max{ x( s) : t ≤ s≤τ( t )} 

Therefore, for all large k, 

k 

0 

0 

≤ max{ x( s) : t ≤ s ≤ t } = x( t ). 

z( τ ( t )) ≥ x( t ) −c x( τ ( t )) ≥ (1 − c ) x( t ) 

k k 0 k 

0 k 

, 

and lim zt ( ) =∞. From (H1) and (30), as in the proof of 

k→∞ 

k 

Theorem 1 [4], there exists t 3 

≥ t 2 

such that for all t ≥ t , 

3 

we have 

In view of (5), (30) and (31), we get 

0 

k 

Δ 

zt () > 0, z () t > 0. (31) 

Δ 

( ( z ) γ 

γ 

α ) 

Δ 

≤−( q( t) − p( t)) z ( δ( t)) < 0. (32) 

Now by using the same proof of Theorem 1, we get a 

contradiction with (29). Thus x (t) is bounded and hence z 

(t) is bounded. 

Also, by using (H1) and the same proof of Theorem 1 

Δ 

in [4], there exist t 4 ≥ t 3 such that z () t > 0on [t 4 , ∞). 

There are two cases. 

Δ 

Case 1 zt () > 0 and z () t > 0. As in the proof of 

Theorem 1, we get a contradiction with (29). 

Δ 

Case 2 zt () < 0and z ( t) > 0 . We claim lim xt ( ) = 0 . 

k 

k 

k 

t→∞ 

Assume not, then there exists { t } ⊆[ t , ∞) 

such that 

k 5 

lim t =∞, 

lim xt ( ) = : b> 0 and x( t ) = max{ x( s): 

t ≤ s 

k 

k 

k 

0 

k→∞ 

t k 

k→∞ 

≤ }. But, by x( τ ( t )) ≤ x( t ), we get 

k 

k 

0 > zt ( ) ≥ xt ( )(1 −c) →b(1 − c) > 0, as k→∞. 

k 

k 

0 0 

Which is a contradiction. This completes the proof. 



T ∗ 

, 

we have 

t 

∗ 

α() 

s 


( s, T )( q( s) − p( s)) − ) Δ s =∞. 

t→∞ 

T 

γ+ 

1 γ 

( γ + 1) s 


0 T 




T ∗ 

, 

we have 

t 

∗ 

limsup ∫ β (, sT)(() qs − ps ()) Δ s=∞. 

t→∞ 

T 


0 T 


We next study a Philos-type oscillation criteria for (5). 

Theorem 4 Assume that (H1) - (H5) hold. Let g (t) be 

as defined in Theorem 1, and H, h∈C rd 

( D, ) 

such that 

H ∈R . Furthermore, suppose that there exists a 

positive rd-continuous function ϕ () t such that (24), (25) 

hold, and for all sufficiently largeT ∗ , we have 

1 t 

∗ 

limsup ∫ { β ( s, T ) g( s)( q( s) − p( s)) H( t, s) 

t→∞ 

t0 

Htt (, ) 

0 

α()( s h (,)) t s 

− } Δ s =∞. 

γ + 1 

− 

γ+ 

1 γ 

( γ + 1) g ( s) 

(33) 


0 T 


Proof Suppose that (5) has a nonoscillatory solution x 

(t), without loss of generality, say xt () > 0, x( τ ( t)) > 0, 

x( δ ( t)) > 0, for all t ≥ t , for some t 

1 

1 

≥ t 0 

. By (H2) - (H5), 

we obtain that (30) holds for all t ≥ t , and zt () and 

1 

Δ 

z () t are of constant sign eventually. Similar to the proof 

of Theorem 3, we claim that x() 

t is bounded. If not, there 

exists{ t } ⊆[ t , ∞ ), for all large k, there exists t 

k 1 

2 

≥ t 1 

, such 

that (31) and (32) hold for t ≥ t . Again we define wt () as 

2 

in the proof of Theorem 1, then there exists t 3 

≥ t 2 

, 

sufficiently large such that for t 

∗ 

≥ t and for t ≥ t ∗ 

, we 

3 

find 

β (, tt) gt ()( qt () − pt ()) 

3 

Δ g () t γ g() 

t 

≤− w () t + w () t − 

( w ()). t 

g t t g t 

Δ 

σ σ λ 

σ 1 γ σ λ 

() α ()( ()) 

And similar to the proof of the theorem 3, we obtain 

1 t 

∫ [ β ( s, t ) g( s)( q( s) − p( s)) H( t, s) 

t 

Htt (, ) 

0 3 

0 

γ + 1 

( h ( t, s)) α( s) − 

γ+ 

1 γ ] s ( 

∗ 

ϕ t ) w ( 

∗ 

t ) 

− Δ ≤ + 

( γ + 1) g ( s) 

(34) 



∗ 

t 

ϕ s β s t g s q s p s s 

t0 3 

∫ 

() (, ) ()(() − ()) Δ 0on [ t 

4 

4 

, ∞ ) . And then there are 

two cases of Theorem 3. As in the proof of Theorem 3, if 

the case 1 holds, we get a contradiction with (33) ; if the 

case 2 holds, we obtain lim xt ( ) = 0 . This completes the 

t→∞ 

proof. 

In Theorem 4, let g (t) =1 and H ( ts , ) = ( t− s) m 

, we 

have the following result. 

Corollary 6 Assume that (H1) - (H5) hold, and m ≥ 1 , 

for all sufficiently largeT ∗ , we have 

1 t 

m 

∗ 

limsup ( ) ( , )( ( ) ( )) 

m ∫ t−s β sT qs − ps Δ s=∞. 

t→∞ 

t0 

t 


0 T 


IV. EXAMPLES 

In this section, we give some examples to illustrate our 

main results. Define 

⎧1 , δ ( t) ≥ t, 

ξ () t = ⎨ γ 

⎩ρ 

(, tt), δ() t ≤ t. 

0 

∗ 

∞ 

1 γ 

β (, tT ) 

Note that ∫ Δ t ( α( t)) 

=∞, implies lim = 1. 

t0 

t→∞ 

ξ () t 

Example 1 Consider the nonlinear neutral perturbed 

dynamic equation 

( t (( x( t) ± x( τ ( t))) ) ) 

t + 1 

Δ 

+ F( tx , ( δ( t))) = Gtx ( , ( δ( t)), x), 

γ−1 1 

Δ γ Δ 

(35) 

for t ∈[1, ∞) 

T 

, where γ is the quotient of odd positive 

integers. Let 

α 

k(1 + δ ( t)) 1 

t δ () t ξ() 

t t 

γ 

γ−1 2 γ 

() t = t , F(, t u) = ( + + u ) u , 

2 γ 

4 

γ 

γ+ 

2 

1 k(1 + δ ( t)) 

u 

ct () = , Gtuv (, , ) = 

, 

2 γ 

2 2 

t+ 1 2 t δ () t ξ()( t u + v + 1) 

where k is a positive constant. Then 

2 

Qt () = k 2 t ξ () t . 

t0 t0 

1 γ γ 1 γ 

Since ∫ ∞ Δ t ( α( t)) 

= ∫ ∞ Δ t t 

− 

=∞, hence the conditions 

(H1) - (H5) are clearly satisfied. And, 

t 

∗ 

α() 

s 


(, sT ) gsQs () () − ) Δs 

t→∞ 

T 

γ+ 

1 γ 

( γ + 1) s 

k 1 

t Δs 

= ( − )limsup , 

γ + 1 ∫ =∞ 

t→∞ 

T 

2 ( γ + 1) 

s 

t 

∗ 

α() 

s 


( sT , ) gs ( )( qs ( ) − ps ( )) − ) Δs 

t→∞ 

T 

γ+ 

1 γ 

( γ + 1) s 

k 1 

t Δs 

= ( − )limsup , 

γ + 1 ∫ =∞ 

t→∞ 

T 

2 ( γ + 1) 

s 

γ + 1 

if k > 2( γ + 1) . Thus it follows from Corollary 1 that 

every solution of (35) + is oscillatory on [1, ∞) 

T 

if k > 

γ + 1 

2( γ 1) , 

+ and it follows from Corollary 4 that every 

solution of (35) − is either oscillatory on [1, ∞) 

T 

or tends 

1 

to zero if k > 2( γ 1) γ + 

+ . 

Example 2 Consider the nonlinear neutral perturbed 

dynamic equation 

1 

t x t − x τ t 

2 + sin t 

Δ 

+ F( t, x( δ( t))) = G( t, x( δ( t)), x ). 

23 Δ 53 Δ 

( (( ( ) ( ( ))) ) ) 

2 

(36) 

23 2 

for t ∈[2, ∞) 

T 

, where α() t = t , γ=53, c() t = 1( 2+ 

sin t) 

Let 

Ftu 1 4 2 5 3 

(, ) = ( + ) , 

tξ 

() t 

t + u u 

and 

11 3 

1 u 

Gtuv (, , ) = 

. 

2 4 

2 tξ 

( t) ( u + v + 2) 

Then qt () − pt () = 12 tξ 

() t . The conditions (H1) - (H5) 

are clearly satisfied. For all t > s ≥ 2 , let m=2, we have 

1 t 

2 

∗ 

limsup 

2 ∫ ( t− s) β ( sT , )( qs ( ) − ps ( )) Δs 

t→∞ 

2 

t 

2 

1 t ( t− 

s) 

= limsup 

t 

2 ∫ Δs 

→∞ 

2 

t 2s 

1 t s t 1 t− 

2 

= limsup[ s s ] . 

t→∞ 

2 ∫ Δ + 

2 ∫ Δ − =∞ 

2 

t 2 2s t 

Thus it follows from Corollary 6 that every solution of 

(36) is either oscillatory on [2, ∞) 

T 



To investigate the oscillatory and asymptotic behavior 

for a certain class of second order nonlinear neutral 

perturbed dynamic equations on time scales. This paper 

proposed some new sufficient conditions for oscillation 

of such dynamic equations on time scales were 

established. The results not only improve and extend 

some known results in the literature, but also unify the 

oscillation of second order nonlinear neutral perturbed 

differential equations and second order nonlinear neutral 

perturbed difference equations. In particular, the results 

are essentially new under the relaxed conditions for the 

parameter function. 


if 

k 

γ + 1 

> 2( γ + 1) . Also, 



This work was supported by a grant from the National 

Natural Science Foundation of China (11161049) and the 

Science Foundation of Zhangjiakou, China (1112027B-1). 

REFERENCES 

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to continuous and discrete calculus”, Results Math., 

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[2] R.P. Agarwal, M. Bohner, D. O’Regan, and A. Peterson, 

“Dynamic equations on time scales, a survey”, Comput. 

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[3] M. Bohner and A. Peterson, Dynamic Equations On Time 

Scales: An Introduction with Applications. Birkhauser, CA: 

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second order nonlinear neutral dynamic equations on time 

scales”, Mathematics in Practice and Theory, vol. 38, pp. 

253–256, September 2008. 

[5] D. X. Chen and J. C. Liu, “Oscillation theorems for second 

order nonlinear neutral dynamic equations on time scales”, 

J. Sys. Sci. & Math. Scis., vol. 9, pp. 1191–1205, September 

2010. 

[6] P.R. Agarwal, D. O’Regan, and S. H. Saker, “Oscillation 

criteria for second-order nonlinear neutral delay dynamic 

equations”, Math. Anal. Appl., vol. 300, pp. 203–217, 

March 2004. 

[7] S. H. Saker, “Oscillation of second-order nonlinear neutral 

delay dynamic equations on time scales”, Comput. Appl. 

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[8] Y. Sahiner, “Oscillation of second-order neutral delay and 

Mixed-type dynamic equations on time scales”, J. Adv.Diff. 

Equ., vol. 3, pp. 1–9, May 2006. 

[9] M. Bohner, S. H. Saker, “Oscillation Criteria for a 

perturbed nonlinear dynamic equations”, Math. Comp. 

Modelling, vol. 40, pp. 249–260, August 2004. 

[10] J. S. Yang, “Oscillation for a class of second-order 

nonlinear dynamic equations on time scales”, J. of Sichuan 

University, vol. 48, pp. 278–283, March 2011. 

[11] E. Thandapani and V. Piramanantham, “Oscillation criteria 

of second order neutral delay dynamic equations with 

distributed deviating arguments”, Electronic J. of Qualitative 

Theory of Diff. Equ., vol. 61, pp. 1–15, April 2010. 

[12] S. Petr and T. Bevan, “Applications of maximum 

principles to dynamic equations on time scales”, J. Diff. 

Eqs. & Appl. vol. 16, pp. 373–388, November 2010. 

[13] D. Anderson, “Oscillation and nonoscillation criteria for 

Two-Dimensional time-scale systems of First-Order 

nonlinear dynamic equations. electronic”, J. of Diff. Eqs. 

Vol. 24, pp. 1–13, January 2009. 

[14] J. S. Yang and B. Fang, “Oscillation criteria of a class of 

second-order dynamic equations on time scales”, Appl. 

Math. A J. of Chinese Universities. Vol. 26, pp. 149–157, 

June 2011. 

[15] J. S. Yang, “Asymptotic behavior of second-order nonlinear 

dynamic equations on time scales”, J. Inner Mongolia 

University. Vol. 41, pp. 153–156, March 2010. 

[16] X. P. Yu, H. Y. Yang and Y. X. Xu, “Oscillation criteria 

for second-order neutral nonlinear dynamic equations on 

time scales”, Proceedings of the 5th ICMB, Vol. 1, pp. 

353–356, June 2011. 

[17] X. P. Yu, H. Y. Yang and J. M. Zhang, “Oscillation criteria 

for nonlinear neutral perturbed dynamic equations on time 

scales”, Ann. Diff. Eqs., in press. 

Xiuping Yu was born in Yu County, Hebei Province, China 

in April 1966. She graduated from Hebei Normal University, 

Shijiazhuang City, China majoring in mathematics with a B.S. 

degree in 1988. And then she earned a Master’s degree in 

applied mathematics from Hebei University, Baoding City, 

China in 2003. 

At present, she teaches in Department of Mathematics and 

Physics and serves as DIRECTOR of BASIC MATHEMATICS 

SECTION in Hebei Institute of Architecture and Civil 

Engineering, Zhangjiakou City, China. In recent years she has 

participated in quite a few international and domestic academic 

conferences during summer vocations. She was once a major 

member of the 5 th International Congress on Mathematical 

Biology and the 2 nd International Conference on Information 

Computing and Applications. She has been mainly engaged in 

functional deferential equation and dynamic system. She has 

completed five provincial-level scientific research projects as 

project leader and principal researcher. Her main achievements 

are interval oscillation criteria for high order neutral deferential 

equations with continuous deviating arguments (Ann. Diff. Eqs. 

vol. 22, pp. 411–417, August 2006), and permanence of 

population with Holling II function response in air pollution 

(Mathematics in Practice and Theory, vol. 37, pp. 102–108, 

October 2007). Currently, she has a strong interest in the 

properties and applications of dynamic equations on time scales. 

Prof. Yu is a member of the National Functional Differential 

Equation Society as well as of the National Biological 

Mathematical Society. She also works as a director of Hebei 

Applied Statistics Society. Her paper, interval oscillation 

criteria for high order neutral deferential equations with 

continuous deviating arguments, won an excellence award at the 

9 th National Functional Differential Equation Conference. 

Another paper, permanence of population with Holling II 

function response in air pollution got the first prize at the 6 th 

Biological Mathematical Conference. The paper, oscillation 

criteria for second order neutral nonlinear dynamic equations on 

time scales was published in Proceedings of the 5 th ICMB by 

World Academic Press. 

Hua Du was born in Zhangjiakou City, Hebei Province, 

China in December 1981. She graduated from Hebei Normal 

University, Shijiazhuang City, China majoring in computer 

information technology with a B.S. degree in 2006. And then 

she earned a Master’s degree in computer application from 

Capital Normal University, Beijing City, China in 2009. 

At present, she teaches in the Information Science and 

Engineering College of Hebei North University, Zhangjiakou 

City, China. In recent years, she has been mainly engaged in 

information management and computer network. 

Hongyu Yang was born in Kangbao Country, Hebei 

Province, China in August 1966. He graduated from Hebei 

Agricultural University, Baoding City, China majoring in 

agricultural machanization with a B.E. degree in 1988. And 

then he earned a Master’s degree in mechanical engineering 

from Chinese Agricultural University, Beijing City, China in 

2012. 

At present, he teaches in Department of Mechanical 

Engineering and serves as DIRECTOR OF DEPARTMENT OF 

MECHANICAL ENGINEERING in Zhangjiakou Vocational 

Technology Institute, Zhangjiakou, China. In recent years he 

has participated in quite a few domestic academic conferences 

during summer vocations. He has been mainly engaged in 

dynamic system. 



Improved Quantum Ant Colony Algorithm based 

on Bloch Coordinates 

Xiaofeng Chen 

Software College, Northeastern University, Shenyang, China 

Email: neucxf@163.com 

Xingyou Xia and Ruiyun Yu 

Software College, Northeastern University, Shenyang, China 

Email: {xiaxy, yury}@mail.neu.edu.cn 

Abstract—The Ant Colony Algorithm is an effective method 

for solving combinatorial optimization problems. However, 

in practical applications, there also exist issues such as slow 

convergence speed and easy to fall into local extremum. This 

paper proposes an improved Quantum Ant Colony Algorithm 

based on Bloch coordinates by combining Quantum 

Evolutionary Algorithm with Ant Colony Algorithm. In this 

algorithm, the current position information of ants is represented 

by the Bloch spherical coordinates of qubits; position 

update, position variation and random behavior of ants are 

all achieved with quantum rotation gate. Simulations of 

function extremum problem, TSP problem and QoS multicast 

routing problem were conducted, the results indicated 

that the algorithm could overcome prematurity, with a faster 

convergence speed and higher solution accuracy. 

Index Terms—quantum computing, Ant Colony Algorithm, 

Quantum Ant Colony Algorithm 


Ant Colony Algorithm (ACA) [1] is a heuristic algorithm 

for solving combinatorial optimization or function 

optimization problems. It has advantages such as positive 

feedback, strong robustness, excellent distributed computing 

mechanism, easy to combine with other algorithms, 

etc., which has been widely used in the NP-complete 

problem. In recent years, ACA has been applied to the 

fields such as knapsack problem [2], Assignment Problem 

[3], Job-shop Assignment [4], Sequential Ordering 

[5], Network Routing [6], Vehicle Routing [7], Power 

System [8] and Controls Parameter Optimization [9], etc. 

and obtained good effect. Meanwhile, like other swarm 

intelligence optimization algorithms, ACA also has some 

shortcomings in the application process, such as: easy to 

fall into local optimization, slow convergence speed, etc. 

A quantum ant colony algorithm (QACO), based on 

the concept and principles of quantum computing can 

overcome this defect. In [17], a QACO-based edge detection 

algorithm was proposed. Quantum bit (qubit) and 

quantum rotation gate are introduced into QACO to represent 

and update the pheromone respectively. Experiments 

and comparisons show that QACO is an efficient 

and effective approach in image edge detection. In order 

to select the optimal parameter, quantum-inspired ant 

colony optimization is employed to select the parameter 

of relevance vector machine in [18]. Quantum-inspired 

ant colony optimization is well suited to multi-objective 

optimization problems with excellent results. By measuring 

experimentally the vibration signals of the gear system 

at different rotating speeds for different faults, the 

testing signals are obtained. In [19], a novel parallel ant 

colony optimization algorithm based on quantum dynamic 

mechanism for traveling salesman problem (PQACO) 

was proposed. The use of the improved 3-opt operator 

provides this methodology with superior local search 

ability. A global optimization method was proposed to 

analyze ground state energy of quantum mechanical systems 

in [20], which It simulates the way that real ants 

find a shortest path from nest to food source and back. To 

eliminate system disturbances and noise from the high 

levels of data, a novel quantum ant colony optimization 

(QACO) algorithm was proposed to select the fault features 

[21]. 

This paper proposed an improved quantum ant colony 

algorithm based on the Bloch Spherical Coordinate [11] 

(BIQACA), and various solution space transformational 

models and fitness functions are planned for different 

optimization problems. Algorithm in this paper is verified 

by function extreme value problem, Traveling Salesman 

Problem and QoS multicast routing problem respectively. 

The result of simulation shows that the algorithm not 

only expresses high efficiency of quantum computing, 

but also maintains the preferable optimizing and robustness 

of colony algorithm. 

II. QUANTUM ANT COLONY ALGORITHM (QACA) 

Any point on the Bloch sphere can be identified via θ 

and ϕ as: ϕ = [ cosϕ 

sinθ,sinϕ 

sinθ, 

cosθ 

] T . Suppose 

there are a total of n ants in the ant colony, where each 

ant carries a group (m units) of qubits, current position of 

ant is represented by Bloch spherical coordinate, corresponding 

to approximate solution of optimization problem. 

A. Initialize Ant Colony 


doi:10.4304/jcp.8.6.1536-1543


Pi 

is set as the location of the ith ant, considering that 

the randomness of coding for ant colony and constraint 

conditions for probability amplitude of the quantum state, 

the initialization of BIQACA is expressed as: 

j 

⎡P 

⎤ 

ix 

⎡cosφi1sinθi1 cosφi 2sinθi2 

cosφim sinθim 

⎤ 

⎢ j ⎥ ⎢ ⎥ 

⎢Piy ⎥ = 

⎢ 

sinφi1sinθi1 sinφi 2sinθi2 

sinφim sinθim 

⎥ 

(1) 

⎢ 

j 

P ⎥ ⎢ 

iz ⎣ cosθi1 cosθi2 

cosθ 

⎥ 

⎣ ⎦ 

 

im ⎦ 

Where ϕij 

= 2πrand 

, θ ij = πrand 

, rand are random 

numbers between (0, 1) ; i ∈ { 1,2, 

, 

n} 

, j ∈ { 1,2, 

, 

m} 

, n 

for number of ant; m for number of qubit. 3 coordinates 

of qubit are regarded as 3 paratactic genes, and each ant 

contains 3 gene chains, which are called X-chain, Y- 

chain and Z-chain respectively, each gene chain stands 

j j j 

for an optimal solution P ix , P iy , P iz . 

B. Transformation of Solution Space 

In the optimization of specific problems in BIQACA, 

transformation between the unit quantum space and solution 

space of optimization problem is needed, making 

each probability amplitude of qubit on ant correspond to 

an optimization variable of solution space. In this paper, 

the function extremum problem, TSP problem and QoS 

multicast routing problem are taken as examples to explain 

the process. 

Solution space transformation approach for function 

extreme-value problem: propose the domain of definition 

j 

of variable X is its solution space [ a j , b j ] , record the jth 

qubit in P i as [ cos ϕ 

] T 

ij sinθij 

,sin ϕij 

sinθij 

, cosθij 

by using 

linear transformation, then the corresponding solution 

space variable is: 

j 

⎡X 

⎤ 1 cos sin 1 cos sin 

ix 

⎡ + ϕij θij − ϕij θij 

⎤ 

⎢ j ⎥ 1 ⎢ b 

1 sin sin 1 sin sin 

j 

X 

ϕ 

iy 

ij 

θij ϕij θ ⎥⎡ 

⎤ 

⎢ ⎥ = ij 

2 

⎢ 

+ − 

⎥⎢ a 

⎥ 

⎢ 

j 

j 

X 

⎥ ⎢ 1+cos θij 

1-cosθ 

⎥ ⎣ ⎦ 

⎣ iz ⎦ ⎣ 

ij ⎦ 

Solution space transformation approach for TSP problem 

and QoS multicast routing problem: this paper has 

designed two-layer transformational model in the aspect 

of solution space aiming at the specific characteristic of 

TSP problem and QoS multicast routing problem, the 

model contains two transformations--linear transformation 

and lead transformation. 

Linear transformation: qubit is transformed from unit 

space to lead space. Propose the definitional domain of 

j 

lead message variable, r , is [0,1] , formula (2) is used to 

calculate corresponding lead solution space variable 

j j j T 

[ τ , τ , τ ] . 

ix iy iz 

Lead transformation: impact strength of lead message 

and inspire message to solution could be regulated by 

adjusting lead factor and inspire factor. Strategy is selected 

according to lead probability and roulette to carry out 

optimal decode. Suppose the current node as i, select 

node j as the next visiting node: 

(2) 

p 

k 

ij 

ω υ 

⎧ rij 

() t iλij 

() t 

j∈ 

allowed 

⎪ 

ω υ 

= ⎨ ∑ ris 

() t i λis 

() t 

(3) 

⎪⎪ 

s∈allowedk 

⎩0 otherwise 

ω υ 

where r () t i λ () t is for message of path, r () t stands 

ij 

ij 

for lead message, ω is lead factor; λ () t represents inspire 

message λ (t)= 1 

ij 

d ij 

ij 

, d 

ij 

means the distance from 

node i to node j, υ is inspire factor; 

allowed = {1, 2, m} 

− tabu means the set of available 

k 

k 

node may selected by ant k at the time t; tabu 

k 

is used to 

keep the routing table which obtained by transforming ant 

k. 

C. Definition of Fitness Function 

A variety of fitness function needs to be designed for 

different optimal problems, the more fitness it is, the better 

solution for individual. 

Fitness function of extreme-value problem: suppose 

f ( X i 

) as the ith solution, fit( X i 

) 

ij 

is the adaptive value 

for the ith solution. min and max denote the minimum 

value and maximum value of function, respectively. 

⎧ 1 

⎪ 

f( Xi 

) ≥ 0 

min fit( X ) 1 ( 

i 

) 

i 

= ⎨ + f X 

⎪ 

⎩1 + abs( f ( X 

i)) f ( X 

i) < 0 

⎧ 1 + f( Xi) f( Xi) ≥ 0 

⎪ 

max fit( X 

i 

) = ⎨ 1 

⎪ 

1 + f( Xi 

) < 0 

⎩ abs( f ( X 

i 

)) 

TSP fitness function: fitness of individual 

X 

i 

= { x1, x2, , xm} 

of TSP is defined as the reciprocal of 

path length represented by individual. 

fit( 

Ti 

) 

(4) 

(5) 

1 

fit( X 

i 

) = (6) 

DX ( ) 

Fitness function for multicast routing problem: 

Wc 

( Wd 

⋅ Φ( 

TD − Dmax 

) + Wdj 

⋅ Φ( 

TDJ − DJ max ) + W pl ⋅ Φ( 

TPL − PLmax 

)) 

TC 

= (7) 

where TD, TDJ, TPL and TC represent the delay, delay 

jitter, packet loss rate and cost of multicast tree 

respectively. Wc=0.5, Wd=0.2, Wdj=0.1 and Wpl=0.2, 

represent the proportion of the cost, delay, delay jitter and 

packet loss rate in the fitness function respectively; 

⋅ Φ(X ) is a penalty function, when ⋅X ≤ 0 , ⋅Φ( X ) = 1 , or 

else, ⋅Φ( X ) = 0. 5 . It can be seen from the above equation 

that, the fitness value is the bigger the better. 

D. Ant Position Update 

In the solution space of optimal problem, suppose 

τ ( X i 

) is the strength of pheromone of kth ant at X 

i 

, initial 

moment all set as some constant: η ( X i 

) stands for 

i 



the visibility at X 

i 

. The basic framework of BIQACA 

described as follows: 

1) Selecting the target position of ant movement 

By applying the principle of randomness, a number of 

qubits in the current position were randomly selected to 

constitute a position update vector S. The transition rule 

and transition probability of ant k from position X to 

position 

where q∈[0, 1] is even-distributed random number, q 0 

∈[0, 1] is probability parameter, P is the set of occupied 

points for ant in unit space, X 

s 

tion as per formula (8) ; α is the update parameter of 

pheromone, β is the update parameter of visibility. 

2) Realizing the movement of ant towards target position 

via quantum rotation gate 

After the ant has selected the target position, its 

movement process can be realized by changing the phase 

of qubit it brought for quantum rotation gate. In unit 

space, suppose the current position for ant at time t is P 

i 

, 

selected target position is P k , update vector of P i is S, 

then the update of phase angle increment at P 

i 

is 

where )} 

t+ 1 t+ 1 t t t t+ 1 t t+ 

1 

⎡cosϕij sinθ ⎤ ⎡ 

ij 

cosϕij sinθ ⎤ ⎡ 

ij 

cos( ϕij +Δ ϕij )sin( θij +Δθ 

) ⎤ 

ij 

⎢ t+ 1 t+ 1⎥ ⎢ t t ⎥ ⎢ t t+ 1 t t+ 

1 ⎥ 

⎢sinϕij sinθij ⎥ = U ⎢sinϕij sinθij ⎥ = ⎢sin( ϕij +Δ ϕij )sin( θij +Δθij 

) ⎥ 

⎢ 

t+ 1 t t t 1 

cosθ ⎥ ⎢ 

ij 

cosθ ⎥ ⎢ 

+ 

ij 

cos( θij θ ) ⎥ 

⎣ ⎦ ⎣ ⎦ ⎣ +Δ 

ij ⎦ (15) 

Apparently, U-gate can rotate the phase of qubit by 

t 1 

ϕ + 

t 1 

Δ 

ij 

and Δ θ + 

ij 

. 

3) Adjustment strategy of search space 

i 

In BIQACA, the search space for each qubit is designed 

as [ lowBd ij , upBdij 

] , the search space at initializa- 

X 

s 

are: 

α 

β 

⎧arg max{ τ ( X 

s) iη 

( Xs)} q ≤ q 

tion is [ 0.25π 

,0.75π 

] , during optimizing process of ants, 

0 

⎪ Xs∈P 

X 

s 

= ⎨ these search spaces are related with the contraction level 

⎪ 

⎩ Xs 

q > q0 

(8) of each qubit, and decrease exponentially, which can significantly 

improve the solution accuracy of the algorithm. 

α 

β 

τ ( Xs) iη 

( Xs) 

t+ 

1 

t 

pX ( 

s 

) = 

α 

β 

τ ( X 

u) η ( X 

u) 

X 

∑ i , 

(9) 

⎡lowBd 

⎤ ⎡ 1 ⎤⎡ ij 

lowBd ⎤ 

ij 

⎢ t+ 

1 ⎥ = ⎢ t ⎥ 

ij 

⎢ t ⎥ (16) 

nL 

⎢ 

s, 

Xu∈P 

⎣ upBdij 

⎥⎦ ⎢⎣nf 

⎥⎦⎢⎣upBdij 

⎥⎦ 

where j ∈ { S(1), 

S(2), 

, 

S( 

sm)} 

, S is the update vector 

of ants, nf = 2 is the constriction factor, nL t represents 

ij 

is the selected target loca- 

the contraction level of t-th iteration. 

4) Processing of ant position variation 

Suppose the current position is P i , update vector of P i 

is S, the search space of P i is [ lowBd ij , upBdij 

] . Then the 

update of phase angle increment at P 

i 

is: 

⎧ Δϕij 

= (2rand 

−1)( 

upBdij 

− lowBdij 

) 

⎨ 

⎩ 

Δϕij 

= sign( 

Δϕij 

)( abs( 

Δϕij 

) + lowBdij 

) (17) 

⎧ Δθij 

= (2rand 

−1)( 

upBdij 

− lowBdij 

) 

⎨ 

⎩ 

Δθij 

= sign( 

Δθij 

)( abs( 

Δθij 

) + lowBdij 

) (18) 

( φkj − φij ) × rand 

t 

⎧⎪ 

j 

φkj ≠φij 

Δ φij 

= ⎨ 

(10) 5) Random behavior of ants 

⎪⎩ Δ φij φkj = φij 

If P i is not improved after continuous limited-time cycles, 

the position should be abandoned, the ants will generate 

a new P ' 

t 

t 

⎧Δ ϕij 

+ 2π Δ ϕij 

< −π 

t+ 

1 ⎪ 

i through random behavior to substtute P i . 

t t 

Δ ϕij = ⎨ Δ ϕij −π ≤ Δϕij 

≤ π (11) 

' 

⎪ Δ 

t 

t 

⎩ ϕij 

− 2π Δ ϕij 

> π 

ϕij = mean( ϕi 

) + Δϕ ij 

(19) 

' 

( θkj − θij ) × rand 

t 

⎧⎪ 

j 

θkj ≠θ 

θij = mean( θi 

) + Δθ ij 

ij 

(20) 

Δ θij 

= ⎨ 

(12) 

⎪⎩ Δ θij θkj = θij 

where i ∈ { 1,2, , 

n} 

, j ∈ { S(1), 

S(2), 

, 

S( 

sm)} 

, S is the 

update vector of current position, Δ ϕij 

and Δ θij 

are updated 

using (17), (18), mean( θ 

t 

t 

⎧Δ θij 

+ π Δ θij 

< −π 

/2 

t+ 

1 ⎪ t t 

i ) is the mean value of 

Δ θij = ⎨Δ θij −π /2 ≤ Δθij 

≤ π /2 (13) 

vector of phase angle θ 

⎪ Δ 

t 

t 

i at P i . 

⎩ θij 

− π Δ θij 

> π /2 

6) Update rules for pheromone intensity and visibility 

When the ant completes a traverse, the current position 

j ∈ { S(1), 

S(2), 

, 

S( 

sm , rand 

j 

is random num- 

is mapped into the solution space of optimal problem 

Δ ϕij 

, Δ θij 

can be obtained using from unit space, fitness function is calculated, and the 

intensity and visibility of pheromone at current position 

should be updated. 

⎧τ( X 

i) = (1 − ρ) τ( Xi) + ρτ( Xi) 

t+ 1 t+ 1 t+ 1 t+ 1 t+ 1 t t+ 

1 

⎨ 

⎡cos Δϕij cos Δθij −sin Δϕij cos Δθij sin Δ θij cos( ϕij +Δϕij 

) ⎤ 

⎢ t+ 1 t+ 1 t+ 1 t+ 1 t t+ 

1 ⎥ 

⎩ τ ( X 

i) = Qfit( X 

i) 

(21) 

U = ⎢sin Δϕij cos Δθij cos Δϕij cos Δθij sin Δ θsin( ϕij +Δϕij 

) ⎥ 

⎢ 

t+ 1 t t+ 1 t+ 

1 

−sin Δθij −tan( ϕij / 2)sin Δθij cos Δθ 

⎥ 

⎣ ij ⎦ (14) 

ber between [0, 1]; 

(17), (18). 

Update of probability amplitude of qubit based on 

quantum rotation gate 



η ( X ) = fit( X ) 

(22) 

i 

where (1 −ρ) ∈ [0,1] is the evaporation coefficient of 

pheromone, Q is the enhancement coefficient of pheromone. 

E. Description of BIQACA 

Taking the function extremum problem as an example, 

BIQACA implementation steps are described as follows: 

Step 1: Setup relevant parameters such as the number 

of ants, maximum number of iterations, number of limits 

limit, contraction level 

nL 

ij 

i 

, constriction factor nf, Maximum 

contraction level MaxL, reset contraction level 

resetL, search space [ lowBd ij , upBdij 

] , etc. 

Step 2: Randomly generate initial position of ants according 

to (1), transform the solution space according to 

(2), and calculate the fitness of each ant according to (5) 

or (6). Update the pheromone intensity and visibility according 

to (21) and (22).Record the current optimum solution, 

i.e. global optimum solution GBest. Initialize the 

conceptual vector trial ( i) 

= 0 , record the number of nonupdates 

at the position of ant. 

Step 3: Update the search space [ lowBd ij , upBdij 

] according 

to (16). 

Step 4: Select a moving target for each ant in the ant 

colony according to (8) and (9), then realize the movement 

of ants using quantum rotation gate in light of (10), 

(12) and (14). 

Step 5: For each ant, according to mutation probability, 

realize the variation of ant’s position using quantum rotation 

gate in light of (17) and (18). 

Step 6: Transform the solution space according to (2), 

calculate the fitness of each ant according to (5) or (6). 

Update the current position if the new position is better 

than the current one; otherwise trial ( i) 

= trial( 

i) 

+ 1 , update 

contraction level nL ( i, 

j) 

= nL( 

i, 

j) 

+ 1 , if 

nL ( i, 

j) 

>MaxL, nL ( i, 

j) 

=resetL. 

Step 7: Determine whether trial (i) 

is greater than the 

limit, if trial (i) 

>limit, abandon the current position of 

the i-th ant, and generate a new position according to (19), 

(20) and (15), perform space transformation in light of 

(2), calculate the fitness of each ant according to (5) or 

(6), trial ( i) 

= 0 . 

Step 8: Update the pheromone intensity and visibility 

according to (21) and (22). Record the current local optimum 

position, Best, and local worst position, Worst. 

Step 9: Determine whether the local optimum position, 

Best is greater than the global optimum position, GBest, 

if Best>GBest, update the global optimal position, GBest 

with local optimum position, Best, otherwise, update the 

local worst position, Worst with global optimum position, 

GBest. 

Step 10: Update the number of iterations t=t+1. If the 

current number of iterations t>maxgen or accuracy of 

convergence is met, stop the search, output the global 

optimum position, or else, turn to Step 3. 

III. SIMULATION EXPERIMENT 

To verify the effectiveness and feasibility of BIQACA 

algorithm, function extremum problem, traveling salesman 

problem and multicast routing problem were selected 

for testing. The simulation programs were programed 

and implemented in MATLAB 2009a, test results were 

obtained in a PC with an Intel Core (TM) i5 CPU running 

at 3.2GHz, and a 2.8GB RAM. 

A. Function Extremum Problem 

Three internationally commonly used functions f1~f3 

were selected to test BIQACA performance when the 

number of independent variables was 2 and 30 respectively 

2 2 

f ( x, 

y) 

= 0.3cos3π x − 0.3cos 4πy 

− x − y − 0.3, −1 

≤ x, 

y 1 (23) 

1 ≤ 

n 

f ( x ) = ∑ ( −x 

sin( x )), − 500 ≤ x 500 (24) 

2 i 

i 

i 

i 

≤ 

i= 

1 

n 

∑ 

2 

f3( xi 

) = ( xi 

−10cos(2π xi 

) + 10), −5.12 

≤ xi 

≤ 5. 12 (25) 

i= 

1 

1) When the number of independent variables is 2 

Test function is f1, the optimization objective is to obtain 

the maximum value. 

Algorithm parameters: maximum number of iterations 

maxgen=500, number of ants n=20, probability parameter 

q 

0 

=0.5, evaporation coefficient 1− 

ρ =0.05, pheromone 

update parameter α =1, visibility update parameter β =5, 

pheromone enhancement coefficient Q =10, mutation 

probability P 

m 

=0.05; the program was terminated when 

the BIQACA algorithm found the optimal solution or had 

run for gen=500 iterations. Simulations were conducted 

using the CQACO algorithm and ACO algorithm in Ref. 

[12] respectively, each algorithm was run for 50 times 

independently under the same conditions, and their optimal 

value (Best), optimal mean value (M-best), number 

of success and average number of iterations were recorded, 

optimization results were compared in Table 1. 

TABLE I. 

COMPARISON OF EXPERIMENTAL RESULTS OF 3 ALGORITHMS WITH TEST 

FUNCTION F 1 

Func/opt 

f 1/ 

0.24 

Status 

Algorithm 

ACO CQACO BIQACA 

Best 0.2400 0.2400 0.2400 

M-best 0.1720 0.2388 0.2400 

Con-times 42 48 50 

Ave-Steps 198.16 84.04 17.06 

It can be seen from Table 1 that, BIQACA algorithm’s 

optimization efficiency is the highest, its optimization 

results is also the greatest, with the success rate of 100%; 

followed is CQACO, with a success rate of 96%; the last 

is ACO, with a success rate of 84%. 

2) When the number of independent variables is 30 

Test functions were f2, f3, optimization goal is to obtain 

the minimum value. 



TABLE II. 

COMPARISON OF EXPERIMENTAL RESULTS OF 3 ALGORITHMS WITH TEST 

FUNCTION F2 AND F3 

B. Traveling Salesman Problem 

Take symmetric-distance TSP as example, five problems 

with different data scale was selected from TSPLIB 

database as cases to verify the performance of the algorithm. 

Compare the result with Common Genetic Algorithm 

(CGA), Common Particle Swarm Optimization 

(CPSO) and Common Ant Colony Algorithm (CACA) 

respectively. 

Algorithm parameters: each algorithm prescribes a 

limit to algebra of 100 and population of 50. in CGA algorithm, 

integer encoding is adopted; in CPSO algorithm, 

integer encoding is also adopted, inertia factor W =0.5, 

self-factor C 

1 

=0.3, global factor C 

2 

=0.7; in CABC algorithm, 

integer encoding adopted as well, other parameters 

with the function extreme value problem; In BIQACA 

algorithm, transfer factor parameter ω = 1, stimulating 

factor parameter υ = 5, other parameters with the function 

extreme value problem. 

Then in every case, 20 experimental data would be 

taken, and table 3 shows contrast of optimization results. 

Figure 1 is the Oliver30 Optimization Results and Figure 

2 is the EIL51 Optimization Results. Figure 3 shows the 

best solution of Oliver30 quantum ant colony algorithm, 

the total distance for 424. Figure 4 shows the best solution 

of EIL51 quantum ant colony algorithm, the total 

distance is 458. 

Func/ 

Opt 

f 2/ 

-12569.5 

f 3/ 

0 

Status 

Algorithm 

OGA/Q LEA BQACA 

M-nfun 302116 287365 236613 

M-best -12569.454 -12569.454 -12569.487 

St.dev 6.447×10 -4 6.831×10 -4 6.5856×10 -6 

M-nfun 224710 223803 223230 

M-best 0 2.103×10 -18 0 

St.dev 0 3.0359×10 -18 0 

Algorithm parameters: maximum number of iterations 

maxgen=1500, number of ants n=100, other parameters 

were the same as test 3.1.1. Simulations were conducted 

using the BIQACA algorithm, as well as the OGA/Q algorithm 

in Ref. [13] and LEA algorithm in Ref. [14] respectively, 

each algorithm was run independently for 50 

times under the same conditions, and their average number 

of function evaluations (M-nfun), optimal mean value 

(M-best) and standard deviation (St. dev) were recorded, 

optimization results were compared in Table 2. 

It can be seen from Table 2 that, the BIQACA algorithm 

is obviously superior to the OGA/Q algorithm and 

LEA algorithm with respect to optimal mean value, average 

number of function evaluations and standard deviation 

of function f2, f3; for f3, the BIQACA algorithm and 

the OGA/Q algorithm could both find the optimal solutions. 

For function f2, the three algorithms all failed to find 

the optimal solutions, but the solution finding quality of 

BIQACA algorithm is significantly better than that of the 

LEA algorithm and OGA/Q algorithm, the standard deviation 

obtained by the BIQACA algorithm is also less than 

that of the LEA algorithm and OGA/Q algorithm. 

Figure 1. The Oliver30 Optimization Results 

Figure 2. The EIL51 Optimization Results 

Figure 3. The Oliver30’s Best Solution by using BIQACA 



Figure 4. 

the EIL51’s Best Solution by using BIQACA 

Statistics analysis of data based on table 3: from time 

perspective, the average time of CPSO algorithm is 

shortest, secondly CGA algorithm, BIQACA algorithm 

followed, and CACA algorithm is the last one; from steps 

perspective, BIQACA algorithm and CACA algorithm 

are at the same level and the convergence rate of them is 

more preferable than the other two algorithms; from the 

perspective of calculation result, the optimal solution of 

BIQACA algorithm and CACA algorithm can reach an 

ideal resolution recommended by TSPLIB database when 

urban scale is small. 

When the urban scale is large, the BIQACA’s optimal 

solution can approach to that of CACA algorithm, and its 

average solution and standard deviation is better than that 

of CPSO algorithm and CGA algorithm. To sum up, 

BIQACA algorithm in this paper is feasible and effective. 

TABLE III. 

TSP CALCULATION RESULTS 

Test library 

Uleysses22 

Oliver30 

EIL51 

EIL76 

GR96 

algorithm 

Optimal Worst solution 

value deviation deviation time step 

Mean Standard Mean-square Mean Average 

solution 

CGA 76.9162 93.5551 85.0164 4.3255 18.7098 1.4645 100.0000 

CPSO 78.9062 125.7221 105.8074 9.7533 95.1269 0.2646 88.8000 

CACA 75.9832 77.3018 76.3748 0.3878 0.1504 1.9651 60.0000 

BIQACA 75.9832 76.6314 76.2579 0.2226 0.0496 1.6571 62.0000 

CGA 482.6800 639.5484 570.9215 37.2503 1387.5816 2.0194 100.0000 

CPSO 729.5129 990.8997 850.9355 84.6154 7159.7655 0.3277 84.7500 

CACA 423.7406 429.7853 426.7401 1.4871 2.2115 3.1717 54.1000 

BIQACA 423.7406 438.6092 428.8924 3.8389 14.7375 2.2512 50.0500 

CGA 558.7636 812.5886 694.0846 60.0962 3611.5476 3.4789 100.0000 

CPSO 1055.4600 1252.3856 1146.5343 60.0677 3608.1277 0.4929 93.4500 

CACA 440.7957 457.3709 450.5731 4.8484 23.5068 10.0465 60.8000 

BIQACA 458.3380 507.1071 492.5977 11.4446 130.9781 5.9311 55.4500 

CGA 949.3124 1200.5125 1082.3078 77.0343 5934.2825 5.3974 100.0000 

CPSO 1698.2136 2090.3629 1885.3653 106.6634 11377.0827 0.6863 94.6500 

CACA 566.8443 576.1675 572.0972 2.8604 8.1822 18.5971 50.4500 

BIQACA 628.7805 670.0715 653.8038 11.0728 122.6080 11.8519 59.4000 

CGA 1082.0048 1467.8411 1232.7158 98.6122 9724.3659 7.1479 100.0000 

CPSO 2274.0041 2885.1164 2567.0244 160.3023 25696.8139 0.8681 90.8500 

CACA 544.8082 558.9636 552.8529 4.3274 18.7262 37.43502 63.7500 

BIQACA 594.9407 648.2708 626.9822 11.5389 133.1465 22.903469 54.1000 

C. QoS Multicast Routing Problem 

In order to compare with the GA algorithm in Ref. [15] 

and QCMR-ACS in Ref. [16], the network architecture 

model the same with them was adopted in the experiment, 

as shown in Figure 5. 

Figure 5. 

8-node network model 

In this typical 8-node network model, network can be 

represented using picture G (V, E), where V (D, DJ, PL, 

C) represents network node set, E (D, DJ, B, C) represents 

link set, and D, DJ, PL, C and B represent delay 

(ms), delay jitter (ms), packet loss rate, cost and bandwidth 

(Mb/s) respectively. 

The core idea of multicast routing algorithm is: in each 

iteration, firstly, qubits pass linear transformation and 

state transition transformation, and complete the conversion 

of quantum information in the routing path; secondly, 

use the routing paths to generate the multicast tree of the 

iteration; thirdly, compute the delay, delay jitter, packet 

loss rate, bandwidth, and cost of the multicast tree; finally, 

calculate the fitness of the multicast tree. 

Multicast tree generation: the original multicast tree is 

generated using the vector information of multiple routing 

paths, and through the conversion from vector to matrix, 

the original multicast tree was pruned and processed 

to obtain the multicast tree. 

Algorithm parameters: source node s=1, destination 

node M=[2, 4, 5, 7], maximum number of iterations 

maxgen=16, number of ants n=8, mutation probability 

P = 0.1. 

m 



Table 4 shows the optimization results of BIQACA algorithm 

when D 46 , DJ 8 , B 70 and 

max = 

max = 

min = 

PL max = 0.001 were constrained; Figure 6 shows the cost 

convergence curves of multicast tree for three algorithms 

(GA, QCMR-ACS, BIQACA) 

Route 

request 

s=1 

M=[2, 4, 

5, 7] 

Figure 6. 

TABLE IV. 

BIQACA ALGORITHM OPTIMIZATION RESULTS 

Optimal 

multicast tree 

(1, 2), (1, 3), 

(3, 4), (3, 5) 

(4, 6), (6, 7) 

Delay 

Delay 

jitter 

Packet 

loss rate 

Cost 

45 7 0.0001 66 

Cost convergence curves of multicast tree for three algorithms 

Table 5 shows the optimization results of BIQACA algorithm 

when D 50 , DJ 6 , B 70 and 

max = 

max = 

min = 

PL max = 0.001 were constrained; Figure 7 shows the cost 

convergence curves of multicast tree for three algorithms 

(GA, QCMR-ACS, BIQACA) 

Route 

request 

s=1 

M=[2, 4, 

5, 7] 

Figure 7. 

TABLE V. 

BIQACA ALGORITHM OPTIMIZATION RESULTS 

Optimal 

Delay Packet 

Delay 

multicast tree 

jitter loss rate 

Cost 

(1, 2), (1, 3), 

(2, 4), (3, 5) 

49 5 0.0002 62 

(4, 6), (6, 7) 

Cost convergence curves of multicast tree for three algorithms 

It can be seen from Figure 6 and Figure 7 that, under 

the conditions of the two multicast routing constraints, 

the three algorithms can all converge to the global optimal 

solution, for GA algorithm in Ref. [15], evolution 

generations during convergence were 12 and 14, respectively, 

QCMR-ACS algorithm in Ref. [16] requires 6 and 

9 generations respectively, while the BIQACA algorithm 

herein requires only 2 generations, its convergence speed 

is much faster than that of the GA and QCMR-ACS 

based QoS multicast routing algorithms, thus the feasibility 

and effectiveness of the BIQACA algorithm are verified. 


In this paper, by combining quantum computation and 

ant colony algorithm, an improved quantum ant colony 

algorithm based on Bloch coordinates is presented, enriching 

the research field of quantum intelligence algorithm. 

From the perspective of quantum computation, this 

algorithm proposes the adjustment strategy of search 

space in accordance with the exponential decrease method. 

A number of qubits at current position of ants are 

selected using the principle of randomness to constitute 

the update vector, the position update, position variation 

and random behavior of ants are all subject to the constraint 

of update vector, thus improving the convergence 

speed of the algorithm. At the same time, the random 

behavior of ants introduced can obviously overcome the 

prematurity of the algorithm. Different solution space 

transformation models and fitness functions are designed 

for different optimization problems, where the overall 

idea of the algorithm remains the same, the algorithm has 

strong versatility. Research results show that the new 

algorithm has certain practical value which can improve 

the efficiency and accuracy. Compared with conventional 

intelligence algorithms, BIQACA has stronger search 

capability and higher efficiency, and is appropriate for 

complex function optimization and combinatorial optimization 

problems. At the same time, as a novel optimization 

algorithm, BIQACA is lack of necessary theoretical 

proof, experimental verification alone is not comprehensive 

enough; further study is needed in the future. 

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Image Fusion Method Based on Directional 

Contrast-Inspired Unit-Linking Pulse Coupled 

Neural Networks in Contourlet Domain 

Xi Cai 

Northeastern University at Qinhuangdao, Qinhuangdao, China 

Email: cicy_2001@163.com 

Guang Han 

College of Information Science and Engineering, Northeastern University, Shenyang, China 

Email: a00152738@sohu.com 

Jinkuan Wang* 

Northeastern University at Qinhuangdao, Qinhuangdao, China 

Email: wjk@mail.neuq.edu.cn 

Abstract—To take full advantage of global features of source 

images, we propose an image fusion method based on 

adaptive unit-linking pulse coupled neural networks 

(ULPCNNs) in the contourlet domain. Considering that 

each high-frequency subband after the contourlet 

decomposition has rich directional information, we employ 

directional contrast of each coefficient as the external 

stimulus to inspire each neuron. Linking range is also 

related to the contrast in order to adaptively improve the 

global coupling characteristics of ULPCNNs. In this way, 

biological activity of human visual systems to detailed 

information of images can be simulated by the output pulses 

of the ULPCNNs. The first firing time of each neuron is 

utilized to determine the fusion rule for corresponding 

detailed coefficients. Experimental results indicate the 

superiority of our proposed algorithm, for multifocus 

images, remote sensing images, and infrared and visible 

images, in terms of visual effects and objective evaluations. 

Index Terms—Image fusion, contourlet transform, unitlinking 

pulse coupled neural network 


Owing to widespread use of multisensor systems, 

much research has been invested to develop the 

technology of image fusion. Ordinarily, 2-D image fusion 

is to merge complementary information from multiple 

images of the same scene, and obtain one single image of 

better quality [1]-[4]. This promotes its increasingly 

extensive application in digital camera imaging, 

battlefield surveillance and remote sensing. As a major 

class of image fusion methods, the ones based on 

multiscale decomposition (MSD) take into account the 

sensitivity of human visual system (HVS) to detailed 

* Corresponding author. 

information, and hence receive better fusion results than 

other methods [5][6]. To improve the performance, MSD 

transforms and fusion rules have become the main focus 

in the fusion methods based on MSD [7]-[9]. 

Typically, MSD transforms include: pyramid 

transform, wavelet transform, curvelet transform, etc. 

With further development of MSD theory, a superior twodimensional 

representation, contourlet transform was 

exploited to overcome limitations of traditional MSD 

transforms [10]. Its characteristics of multidirection and 

anisotropy make it sensitive to directions and sparse 

while representing objects with edges. Especially, 

contourlet transform allows for different and flexible 

number of directions at each scale, and hence can capture 

detailed information in any arbitrary direction. These 

advantages make the contourlet transform quite attractive 

to image fusion [11]-[14]. In most contourlet-based 

fusion methods, researchers adopt fusion rules to choose 

more salient high-frequency information, for example, 

[12] and [13] respectively chose the coefficient with the 

maximum region energy and the maximum edge 

information. 

However, the traditional fusion rules could not make 

good use of global features of images, for they were most 

based on features of a single pixel or local regions. In our 

study, we present a bio-inspired salience measure based 

on unit-linking pulse coupled neural networks 

(ULPCNNs), and capture the global features of source 

images by using the global coupling properties of the 

ULPCNNs. PCNN originated from the experimental 

observations of synchronous pulse bursts in cat visual 

cortex [15], and is capable to simulate biological activity 

of HVS; ULPCNN is a simplified version of the basic 

PCNN with fewer parameters [16]. When motivated by 

external stimuli from images, ULPCNNs can generate 

series of binary pulses containing much information of 

features such as edges, textures, etc. 


doi:10.4304/jcp.8.6.1544-1551


In this paper, we propose an image fusion method 

based on directional contrast-stimulated ULPCNNs with 

adaptive linking range in the contourlet domain (CT- 

ULPCNN). ULPCNN neurons are inspired by directional 

contrast revealing the prominence of each directional 

subband, and such a ULPCNN is expected to possess 

good sensitivity to directional information of objects in 

images. The linking range is also determined by 

corresponding directional contrast. In this way, the global 

coupling character of the ULPCNN is better represented 

than that with constant linking range, especially for the 

strong stimulus. In our fusion rules, the first firing time of 

each neuron is chosen as the salience measure. 

Experimental results suggested that CT-ULPCNN has 

better fusion results for multifocus images, remote 

sensing images, and infrared and visible images, which 

actually proves the advantages of the proposed method 

capturing the prominent directional features of each 

subband in the contourlet domain. 

The outline of the rest of the paper is as follows. 

Contourlet transform is briefly introduced in Section II. 

In Section Ⅲ, we describe the theories of basic PCNN 

and ULPCNN, respectively. Detailed procedure of CT- 

ULPCNN algorithm is proposed in Section Ⅳ, and its 

effectiveness is certified and analyzed in Section Ⅴ . 

Finally, conclusion is drawn in Section Ⅵ. 

II. CONTOURLET TRANSFORM 

Contourlet transform is a multi-scale and multidirectional 

transform. It was initially developed in 

discrete domain, and hence easy for digital 

implementation. Contourlet transform combines 

Laplacian Pyramid (LP) and Directional Filter Bank 

(DFB) into a double filter bank structure, so it is also 

called Pyramidal Direction Filter Bank (PDFB). In 

essence, LP is first executed to capture the point 

discontinuities, and then followed by DFB to link point 

discontinuities into linear structures. Fig. 1 shows the 

contourlet decomposition in the frequency domain, where 

shaded parts denote the support regions of corresponding 

filters. During the contourlet decomposition, an image is 

first decomposed by LP into a low-frequency subband 

and mutiple high-frequency subbands, and then each 

high-frequency subband is fed into DFB to generate 

multiple directional subbands. 

In the contourlet transform, the number of directional 

n 

subbands in each scale is usually 2 ( n∈ N) 

and quite 

flexible when n is set differently. Therefore, the 

contourlet transform is able to provide detailed 

information in any arbitrary direction, which is its major 

advantage over the other MSD transforms. Meanwhile, 

after the contourlet decomposition, majority of the 

contourlet coefficients of an image are close to zero, 

concentrating the most information and energy, which 

indicates the sparsity of the contourlet transform. 

Ⅲ. PCNN AND ULPCNN 

A. Basic PCNN 

PCNN is a feedback network in a single layer with 

neurons laterally interconnected, which can imitate the 

biological characteristics of HVS. Basically, each neuron 

consists of a receptive field, a modulation product and a 

pulse generator. For the neuron located at ( i, j ) in a 

PCNN, the receptive field involves a linking input L ij 

and a feeding input F ; The modulation product 

ij 

combines F with the biased L to form a total internal 

ij 

ij 

activity 

U ; The generator Y 

ij 

ij 

will produce a pulse (i.e. 

firing) if U ij 

exceeds the dynamic threshold θ ij 

. When 

inspired by external stimulus S ij 

and influenced by 

signals from neighboring neurons { Y kl 

} 

mathematical equations for F ij 

, 

L , 

ij 

, the discrete 

U , Y and θ can 

ij ij 

ij 

be described as follows. 

−α 

F ( n) = e F ( n− 1) + V M Y ( n 1) S 

F 

ij ij F ∑ − + , (1) 

ijkl kl ij 

kl 

−αL 

L ( n) = e L ( n− 1) + V W Y ( n 1) 

ij ij L∑ − , (2) 

ijkl kl 

kl 

U ( n) = F ( n) ⋅ (1 +β L ( n)) 

, (3) 

Y ( n) 

ij 

ij ij ij 

1, U ( n) >θ ( n−1), 

ij 

ij 

0 , otherwise , 

= ⎧ ⎨ ⎩ 

(4) 

θ ( n) = e −α θ 

θ ( n− 1) + VY ( n) 

. (5) 

ij ij θ ij 

Figure 1. Frame of contourlet decomposition in the frequency domain. 

Fig. 2 illustrates the basic model for a single neuron 

located at ( i, j ) in a PCNN. Output pulses of neurons in 

the k× l neighborhood centered at ( i, j ) enter into the 

neuron at ( i, j ) and then influence its next output, where 

k× l is called linking range. L ij 

receives pulses from 

surrounding neurons ((2)), and F ij 

receives not only the 

neighboring signals but also the external stimulus S ij 



Figure 2. Basic model for a single PCNN neuron. 

((1)). U is obtained by multiplying F with the biased 

ij 

ij 

L ((3)). If U is above the neuromime threshold θ , Y 

ij 

ij 

ij ij 

will generate a pulse ((4)), and simultaneously θ ij 

will 

increase enormously ((5)) to block another pulse in the 

next iteration. Without an output pulse, θ ij 

would decay 

exponentially ((5)), until it drops below the internal 

activity and at that time a pulse will be outputted again. 

In this way, these processes run over and over again. In 

(1)-(5), n denotes the iteration times; α F 

, α , α and 

L θ 

V , V , V θ 

are attenuation time constants and inherent 

F 

L 

voltage potential of F ij 

, L and θ , respectively; 

ij 

ij 

W signify synaptic weight strength for F 

ijkl 

ij 

and 

M and 

ijkl 

L ; 

ij 

β indicates linking strength determining contribution of 

the linking input to the internal activity. 

B. ULPCNN 

PCNN is qualified to imitate the biological features of 

HSV and hence apply to image processing [17]-[19]; 

however, so many parameters in the model should be set 

during use. So far, the relation between model parameters 

and network outputs is still ambiguous, and it is really 

difficult to determine the proper PCNN parameters. 

Therefore, ULPCNN is presented to simplify the PCNN 

by means of decreasing parameters and making the 

linking inputs of ULPCNN neurons uniform [16]. Fig. 3 

displays the simplified model for a single ULPCNN 

neuron. The processes of a single ULPCNN neuron are 

displayed as 

F ( n) 

= S , (6) 

ij 

∑ 

1, Y ( n− 1) > 0, 

⎧⎪ 

kl 

L ( n) 

= 

kl 

ij ⎨ 

⎪⎩ 0 , otherwise , 

ij 

(7) 

U ( n) = F ( n) ⋅ (1 +β L ( n)) 

, (8) 

ij ij ij 

Figure 3. Simplified model for a single ULPCNN neuron. 

Y ( n) 

ij 

1, U ( n) >θ ( n−1), 

ij 

ij 

= ⎧ ⎨ (9) 

⎩ 

0 , otherwise , 

θ ( n) = e −α θ 

θ ( n− 1) + VY ( n) 

. (10) 

ij ij θ ij 

According to (7), if any neuron in the k× 

l 

neighborhood fires, L ij 

will have a unity input, and then 

the centered neuron will be encouraged to fire. Obviously, 

impulse expanding behavior is much clearer and more 

controllable with much fewer parameters than the basic 

PCNN. 

IV. THE PROPOSED IMAGE FUSION METHOD 

Considering that HVS is very sensitive to detailed 

information, researchers commonly employ fusion rules 

to choose more significant information in high-frequency 

subbands. In our study, we provide a new image fusion 

method based on directional contrast-inspired ULPCNN 

in the contourlet domain. Directional features are fed into 

ULPCNN to imitate the biological activity of HSV, and 

then transmitted in the form of pulses. The linking range 

for each neuron is adaptive to corresponding directional 

contrast. The first firing time of each neuron is used to 

determine the decision in fusion rules. Because of the 

global coupling characters of the ULPCNNs, global 

features of images can be made good use of during fusion 

in our proposed method. 

Fig. 4 shows the flowsheet of our proposed method. 

Detailed procedure of the CT-ULPCNN method is given 

as follows. 

• Source images A and B are decomposed by the 

A A 

contourlet transform to coefficients { a , d } and 

, 

B 

{ a , d }, respectively. Denote the coefficients of 

R 

B 

r, 

p 

F F 

the fused image F by { a , d }. Here, R is the 

R r, 

p 

decomposition level, a X (X=A,B,F) denotes the 

R 

coefficients in the low-frequency subband of 

X 

image X, and d (X=A,B,F) denotes the 

r, 

p 

R 

r p 



Figure 4. Flowsheet of our proposed method. 

coefficients in the pth directional subband at the 

rth (1 ≤ r ≤ R) 

scale of image X. 

• In each directional subband, directional contrast at 

location (, ) i j can be calculated as 

Ctr (, i j) = d (, i j) a ( u, v) 

. (11) 

X X X 

r, p r, 

p r 

X 

where a indicates the low-frequency subband at 

r 

the rth scale of image X, and the coarse 

coefficient at location ( uv , ) corresponds to the 

X 

X 

same region as d , 

(, i j ) does. Then Ctr (, i j ) 

, 

r p 

is imported as the external stimulus S ij 

into the 

ULPCNN neuron located at ( i, j ). Its linking 

range is fixed according to 

k 

ij 

or l 

ij 

r p 

5, 

X 

X 

Ctr ( i, j) ≥ max( Ctr ) 2 , 

r, p 

r, 

p 

3, otherwise. 

= ⎧ ⎨ 

⎩ 

(12) 

The ULPCNN operates iteratively as (6)-(10), 

until all neurons are fired at least once. The first 

firing time of the neuron at location (, i j) 

in the 

pth directional subband at the rth scale of image X 

X 

should be recorded as T (, i j ) (X=A,B). 

, 

F F 

• 

R r, 

p 

{ a , d } are obtained by the following rules. 

For the low-frequency, 

r p 

( ) 

F A B 

a (, i j) = a (, i j) + a (, i j) 2 , (13) 

R R R 

For the high-frequency, 

d 

F 

r, 

p 

(, i j) 

A A B 

d (, i j), T (, i j) < T (, i j), 

⎧ r, p r, p r, 

p 

= ⎨ (14) 

B 

⎩ 

d 

r, 

p 

( i, j), otherwise. 

• The fused image F is finally achieved via 

F F 

contourlet reconstruction from { a , d }. 

R r, 

p 

V. EXPERIMENTAL RESULTS 

To certify the effectiveness of our proposed method, 

we have performed the CT-ULPCNN method on many 

pairs of images. Considering limitation of space, we take 

three pairs of images (shown in Fig. 5) as examples to 

provide the experimental results. Fig. 5(a) is a pair of 

multifocus images focusing on different objects of the 

same scene, Fig. 5(b) displays a pair of remote sensing 

images taken from different wavebands, and Fig. 5(c) is 

a pair of infrared and visible images. 

In this section, following two sets of tests are designed 

to prove the validity of our proposed method. In Test 1, 

we highlight the advantage of the adaptive ULPCNNs 

model in our proposed method by comparing its behavior 

to three existing contourlet-based image fusion 

algorithms, including CT-Miao [12], CT-Zheng [13], and 

CT-Yang [14]. Test 2 demonstrates the prominence of 

the CT-ULPCNN method by its comparison with some 

typical MSD-based image fusion methods, namely, the 

gradient pyramid-based method (Gradient) [20], the 

conventional discrete wavelet transform-based method 

(DWT) [21], the curvelet transform-based method 

(Curvelet) [22], and the nonsubsampled contourlet 

transform-based method (NSCT) [23]. 

In our experiments, images were all decomposed into 

four levels in use of the above MSD-based fusion 

methods. Especially, for the contourlet-based image 

fusion methods, the decomposed four scales were 

divided into 4, 4, 8, and 16 directional subbands from 

coarse to fine scales, respectively. Furthermore, in our 

proposed method, parameters were set as α = 0.5 , 

θ 

V θ 

= 20 and β = 3 . 

A. Test 1 

Fig. 6-Fig. 8, respectively, provide the fusion results 

of pepsi, remote and camp using the CT-ULPCNN, CT- 

Miao, CT-Zheng, and CT-Yang methods. To show more 

clearly, we select a section of each result to enlarge. 

As can be seen from Fig. 6, for multifocus images, the 

CT-Miao, CT-Zheng, and CT-Yang methods all have the 

problem of ring artifacts in their fusion results, and the 

partial result of the CT-Zheng has the severest ghost 

image even with a post-processing of consistency 

verification (CV) to intentionally reduce the ringing 

artifacts; whereas our proposed method possesses a result 

with the fewest ringing artifacts, highest contrast and 

finest details without the CV. 

As seen from Fig. 7, the CT-ULPCNN method still 

has the best performance with the smoothest surface in 

the flat regions. However, the result of the CT-Yang 



(a) (b) (c) 

Figure 5. Three pairs of test images: (a) pepsi, (b) remote and (c) camp. 

(a) (b) (c) (d) 

(e) (f) (g) (h) 

Figure 6. Fusion results of pepsi: (a) our method, (b) CT-Miao, (c) CT-Zheng, (d) CT-Yang, 

and (e)-(h) are partial enlargements of (a)-(d), respectively. 

method is visually unsatisfactory. This is because the 

fusion rule of the CT-Yang method for the lowfrequency 

subband is to choose the low-frequency 

coefficient with the maximum region variance, and such 

a rule makes the fused approximated image unsmooth 

when applying to source images with distinct basic 

illuminations, such as remote sensing images in different 

wavebands. 

Likewise, for the pair of infrared and visible images, 

the CT-Yang method generates the worst fusion result; 

whereas the hot target (i.e. the man) is the most 

distinguishable in the result of our proposed method (Fig. 

8(a)). 

Obviously, the CT-ULPCNN achieves superior visual 

quality over the other three contourlet-based fusion 

methods. 



(a) (b) (c) (d) 

(e) (f) (g) (h) 

Figure 7. Fusion results of remote: (a) our method, (b) CT-Miao, (c) CT-Zheng, (d) CT-Yang, 


(a) (b) (c) (d) 

(e) (f) (g) (h) 

Figure 8. Fusion results of camp: (a) our method, (b) CT-Miao, (c) CT-Zheng, (d) CT-Yang, 


To evaluate the fusion effects more objectively, we 

introduce average gradient (AG), spatial frequency (SF), 

mutual information (MI), Q AB/F [24] and a universal 

image quality index (UIQI) [25] as fusion indices. 

Generally, the larger the above five objective indices, the 

better the fusion result is. 

Table Ⅰ-Ⅲ show the indices for fusion results of the 

three pairs of images in Fig. 5, respectively. According 

to these tables, the results of our method always have the 

largest values in the average gradient, spatial frequency, 

mutual information, Q AB/F and the universal image 

quality index, no matter for the pair of multifocus images, 

or the pair of remote sensing images, or the pair of 

infrared and visible images. This clearly proves the 

superiority of our proposed method on the objective 

evaluations. 

B. Test 2 

We also make a comprehensive comparison of our 

proposed method with other four classical MSD-based 

fusion methods, including the Gradient [20], DWT [21], 

Curvelet [22] and NSCT [23]. 

Because of the limitations of space, we only exhibit 

the fusion results of pepsi in Fig. 9. Apparently, the 

result of the Gradient method has the lowest contrast, 

and the Curvelet and the NSCT methods also generate 



(a) (b) (c) (d) (e) 

(f) (g) (h) (i) (j) 

Figure 9. Fusion results of pepsi: (a) our method, (b) Gradient, (c) DWT, (d) Curvelet, (e) NSCT 

and (f)-(j) are partial enlargements of (a)-(e), respectively. 

results with relatively lower contrast, and the results of 

the NSCT and especially the DWT methods have heavy 

ringing artifacts; whereas our proposed method produces 

a result with the highest contrast and the fewest ringing 

artifacts. Visually, the advantage of our proposed method 

is prominent. 

Table Ⅳ shows the fusion indices of results by using 

the above five image fusion methods for pepsi. The 

result of our proposed method has the largest mutual 

information, Q AB/F , and the universal image quality index, 

except that, it has lower average gradient and spatial 

frequency than those of the DWT and the NSCT methods. 

This is because that, for pepsi, severe ringing artifacts in 

the results of the DWT (Fig. 9(h)) and the NSCT (Fig. 

9(j)) may cause larger values in the average gradient and 

the spatial frequency. 

Experimental results demonstrate that, the superiority 

of the proposed method, in the field of visual quality and 

objective evaluations, is prominent. This mainly benefits 

from the global coupling characteristics of the 

ULPCNNs model. By using the features extracted from 

the output pulses of the ULPCNNs, the biological 

activity of the HVS to detailed information of images can 

be reflected very well. 


In this paper, we provide a new image fusion 

algorithm based on the ULPCNNs in the contourlet 

domain. Directional contrast is fed into the ULPCNNs to 

imitate the biological activity of HVS to directional 

information. Linking range is also determined by the 

contrast, flexibly making good use of global features of 

images. Experimental results illuminate that, the CT- 

ULPCNN method outperforms the other methods in both 

the visual and the objective fields. 


This work was supported by the Fundamental 

Research Funds for the Central Universities 

(N110323004) and the Natural Science Foundation of 

Hebei Province under Grant No.F2012501001. 

Method 

TABLE I. 

FUSION INDICES FOR PEPSI 

Metrics 

AG SF MI Q AB/F UIQI 

CT-ULPCNN 5.6722 13.986 6.7704 0.74015 0.89467 

CT-Miao 5.5759 13.923 6.4653 0.73644 0.85769 

CT-Zheng 5.4912 13.833 6.2256 0.71153 0.84454 

CT-Yang 5.5684 13.933 6.4987 0.73185 0.85492 

Method 

TABLE II. 

FUSION INDICES FOR REMOTE 

Metrics 


CT-ULPCNN 7.0993 15.362 1.6673 0.56055 0.69729 

CT-Miao 6.6244 14.646 1.4599 0.53364 0.64608 

CT-Zheng 6.6965 14.526 1.4182 0.49636 0.63166 

CT-Yang 7.0883 15.037 1.1027 0.46923 0.50629 

Method 

TABLE III. 

FUSION INDICES FOR CAMP 

Metrics 


CT-ULPCNN 7.2227 13.506 1.5600 0.46466 0.63175 

CT-Miao 6.8137 12.747 1.3814 0.4067 0.56411 

CT-Zheng 6.7682 12.529 1.3594 0.38244 0.55494 

CT-Yang 7.0183 13.064 1.5026 0.38959 0.51602 

TABLE IV. 

FUSION INDICES FOR PEPSI 



Method 

Metrics 


CT-ULPCNN 5.6722 13.986 6.7704 0.74015 0.89467 

Gradient 4.7795 11.987 6.135 0.73947 0.88898 

DWT 5.8093 14.173 6.3616 0.72958 0.86539 

Curvelet 5.6215 13.977 6.5344 0.73633 0.88186 

NSCT 7.7004 18.99 6.7607 0.68791 0.78435 

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Xi Cai received her B.S. and Ph.D. degrees from the School of 

Electronic and Information Engineering, Beihang University, 

China, in 2005 and 2011, respectively. Now she is a teacher at 

Engineering Optimization and Smart Antenna Institute, 

Northeastern University at Qinhuangdao, China. Her research 

interests include image fusion, image registration and object 

detection. 

Guang Han received his B. Eng. and M. Eng. degrees from the 

School of Electronic and Information Engineering, Beihang 

University, China, in 2005 and 2008, respectively. Now he is a 

Ph.D. candidate at College of Information Science and 

Engineering, Northeastern University. His research interests 

include object detection and object tracking based on video 

sequences. 

Jinkuan Wang received the M.Eng. degree from Northeastern 

University, Shenyang, China, in 1985, and the Ph.D. degree 

from the University of Electro-Communications, Chofu, Japan, 

in 1993. 

In 1990, he joined the Institute of Space and Astronautical 

Science, Sagamihara, Japan, as a special member. He was an 

Engineer with the Research Department, COSEL Company, in 

1994. He is currently the President of the Northeastern 

University at Qinhuangdao, Hebei, China, where he has been a 

Professor since 1998. He has been a main researcher in several 

National Natural Science Foundation research projects of China. 

His main interests are in the areas of intelligent control, 

adaptive array, wireless sensor networks and image processing. 



The Critical Legal Contention under the 

Challenge of Information Age and the 

Predominant Social Interests Concern for 

Developing Intelligent Vehicle Telematics in the 

United States 

Fa-Chang Cheng 

National Kaohsiung First University of Science and Technology/Graduate Institute of Science and Technology Law, 

Kaohsiung City, Taiwan 

Email: fachang1@hotmail.com 

Wen-Hsing Lai * 

National Kaohsiung First University of Science and Technology/Dept. of Computer and Communication Engineering, 

Kaohsiung City, Taiwan 

Email: lwh@nkfust.edu.tw 

Abstract—Intelligent Vehicle Telematics has been a 

promising industry in the world. This new development of 

telecommunication technology has emerged with some legal 

concerns, especially in the liability for failure of safety 

devises and the protection of information privacy within 

Intelligent Vehicle Telematics. The purpose of this article is 

to gain experiences from the discussion for these concerns in 

academic papers and related cases within the United States, 

in order to depict the possible solution for safety related 

legal concerns and the protection of information privacy 

which is based upon not only the concern of information age 

but also the concern of national security with regard to 

developing Intelligent Vehicle Telematics. The purpose of 

this article is intended to offer some valuable reference to 

other countries which are also involving in the development 

of intelligent Vehicle Telematics. 

Index Terms—Intelligent Vehicle Telematics, product 

liability, strict liability, information privacy 


The Intelligent Vehicle Telematics is highly valued by 

the government in the world as having a lot of beneficial 

potential to the transportation infrastructure in such 

sovereignty. The features of safety design are critical to 

the Intelligent Vehicle Telematics and have some 

significant meaning to the legal infrastructure. Those 

safety devises may increase the safety of transportation 

which benefits to the society as a whole. Conversely; the 

failure of such safety devises may cause a lot of trouble. 

Manuscript received September 20, 2012; revised September 20, 

2012; accepted September 20, 2012. 

* Corresponding author 

Therefore, the liability for system provider and devise 

manufacture (distributor) is one significant safety legal 

issue with regard to Intelligent Vehicle Telematics. Apart 

from the safety related legal concerns, the protection of 

privacy in the operation of Intelligent Vehicle Telematics 

is also another critical legal issue for Intelligent Vehicle 

Telematics. The intention of this article is to introduce 

the concept of information privacy in the United States 

and bring up the suggestion of how to comprise the 

conflictions between protecting information privacy and 

other legal interests. Since this paper is mainly talking 

about the concerns from the prospective of the United 

States because due to the United states advancing in 

Intelligent Vehicle Telematics research field, except the 

general technology description of Intelligent Vehicle 

Telematics, including the safety features, in the beginning, 

this article will center the discussion on these concerns to 

academic papers and related cases within the United 

States, in order to depict the possible solution for safety 

related legal concerns and the protecting privacy concerns 

with regard to developing Intelligent Vehicle Telematics 

to other following countries. 

II. THE TECHNOLOGY OF INTELLIGENT VEHICLE 

TELEMATICS AND ITS SAFETY FEATURES 

Vehicle Telematics is the integrated use of 

telecommunications and informatics within road vehicles. 

The objectives of Intelligent Vehicle Telematics are to 

improve safety, reduce traffic congestion, fuel 

consumption and carbon dioxide emissions, and increase 

comfort and convenience or even entertainment, and the 

future trends focus on making automobiles greener, 

smarter, and merging transportation and information 


doi:10.4304/jcp.8.6.1552-1559


networks [1]. Most vehicle telematics projects were 

developed isolate. However, in some regions, like 

European Commission, have decided to act forwards 

harmonizing the deployment and use of ITS in road 

transport across Europe by means of the ITS Action Plan 

and the European ITS Directive [2]. 

Wireless communications and networking is a core 

enabling technology for ITSs (intelligent transport 

systems). A vehicle may communicate with other 

vehicles (vehicle-to-vehicle, V2V) or the infrastructure 

(vehicle-to-infrastructure, V2I) by using Dedicated Short 

Range Communication (DSRC), cellular communication, 

satellite communication, WiFi, Bluetooth or RFID. 

Among them, DSRC is short to medium range wireless 

communication promoted by US Department of 

Transport and specifically designed for vehicle use. US 

Federal Communications Commission (FCC) has 

allocated 75MHz in the 5.9GHz band for DSRC. Longer 

range communications can be accomplished by GSM, 3G, 

or WiMAX. It is noted that to prevent accidents, very low 

latency and short response times are needed for vehicleto-vehicle 

communications [3]. IEEE 802.11p, which is 

the groundwork for DSRC, is an IEEE standard to add 

wireless access in vehicular environments (WAVE). It 

defines enhancements to 802.11 to support ITS. That is, it 

is specially designed for data exchange among moving 

vehicles and road infrastructure. 

Generally speaking, in vehicle transportation, safety 

normally gets top priority, though entertainment and 

convenience have rapidly caught up to safety as the 

impetus for new in-car electronics development [4]. 

Examples of many applications of vehicle safety systems 

are: Cooperative forward collision warning, Emergency 

braking notification, Lane or road departure warning, Precrash 

sensing, Curve speed warning, Right turn assistance, 

Give way junction assistance, Traffic signal violation 

warning, Intersection collision warning, Road / rail 

collision warning, Road condition warning, Approaching 

emergency vehicle warning, Emergency vehicle signal 

pre-emption, Road works warning, and Motorway merge 

assistance [5]. 

The above safety related application systems or 

functions of intelligent vehicle system generally focuse 

on assisting drivers and preventing driver errors while 

full autonomous, unmanned vehicles are still remained as 

a research topic. However, these systems which designed 

to improve safety may, instead, compete for driver 

attention and provide confusing message [6]. That causes 

the telematics use becoming a contributing factor for 

crashes, mostly due to multitasking, distraction and 

longer duration usage time than conventional in-vehicle 

tasks [7]. Besides, more and more car innovations are 

from computer systems and software, and such 

complexity brings with it reliability concerns [8]. Ivan 

Berger [9] questioned three growing challenge for 

carmakers. First, the more complex a car electronic 

system, the more failure points it offers. Second, the 

growing reliance on software raises more risk of fail. 

Third, the hardware environment becomes more 

demanding because of heat and electromagnetic 

interference (EMI). 

Some methods have been proposed to solve the safety 

concerns. For example, a workload manager is set to help 

determine if a driver is overloaded or distracted [7], and a 

structured procedural safety assessment of intervening 

systems is proposed [10]. Nevertheless, unless we can 

totally understand the driving behavior [11] - [13], 

including driver intentions, how people make decisions, 

and how people interact with vehicle, and model the 

behavior, there are still risks. 

In addition, there is privacy concern to aware. 

Knowing the accurate position and status of vehicles is 

the first thing to do to make the transport intelligent. 

Global Positioning System (GPS) is a convenient way to 

calculate the information. However, the accuracy of 

standard GPS, which is generally 5 to 10 meters, is not 

always enough, and the accuracy and reliability of GPS 

are degraded in urban environments due to satellite 

visibility and multipath effects. Other technologies like 

Triangulation Method using mobile phones or inertial 

navigation by the sensors via dead reckoning could be 

integrated to improve the accuracy. Video cameras can 

also be fused [14] to help measure traffic flow or the 

distance between lane lines. The computer vision 

technology can not only be used to look out of the vehicle 

to detect and track roads, but simultaneously look inside 

the vehicle to monitor the attentiveness or intentions of 

the driver [15]. Besides camera, multiple Sensors 

including radar and lidar can be used to help detect 

various statistic or moving on-road obstacles [16]. Using 

standard statistics of telecom switches without extra 

effort in telecom network is also used to compute the 

speeds of vehicles [17]. By using the above techniques, 

accurate position or status information is obtained and 

then, these information is generally shared with other 

vehicles and infrastructure by communication. If privacy 

filtering is not applied, serious privacy risk happens. 

Some applications like Pay-As-You-Drive Insurance 

model [18] have noticed it. The system performs the 

premium calculations locally in the vehicle, and send 

only aggregated data to the insurance company without 

leaking location information. 

Another trend to aware is that cloud computing is 

expected to play a pivotal role in future automotive 

telematics services. It particularly makes the security and 

privacy in clouds an important issue in ITS. 

III. THE LIABILITY OF SYSTEM PROVIDER AND DEVISE 

MANUFACTURE (DISTRIBUTOR) FOR SAFETY LEGAL 

CONCERNS 

The safety concern for the Intelligent Vehicle 

Telematics is by far the most concerned topic both from 

the technical and the legal perspective. Discussing from 

the legal perspective for safety concern to Intelligent 

Vehicle Telematics, at first sight, there could be three 

potential possible kinds of liability, negligence, warranty 

in contract or strict liability, for the system provider and 

four potential possible kinds of liability for devise 

manufacture (distributor) with regard to the safety legal 



concerns, adding product liability to the three just 

mentioned before. The difference between the system 

provider and the devise manufacture (distributor) for 

potential liability to the safety legal concerns the product 

liability because the product liability is only eligible for 

the harm done by the tangible product, but not the 

services. For the purpose of elucidating the discussion 

here, briefly introducing the concepts of negligence, 

warranty, strict liability and product liability is necessary. 

And the assertion of this article will insist that strict 

liability theory is most appropriate to those situations 

based on the understanding and characteristics of those 

legal infrastructures since there is no real case handed 

down related to the safety legal concerns for Intelligent 

Vehicle Telematics in the United States judicial system. 

Regarding this section here, the discussion will be 

divided into three parts discussion: the first part of 

theories among negligence, warranty, product liability 

and strict liability; the second part of comparing among 

negligence, warranty, product liability and strict liability 

for the culpability; and the third part of the reason to 

choose strict liability for the system provider and devise 

manufacture (distributor) as the liability solution for the 

related safety legal concerns to Intelligent Vehicle 

Telematics. 

A. The Theories among Negligence, Warranty, Product 

Liability and Strict Liability 

The first safety liability theory for system provider and 

devise manufacture (distributor) to Intelligent Vehicle 

Telematics is negligence. Generally speaking, the theory 

of negligence is really based upon the idea of fault. To 

indicate a defendant is negligent means that the defendant 

in the case violates the duty of care imputed by the 

society. And, except for some specific circumstances, the 

standard of care is either based upon the reasonable 

person [19] or professional reaction [20] under the 

ordinary cases. Another specific feature for the theory of 

negligence is the requirement for proximate cause of 

which the legal meaning is to define the amount of 

damages. The cause in fact between the wrongdoer and 

the consequences invoked by such wrongdoer is required 

in every tortious cause of action, the proximate cause is 

not a prerequisite for the cause of action in torts, for 

example the intentional torts or product liability etc. and 

the proximate cause is really a means to the policy 

concern’s ends [21]. So, in order to substantiate in a 

negligence case, there are four elements need to be 

proved: duty of care, breach duty of care, causation 

(including the cause in fact and proximate cause) and 

damages. 

The second possible legal theory of the liability for 

system provider and devise manufacture (distributor) 

related to the safety devise for Intelligent Vehicle 

Telematics is warranty. Warranty cause of action is 

really something between the contract theory and the torts 

theory. Two kinds of warrant theory fall under this 

category; one is called the express warrant, the other is 

named the implied warranty. In the express warranty, it 

could be the contract liability which needs to prove the 

contract privity between the parties involved in the 

warranty dispute. The express warrant could also be the 

torts liability which needs to prove the reliance of the 

injured party, even though there is no requirement for 

proving the privity between the parties [22]. And the 

adoption of implied warrant theory is, to some extent, 

depending on the willingness of the court and mostly 

used in the dispute of fitness of the object to its common 

application [23]. 

The third possible legal theory to the mentioned 

liability is strict liability. In the strict liability theory, 

there is no need to prove the defendant’s fault, the 

contract privity, the reliance of the injured or even 

pending on the court’s interference. To prove some basic 

facts and establish that these facts results in the 

consequences is the only requirement to assert the strict 

liability. Traditionally, two types of strict liability are 

accepted in cases: the wild or vicious animal strict 

liability and the extremely dangerous activity strict 

liability. However, even under this stringent liability, 

some exceptions exist to the general rule, like the 

comparative negligence of plaintiff [24] or the Act of 

God [25]. 

The last possible legal theory of the liability mentioned 

in this paragraph for system provider and devise 

manufacture (distributor) related to the safety devise for 

Intelligent Vehicle Telematics is product liability. The 

main purpose of product liability is to protect the user or 

consumer from injured by the product threw in the stream 

of commerce. Theoretically, this legal theory contains 

three different types of product liability claims: 

manufacturing defect, design defect and lack of warning 

[26]. Several possible legal interpretations can delineate 

the meaning of product liability. To make the statement 

more clear, under the title of product liability, a product 

liability case can really be a negligence case [27], a 

warrant case [28] or a strict liability case [29]. When a 

product liability case is based upon the strict liability 

theory, the distributor or the manufacture for the product 

would easily be involved in such case. The provision in 

the Restatement (Second) of Torts embodies the strict 

liability approach. According to Restatement (Second) of 

Torts § 402A which is accepted by some of the states in 

the United States, one who sells any product in a 

defective condition unreasonably dangerous to the user or 

consumer or to his property is subject to liability for 

physical harm thereby caused to the ultimate user or 

consumer, or to his property, even the seller has exercised 

all possible care in the preparation and sale of his product 

or the user (or consumer) has not brought the product 

from or entered into any contractual relation with the 

seller. Even the Restatement (Second) and following 

courts take the position that both the manufacture and the 

distributor shall bear the strict liability [30], there are still 

some jurisdictions which partially follow the Restatement 

(Second) would like to prove the breach of duty to the 

manufacture which is based upon design defect and lack 

of warning claims in a product liability litigation [31]. 

And just similar to the strict liability, there are also a 

couple possible defenses, comparative negligence of 

plaintiff [32] and statutory immunity (preemption) [33] or 



unforeseeable misuse of the product [34], could be used 

as the defense against the product liability. To sum up 

the description regarding the product liability, the product 

liability is the liability to harm caused by the product 

which liability can present either one of the three possible 

choices: negligence, breach of warranty or strict liability. 

B. The Comparison among Negligence, Warranty, 

Product Liability and Strict Liability for the Culpability 

of Wrongdoer 

From the explanation in this previous paragraph, the 

conclusion for comparing different legal theories for the 

safety related legal dispute can be summarized as the 

following. First of all, the negligence cause of action is 

the most difficult liability to prove because, unlike 

warranty or strict liability, the duty of care needs to be 

substantiated. And the strict liability might be the easist 

legal theory to satisfy in the burden of providing evidence. 

As to the warranty cause of action, the liability would 

either rely on the contract privity or reliance in express 

warranty or count on the court intervention in implied 

contract. To estimate the strength of liability or 

culpability, the warranty cause of action seems to stand in 

between of the negligence and the strict liability. The last 

possible liability mentioned in this article-product 

liability, is really a mixture type of theory of liability 

among the negligence liability, warranty liability and the 

strict liability. Observing the history of the policy 

attitude toward the product liability, the substance to 

contend product liability is really swinging between the 

negligence and the strict liability and some commentator 

believes the current court attitude in applying the product 

liability is more lenient toward the manufacture [35]. 

C. The Reason for Choosing Strict Liability for the 

System Provider and Devise Manufacture (Distributor) 

as the Liability Solution for the Related Safety Legal 

Concerns to Intelligent Vehicle Telematics 

This article would like to indicate that those safety 

devises to Intelligent Vehicle Telematics are presenting 

really high social responsible concerns. Therefore, the 

primary policy thinking should be that the manufacture of 

these safety devise to Intelligent Vehicle Telematics is 

going to hold the highest legal responsibility under the 

current legal theory to the injured person or property 

based upon the strict product liability. And the system 

provider for the operation of these safety devises to 

Intelligent Vehicle Telematics is the same important as 

the manufacture. If anything goes wrong with the system, 

it could cause a catastrophe to the transportation. 

Therefore, the system provider for the operation of these 

safety devises to Intelligent Vehicle Telematics should 

also take the strict liability. The liability for both the 

manufacture and the system provider here is nothing like 

the liability to the cell phone manufacture or the 

communication services provider for the user talking over 

the cell phone while he or she was driving because the 

cell phone is not designed to the protection of 

transportation safety and the user who initiates 

communication and cause the distraction which results in 

the traffic incident should be responsible for his or her 

behavior [36]. As to the distributor between the 

manufacture and the user or consumer, because the 

distributor doesn’t directly contribute to the safety legal 

issue regarding the safety devises within Intelligent 

Vehicle Telematics, it is suggested the distributor doesn’t 

need to be strictly liable to the injury based upon product 

liability by the failure of these safety devises. The 

current situation as to different options for liability to the 

distributor should remain the same for further 

consideration through the case decision in the future. 

IV. THE PROTECTION OF INFORMATION PRIVACY IN 

INTELLIGENT VEHICLE TELEMATICS 

As mentioned in the beginning of this article, in 

applying Intelligent Vehicle Telematics to the real world, 

often times, it will acquire, collect or use personal 

information in the process of operating these devises or 

systems. This could arouse a lot of concerns to the legal 

issue of information of privacy. In this section, it intends 

to introduce the idea of information privacy in the United 

States, the protection of this legal interest in the United 

States. Not only will several inclined tendencies to the 

protection based on the concern of information age be 

indicated here but also is the suggested hierarchy of 

methods to build up such protection in the legal arena for 

Intelligent Vehicle Telematic going to be discussed. One 

additional future possible concern to the protection of 

critical infrastructure based upon the reason of national 

security will also be briefly discussed for the purpose of 

this article. The purpose of all these discussions is to 

make projection of what would have happened if the 

issue of information privacy emerged once the industry of 

intelligent vehicle telematics becomes mature. 

A. The Concept of Information Privacy and the 

Protection in the United States 

The protection of “privacy” is not articulated in the 

Constitution in the United States, instead it is interpreted 

by the Supreme Court to say “The forgoing cases suggest 

that special guarantees in the Bill of Rights have 

penumbras, formed by emanations from those guarantees 

that help give them life and substance. Various 

guarantees create zones of privacy.” in order to “create” 

the protection of privacy [37]. Through the years, the 

Supreme Court has recognized several kinds of privacy as 

the fundamental human rights [38], for example the right 

to marriage, breeding the child etc., but not the 

information privacy. The significant legal meaning of 

information privacy as a non-fundamental human rights 

on the Constitutional level is that the right of privacy will 

probably be restricted when it directly conflicts with the 

protection of other fundamental human rights or 

important social rights, for example the freedom of 

speech [39]. And it is fairly to say, other than conflicting 

with the protection of other fundamental human rights or 

important social rights, the protection of information 

privacy is really the balance of interests between the 

protection of privacy and other affected legal interests, 

except it wouldn’t affect any legal interests, for example, 

to the protection against unauthorized invasion of 



information privacy. From the experience of the United 

States in protection of information privacy, there are three 

auspicious preventive and one remedial trends worth to 

draw attention. The first preventive trend is to use 

informed consent mechanism for reducing or eradicating 

the controversy of reasonable expectation of privacy. 

The second preventive trend is to emphasize the 

importance of technology prevention of information 

privacy infringement. And the last one preventive trend 

is to enhance the liability of data collector for notification 

of the security breach to the information provider in case 

of some special kind of personal information been 

unauthorized disclosed by the third party. As to the 

remedial trend related to the protection of information 

privacy for intelligent vehicle telematics, the focus will 

be the secondary liability to the internet service provider. 

Especially a secondary liability case of internet service 

provider about trademark infringement in recent years is 

going to be discussed here since there seems no direct 

judicial verdict to address the secondary liability of 

information privacy infringement to the internet service 

provider. 

B. The Three Observations to the Preventive Measure in 

the Protection of Information Privacy 

First of all, the best way to eliminate the issue of 

whether or how the information privacy shall be 

protected is to receive the consent of personal 

information provider in gathering the personal 

information. The legal thinking behind this is that the 

information privacy is a personal right and can be 

reduced or eliminated by way of the consent of the 

information provider. It can be seen from a flood of 

statements related to privacy policy within a variety of 

contract in the United States. Also, this idea of executing 

informed consent appears in some federal legislation and 

administrative regulation. For example, in HIPAA 

(Health Insurance Portability and Accountability Act) 

[40], the Congress require in this act that the entities for 

health care will basically get the informed consent for any 

disclosure of personal medical information. The new 

drug application for biological product and the human 

body test for genetic therapy will need the informed 

consent from the test or research subject before the 

approval of such application or test [41]. And, the 

informed consent requirement also happens in The 

Gramm-Leach-Bliley Act and Privacy of Consumer 

Financial Information, Regulation P for electronic 

commerce. 

Secondly, beside the informed consent methodology, 

to put a high value of technology prevention in protecting 

information privacy is the other current trend of 

preventive measure for the information privacy 

infringement. The best example for the emphasis of 

technology security is the infrastructure for establishing 

technology standard in American Recovery and 

Reinvestment Act of 2009 [42]. Generally speaking, 

from Subtitle C SEC 3001-3003 in American Recovery 

and Reinvestment Act of 2009, Congress design to 

establish the Office of the National Coordinator for 

Health Information Technology for the purpose of setting 

up the technology standard, including the purpose of 

protection in information privacy, in order to promote the 

electronic medical records system. 

The last observed tendency for the issue of protecting 

information privacy is to add the obligation of 

notification to who preserves the individual information 

when such information has been unauthorized accessed 

by the third party. This measurement is a fairly new legal 

remedy for the harm to the information privacy. For 

example, the detailed mechanism for how to work the 

requirement of notification in electronic medical records 

security breach is regulated in Subtitle D Part I SEC 

13400 and 13402 of American Recovery and 

Reinvestment Act of 2009. There are also other 

legislations in the United States embracing the similar 

regulation [43]. 

C. One Potential Prediction to the Secondary Liability to 

the Internet Service Provider in the Protection of 

Information Privacy 

Beside the above-mentioned three preventive measures 

in the protection of information privacy, the secondary 

liability to the internet service provider for information 

privacy invasion is potentially viable in the information 

age, especially in case of intelligent vehicle telematics. 

Until now, there is no general federal or state law to 

regulate the secondary liability of the internet service 

provider for information privacy invasion, At the same 

time, even there seems no direct judicial verdict to the 

secondary liability of the internet service provider for 

information privacy invasion in the United States; the 

article would think probably one important reason is 

because the court of the United States is still struggling to 

delineate the scope of information privacy within Internet. 

But this status quo is by no means to say the protection of 

information privacy within Internet is insignificant. On 

the other hand, ensuing the highly developed technology 

of telecommunication and the more dependency of our 

society to such technology, the protection of information 

privacy within Internet is deemed to be an important issue 

in the information age. Although there is no judicial 

decision to the secondary liability of the internet service 

provider for information privacy invasion at this moment, 

the court in the United States did make some decision 

with regard to the secondary liability to the internet 

service provider in recent years and revealed the court’s 

leniency to the internet service provider through the 

following case related to the trademark infringement 

within Internet. In Tiffany v. Ebay [44], Tiffany file the 

suit for multiple causes of action against eBay. For the 

purpose of this discussion in this article, the focus of this 

case is centered on the issue of contributory infringement 

of trademark. The facts for this case are relatively simple. 

eBay offers the platform for online purchases to be 

concluded. Tiffany, the high-quality jewelry producer, 

was unhappy there are counterfeiting Tiffany jewelry 

circulating on eBay’s online purchasing platform and 

filed the secondary liability litigation for trademark 

infringement to eBay, even eBay did have taken some 

kind of anti-fraud measurement for preventing the 

counterfeited product in its operation system. To the 



issue of secondary liability to the trademark infringement, 

based upon the interpretation of the Supreme Court in 

Inwood case [45], the liability lies when “a manufacturer 

or distributor intentionally induces another to infringe a 

trademark, or if it continues to supply its product to one 

whom it knows or has reason to know is engaging in 

trademark infringement.” eBay definitely did not induce 

the trademark infringement in this case, that left the 

question to whether eBay was contributory liable to the 

trademark infringement. The court in this case discarded 

the “reasonable anticipation standard” as the meaning of 

“knows or has reason to know”, instead the knowledge 

requirement is “a contextual and fact-specific test” judged 

by all the surrounding circumstances, for example the 

specific incident of trademark infringement, which is a 

higher standard than “reasonable anticipation standard”. 

In this case, the court concluded that Tiffany could not 

satisfy with the high criteria for “knows or has reason to 

know” requirement, especially eBay has abovementioned 

anti-fraud measurement in force, and eBay 

was not liable for contributory trademark infringement. 

The Tiffany case demonstrates two kinds of policy 

attitude. One observation is that the court in the United 

States is reluctant to impute the liability to the internet 

service provider probably due to the concern of free flow 

of information. And the other observation is the court 

would enhance the mental requirement for the secondary 

liability infringer to some extent, at least near to the 

requirement of “willful blindness” instead of reasonable 

anticipation. From the description of shifting attitude to 

the secondary liability of the internet service provider, 

this judicial attitude also put the preventive measure to 

the protection of information privacy within Internet in 

the even more important position for such infrastructure. 

D. The Definition of Information Privacy and the 

Suggested Model Building Up the Information Privacy 

Protection for Intelligent Vehicle Telematics 

After understanding the general idea of information 

privacy and the tendency of protecting such legal interest 

in the United States, how to build the protection 

infrastructure of information privacy and strike the 

balance with other kinds of conflicting legal interest for 

Intelligent Vehicle Telematics operation brings the 

discussion to the next level. With regard to the issue of 

protection of information privacy in Intelligent Vehicle 

Telematics operation, this article would attempt to divide 

it into two different aspects: non-legal –binding self 

regulation and legal measurements for preventive or 

remedial purpose to the system operator. First, to the part 

of self regulation within the system operator, the 

proposed estimation in this article is that the self 

regulation wouldn’t be able to play any significant role in 

striving to preserve the legal interest of information 

privacy before the competition in market has reached 

sufficient status. That is not to say the idea of selfmanagement 

for the information privacy protection is not 

important. The statement is just to express the thinking 

that to establish the management system for the 

protection of information privacy is not easy compared 

with the intellectual property management system 

because the concept of information privacy is further 

developing. So, it is argued in this article, in this stage, 

there is no substantial meaning to emphasize the 

mechanism of self regulation. As to the preventive or 

remedial legal measurements for the protection of 

information privacy related to the system provider for 

Intelligent Vehicle Telematics, the bottom line is 

described as the old saying: “One stitch in time safes 

nine.”. That leads to the indication that the preventive 

measurements of informed consent and technology 

prevention are much better than the remedial 

measurements (the obligation of notification, civil 

liability or even criminal punishment). To sum up the 

infrastructure for the protection of information privacy in 

Intelligent Vehicle Telematics, it is fairly to say in 

protecting information privacy in operating Intelligent 

Vehicle Telematics, there is a hierarchy to construct the 

protection, from the legal to the non-legal in general 

concept, from the preventive to the remedial 

measurement in real practice. 

As to the definition of information privacy, this really 

means the balance of interest. In comparing the different 

interests to confirm the legitimacy of information privacy 

in the situation of Intelligent Vehicle Teleatics, the safety 

concern will definitely get its priority to the information 

privacy concern. To other comparisons between the 

protection of information privacy and proprietary 

interests of the system operator, the odds are that the 

information privacy will have a good chance to fight in 

the battlefield of balancing interests. One problematic 

situation of protecting information privacy within the 

environment of intelligent vehicle telematics is its 

possible interaction with the concept of protecting critical 

infrastructure. General speaking, under the idea of 

protecting critical infrastructure, the Bureau of Homeland 

Security can acquire and reasonably use the information 

related to the critical infrastructure processed by the 

private sector or government agencies for the purpose of 

anti-terrorism, which information might be under the 

protection of information privacy [46]. Even under the 

balance of interest approach, the legal interest of 

information privacy will be no doubt succumbed to the 

interest of national security if these two kinds of interest 

directly conflict with each other, the question is whether 

the environment of intelligent vehicle telematics would 

be treated as the critical infrastructure and to what extent 

of using the information contained within is reasonable 

[47]. The potential impact of critical infrastructure 

protection to information privacy protection is unknown 

and needs to wait and see. As the protection of 

information privacy is getting more and more importance 

in the hierarchy of different kinds of legal interest, the 

national security remains the strongest opposition. What 

is the line need to be drawn between the protection of 

national security and information privacy, especially in 

talking about the intelligent vehicle telematics 

environment, cannot be answered until the day comes. 

V. CONCLUSION 



It often times comes with the legal concern when the 

advanced technology seems to promise the society a 

better life. And this is exactly what happens to the 

Intelligent Vehicle Telematics. These two mainly legal 

concerns which are the liability both for the safety devise 

manufacture and the system provider, and also the 

protection of information privacy, under the discussion in 

this article, shall move toward the intensive way to go. 

There should be nothing wrong to be cautious about the 

new technology after balancing the benefits and the 

potential harm of such technology to reveal that it could 

do more harm than good to the society as a whole, 

especially such harm is imminent. And it is suggested in 

this article that the potential harm to the safety devise in 

Intelligent Vehicle Telematics could be a disaster for the 

reason of estimating human life as high-value. And also 

the same seriousness to the invasion of information 

privacy would happen especially the unauthorized use or 

security breach of the extensive gathering of personal 

information in operating Intelligent Vehicle Telematics 

could be fatal to the trend of enhanced protection of 

information privacy. For all the reasons mentioned here, 

this article will hold the position that the most restrictive 

legal responsibility under the current legal theory shall 

apply to these two concerns respectively. But, even the 

legal interest of information privacy is moving its way 

toward the ultimate position which is one kind of the 

fundamental human rights, its legal hierarchy still hasn’t 

reached that stage yet. And the difficulties and dilemma 

to protect the information privacy in the information age, 

especially in the intelligent vehicle telematics 

environment, make the preventive measure to protect the 

information privacy get its priority and alleviate the 

secondary liability of the internet service provider to 

some extent. The influence of national security to the 

protection of information privacy in the environment of 

intelligent vehicle telematics will be the potential 

problem need to be resolved since there is no direct or 

similar judicial decision can be refered. The development 

of Intelligent Vehicle Telematics technology is still in its 

primitive stage. And it is the purpose (intention) of this 

article to pinpoint the legal concerns for Intelligence 

Vehicle Telematics in front and try to come up the 

positive solutions in the hope of that the discussion could, 

at least, have some referential value for the possible 

future policy making decision. 

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Fa-Chang Cheng received LL.M. degree from Golden Gate 

University and J.D. (Juris Doctor) degree from Ohio Northern 

University, U.S.A., in 1997 and 2001, respectively. 

He is a full-time associate professor in Graduate Institute of 

Science and Technology Law of National Kaohsiung First 

University of Science and Technology. His major research area 

is focusing on the legal issues for both Telecommunication and 

Biotechnology. 

Wen-Hsing Lai received the Ph.D. degrees in communication 

engineering from National Chiao Tung University, Hsinchu, 

Taiwan, in 2003. 

In 2006, she became an Assistant Professor of the 

Department of Computer and Communication Engineering, 

National Kaohsiung First University of Science and Technology, 

Taiwan. Her major research area is focusing on digital signal 

processing. 



MPC Controller Performance Evaluation and 

Tuning of Single Inverted Pendulum Device 

Chao Cheng 

Department of Automation, Beijing University of Chemical Technology, Beijing, China 

Email: beryle117@163.com 

Zhong Zhao 1 , Haixia Li 

Department of Automation, Beijing University of Chemical Technology, Beijing, China 

Email: zhaozhong@mail.buct.edu.cn 

Abstract—Inverted pendulum is a non-linear, multivariable 

and unstable device, a model predictive control (MPC) 

performance evaluation and tuning method for inverted 

pendulum device is proposed. MPC was designed to control 

the inverted pendulum device, and the minimum variance 

covariance constrained control (MVC 3 ) was applied to 

evaluate the performance of the MPC controller and tune its 

parameters. The application results to a single inverted 

pendulum device have verified the feasibility and 

effectiveness of the proposed method. 

Index Terms—Inverted pendulum, Model Predict Control, 

Minimum Variance Covariance Constrained Control, 

Performance evaluation, Controller-tuning 


Inverted pendulum is a non-linear, strongly coupled, 

multivariable and unstable system. Because it can 

effectively reflect a lot of key control problems, such as 

the stabilization, robustness, tracking performance, many 

control theories and control methods can be verified with 

the inverted pendulum experiment. Google Technology 

LTD [1] designed its LQR controller. D. Chatterjee et al. 

[2] described the swing-up and stabilization with a 

restricted cart track length and restricted control force 

using generalized energy control methods. M. Bugeja [3] 

presented a swing-up and stabilizing controller on 

inverted pendulum non-linear model. S.Y. Zhang [4] and 

Y. Fan et al. [5] designed the fuzzy controllers for 

inverted pendulum. L.X. Deng [6] designed a controller 

based on back stepping for inverted pendulum. 

Model Predictive Controllers (MPC) was proposed by 

J. Richalet et al. in 1978[7]. It is a model-based optimal 

control strategy [8]. Its ability to incorporate meaningful 

limits on manipulative as well as control variables has 

allowed the industry to move away from traditional 

regulation-type control and focus on the economics of 

operating point selection [9]. Model predictive control 

has been widely applied to process control [10]. On the 

1, Corresponding author, zhaozhong@mail.buct.edu.cn; 

other hand, it is noted that less effort has been made on 

the performance monitoring of MPC applications, while 

the performance monitoring of conventional controllers 

has been well studied such as in Harris (1989) [11], 

Harris, Boudreau, and Macgregor (1996) [12], Huang, 

Shah, and Kwok (1997) [13], Huang and Shah (1999) 

[14], Jelali (2005) [15], Srinivasan, Rengaswamy, and 

Miller (2005) [16] [17], Xu, Lee, and Huang (2006) [18], 

Salsbury (2007) [19] and Bauer and Craig (2008) [20]. 

The Minimum Variance Covariance Constrained 

Control (MVC 3 ) principle was proposed by R.E. Skelton 

et al. [21] as the solution of linear feedback control 

problem. For multivariable systems, D.J. Chmielewski* 

et al. [22] solved it with LQR method. In this work, the 

model predictive control (MPC) performance evaluation 

and tuning system has been developed by extended 

MVC 3 and applied to a single inverted pendulum device. 

The application results have verified the feasibility and 

effectiveness of the developed system. 

II. THE MATHEMATIC MODEL OF LINEAR SINGLE 

INVERTED PENDULUM 

The linear single inverted pendulum can be described 

as a system composed of a cart and a homogeneous rod 

without air resistance and all kinds of frictions, as is 

illustrated in Fig. 1. 

Figure 1. Linear single inverted pendulum model 

Where, M , m , x , F , l ,θ ,denote cart weight, rod weight, 

cart level displacement, force on cart, the length from the 


doi:10.4304/jcp.8.6.1560-1570


axis of the rod angle to the center of rod mass, the angle 

of the rod from the vertical upward direction respectively. 

A. State Space Model of Linear Single Inverted 

Pendulum 

The method of this work is based on linear constant 

state space model as: 

x 

= Ax + Bu 

. (1) 

y = Cx + Du 

The mathematical model of single inverted pendulum can 

be obtained by mechanism analysis [1], shown in (2), 

where, u , is cart angular velocity. x andθ , are the same 

as shown in Fig 1. 

⎛x 

⎞ ⎛0 1 0 0⎞⎛x 

⎞ ⎛0⎞ 

⎜ 

x 

⎟ ⎜ 

0 0 0 0 

⎟⎜ x 

⎟ ⎜ 

1 

⎟ 

⎜ ⎟ 

 

= ⎜ ⎟⎜ ⎟+ 

⎜ ⎟u 

⎜ θ ⎟ ⎜0 0 0 1⎟⎜θ 

⎟ ⎜0⎟ 

⎜ 

θ ⎟ ⎜ ⎟ 

0 0 29.4 0 ⎜θ 

⎟ ⎜ ⎟ 

⎝ ⎠ 

 

⎝ ⎠ 

⎝ ⎠ ⎝3⎠ 

⎛x 

⎞ 

⎜ 

x 1 0 0 0 x 

⎟ 

⎛ ⎞ ⎛ ⎞ ⎛0⎞ 

y = ⎜ ⎟ 

⎜ = + u 

θ 

⎟ ⎜ 

0 0 1 0 

⎟⎜θ 

⎟ ⎜ 

0 

⎟ 

⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 

⎜ 

θ ⎟ 

⎝ ⎠ 

B. Controllability & Observability Analysis of Single 

Inverted Pendulum 

The controllability and observability of a system is 

prerequisite for analysis and controller design. Here, 

n− 

Uc = B AB A 1 B and 

Controllability matrix ( ) 

n 

observability matrix Uo ( C CA CA −1 

) 

T 

(2) 

= were 

obtained and then rank criterion was employed to 

analysis its controllability and observability. It has been 

proved that the system as (2) has both controllability and 

observability. 

C. Stability Analysis of Single Inverted Pendulum 

The extended MVC 3 performance evolution and MPC 

tuning system is based on the stabilization system. Hence, 

Stability analysis is necessary. The poles of the inverted 

pendulum as (2) are ( 5.4222 − 5.4222 0 0) 

, where 

positive real root appears. It shows that the system as (2) 

is instable and this requires a stabilizer before designing a 

MPC controller for the generalized controlled system [23]. 

III. MPC PERFORMANCE EVOLUTION AND TUNING 

METHODE BASED ON EXTENDED MVC 3 

A. Introductions of LMI and Lemmas 

• About LMI: 

Assume a linear matrix inequality (LMI) can be stated 

as: F( x) = F0 + x1F1+⋅⋅⋅+ xmFm 

< 0 .Where, variable 

x constitutes a convex set, LMI can be solved using the 

method of convex optimization problem [24]. 

1) Feasible solution of LMI: 

If there exists x makes, F( x ) < 0 , established, then the 

LMI is feasible [24].This can be expressed using the 

following formulation: 

min. t 

. 

s.. tF( x) 

< tI 

2) Minimization problem of LMI: 

The problem can be stated as a optimality problem that 

minimize the largest eigenvalue, λ , of the matrix 

Gx ( ) under inequality constraint H( x ) < 0 [24]: 

st .. 

Another expression is as: 

T 

min λ 

G < λI 

. 

< 0 

( x) 

H ( x) 

T 

min c x 

, 

st .. F < 0 

( x) 

where, c x is object function. 

• Lemmas: 

Consider a linear time-invariant state-space system: 

x( k + 1) = Ax( k) + Bu( k) + Ew( k) 

, (3) 

y( k) = Cx( k) 

where, x (k) 

, u ( k ) , y( k ) are state variable, manipulative 

variable and control output variable respectively, 

A , B , C and E are process model matrix, w ( k) 

denotes 

stationary, Gaussian noise with zero mean and covariance 

as ∑ w . 

State feedback controller can be expressed as: 

u( k) = Kx ( k) 

. (4) 

Then, the closed-loop system can be written as: 

x( k + 1) = ( A+ BK) x( k) + Ew ( k) 

. (5) 

Lemma1: LMI of MVC 3 [22]: 

For system (5), ∃ stabilizing K and ∑x ≥ 0 s.t. 

∑ , = 1... p 

yi i 

T 

T 

x w x 

T 

∑ y = ϕ 

i iC∑ 

xC 

ϕi 

2 

∑ y < y , 1 

i i i = … p 

( A+ BK) ∑ ( A+ BK) 

+ E∑ E = ∑ 

If and only if ∃ W, X > 0and Yi , = 1... ps.t. 

⎡ 

T 

X − E∑ 

E AX BW⎤ 

w + 

⎢ 

⎥> 

0 

T 

⎢⎣( AX + BW ) X ⎥⎦ 

⎡ Yi 

ϕiCX⎤ ⎢ 

( ) T 0 

T 

⎥ > 

⎢⎣ 

CX ϕi 

X ⎥⎦ 



Y i2 i < y , i = 1… p, 

where, K is the linear state feedback gain; ∑ x is the state 

variables covariance; ∑ is the i th variable of output 

covariance ∑ y ; 

y i 

2 

y i is constraint of 

Lemma2: Schur complements [25]: 

For symmetric matrix: 

⎡S 

S = ⎢ 

⎣S 

11 

21 

∑ yi . 

The following three conditions are equivalent: 

1) S < 0 

T −1 

22 12 11 12 0 

2) S 11 < 0 , S − S S S < 

−1 

T 

11 12 22 12 0 

3) S 22 < 0 , S − S S S < . 

B. Extended MVC 3 Problem and Its LMI Solution 

In this work, constraints on manipulative variables 

were included in the MVC 3 scheme. The extended MVC 3 

can be described as: 

S 

S 

12 

22 

⎤ 

⎥ 

⎦ 

p 

m 

min qi ∑ yi + rj ∑u j 

∑ x, KY , i, Uj 

i= 1 j= 

1 

∑ ∑ (6) 

s.t. ( A+ BK) ∑ ( A+ BK) T + E∑ E 

T = ∑ (7) 

x w x 

T 

yi ϕiC 

C ϕi 

∑ = ∑ x (8) 

T 

uj ϕ jK 

K ϕ j 

∑ = ∑ x (9) 

2 

i 

∑ < y , i = 1... p 

(10) 

yi 

2 

j 

∑ 

uj 

The main design target of the extended MVC 3 is 

obtaining linear feedback gain K to make object function 

(6) minimum, additionally, to make the steady-state 

control outputs and the covariance of manipulative 

variables satisfy a set of bounds respectively. The above 

problem can be converted to a convex form of LMI as 

follows. 

Theorem 1: If and only if ∃W, X ≥ 0 and Y i , 

U , i = 1... p, j = 1... m s.t. 

j 

p m 

min qY i i+ 

rU j j 

XWYU , , j j i= 1 j= 

1 

∑ ∑ (12) 

⎡ 

T 

X −E∑ E AX BW⎤ 

w + 

s.t. ⎢ 

⎥> 

0 

T 

⎢⎣( AX + BW ) X ⎥⎦ 

(13) 

⎡ Yi 

ϕiCX⎤ ⎢ 

0 

T T ⎥ > 

⎣( CX ) ϕi 

X ⎦ 

⎡ U j ϕ jW⎤ ⎢ T T ⎥ > 0 

⎢⎣ 

W ϕ j X ⎥⎦ 

(14) 

(15) 

Y i2 i < y , i = 1... p 

(16) 

U j2 j 

(17) 

−1 

Then, u= Kx( k) = WX x( k) 

is the extended MVC 3 linear 

feedback controller of system (2), satisfying covariance 

constraints. 

Proof: If the closed-loop system (2) is stable, the steady 

state covariance matrix can be expressed 

T 

as ∑ x = lim{E[ x( k) x ( k)]} 

, and ∑ 

x 

satisfies (7). From 

k→∞ 

the definition of covariance, it is easily to get the 

T 

T 

expression ∑ = ϕC∑ x C ϕ , ∑ = ϕ K∑ x K ϕ , 

where, 

yi i i 

2 

u j 

∑ 

yi 

< y i 

, 

uj j j 

2 

j 

∑ 

∃∑ x < X , Makes the state covariance constraint (7) is 

T 

equivalent to LMI (13). Let ϕiCXC ϕ i < Yi, i = 1, … p , 

T 

ϕjKXK ϕ j 

U j2 j 

p 

m 

p m 

qi ∑ yi + rj ∑u j ≤ qY i i + rU j j 

i= 1 j= 1 i= 1 j= 

1 

∑ ∑ ∑ ∑ . 

Then, minimizing the function 

ensure the object function 

p m 

qY i i + rU j j 

i= 1 j= 

1 

p 

m 

qi yi + rj uj 

i= 1 j= 

1 

∑ ∑ will 

∑ ∑ ∑ ∑ be 

minimized too. Still use Lemma 1, (14)-(17) can be 

derived. 

From the definition of extended MVC 3 problem, 

controller feedback solution K ∗ can be solved by 

∗ ∗ ∗−1 

K = W X with LMI. Where, W ∗ and X ∗ denote the 

optimal solution matrices of the extended MVC 3 problem. 

Conditions (14)-(17) are exactly that required to 

determine the feasibility of the extended MVC 3 problem. 

If the problem turns out to be infeasible, then the 

2 2 

bounding region defined by yi 

and u j terms should be 

enlarged. 

C. Performance Evolution Based on Extended MVC 3 

For closed-loop system (5) the multi-variable form of 

LQG performance benchmarks can be defined as 

T 

T 

J 

LQG 

= E( 

y Qy) 

+ λ E( u Ru) 

. In order to evaluate 

controllers under constrains, the covariance constrains are 

included in the LQG performance evaluation benchmarks. 

New performance evolution is exactly an advanced 



MVC 3 problem. After deformation, the problem can be 

solved by technology of LMI: 

If and only if ∃W, X ≥ 0 , λ > 0 and Y i , U j , i = 1... p , 

j = 1... m and the following optimization as (18) can be 

solved, 

p 

m 

min qY i i+ 

λ rU j j 

XYUWi , , , = 1 j= 

1 

∑ ∑ (18) 

s.t. (13)-(17). 

Then, according to the change of λ , optimized curve of 

control outputs variance Var( y) 

and manipulative variable 

variance Var( u ) can be obtained. This optimized curve 

can be used as the benchmark to evaluate controller 

performance. 

According to optimization objective function: 

T 

T 

J = E( y Qy) + λ E( u Ru) 

= Trace( Q ∑ y + λR 

∑u) 

. 

T 

T 

= QTrace( C ∑ xC ) + λRTrace( K ∑x 

K ) 

T 

T 

≤ QTrace( CXC ) + λRTrace( KXK ) 

T 

T 

Let CXC < Y , KXK inimizing 

QTrace( Y ) + λRTrace( U ) can ensure J be minimized 

too. Object function can be rewritten as 

3 

MVC 

p 

m 

i i λ j j 

i= 1 j= 

1 

J = ∑qY + ∑ rU . (13)-(17) can be obtained as 

the same as LMI of advanced MVC 3 . 

The MVC 3 benchmark curve is the lower limit of the 

controller performance. That is, all linear controllers can 

only be located in operating area above the curve. 

Comparing actual run-time steady state outputs and 

manipulated variables covariance with the MVC 3 

benchmark cure, closer distance means better 

performance. In practice, a benchmark 

3 

MVC 

p m 

i= 1 

i i 

j= 

1 

j j 

J = ∑qY + ∑ rU can be calculated as λ = 1, then, 

judge controller performance by the ratioη which is the 

value of benchmark J 3 divided by actual operation 

MVC 

steady state covariance J arh .η closes to 1 means better 

performance. 

D. Extended MVC 3 and Infinite Horizon MPC 

• Solution of infinite horizon MPC 

For linear system, solving infinite horizon MPC is 

equivalent to solving the LQR control problem as follows, 

∞ 

min ∑ x( k) Qx( k) + u ( k) Ru( k) 

(19) 

u( k ) k = 0 

T 

x( k + 1) = Ax( k) + Bu( k) 

s.t. 

. 

y( k) = Cx( k) 

T 

Let 

T 

p 

Q= C DC,( D= ∑ qϕ ϕ ) , and let feedback 

i= 

1 

T 

i i i 

controller be u( k) = Kx ( k) 

, then, 

T −1 

T 

K =− ( B PB + R) 

B PA , where, 

T T T −1 

T 

P = A PA − A PB( B PB + R) 

B PA + Q . 

• LQG control problem 

LQG control problem can be described as: 

1 T 

T 

T 

min lim ∑ E[ y( k) Qy( k) + u( k) Ru ( k)] 

(20) 

u T 

( k) T→∞ k = 0 

x( k + 1) = Ax( k) + Bu( k) + Ew( k) 

s.t. 

, 

y( k) = Cx( k) 

where feedback controller can be solved by 

T −1 

T 

K =− ( B PB + R) 

B PA , here, PQis , the same as the 

solution of infinite horizon MPC. Rewrite the object 

function in (21) as, 

1 T 

T 

T 

J = lim ∑ E[ y( k) Qy( k) + u( k) Ru( k) 

T →∞ T k = 0 

T 

T 

= lim E[ y( k) Qy( k) + u( k) Ru( k)] 

k→∞ 

. 

= Trace ∑ + ∑ 

{ Q y R u} 

p 

m 

T 

T 

∑qiϕi yϕi ∑ rjϕ j uϕ 

j 

i= 1 j= 

1 

= ∑ + ∑ 

• Extended MVC 3 control problem without 

constraints 

Extended MVC 3 control problem can be described as: 

p m 

qY i i+ 

rU j j 

∑ x i= 1 j= 

1 

min ∑ ∑ (21) 

s.t. ( A+ BK) ∑ ( A+ BK) + E∑ w E = ∑ 

x 

T T 

i ∑ x ϕi = i, = 1 

ϕ C C Y i p 

T 

T 

ϕ jK ∑ x K ϕ j = U j, j = 1… m . 

The goal is to get a feedback gain matrix K by minimize 

p m 

the objective function ∑qY 

+ ∑ rU . 

T 

i i j j 

i= 1 j= 

1 

Assumption 1. R > 0 , Q ≥ 0 . 

Assumption 2.The pairs ( A, B ) and ( A, Q) 

is stabilizable 

and detectable, respectively. 

T 

Assumption 3.The pair ( A, G∑ w G ) is controllable. 

Let hypotheses 1-3 hold; then the solution to of MVC 3 

problem as (21) is coincident with the solution of infinite 

horizon MPC as (19). Hypotheses 1-2 indicate that the 

solutions of problems (19) and (20) are unique and 

stabilizing. Hypotheses 1-3 ensure that the solution of 

problem (21) is unique and stabilizing. From the 

construction of problem (20), it is equivalent to problem 

(21), in the sense that the linear feedback generated by 

T 

x 



(21) is the solution to problem (20). Finally, certainty 

equivalence between problems (20) and (19) completes 

the proof. 

Theorem 2: Let hypotheses 1-3 hold; then the solution 

of K ∗ , to problem (12)-(17) is coincident with the 

solution of appropriate weighted infinite horizon MPC 

problem (19). 

Proof. Problem (6)-(11) can be exactly restated as the 

existence of Lagrange multiplier, , s.t. 

1 1 

s.t. ⎢ 0 

T ⎥ 

⎣S1 I1⎦ 

⎡ T2 S2⎤ ⎢ 0 

T ⎥ > 

⎣S2 I2⎦ 

T 

λ 

i 

, γ 

A PA 1 P1 Q 0 

j 

⎧ 

p m ⎫ 

T1 ρ1I1 

⎪ 

min { ∑qY 

i i+ ∑ rU j j + 

K, ∑x≥ 0, Yi, U 

⎪ 

j i= 1 j= 

1 

⎪ 

⎪ 

⎪ 

p 

m 

2 2 ⎪ 

T2 ρ2I2 

⎪∑λi( Y i− yi ) + ∑γ 

j( U j −uj 

)} ⎪ 

i= 1 j= 

1 

T 

⎪ 

⎪ where, 1 ( ) ( ) 

max ⎨ 

T 

s. t. ( A+ BK) ∑ ( A+ 

BK) 

⎬. (22) 

λi≥0, γ j≥0 

x 

T 

T 

⎪ 

⎪ S2 

RK B PBK B PA 

T 

⎪ + E∑ w E =∑x 

⎪ LQR inverse-optimal Control, , 

⎪ 

T T 

⎪ 

⎪ ϕiC∑ x C ϕi = Yi 

⎪ 

⎪ 

T T 

⎪ 

∃P 

≥ 0 , Q ≥ 0 , R > 0 , P 1 > 0 , s.t. 

⎪⎩ 

ϕ jK∑ x K ϕ j = U j ⎪⎭ 

If rewrite the minimization objective function as: 

p 

m 

T 

T 

min { ∑( qi + λi) Y i+ ∑ ( rj + γ j) U j} 

RK B PBK B PA 

K, ∑x≥ 0, Yi, U j i= 1 j= 

1 

, 

p 

m 

T 

2 2 

A PA 

− ∑λiyi − ∑γ 

ju 

1 P1 

Q 

j 

i= 1 j= 

1 

λ i≥ γ j ≥ .This indicates 

∗ 

λ i γ j dependent solutions, K ( λi, γ j) 

,coincide 

⎡ T1 S1⎤ ⎢ 0 

T ⎥ > 

⎣S1 I1⎦ 

i = qi + i i = rj + j). 

T T T T 

1 

Because of the variance constraints (16) and (17), 

T 

problem cannot be equivalent to the infinite 

1 ≤ ρ1I1 

⎡ T1 S1⎤ and Lemma 2, ⎢ 0 

Theorem 2 guarantees that the MVC 3 T ⎥ > 

problem would 

⎣S1 I1⎦ 

∗ 

T 

T 

K λi 

γ j such that there to T 1 − S 1 S 1 > 0 , that is 1 I 1 SS 1 1 

⎡ T2 S2⎤ λ , γ j . But, weighted matrix Q , R of infinite 

⎢ 0 

T ⎥ > 

⎣S2 I2⎦ 

T 

T 

2 = + + 

T2 ≤ ρ2I2 

LQR inverse-optimal control can be described as: 

If ∃P 

≥ 0 , Q ≥ 0 , R > 0 , P 1 > 0 and symmetric 

min ρ 1 + ρ 2 

(23) PPT , , , T, QR , 

then, it is clear that the above three assumptions are 

satisfied for all values of 0, 0 

that all , 

with the solution to some infinite horizon MPC problem 

( λ λ , γ γ 

MVC 3 

horizon MPC problem (19). Theorem 2 shows that 

introducing variance constraints to MVC 3 problem (21), 

is exactly the reason to adjust the MPC controller weight 

matrix, Q , R . 

generate a linear feedback ( , ) 

exists a feasible solution for infinite horizon MPC 

problem. Unfortunately, the exact form of this infinite 

horizon MPC problem is unclear, unless the MVC 3 

solution procedure provides us with the optimal 

Lagrangians i 

horizon MPC can be solved by given feedback gain, K . 

Then, it can be updated with the Riccati equation. 

E. LQR Inverse-Optimal Control and Its LMI Method 

matrices, T 1 , T 2 that 

1 1 2 

⎡ T S ⎤ > 

(24) 

(25) 

− − < (26) 

< (27) 

< , (28) 

S = A+ BK P A+ BK − P+ Q+ K RK , 

= + + .Then, through the solution of 

QR,can be obtained. 

LQR inverse-Optimal Control [27] is described as: 

T T T T 

A PA − P −K RK − K B PBK + Q = 0 (29) 

+ + = 0 (30) 

− < , (31) 

where, (31) ensures that ( A, Q ) is detectable. As (29) 

cannot be converted to the LMI form, it can be 

constructed as, 

S = A PA −P −K RK − K B PBK + Q , 

where, T 1 is symmetric matrix; ρ 1 is a scalar; I 1 is a 

unit matrix of appropriate dimension. From LMI theory 

is 

T 

equivalent 

ρ > .Then, approximate 

solution of equation (29), R , P , can be gotten through 

choosing a small enough ρ 1 . Similarly, 

S RK B PBK B PA 

Equation (26) is the rewriting of (31). Then, the LMI 

form of LQR inverse-Optimal Control can be gotten. 

Equations (29)-(31) are constructed to LMI form to get 

parameters QR. , However, Matrix Q here is nondiagonal 

matrix, practical application is inconvenience. 



From LMI and ARE equivalence relation [28], S1 

is equal 

to: 

T T T T 

S1 = A PA + A PBK + ( BK) PA + BK P( BK) 

T 

T 

− P+ Q+ 

K RK 

= ( A+ BK) P( A+ BK) 

− P+ Q+ 

K RK 

Therefore, LMI form of (23)-(28) can be gotten and the 

solution of Q is diagonal matrix. 

F. MPC Tuning Based on Extended MVC 3 

Consider system (3), outputs and manipulative variable 

constraints are as y ( k) 

< y and u ( k) 



i 

i 

where, yi ( k) 

is i th element of y( k ) and u j ( k) 

is j th 

element of u ( k ) . When the MPC controller is put into 

operation, extended MVC 3 performance evaluation 

criteria is used to monitor controller performance. If the 

performance evolution indexη is below the thresholdψ , 

weighted parameter R can be updated with extended 

MVC 3 to improve the robustness of the controlled system. 

The block diagram of MPC tuning is shown in Fig. 2. 

Figure 2. Block diagram of MPC controller-tuning 

IV. MPC CONTROLLER PERFORMANCE EVALUATION 

AND TUNING SYSTEM IN SINGLE INVERTED PENDULUM 

CONTROL 

A. Model Preprocessing 

• Stabilizer design 

The single inverted pendulum is unstable system, 

while, tuning system of infinite MPC require a stable 

controlled object. Hence a stabilizer u =− Kx+ v is 

needed. For the inverted pendulum system (2), Use 

command K=acker(A,B,P) in Matlab, to configure 

closed-loop pole to: 

( 8 8 2 2 2 2 ) 

j 

P = − − − + i − − i . (32) 

j 

T 

. 

The feedback gain is obtained as: 

K = ( −17.4150 − 13.0612 60.9383 11.0204) 

. (33) 

The generalized system matrix after stabilization is as 

follows: 

⎛x 

⎞ ⎛ 0 1 0 0 ⎞⎛x 

⎞ ⎛0⎞ 

⎜ 

x 

⎟ ⎜ 

0 0 1 0 

⎟⎜ x 

⎟ ⎜ 

1 

⎟ 

⎜ ⎟ 

 

= ⎜ ⎟⎜ ⎟+ 

⎜ ⎟u 

⎜ θ ⎟ ⎜ 0 0 0 1 ⎟⎜θ 

⎟ ⎜0⎟ 

⎜ θ ⎟ ⎜ ⎟ 

512 384 136 20 ⎜θ 

⎟ ⎜ ⎟ 

⎝− − − − ⎠ 

 

⎝ ⎠ 

⎝ ⎠ ⎝3⎠ 

. (34) 

⎛x 

⎞ 

⎜ 

x 1 0 0 0 x 

⎟ 

⎛ ⎞ ⎛ ⎞ ⎛0⎞ 

y = = ⎜ ⎟ 

⎜ + u 

θ 

⎟ ⎜ 

0 0 1 0 

⎟⎜θ 

⎟ ⎜ 

0 

⎟ 

⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 

⎜ 

θ ⎟ 

⎝ ⎠ 

The following MPC controller performance evaluation, 

tuning system based on extended MVC 3 was built on the 

stabilized generalized system (34). 

• Discretization 

Since the derivation of the above extended MVC 3 

algorithm is based on discrete state space model (3), 

discretization of system (34) and constructing a suitable 

noise are needed. Use command sys=c2d(A,B,Ts) in 

Matlab, here Ts = 1s 

, and consider the noise to be 

stationary, Gaussian White-noise processes, the following 

system can be obtained as: 

⎛ xk ( + 1) ⎞ ⎛ 0.2584 0.1707 0.0306 0.0017 ⎞ 

⎜ 

xk ( 2) 

⎟ ⎜ 

0.8519 0.3805 0.0556 0.0027 

⎟ 

⎜ 

+ 

⎟ 

− − − − 

= ⎜ ⎟ 

⎜θ 

( k + 1) ⎟ ⎜ 1.3646 0.1716 −0.0181 −0.0023⎟ 

⎜ ⎟ ⎜ ⎟ 

⎝θ 

( k + 2) ⎠ ⎝ 1.1850 2.2534 0.4863 0.0282 ⎠ 

⎛ xk ( ) ⎞ ⎛ 0.2319 ⎞ ⎛0⎞ 

⎜ 

xk ( + 1) 

⎟ ⎜ 

0.1757 

⎟ ⎜ 

⎜ ⎟ 

1 

⎟ 

× + ⎜ ⎟uk 

( ) + ⎜ ⎟wk 

( ) 

⎜ θ ( k) ⎟ ⎜−1. 

3885⎟ ⎜0⎟ 

⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 

⎝θ 

( k + 1) ⎠ ⎝ 0.1646 ⎠ ⎝1⎠ 

where, ∑ w = 0.01 . 

⎛ xk ( ) ⎞ 

xk ( ) 1 0 0 0 

⎜ 

xk ( 1) 

⎟ 

⎛ ⎞ ⎛ ⎞ + 

yk ( ) = ⎜ ⎟ 

⎜ 

θ( k) ⎟= 

⎜ 

0 0 1 0 

⎟ , (35) 

⎝ ⎠ ⎝ ⎠ ⎜ θ( k) 

⎟ 

⎜ ⎟ 

⎝θ 

( k + 1) ⎠ 

B. MPC Tuning Design 

• MPC controller 

For system (35), choose the initial objective function 

of extended MVC 3 as 

J = Y + Y + U ,where R = 1, Q = diag(1,1) 

,output 

1 2 

variance bounds as yi 

= 0.3, i = 1,2 , manipulative 

variable variance bounds to be u = 0.8 .Using the 

command of LMI toolbox in Matlab ,the MPC controller 

weight matrix of the nominal model (35), R = 0.0167 , 

Q = diag(0.0204,0.1234,0.0007,0.0160) can be gotten. 



• Mismatch model 

In order to create performance degradation condition, 

A disturbance, Δ A was added to the nominal model (2), 

to construct a man-made mismatch model as, 

⎛ 0 1 0 0 ⎞ 

⎜ 

0 0 1 0 

⎟ 

A' 

= A+Δ A= ⎜ 

⎟. (36) 

⎜ 0 0 0 1 ⎟ 

⎜ 

⎟ 

⎝−600 −300 −100 −30⎠ 

• MPC tuning parameters 

Based on the extended MVC 3 algorithm combined 

with LQR inverse optimal, the MPC controller matrixes 

of above mismatch model can be gotten. 

R = 0.0388 , Q = diag(0.0706 0.0002 0.0357 0.000) 

Through MVC 3 performance evaluation, controller 

performance declining was detected. If it dropped below 

threshold, ψ , (here, ψ is set to 0.8), then, weight 

parameter of manipulated variable in MVC 3 , R ,is 

updated by R' 

= R+ ξ I ,(here,ψ is set to 0.5). Repeat the 

MPC weight matrix calculation process to update Q, 

R, 

the new MPC controller parameters 

as R = 0.0952 

, 

Q = diag(0.1703 0.0006 0.0552 0.0000) can be 

gotten. Apply the new controller parameters to operation 

to restore the desired operational performance. 

V. SIMULATION AND ANALYSIS OF MPC CONTROLLER 

A. Simulation and Comparison of MPC Controller and 

the LQR Controller 

• Simulation of LQR controller 

LQR controlled system in the Simulink of Matlab was 

shown in Fig. 3. Parameter of LQR block was set to 

K = ( −31.623 − 20.151 72.718 13.155) 

, which was 

provided by Googol Technology LTD. 

Figure 3. Simulation block of LQR control loop 

• Simulation of MPC controller 

MPC controlled system in the Simulink was shown in 

Fig. 4, where, parameter of Acker block was set to 

stabilizer feedback gain. Weighted matrixes of MPC 

block were set the parameters calculated by the nominal 

model. 

Figure 4. Simulation block of MPC control loop 

• Analysis of simulations results 

Simulation curve charts of MPC controller and LQR 

controller are shown in Fig. 5, where, u denotes 

manipulative variable, which is cart angular velocity. 

angle, pos denote outputs, they are pendulum angle and 

cart position. 

The maximum deviation of MPC controller and LQR 

controller are shown in Table I and comparison bar chart 

is shown in Fig. 6. 

TABLE I. 

MAXIMUM DEVIATION COMPARISON 

u angle pos 

MPC 0.8240 0.0096 0.0093 

LQR 34.4589 0.3101 0.3533 

Obviously, due to the introduction of steady state 

manipulative variable and outputs covariance constraint, 

MPC controller can make the maximum deviation 

significantly reduced than LQR controller, which greatly 

improved the system dynamic performance. 

B. Simulation of MPC Controller Tuning 

• Simulation of MPC controller tuning 

MPC controller tuning dynamic curves was obtained 

by replace original weight matrix Q , R of MPC controller 

with mismatched and Controller-tuned parameters, shown 

in Fig. 7, where, the legend (good, bad and tuned) means 

controller running under, nominal model, mismatch 

model and MPC controller tuned. 

Through curves, if using original controller parameters 

to control mismatch model, it would lead an increase on 

manipulative variable and outputs deviation. After 

adjusting controller parameters by controller tuning 

system, the deviation reduced to some extent. This proves 

the feasible of MPC controller tuning algorithm. 

• Extended MVC 3 performance evaluation method 

The extended MVC 3 performance evaluation curve is 

shown in Fig. 8. 

Set λ = 1 in the MVC 3 performance evolution object 

function (18) and get 

p m 

i= 1 

i i 

j= 

1 

j j 

−7 

benchmark J 3 = ∑qY + ∑ rU by LMI method, 

MVC 

here, J 3 = 1.3217 × 10 .Then actual run-time 

MVC 

variance was compared with this benchmark, get η 



40 

30 

MPC 

LQR 

0.35 

0.3 

MPC 

LQR 

0.3 

0.2 

MPC 

LQR 

0.25 

20 

0.2 

0.1 

u 

10 

0 

angle 

0.15 

0.1 

pos 

0 

-0.1 

-10 

0.05 

0 

-0.2 

-20 

-0.05 

-0.3 

-30 

0 20 40 60 

T 

-0.1 

0 20 40 60 

T 

-0.4 

0 20 40 60 

T 

Figure 5. Simulations curves charts of MPC and LQR control loop 

35 

0.35 

0.4 

30 

0.3 

0.35 

25 

0.25 

0.3 

20 

0.2 

0.25 

u 

15 

angle 

0.15 

pos 

0.2 

0.15 

10 

0.1 

0.1 

5 

0.05 

0.05 

0 

MPC 

1 

LQR 

0 

MPC 

2 

LQR 

0 

MPC 

3 

LQR 

Figure 6. Bar charts of MPC and LQR simulations curves maximum deviation 

1.5 

1 

good 

bad 

tuned 

12 

10 

good 

bad 

tuned 

0.01 

0.005 

good 

bad 

tuned 

8 

u 

0.5 

0 

angle 

14 x 10-3 T 

6 

4 

pos 

0 

-0.005 

2 

-0.5 

0 

-0.01 

-2 

-1 

0 20 40 60 

T 

-4 

0 20 40 60 

-0.015 

0 20 40 60 

T 

Figure 7. Dynamic curves of nominal model, mismatch model and MPC controller-tuned 

as: 

J 3 

MVC 

η 1 = = 0.9803 ; 

J 

arh 

1 

J 3 

MVC 

η 2 = = 0.7551 ; 

J 

arh 

2 

J 3 

MVC 

η 3 = = 0.9143 , where, 

J 

arh 

3 

J , J , J denote 

arh1 arh2 arh3 



11.5 x 10-8 Var(U) 

11 

MVC3 curve 

good 

bad 

tuned 

10.5 

Var(Y) 

10 

9.5 

9 

8.5 

8 

1 2 3 4 5 6 7 8 9 

x 10 -8 

Figure 10. Single inverted pendulum device 

Figure 8. MVC 3 performance evolution curve 

steady state error of good, bad, tuned. η 1 , η 2 , η 3 denote 

their corresponding ratio. The bar chart is shown in Fig. 9. 

It confirms the correctness and feasibility of MPC tuning 

method. 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

Figure 11. MPC control loop 

0.4 

0.3 

0.2 

0.1 

0 

good bad tuned 

Figure 9. Bar chart of performance evolution 

VI. ACTUAL CONTROL ON THE DEVICE 

A. Construct MPC Controller 

The photo of single inverted pendulum device 

provided by Googol Technology LTD is shown in Fig.10. 

MPC controlled system was constructed on Matlab 

real-time control platform provided by Googol 

Technology LTD shown in Fig. 11. 

Parameters of k_acker block was set to stabilizer 

feedback gain and weight matrixes QR , of MPC 

controller was set to which calculated from nominal 

model. Run-time curves were shown in Fig.12. 

Obviously, under the permission of variance 

constraints, MPC controller can reach steady state in a 

short period of time. 

B. Tuning Process 

Run the MPC controller tuning system, and preprocess 

manipulated variable u by limiting filter, the effect 

curves can be shown in Fig. 13. 

Figure 12. MPC run-time operating curves 

Steady state variance of manipulative variable and 

outputs were calculated and shown in Fig. 14. 

Bar charts shows MPC controller performance has 

been restored and the tuning system is feasible. 

VII. CONCLUSION 

In this work, an extended MVC 3 method and its LMI 

solution were applied to infinite MPC controller 

performance evaluation and parameters tuning system. 

Using extended MVC 3 principle to monitor controlled 

system, if controller performance declined is detected, it 

can be improved by resetting MPC weighted matrixes 

with controller tuning algorithm. Simulation and device 

operation on single inverted pendulum device provided 

by Googol Technology LTD reaffirm the correctness of 

this system. Also, the introduction of LMI solution makes 



1 

-3.12 

0.05 

0.8 

-3.125 

0.04 

0.6 

0.4 

-3.13 

0.03 

0.02 

0.2 

-3.135 

0.01 

u 

0 

angle 

-3.14 

pos 

0 

-0.2 

-3.145 

-0.01 

-0.4 

-0.6 

-3.15 

-0.02 

-0.03 

-0.8 

-3.155 

-0.04 

-1 

0 200 400 600 800 

T 

-3.16 

0 200 400 600 800 

T 

-0.05 

0 200 400 600 800 

T 

Figure 13. Real-time operating curves of MPC controller-tuning system 

Figure 14. Steady state variance comparison bar charts 

the system easy to extend and analysis, this will provide a 

new way for later controller performance evaluation and 

tuning research. 


This work is supported by National Science 

Foundation of China under Grant 60974065. 

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Chao Cheng was born in Shanxi, China, 

1983. She received the bachelor degree 

in Beijing Institute of Fashion 

Technology in 2004. From August 2004 

to January 2007, she worked as control 

engineer in Jiangsu Yangnong Chemical 

Group Co.,Ltd. She is currently a second 

grade postgraduate student in 

Department of Automation in Beijing 

University of Chemical Technology. Her research interests 

include MPC and other advanced control. 

Zhong Zhao was born in Henan, China, 

1970. He received bachelor degree in 

Zhejiang University in 1992 and master 

degree and Ph.D. from East China 

University of Science and Technology in 

1995 and 1998 respectively. 

From 1998 to 2000, he worked as a 

postdoctol in Tsinghua University, from 

2000 to 2002 as Senior Engineer in 

Honeywell Hi-Spec Solutions and 

Visiting fellow in Max-Planck-Institute. From 2002 to 2004 he 

employed as a lecturer by University of Saga, Japan. 

He is currently a professor in the Department of Automation, 

and deputy director of Institute of Automation in Beijing 

University of Chemical Technology, also, member of U.S. IEEE 

and Japan, SICE. His research interests are the advanced control 

of complex industrial processes, process monitoring, and multiscale 

process signal analysis. 

Haixia Li was born in Gansu, China, 

1984. She received her bachelor degree 

and master degree in Information 

Science and Technology Institute of 

Beijing University of Chemical 

Technology in 2007 and 2010 

respectively. Her research direction is 

advanced control of industrial process. 



A Metadata-driven Cloud Computing Application 

Virtualization Model 

Yunpeng Xiao 1,2,* 

1. Chongqing Engineering Laboratory of Internet and Information Security, Chongqing University of Posts and 

Telecommunications (CQUPT), Chongqing, China 

2. Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and 

Telecommunications (BUPT), Beijing, China 

Email: shineagle2005@hotmail.com 

Guangxia Xu 1 , Yanbing Liu 1 and Bai Wang 2 

1. Chongqing Engineering Laboratory of Internet and Information Security, Chongqing University of Posts and 

Telecommunications (CQUPT), Chongqing, China 

2. Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and 

Telecommunications (BUPT), Beijing, China 

Email: {xugx, liuyb}@cqupt.edu.cn, wangbai@bupt..edu.cn 

Abstract—In order to meet the requirements of 

standardization of virtualization in cloud computing 

platform, improve the flexibility and expansibility of the 

system and enhance the capability of management-control 

of the platform, by means of introducing the features of 

decoupling and semantic of metadata, a Metadata-driven 

Cloud Computing Application Virtualization 

Model(MCCAVM) in software level is proposed in the 

paper based on Turing machine model and Von Neumann 

computer architecture. The model achieves the complete life 

cycle management of the capabilities and services. Based on 

the formal definition, analyzing the hierarchical structure 

with multi-role and multi-dimensional view, the paper 

proposes a Metadata-driven Cloud Computing Application 

Virtualization System(MCCAVS). Taking the production of 

virtual cloud storage service as example, this paper gives 

formal analysis of system running and compares with other 

relating work. The results show that the model presents 

good reference on the construction of cloud computing 

application virtualization platform. 

Index Terms—MCCAVM, metadata, cloud computing, 

application virtualization, software architecture 


The internet is gradually becoming a kind of 

computing platform in peace with the rapid expansion 

and popularization of computer communication 

technology. As a new computing mode, cloud computing 

describes a mode of increment, use and delivering for a 

new type of IT services based on internet. It usually 

means to apply dynamic scalable and virtual resources 

through internet[1, 2]. Wikipedia defined cloud 

computing scenario as follow: Users or clients can submit 

Manuscript received August 20, 2012; revised October 8, 2012; 

accepted October 14, 2012. 

Corresponding author: Yunpeng Xiao (xiaoyp@cqupt.edu.cn). 

a task, such as word processing, to the service provider, 

without actually possessing the software or hardware[3]. 

This description shows that a core issue of cloud 

computing research is how to achieve virtualization and 

large-scale application scalability and availability in the 

virtual environment. 

A broadly understood of virtualization is that 

computing elements run on the virtual basis. That is a 

kind of solution to simplify management and optimize 

resources. The key question highlights platform 

standardization, improvement of the platform flexibility 

and dynamic scalability, reduction of the degree of 

coupling of platform components and other aspects. 

There are many virtualization technology researches and 

explorations: Research [4] and [5] put forward 

virtualization platform architecture through researches 

based on service-oriented architecture (SOA), [6] and [7] 

focus on platform flexibility and dynamic capacity 

expansion, [8, 9, 10] study on virtualization from storage 

virtualization, virtual device, network virtualization, and 

other aspects. 

Application virtualization uncouples the applications 

from operating systems, provides a virtual operating 

environment for the applications. In this environment, not 

only includes the application executable file, but also 

includes the runtime environment it requires. In essence, 

application virtualization is abstracted dependent between 

low-level application systems and hardware. It can solve 

the problem of version incompatibility, the limitation of 

terminal capacity, application system hosting mass, realtime 

deployment of application, disaster recovery and so 

on. 

Metadata is descriptive information about the data. It is 

semantics on the basic concepts, basic relationships and 

basic constraints of data model. The metadata can solve 

problems that model layer can not resolve, such as fuzzy 

semantic of data model, model integration and sharing of 

information. By using metadata we can translate 


doi:10.4304/jcp.8.6.1571-1579


functional strong coupling relationships into data type 

weak coupling relationships. Metadata research is widely 

used in data-driving system such as file system, 

information system and so on [11, 12]. On the other hand, 

the abstract computational model: Turing machine, which 

can simulate any human computing process, is equivalent 

to any finite mathematics of logic process. The Turing 

machine is also a general-purpose computer and an ideal 

model of universal definition. Its abstract definition is a 

kind of mathematical logic machine [13]. Von Neumann 

implemented the ideal model, designed store-based 

computer architecture [14]. The Von’s thinking is 

inherited by modern computer architectures, since its 

clear structure and feasibility [15]. 

Taking into account the needs of application 

virtualization mentioned above, and by means of 

metadata, Turing machine and Von Neumann architecture, 

a Metadata-driven Cloud Computing Application 

Virtualization Model(MCCAVM) in software level is 

proposed in this paper. A Metadata-driven Cloud 

Computing Application Virtualization System 

(MCCAVS) is implemented based on MCCAVM by 

then. We make the following three major contributions: 1) 

Metadata is used to drive the whole system, so that the 

description of the system is standard and uniform. The 

decoupling purpose is well done besides. 2) We propose 

an application virtualization model in software level by 

refering Von Neumann architecture. All kind of 

applications and services can be managed by software 

bus. 3) Not only implemented engineering, the entire 

model and system are defined and verified formally by 

using Turing machine. 

The rest of this paper is organized as follows: after the 

introduction in Section 1, Section 2 describes the formal 

definition and gives the system model; Section 3 designs 

system and explains each module in detail; Section 4 

presents our MCCAVS and verifies it engineering and 

formally respectively; Section 5 concludes this paper. 

II. MODEL 

A. Formal Definition 

Before giving model description formally, the 

definition of capability and Service in the model is 

described firstly. 

Definition 1. Capability. Any underlying hardware 

and software resource in the cloud server side. 

Definition 2. Service. Product generated by a variety 

of capabilities, through assembling and reprocessing 

pattern. 

In fact, a virtual application in the cloud server side is 

combined of Capability and Service. According to Von 

Neumann architecture, computers must have five basic 

components: input data and devices, memory program 

and data memory, data processing computing device, 

control program execution controller, output device. 

Drawing on the thinking of the Von Neumann computer 

architecture, model regards Capability and Service as an 

external device. Various external devices mounted to the 

model via a software bus and driven by model controlled 

components. The work of the model is based on 

predefined tasks, makes multiple types of Capability and 

Service work together, and provides virtualization 

technology by using the basis of hardware, software 

resources and the upper applications supplied by these 

devices. Regarding Capability and Service as an external 

device, the collaborative process can be considered as the 

calculation of the finite number of steps. Based on formal 

definition, the paper proposed a Metadata-driven Cloud 

Computing Application Virtualization Model(MCCAVM) 

considering Turing machine computation model and the 

von Neumann computer system structure of these devices. 

Definition 3. Formal definition of the model. A 

Metadata-driven cloud computing application 

virtualization model can be formalized as a ten-tuple: T = 

(Q,Σ,Γ 1 ,Γ 2 ,Γ 3 ,Γ 4 ,δ,q 0 ,q a ,q r ) 

Q is the set of states; 

Σ is the input alphabet, which does not contain a 

special blank symbol B; 

Γ 1 is the capability to take the alphabet, where B∈Γ 1 

and Σ∈Γ 1 ; 

Γ 2 is the service with the alphabet, where B∈Γ 2 and 

Σ∈Γ 2 ; 

Γ 3 is the result with the alphabet, where B∈Γ 3 and Σ 

∈Γ 3 ; 

Γ 4 is a task with an alphabet, where B∈Γ 4 andΣ∈Γ 4 ; 

δ : Q×Γ 4 →Q×Γ 4 ×{L,R} 4 is the transfer function, 

where L, R indicates that the read-write head to the left or 

to the right; 

q 0 ∈Q is the initial state; 

q a ∈Q is an accepting state; 

q r ∈Q is the denial of state and q r ≠q a ; 

Capability alphabet and service alphabet need to be 

processed were recorded on work tapeΓ 1 and Γ 2 ; Γ 3 

records the results; Γ 4 records work processes alphabet of 

different virtualization tasks. 

Theorem 1. MCCAVM is a general computing model 

which is equivalent to the universal Turing machine. 

Proof: Firstly, in Definition 3, depending on the 

differences of storage function, defining a number of 

working tapes. Obviously, MCCAVM is multi-tape 

Turing machine, and multi-tape Turing machine is 

equivalent with Turing machine, so MCCAVM is 

equivalent with Turing machine. 

Secondly, we set the capability alphabet, service 

alphabet, results alphabet and tasks alphabet as 

T1,T2,T3,T4 in T's each computing step. Turing machine 

M is a seven-tuple. The current state, the current tape 

content and the location of the read-write head constitute 

the pattern of M. The specific calculation process of M is 

conversion from one pattern to another, based on the 

conversion rules described in the transition function δ. 

The essence of the Turing machine is an algorithm or 

function, given data x, a mapping rule according to the 

function f, calculating the corresponding f(x), that is, M is 

equivalent to a dedicated machine for a particular 

calculation. For a specific task, it completes a specific 

calculation or mapping process by MCCAVM according 

to task process. 



For a particular task, we can fix an algorithm Mi from 

process of tasks alphabet T4. The implementation process: 

Given T1, T2, transferring function δ is first fixed 

according to algorithm Mi, making T from one pattern to 

another. Each task corresponds to a process and each 

process corresponds to a Turing machine. Therefore, the 

algorithm is equivalent to a Turing machine. The 

calculation of (T1, T2) inputted on Turing machine Mi 

and array (T1, T2, T4) on MCCAVM are equivalent. 

That is, to any input of Turing machine Mi, MCCAVM 

can emulate the calculations of Mi, MCCAVM 

equivalent to interpreter for Mi. Therefore, MCCAVM is 

equivalent to a universal Turing machine. 

B. Role View of Model 

From the perspective of model development and 

management control, the model role is divided into 

developers and system operators. Among them, the 

developers are divided into capability developers and 

service developers. Developers produce capabilities or 

services by using interface language. The system 

operators use the system language to complete the control 

of model. Interface instruction set is related to interface 

language, system instruction set is related to system 

language. We will explain separately bellowed. 

Definition 4. Interface language. It is a set of grammar 

rules facing capability and service developers. Following 

this rule, developers can operate MCCAVM directly and 

complete the operating tasks accurately. Interface 

language enabled developers to manage full life-cycle of 

capability and service. In order to facilitate developer, 

interface language uses simple instruction. 

Definition 5. Interface command set. This is a set of 

commands which make MCCAVM to complete all kinds 

of basic operating actions according to interface language 

syntax framework. To complete a certain capability or 

service development tasks, a number of interface 

commands are combined together according to the 

workflow. And each command can also be used to carry 

out specified action. The commands are made up of 

parameters and interface functions. Interface functions 

instructs MCCAVM to complete the basic operating 

actions. Parameter stands for the executing target of 

operating instructions and the association attributes of 

operational objectives. 

Definition 6. System language. A set of grammar rules 

which can be discerned and read directly by the central 

processing unit of MCCAVM. Under the rules of 

grammar in the system language, each interface 

command corresponds to a number of system commands. 

Definition 7. System commands. Basic system 

commands set which meet the system language syntax 

rules. System commands directly relate to a variety of 

metadata operating, and they are significant minimum 

driving force of model. Model task input will be turned 

into system instructions sequence finally. 

In the MCCAVM, the interface language is source 

language and the system language is target language. The 

interface language is developer-oriented, which presents a 

simple way and shields complex logic operating involved 

with metadata in the model. The system language is the 

model executable language, which can complete internal 

behaviors with the core of metadata-driven. 

Figure 1. MCCAVM architecture 

C. Model Architecture 

According to the formal definition of the model, model 

architecture is shown in Fig.1. There are five parts: 

metadata entities, metadata management engine, bus 

architecture, the input-output system and the client 

interface. Referencing to the Von Neumann computer 

architecture, capability and service in MCCAVM are 

equivalent to the "peripheral" in computer hardware; the 

metadata entity is memory and driver of peripheral; 

Metadata management engines are belonged to the central 

controller unit. Capability and service are mounted to the 

corresponding bus through the metadata entity drive and 

in form of peripheral, completing interaction with 

metadata management engine. Capability and service are 

managed and controlled by metadata management engine. 

The central controller will eventually register service and 

capability to the user interface and release in a 

standardized form of web service. The form will be 

transferred by client, implements transparent access to 

cloud resources through clients. 

1) Metadata entity 

The metadata entity is the core part of the model basis. 

It is generated by metadata generator when Capability or 

Service enters the MCCAVM. The metadata entity is 

divided into two categories: descriptive metadata and 

administrative metadata. Descriptive metadata includes 

resource description metadata, capability description 

metadata and service description metadata. Resource 

description metadata is a summary list of capability and 

service of the model, describing available resources of the 

entire model. Administrative metadata includes the 

capability management metadata, the service 

management metadata and the control metadata. 

Metadata management engine controls the capability and 

service through the administrative metadata. 

2) Metadata management engine 

Metadata management engine is institution of control 

and scheduling of model, completes unified monitoring, 

management and coordination work of capability and 



service and other resources. Firstly, after capability (or 

service) enters the model metadata generator. Metadata 

generator requests metadata management engine to 

process by using interruption. Then engine mounts the 

corresponding resource on model bus by using metadata 

entity, completes the registration task of service and 

capability, informs MCCAVM that the capability (or 

service) has been in a state of readiness, then 

accomplishes work of further assembly and 

configuration of resource by deploying the capability (or 

service), coordinates with other related equipments and 

components in order to make the resource executable; 

realizes the management and control of model resource 

through capability (or service) monitoring. For any 

update of the capability(or service), metadata generator 

requests engine to process by using the interrupt 

mechanism similarly. The simple mechanism makes the 

MCCAVM model have favorable agile characteristic and 

dynamic extension property. 

3) Bus architecture 

Important ligament and prominent feature of 

MCCAVM is bus architecture. In the structure of 

computer hardware, rational task division of data bus, 

address bus and control bus promotes module production 

which is suitable for computer components, boosts the 

popularity of computers. The bus architecture of 

MCCAVM is constituted by capability metadata bus, 

service metadata bus and control metadata bus. 

Capability metadata bus and service metadata bus finish 

the carry of service and capability. Control metadata bus 

transmits control signals, communicate capability 

management metadata and service management metadata 

at the same time, makes MCCAVM unified. 

4) Input and output interface system of server side 

Server-side provides the capability and service for the 

system by using metadata, through the capability 

metadata generator and the metadata generator. 

Capability and service are provided to MCCAVM model 

in the form of peripheral through description and 

expansion of metadata. On the output side, further 

assembly and deployment of the model are provided to 

the client system in the unified form of web service. 

5) Client interface 

Client gets kinds of cloud applications from server side 

by using virtual desktop. Firstly, client virtual desktop 

gets service list from cloud side. User orders the apps 

which he/she likes subsequently. The load engine 

completes the transparent access to capability and service 

of cloud side at last. 

Ⅲ. SYSTEM DESIGN 

An open, dynamic scalable and data loosely coupled 

MCCAVS is designed based on MCCAVM in this 

section. 

A. System Architecture 

Based on the model design, MCCAVS architecture is 

shown in Fig.2. Corresponding to the model, the whole 

system includes metadata entities, metadata management 

engine, and bus structure, the input and output interface 

system of server side and client interface. Moreover, 

capability pool and service stores are implemented, used 

for storing capability and service. 

Figure 2. MCCAVS architecture 

B. Metadata Entity 

In MCCAVS, metadata entity components are series 

files of system capability and service for describing, 

controlling and managing (.meta). As the extensible 

markup language (eXtensible Markup Language, XML) 

provides standard methods of metadata information 

exchange methods, we use XML-based metadata file 

format. Resource metadata files (resource.meta) record 

all available capability and service in system; Capability 

description metadata file(capability_description.meta) 

and capability manager meta data files 

(capability_manager.meta) record detail information of 

specific capability; Similarly, service description 

metadata file (service_description.meta) and service 

managing data files (service_manager.meta) record detail 

information of specific service; Control metadata files 

record permissions related to capability and service, 

information of roles and life-cycle state control and so on. 

The resource metadata file (resource.meta) is given as 

followed for example: 

 

 

 

*** 

*** 

*** 

 

...... 

 

 

 

*** 

*** 

*** 

 

...... 

 

 

From above we can conclude that resource metadata 

file includes all the current capability and service list. 

Each capability or service has a system unique id 

identifier, which is assigned by the system when this 

capability or service enters the system and registers to the 

metadata engine. Based on Von Neumann architecture, 



we regard capability and service as “peripheral”, thus 

capability or service id is these “peripherals” address. 

Metadata management engine, which is the CPU of 

MCCAVS, can locate any capability or service according 

to the "peripheral” id through meta-data bus. Individual 

capability or service metadata description file and path to 

the file metadata management are stored in the tag 

meta_location. We take capability described metadata file 

as an example to expound the entity format of individual 

capability metadata in the following 

 

 

*** 

*** 

*** 

*** 

*** 

*** 

*** 

** 

...... 

 

 

Besides containing the capability id and other basic 

information, capability description metadata file also 

contains version tag used for controlling capability 

version information, location tag indicates the real 

location of the capability products in the capability pool, 

loadclass tag indicates the entrance classes of the 

capability part; dependentCapability tag indicates 

dependency relationship with other capability 

components. 

Figure 3. Interface language UML static structure 

C. Metadata Management Engine 

Metadata management engine, which takes responsible 

for parsing the interface command and translates it into 

system commands, is the "central processor" and the core 

component of the system. We define a set of interface 

commands based on object-oriented language JAVA to 

facilitate developers. As shown in fig.3, interface 

language is divided into three categories: the system input 

and output (IOSystem), the scheduling interface 

(Schedule), and the web service interface(WS). Interface 

command is the abstraction method provided by these 

interfaces and the command parameter is the method 

parameter. Table 1 shows a typical interface and the 

interface commands. 

D. Bus Structure 

According to the design of the bus structure in the 

model, three types of buses in the MCCVAS system are 

defined: capability bus, service bus and control bus. For 

the purpose of quick addressing and maintaining 

resources of storage efficiently, HashMap, which can 

complete key-value mapping and time complexity is O(1), 

is used to organize system capability and service. 

Capability or service id is the key and capability or 

service object instance is the value. Three bus 

declarations are followed: 

protected class ControlBus extends HashMap 

implements Bus 

protected class CapabilityBus extends HashMap 

implements Bus 

protected class ServiceBus extends HashMap implements 

Bus 

Interface 

IOSystem 

Schedule 

WS 

TABLE I. 

TYPICAL INTERFACE AND INTERFACE COMMAND 

Interface 

commands 

join() 

exit() 

login() 

load() 

start() 

update() 

Parameter 

Component: the 

Parent interface 

of Capability and 

Service 

ditto 

ditto 

ditto 

ditto 

ditto 

Function Declaration 

To Generate metadata entity 

when Capability or Service 

enters. 

To make Capability or 

Service exits the system. 

To allocate component ID 

when register to the system 

Capability or Service. 

To load Capability or Service 

on the system, which requests 

metadata management engine 

mounted components to the 

corresponding metadata bus 

through interrupt mode. 

To start-up Capability or 

Service. 

To update Capability or 

Service. 

stop() ditto To stop Capability or Service. 

logout() ditto 

To log out Capability or 

Service, log out components, 

exit the bus system. 

To generate service.xml and 

convert() ditto wsdl.xml for Capability or 

Service. 

publish() ditto 

To publish Capability or 

Service as a web service. 

E. Input and Output Interface in Server Side 

Server-side input interface includes capability 

metadata generator and service metadata generator. It 

shields metadata manipulation for outside of the system 

and generates metadata entity as described in Section 3.2. 

Output interface releases system capability and service to 

meet the invoking of terminals by using standardization 

web service interface. As shown in fig.2, we use AXIS2 

as release engine. 

F. Client Access 

As the server-side uses web service technology to 

provide resources, the system supports transparent access 

heterogeneous multi-platform capability and service of 

cloud side. Client interface work steps are as follows: 



a. Regarding all cloud resources (Capability and 

service) in cloud side as the services, and getting the list 

of services through parsing engine. 

b. Users order corresponding services when enter the 

list of services. 

c. User ordering events will trigger service parsing 

engine and get metadata file of their subscription services. 

d. Service load engine loads the service of client 

components according to service metadata file, achieving 

transparent accessing to virtual resources of the cloud. 

G. Capability Pool and Service Store 

Capability pool and service stores are components 

which storage system peripherals (Capability and service). 

System bus manages peripheral by using HashMap. 

Capability or service id is the key and capability or 

service object instance is the value. Correspondingly, the 

capability pool and service store are stockpiles of the 

value. So, here we use two instances of simple data 

structures (class Set) to implement the two components 

separately. 

network and using Google nexus s, Samsung and HTC 

etc. as test termination. 

The MCCAVS includes three subsystems, 

corresponding three user roles: 1) Virtual desktop 

subsystem, which is client software, corresponding to end 

user. As shown in fig.5, end user can enjoy cloud storage, 

browse cloud app list and virtual install apps which 

he/she likes. 2) Developer subsystem, which is a platform 

in the cloud side for the developers. As shown in fig.6, 

developers can upload, submit for review, and release 

apps. 3) Administrator subsystem, which is a platform in 

the cloud side for administrator. As shown in fig.7, 

administrator can use it for checking, configuring, 

monitoring and deploying everything in the cloud system. 

a) home page b) cloud storage view c) cloud apps view 

Figure 4. Snapshot of experimental environment 

d) home page after installing cloud apps e) configure cloud server 

Figure 5. Virtual desktop subsystem 

IV. SYSTEM IMPLEMENTATION AND VERIFICATION 

A. System Implementation 

The experimental environment of the system is as 

follows: The cloud cluster is made up of 14 PCs in which 

master node uses memory bank of 4G, Intel(r) core(tm)2 

duo 2.93GHz, hard disk of 500G and 13 slave nodes are 

of the same configuration of Pentium(r) dual-core 

3.20GHz,use memory bank of 2G,hard disk of 250G. 

MCCVS prototype system hosted by the master node, as 

shown in fig.4. The IaaS layer resources and the 

environment are made up of 13 slave nodes, which have 

installed Hadoop0.20, choose one as NameNode from the 

13 slave nodes. In MCCAVS, as IaaA basic resources 

made up of 13 slave nodes are regarded as a common 

"capability" enter system and MCCAVS manages IaaS 

resources through NameNode, IaaS layer can expand 

arbitrary amount of nodes at any time according to 

demand while there is not effect on MCCAVS. The inner 

bandwidth of the cluster is 100Mbit/s, outlet bandwidth 

of the server is 10Mbit/s; The operating system is 

ubuntu11.04, the version of Java virtual machine is Java 

SE6; The Web container is Tomcat 5.5.17; Client test 

platform is Android2.2, working in China Mobile EDGE 

a) home page for developer b) app upload view 

c) app checking result view d) cloud app list view 

Figure 6. Developer subsystem 

a) login page for administrator b) home page 



c) app monitor view d) app check view 

Figure 7. Administrator subsystem 

B. System Verification 

Due to lack of space, we elaborate formal description 

and experimental analysis based on Turing machine by 

using an example of virtual cloud storage services in this 

section. 

1) Service Description 

Virtual cloud storage is a destination service system, 

which makes numerous different kinds of storage 

equipments in network co-operate and provides data 

storage and service access function jointly. To the 

movable termination which is resource-constrained 

system, virtual cloud storage can extend the storage 

capability of mobile terminals. In MCCAVS, virtual 

cloud storage implementation involves four steps: First, 

the system IaaS layer underlying storage resource 

(Hadoop HDFS) enters the system as a capability, as 

shown in fig.2; Then development storage services log-in 

the system; Moreover, system transfers store service to 

standard web service and releases it; Finally, the terminal 

device finds and loads the service, to provide users with a 

virtual storage service. Using the system interface 

instruction defined in the 3.3 section, the service specific 

implementation steps are as follows: 

a. In IaaS layer, HDFS file system as a capability to 

enter the system and invokes interface IOSystem join() 

method. 

b. Based on HDFS, we develop cloud storage control 

components as service, invoking join() method of 

IOSystem. 

c. Storage capability registers to the system, invokes 

login() method of Schedule interface. 

d. Storage service registers to the system, invokes 

login() method of Schedule interface 

e. Invoke load() method of interface Schedule, load the 

storage capability. 

f. Invoke load() method of interface Schedule, load the 

storage service. 

g. Invoke start() method of interface Schedule to start 

the storage capability. 

h. Invoke start() method of interface Schedule to start 

the storage service. 

i. Invoke convert() method of interface Schedule; make 

Storage service as standard web service. 

j. Invoke publish() method of interface Schedule, 

release storage web service. 

In this section, the order of step a, b is fixed. Step c, e 

and d, f is the registration and loading of the capability 

and service, order cannot be changed. The order of 

process g, h, i, j is also fixed. 

2) Formal Verification 

According to the description of the services, virtual 

cloud storage model of the Turing machine can decode 

the symbol string S=(a b N g h i j), in which N stands for 

symbol string sequence combination of the fixed 

alphabetical order c, e and d, f. S is the symbol sequence 

after the combination of these symbols. Symbols come 

from a finite alphabet Σ and all the sequences of symbols 

constitute a language L. Therefore, the problem is 

transformed to a Turing machine T which can identify the 

language L. The Turing machine formal description is 

given in the following: 

T = (Q,Σ,Γ,δ,q 0 ,q a ,q r ) 

Q = {q 1 ,q 2 ,…,q 8 ,q a ,q r } 

Σ= {a, b, c, d, e, f, g, h, i, j} 

Γ= {a, b, c, d, e, f, g, h, i, j, B} 

δ:Q×Γ→Q×Γ×{L,R} is the transfer function. 

q 0 ∈ Q is the initial state; 

q a ∈ Q is the accepting state; 

q r ∈ Q is the reject state and q r ≠q a ; 

The initial state of Turing machine is q 0 , write symbol 

sequence S= (a b N g h i j), which needed to be read, on 

the work tape. Read-write head is scanned from left to 

right, Each reading of a symbol will trigger a process of 

metadata management engine, transferring to a new state. 

That is, transferring from q 0 to q 1 is a→b, R, its state 

transition function is δ(q 0 , a ) = (q 1 , b, R). The service 

production of the state transition is shown in fig.8. 

Figure 8. State diagram of virtual storage 

3) Experimental Analysis 

For virtual storage, cloud capability is much larger 

than the terminal capability, so, time performance index 

of the system is more important than the storage capacity 

index. Fig.9 describes the relationships between capacity 

and response time when terminal equipment access cloud 

storage service. Three experimental data in the same test 

are showed. In every test, besides testing machine, 15 

clients are simulated to test system concurrent effect. We 

can see, response time is mainly determined by the 

terminal connection bandwidth, system processing time 

can meet user requirement. On the other hand, 

virtualization technology will be the main computing 

tasks hosted by the cloud. 



time(ms) 

300000 

250000 

200000 

150000 

100000 

50000 

upload to cloud 

download from cloud 

0 

0 500 1000 1500 2000 2500 3000 3500 

file size(KB) 

Figure 9. Relationship between cloud storage capacity and response 

time 

amount of code(line) 

24000 

22000 

20000 

18000 

16000 

14000 

12000 

10000 

8000 

6000 

4000 

2000 

0 

amount of code in client 

amount of code in cloud side 

1 2 3 4 5 

service ID 

Figure 10. Compare amount of code between cloud and client 

Fig.10 compares code quantity of 5 services released in 

Section 4.1 (by serial number, they are instant 

messaging[16], cloud storage, campus assistant, online 

words, mobile TV) in the clouds and the terminal to 

compare the amount of computations roughly. As the 

figure shows, numerous computing tasks focus on the 

cloud by virtualization, even respective code quantity of 

service terminal is relatively more; it is also be 

concentrated in user interface to be processed with. In 

addition, fig.10 shows that when service scale is small, 

for improving user experience, the calculation of client 

may closer to the cloud. However, more large-scale 

applications are more suitable for deployment in cloud 

computing virtualization platform. 

C. Compare with Related Work 

In virtualization architecture, typical system is 

designed by Chinese Academy of Sciences, named 

Virtual Management Architecture (VMA)[4]. The model 

aims to establish a unified resource management 

infrastructure for enterprises to realize the unified 

management of resources, resource systems and ondemand 

service of resource. The VMA focuses on 

management and use of underlying hardware facilities. 

This is completely different in form and nature with 

MCCAVM in this paper. 

VMA is a resource management framework model, 

based on virtualization technology and equipped with the 

technique of independent scheduling, which unified the 

management and use of interface. VMA is made up of a 

number of resource management systems; each individual 

resource management system provides a kind of virtual 

resource services. VMA provides reasonable and uniform 

resource management infrastructure of the system by 

unifying these virtual resources management functions to 

a unified and consistent management platform. 

MCCAVM is a Cloud computing, virtualization model 

based on Metadata-driven. According to the formal 

definition of the model, it includes metadata entities, 

metadata management engine, the bus architecture, inputoutput 

system and customer termination. From the 

perspective of model development and control, besides 

end users, the model role is divided into two major 

categories of developers and system operators. Among 

them, the development is divided into capability 

developers and service developers. Developers use the 

interface language to develop capability or service, the 

system operator uses the system language to complete the 

model management control task, Table 2 shows the 

comparison between the two roles. 

TABLE II. 

COMPARE MCCAVM WITH VMA 

MCCAVM 

VMA 

Model role 

Developers, system 

operators 

Resource users 

realization mode Metadata-Driven SOA 

Virtual level 

Hardware resources , 

software services 

Hardware source 

objective 

Dynamic scalability for 

Unified management 

capability and service, 

of basic resources , 

platform versatility and 

on-demand use 

capability to control 

Hierarchy 

Five parts: Metadata 

entities ,metadata 

management engine, bus 

architecture, input, output 

systems and customer-side 

interface 

Consists of one or 

more virtual resources 

management services 

(VMS) and a system 

of registration and 

inquiry services 

( SRCS ) 

From the table above we can conclude that VMA 

focuses on the basic integration of resources and rational 

management. It is equivalent to an integration of 

resources and scheduling platform, which can achieve the 

efficient use and reasonable allocation of resources. 

MCCAVM achieves a reasonable distribution of 

resources, and forms a broader perspective to understand 

the connotation and extension of the capability and 

service. Through fig.2, we can find that the capability 

includes not only just basic resources in IaaS layer of 

cloud computing, but all the basic hardware and software 

in MCCAVS. At the same time, all the production based 

on the capability or reproduced through the combination 

of capability are all service, which reflects the idea 

EaaS(Everything as a Service). And the model realizes 

the dynamic expansion of service and capability and hotswappable, 

which further enhances the versatility and 

scalability of the model. 



V. CONCLUSION 

This paper proposes a metadata-driven cloud 

computing virtualization model MCCAVM, based on the 

discussion and analysis of real needs which exists in 

cloud computing virtualization technology currently. The 

corresponding system MCCAVS is implemented also. 

We formally define and verify the model based on data 

experiments. Compared with previous work, this model 

has good reference value which mainly reflected in: 1) 

Architecture which proposed by the model based on the 

Turing machine model and the Von Neumann computer 

is clear and simple. Simultaneously, it implements 

original intention of design efficiently. 2) The concept of 

cloud computing platform capability and service with a 

broader perspective is proposed. The full life cycle 

management of capability and service is implemented. 

The model regards capability and service as "peripheral", 

making the model has a good dynamic scalability. 3) The 

form of a metadata-driven not only make the model has 

management-control ability, a simple mechanism and 

versatility, but also transform the traditional strong 

function coupling relationship to loosely data coupled 

relationship of the various components in the model, 

which plays an important role in the decoupling. 


This research is supported by import National Science 

and Technology Specific Project under grants of 

2011ZX03002-004-03, Science & Technology Research 

Program of the Chongqing Municipal Education 

Committee under grants of KJ110529, Special 

Foundation of Cloud Computing of Chongqing 

University of Posts and Telecommunications A2010-13, 

Educational Reform Projects of Chongqing University of 

Posts and Telecommunications XJG1216. 

REFERENCES 

[1] Gartner.com. Gartner Say's Cloud Computing Will Be As 

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721. 

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Yunpeng Xiao, born in 1979, Ph.D. candidate. His research 

interests include cloud computing, data mining and complex 

network. 

Guangxia Xu, born in 1974, Ph.D., Associate professor. Her 

research interests include cloud computing and data mining. 

Yanbing Liu, born in 1971, Ph.D., professor, Ph.D. supervisor. 

His research interests include network management and control, 

strategy and security. 

Bai Wang, born in 1962, Ph.D., professor, Ph.D. supervisor. 

Her research interests include distributed computing and data 

mining. 



Robust Portfolio Optimization with Options 

under VE Constraint using Monte Carlo 


Department of Mathematics & Applied Mathematics Humanities & Science and Technology Institute 

of Hunan Loudi, 417000, P.R. China 

Email:hnyuxing@163.com 

Abstract—this paper proposes a robust portfolio 

optimization programming model with options. Under 

constrains of variance efficiency and shortfall preference 

structure, we derive optioned portfolios with the maximum 

expected return of robust counterpart. A numerical example 

using Monte Carlo illustrates some of the features and 

applications of this model. 

Index Terms—Robust portfolio optimization; VE constraint; 

Monte Carlo 


The main problem an investor faces is to make an 

optimal portfolio. The classical portfolio model is 

generally only associated with stocks. The derivative 

instruments are no more considered as the hedging 

instruments, but now they are considered as the 

investment instrument. For example, options are the 

derivative instruments which can increase the liquidity 

and flexibility of return from the investment. And at the 

same time, they also can be regarded as an asset to be 

invested. 

Numerous studies have investigated the integration of 

options in portfolio optimization models. Alexander, 

Coleman and Li (2006) [1] analyzed the derivative 

portfolio hedging problems based on value at risk (VaR) 

and conditional value at risk (CVaR). Papahristodoulou[2] 

proposed optioned portfolio model, and based on Black- 

Scholes(B-S)formula, they derived the values of all 

the Greek letters of the portfolio ΔΓΘto , , hedge risk. 

Their objective was to maximize the difference between 

the theoretical value and the market value of a portfolio 

with options. And they transformed the problem to a 

linear programming model. Their model is simpler, but it 

is tractable. Horasanli[3] extended the model proposed by 

Papahristodoulou to a multi-asset setting to deal with a 

portfolio of options and underlying assets. Gao[4] also 

extended the existing literature on options strategies. 

With the model and the method they mentioned, the 

investors can take the options strategies in terms of one’s 

subjective personality, and meanwhile, adjust the risks to 

suit the needs of the market change. Gerhard 

Scheuenstuhl, Rudi Zagst[5] examined the problem of 

managing portfolios consisting of both, stocks and 

options, However , the target function of their models 

associated with the stochastic properties of the portfolio 

return,which is intractable. Because we have to deal 

with the stochastic dynamics price model of the expected 

final portfolio value. 

The mentioned above are related to the problem of 

parameter estimation. However, the framework requires 

the knowledge of some inputs, such both mean and 

covariance matrix of the asset returns, which practically 

are unknown and need to be estimated. The standard 

approach, ignoring estimation error, simply treats the 

estimates as the true parameters and plugs them into the 

optimal portfolio optimization model. But most 

frequently the uncertain parameters play a central role in 

the analysis of the decision making process. So the 

peculiarity of these parameters cannot be ignored without 

the risk of invalidating the possible implications of the 

analysis Wets [6]. 

During the last two decades, the idea of robust 

optimization has become an interesting area of research. 

Soyster [7] is the first who introduced the idea of robust 

optimization, but his idea turns to be very pessimistic 

which makes it unfavorable among practitioners. Ben-Tal 

and Nemirovski [8] developed new robust methodology 

where the optimal solution is more optimistic. Their idea 

uses interior point based algorithm to find the robust 

solution on a counterpart of the initial model. They also 

apply their robust method on some portfolio optimization 

problems and show that the final optimal solution 

remains feasible against the uncertainty on different input 

parameters. Steve Zymler proposed a novel robust 

optimization model for designing portfolios that include 

European-style options. This model trades off weak and 

strong guarantees on the worst-case portfolio return. The 

weak guarantee applies as long as the asset returns are 

realized within the prescribed uncertainty set, while the 

strong guarantee applies for all possible asset returns. 

Nemirovski[9] proposed robust portfolio selection under 

ellipsoidal uncertainty. There is rare literature about 

robust portfolio optimization with options as far as we 

know. Steve Zymler[10] proposed a novel robust 

optimization model for designing portfolios that include 

European-style options, extending robust portfolio 

optimization to accommodate options. But they only paid 

attention to portfolio return and ignored risk. Ai-fan 

Ling.etc [11] proposed robust portfolio selection models 

under so-called ‘‘marginal + joint’’ ellipsoidal 

uncertainty set and to test the performance of the 


doi:10.4304/jcp.8.6.1580-1586


proposed models. In their paper one more robust portfolio 

selection model with option protection is proposed by 

combining options into the robust portfolio selection 

model. This paper considers the optioned robust portfolio 

return. 

The rest of the paper is organized as follows. In 

section 2 we review robust portfolio optimization. In 

Section 3 we show how a portfolio that contains options 

can be modeled in a robust optimization framework. 

Section 4 gives an example based on Monte Carlo 

simulation to illustrate the application of the model and 

the method. Conclusions are also drawn. 

II. ROBUST PORTFOLIO OPTIMIZATION 

We consider the portfolio includes several European 

call options and put options on different stocks. This 

portfolio makes extensive use of options to achieve the 

desired payoff profile. As we all know, the return of 

options depends on the return of the corresponding 

underlying stocks. And the inputs such as mean or 

variance are uncertain, which is lead to the returns of 

option are uncertain. However, if the uncertain sets of 

underlying inputs are determined, the ones of options are 

corresponding to. Mostly portfolio model integrated into 

options are only emphasized on portfolio return at the end 

of the investment horizon. Due to the resulting 

asymmetric portfolio return distribution mean–variance 

analysis will be not sufficient to identify optimal optioned 

portfolios. From the second half of the last century, 

options have been praised for their ability to give stock 

holders protection against adverse market fluctuations. A 

standard option contract is determined by the following 

parameters: the premium or price of the option, the 

underlying security price, the expiration date, and the 

strike price. A put (call) option gives the option holder 

the right, but not the obligation, to sell to (buy) from the 

option writer the underlying security by the expiration 

date and at the prescribed strike price. American options 

can be exercised at any time up to the expiration date, 

whereas European options can be exercised only on the 

expiration date itself. We will only aim at European 

options, whose expiration is at the end of investment 

horizon, that is, at time T. We will pay attention to these 

instruments because of their simplicity and since they 

naturally in the single period portfolio optimization 

framework of the previous section. 

A. An Introduction to Option Pricing 

It is necessary to introduce call option first. Suppose an 

investor is presented with an opportunity to enter into a 

position in a European call option written on a stock, with 

strike price K and expiration date T. The stock price 

process is assumed to follow a geometric Brownian 

motion with mean rate of return μ> 0 and volatility 

σ> 0 : 

dSt =μ Stdt +σ StdWt 

where { W,t 

t 

≥ 0} 

is a standard Brownian motion with 

W0 

= 0. The basic model for call option of the B–S is: 

−rT 

( ) ( ) 

C= SN d − Ke N d 

1 2 

2 

( ) ( ) 

d1 

= ⎡ln S/K r /2 T ⎤ 

⎣ 

+ +σ 

⎦ 

/ σ T 

d2 = d1−σ 

T 

where 

C call option price; 

S current stock price; 

K striking price; 

r riskless interest rate; 

T time until option expiration; 

σ standard deviation of return on the underlying 

security; 

N( d 

i ) cumulative normal distribution function evaluated 

at d 

i 

. 

The same as put option: 

−rT 

P = Ke N( d2) − SN( d1) 

where P is put option price; 

The meanings of the rest letters are similar to the 

formers. 

Next, we will improve B-S formula using analytical 

method. It is well known that the basic assumption of B-S 

model is to assume the underling price follows Geometric 

Brown motion: 

dSt = μ Stdt +σ StdWt 

Call option is an option is a security that gives its 

owner the right to trade in a fixed number of shares of a 

specified common stock at a fixed price at any time on or 

before a given date. The act of making this transaction is 

referred to as exercising the option. The fixed price is 

termed the strike price, and the given date, the expiration 

date. A call option gives the right to buy the shares; a put 

option gives the right to sell the shares. 

For an European call option its value at the expired 

time T is 

CT 

= ( ST 

− K ) 

+ 

Because the future is uncertain, it is stochastic. And 

we need to know the current value of option. So it should 

to deduce from its expectation ES ( T 

− K ) 

+ 

The financial market is perfect, that is the current value 

is equal to the discount of future value. 

−rT 

C0 = e E( ST 

− K ) 

+ 

Now, to calculate the expectation based on the hypothesis 

of lognormal distribution. 

2 

+ 

⎛ σ ⎞ 

⎛ σ TZ+ r− 

T ⎞ 

+ 

⎜ 2 ⎟ 

⎝ ⎠ 

E ( ST 

− K) 

= E⎜S0e −K⎟ 

⎜ 

⎟ 

⎝ 

⎠ 

where Z∼ 

N( 0,1) 

whose density function is 

Let Se 

1 

f ( x) 

= e 

2π 

2 

Ta ⎛ 

r σ ⎞ 

σ + ⎜ 

− 

2 ⎟ 

T 

0 

K 0 

2 

x 

− 

2 

⎝ ⎠ 

− = then 



2 

⎛ ⎞ ⎛ ⎞ 

K σ 

ln ⎜ ⎟−⎜r − ⎟T 

S0 

⎝ 2 ⎠ 

a = 

⎝ ⎠ 

σ T 

And the integral interval is divided to two parts 

( −∞,a] ∪ [a, +∞ ) 

⎛ 

⎞ 

e E S K S e K e dx 

⎛ 2 ⎞ 

2 

+∞ σ 

σ Tx+ ⎜ 

r− 

2 ⎟ 

T 

x 

+ 

1 − 

−rT 

⎝ ⎠ 

2 

( − ) = ⎜ 

⎟ 

T ∫ 0 

− 

⎜ 

⎟ 

a 

2π 

where 

⎝ 

= I + I 

1 2 

2 2 

x ⎛ ⎞ 

+∞ − +σ Tx+ r− T 

rT S 

σ 

− 0 2 ⎜ 2 ⎟ 

⎝ ⎠ 

∫ 

I1 

= e e dx 

2π 

a 

2 

+∞ 

x 

rT K − 

− 

2 

∫ 

I2 

=−e e dx 

2π 

For I 1 

, 

a 

2 2 

x ⎛ ⎞ 

+∞ − +σ Tx+ r− T 

rT S 

σ 

− 0 2 ⎜ 2 ⎟ 

⎝ ⎠ 

∫ 

I1 

= e e dx 

2π 

= 

a 

2 2 

σ +∞ x 

− T σ Tx− 

0 2 2 

S e ∫ e dx 

2π a 

( x−σ 

T) 

⎛ 

⎞ 

e exp dx 

2 2 

⎛ ⎞ 

r− T 

2 

S 

σ +∞ 

⎜ 

0 2 ⎟ 

⎝ ⎠ 

σ T 

= 

⎜ 

⎟ 

∫ − + 

2π a 

2 2 

⎜ ⎟ 

Let y= x−σ T then 

⎝ 

2 2 

σ T +∞ y 

− 

0 2 2 

S 

I1 

= e ∫ e dy 

2π a−σ 

T 

( ( )) 

( ( )) 

= −Φ −σ 

rT 

Se 

0 

1 a T 

= − −σ 

For I 

2 

, 

rT 

Se 

0 

N a T 

2 

+∞ x 

rT K − 

− 

2 

I2 

=−e ∫ e dx 

2π ( ( ))( ) 

−rT 

( a) 

= −Φ − 

−rT 

e 1 a K 

=−Ke 

Φ − 

a 

B. Basic Model 

The basic notion follows [12]. Consider a portfolio 

X = x x x ′ of stocks1, 2 

n 

consisting of quantities ( ) 

1, 2 n 

with the return vector R= ( r1, r2 r 

n ) 

′ . We assume that for 

each stock there are m put and m call options that mature 

in one year. The m strike prices of the put and call 

options for one particular stock are located at equidistant 

points between 70% and 130% of the stock's current 

price. C 

R , R are denoted the corresponding calls and 

ik 

Pik 

puts returns in the portfolio with stock price 

S , k = 1, 2m 

means the k -th strike price based on the 

i 

th 

i stock,call price C ik 

, and put price P ik 

, whose exercise 

⎠ 

⎠ 

prices are K ik 

, β and 

ik 

γ denote the (decision) variables on 

ik 

the numbers of the corresponding calls and puts option. 

0 

S denotes the initial price of stock ,which then can be 

i 

expressed as S 0 ir at the end of the period. Using the 

i 

payoff functions of call and put options, we can explicitly 

express the returns of options as: 

C 1 0 

R 

ik 

= max { 0, Si ri − Kik} = max { 0, aik + bikri 

} 

Cik 

with 

K S 

ik 

0 

aik 

=− , bik 

= 

P C 

ik 

ik 

Similarly, the return of a put option is 

P 1 0 

R 

ik 

= max { 0, 

i 

Kik − Si ri 

} 

Pik 

= max{ 0, aik 

+ bikri 

} 

S K 

with 

0 

ik 

aik 

=− , bik 

= 

Pik 

Pik 

where P 

ik 

, C will be calculated from Black–Scholes 

ik 

formula. 

Within this investment framework, the value a 

portfolio at the expired time the investor wishes to 

maximize can thus be formulated as: 

n 

m 

⎧ 

C P⎫ 

maxV = ∑⎨xr i i 

+ ∑ βik Rik + γik Rik 

⎬ 

i= 1 ⎩ k= 

1 

⎭ 

Constrains concluded in this paper will be developed 

based on [13], whose model also contained in optioned 

portfolio. The risk-return preferences of the investor are 

specified as mean–variance efficiency with additional 

shortfall constraints expressing the downside risk 

preferences. 

−1 

( I − L) wxβγ 

= C r and 

a 

QV ( ≥ Bα ( )) ≥1− 

α 

where the meanings of the parameters are explained 

as: w βγ 

is the share vector of stocks, call options and put 

x 

− 1 

options. Set L = C rr′ 

and I being the matrix with 1 in the 

c 

diagonal and 0 else. Let C be the covariance matrix of 

the (discrete) returns, r ( r1, r2 

rp 

) 

= the vector of 

expected returns and e the p -dimensional vector filled 

with 1 in each component of the instruments. 

The steps of calculating the parameters are follows: 

(1) Covariance matrix of the (discrete) returns C is 

estimated from history data. 

r = r r r is also 

(2) Expected returns vector ( 1, 2 p ) 

estimated from history data. 

(3) a = eC ′ − r, b= rC ′ − r, c= eC ′ 

− e, 

d = bc− 

a 

⎛b− 

ari 

⎞ ⎛crj 

− a ⎞ 

ra 

= ⎜ ⎟ , rc 

= ⎜ ⎟ 

⎝ d ⎠i= 

1,2 

p ⎝ d ⎠j= 

1,2 

p 

−1 

(4) ( ) 

1 1 1 2 

I − L w = C r 

xβγ 

a 

The following portfolio optimization problem 

corresponds to this model: 



max 

⎧ 

n 

m 

C P 

∑⎨xr i i 

+ ∑ ( βik Rik + γik Rik 

) 

⎩ 

−1 

⎧⎪ 

( I − L) 

wxβγ 

= C ra 

⎨ 

⎪⎩ 

QV ( ≥ B( α )) 

≥1−α 

i= 1 k= 

1 

st . 

C. Parameter Uncertainty 

Most of the parameter such as the expected returns and 

covariance are estimated from noisy data. Hence, these 

estimates are no accurate. As a result, if the model 

amplifies any estimation errors, the portfolios yielding 

will extremely perform badly in out-of-sample tests. So it 

needs to solve this problem. And the robust optimization 

is a good choice. Generally speaking, robust optimization 

aims to find solutions to a given optimization problems 

with uncertain parameters which could achieve good 

objective values for all or most of realizations of the 

uncertain parameters. We will assume that the estimate 

covariance is reasonably accurate such that there is no 

uncertainty about it. This assumption is justified since the 

estimation error in expectation by far outweighs the 

estimation error in covariance, see e.g. [14]. So, in 

decision-making uncertainty is unknown. There are many 

factors that affect the decision-making, including human 

psychology state, external information input, which is 

usually difficult to be derived in terms of probabilistic or 

stochastic measurement. The well known B–S model has 

a number of assumptions such as the riskless interest rate 

and the volatility are constant, which hardly catch human 

psychology state and external information input although, 

B–S model has been improved. 

Now, it needs to introduce robust optimization and 

portfolio selection [15]. The robust counterpart of an 

uncertain mathematical program is a deterministic worst 

case formulation in which model parameters are assumed 

to be uncertain, but symmetrically distributed over a 

bounded interval known as an uncertainty set U. The 

structure and scale of U is specified by the modeler, 

typically based on statistical estimates. Structure refers to 

the geometry or shape of the constraint set U, such as 

ellipsoidal or polyhedral. Scale refers to the magnitude of 

the deviations of the uncertain parameters from their 

nominal values; it can be thought of as the size of the 

structure defining U. A general form of the robust 

counterpart to an uncertain LP is given as 

T 

max ⎡min c x ⎤ 

⎣ 

( ) 

Subject to Ax≤b, ∀( A,b,c) 

∈ U 

There are two forms for transfer the robust into a set, 

linear or Ellipsoidal. 

(1) Linear interval 

In the robust optimization framework, the true value 

a is not certain which is given by the following equation 

i 

⎦ 

− ^ 

ai 

= ai+ a iηi, ∀ i 

where a − 

i is an estimate for a i 

, and a ^ 

i is the maximum 

distance that a i 

deviated from a − i and ηi 

is a random 

⎫ 

⎬ 

⎭ 

variable which is bounded by and symmetrically 

distributed within the interval[-1,1]. That is, the true 

value ai 

is symmetrically distributed with respect to i on 

− ^ − ^ 

⎡ 

⎤ 

the interval ai− a i,ai+ 

ai 

⎢ 

⎣ 

⎥ 

⎦ . 

(2) Ellipsoidal uncertainty sets are given by 

2 

⎧ 

− 

⎛ ⎞ ⎫ 

⎜ai 

− ai 

⎟ 

⎪ 

2 

a: 

⎝ ⎠ ⎪ 

⎨ ∑ 

^ 2 ≤Ω ⎬ 

⎪ a ⎪ 

i 

⎪⎩ 

⎪⎭ 

where Ω is a user defined parameter and adjusts the 

trade-off between robustness and optimality. 

Next, the problem is how to transfer the uncertain set 

to a series equations or in-equations. 

Let J be the number of parameters. For Soyster’s and 

Ben-Tal and Nemirovski’s model[16], 

or 

∑ 

i 

i 

a 

∑ 

i 

^ 

i 

− 

i 

− a 

a 

η = 

i 

Bertsimas and Sim (2004) relaxed this condition by 

defining a new parameter Γ (the budget of uncertainty) as 

the number of uncertain parameters that take their worst 

− ^ 

case value ai 

− ai 

.Therefore ηi 

≤Γ,such that Γ ∈⎡⎣ 0, J ⎤⎦ , 

then the optimal problem can be rewritten as 

− 

^ 

⎛ 

⎞ 

max⎜∑ai 

wi + min∑aiη 

iwi⎟ 

⎝ 

ηi 

⎠ 

S.t w = 1 

∑ 

∑ i 

i 

η ≤Γ 

wi 

≥0, −1≤ηi 

≤1, ∀ i 

It also can be rewritten as 

− 

^ 

⎛ 

⎞ 

max⎜∑ai 

wi −max∑ 

ai 

ηiwi 

⎟ 

⎝ 

ηi 

⎠ 

S.t w = 1 

∑ 

∑ i 

i 

η ≤Γ 

wi 

≥0,0≤ηi 

≤1, ∀ i 

However, this problem is not well-defined. Because it 

is difficult to obtain a different optimal solution for each 

return realization, there are multiple ways to specify the 

linear set. A nature choice is to construct an ellipsoidal 

uncertainty set 

T − 

Θ = r : r − μ Σ 

1 r − μ ≤ δ 

2 

r 

{ ( ) ( ) } 

~ 

According to EI Ghaoui et al [17],when r has finite 

second-order moments, then, we can choice 

δ p 

= 1− p 

for p ∈[0,1 ) and δ = +∞ 

for p = 1 , it means the following probabilistic 

guarantee for any portfolio w : 

= 

J 

J 

a − 



~ 

T 

T 

{ r∈Θ 

} 

r 

P w r ≥minw r ≥ p 

The optimal problem reduces to a convex second-order 

cone program[18]. 

T 

2 T 

max w μ − δ Σ 

1/ w 1 = 1, 

l ≤ w ≤ u 

w 

{ } 

2 

According to the Central Limit Theorem, it is 

^ 

concluded that the sample mean μ is approximately 

normally distributed. That is ,it follows: 

^ 

⎛ Σ ⎞ 

μ ~ N ⎜ μ, 

⎟ 

⎝ n ⎠ 

Similarly, the ellipsoidal uncertainty set for the 

mean μ can be expressed as 

Θ 

μ 

−1 

⎪⎧ 

^ 

⎛ Σ 

^ 

⎛ ⎞ ⎞ ⎛ ⎞ ⎪⎫ 

2 

= ⎨μ 

: ⎜ μ − μ ⎟⎜ 

⎟ ⎜ μ − μ ⎟ ≤ κ ⎬ 

⎪⎩ ⎝ ⎠⎝ 

n ⎠ ⎝ ⎠ ⎪⎭ 

where κ = q / 1− 

q for some q ∈[0,1) 

The problem reduces to 

⎪⎧ 

1/ 2 

^ 

⎛ Σ 

^ 1/ 2 

⎪⎫ 

T ⎞ 

T 

max⎨w 

μ−κ 

⎜ ⎟ w −δ 

Σ w w 1 = 1, l ≤ w ≤ u⎬ 

w 

⎪⎩ 

⎝ n ⎠ 

2 

2 

⎪⎭ 

See[19] the problem is finally reduced to 

⎪⎧ 

^ 

^ 1 / 2 

⎪⎫ 

T 

1 / 2 

T 

max⎨w 

μ − κ Ω w − δ Σ w w 1 = 1, l ≤ w ≤ u⎬ 

w 

2 

⎪⎩ 

2 

⎪⎭ 

where 

Σ 1 Σ T Σ 

Ω = − 11 

n T Σ n n 

1 1 

n 

In this paper, firstly, we consider the uncertain set for 

return mean. We define r′ is the estimation of real 

value r , the uncertainly set I as 

{ : i 

′ i i i 

′ i } 

I = r r −s ≤r ≤ r + s for mean μ . 

According to Anna[20], the robust counterpart: 

rx ≥ r 

∑ 


i i p 

can be transferred to the following form: 

⎧∑rx ′ 

i i 

−∑sm i i 

≥rp 

⎪ 

⎨ mi 

≥ xi 

⎪ 

⎩ si 

≥ 0 

The robust counterpart of objective function is 

n 

m 

⎛ ⎧ 

C P ⎫⎞ 

max ⎜∑⎨xr i i 

+ ∑ { βik Rik + γik Rik} 

⎬⎟ 

x, βγ , 

⎝ i= 1 ⎩ k= 

1 

⎭⎠ 

let x αβγ 

is the share of stock and options. 

The goal is to determine the solution of above problem 

under the constraints. 

Ⅲ.MONTE CARLO SIMULATION AND EMPIRICAL EXAMPLE 

A. Monte Carlo Method and the Simulation Process 

Comparing with other numerical methods, Monte 

Carlo simulation has two major advantages: first, more 

flexible, easy to implement and improvement; secondly, 

the simulation of estimation error and convergence speed 

in solving the problem has strong independence of 

dimension. European option because of its execution time 

is fixed, not to be executed in advance, therefore it only 

need to calculate the earnings of the option of each 

sample path at expiration date, which is available by 

Matlab programming. [21-23] discuss the application of 

the simulation methods in various area. Monte Carlo 

method can overcome the obstacle and we use it further 

to improve the accuracy of simulated price with the 

enhancement of reduction variate technique for more 

complex options whose payoff function is dependent on 

the underlying asset path and sum of asset is more than 

one. 

Now, we illustrate the key steps in Monte Carlo. It is 

saw that to draw samples of the terminal stock price 

S( T ) it suffices to have a mechanism for drawing 

samples from the standard normal distribution. For now 

we simply assume the ability to produce a sequence 

Z1, 

Z2 of independent standard normal random 

variables. Given a mechanism for generating the Z 

i 

, we 

rT 

can estimate E⎡ 

− 

e ( ST 

− K ) 

+ ⎤ using the following 

⎣ 

⎦ 

algorithm: 

For i = 1, 2n 

generate 

Z 

i 

⎛⎡ 

1 ⎤ ⎞ 

Si 

T = S0 

exp⎜⎢ 

r− σ + 

2 ⎥ 

T σ TZi⎟ 

⎝⎣ 

⎦ ⎠ 

set ( ) 

2 

C = e S −K 

−rT 

set ( ) + 

^ 

i 

set n = ( + + + ) 

T 

C C C C n 

1 2 n 

/ 

For any n ≥ 1, the estimator C n is unbiased, in the 

sense that its expectation is the target quantity: 

^ 

⎛ ⎞ 

− rT 

+ 

E⎜Cn 

⎟= C = E⎡ 

⎣e ( ST 

−K) 

⎤ 

⎝ ⎠ 

⎦ 

The estimator is strongly consistent meaning that as 

n →∞. 

In this paper, we suppose z = z() 

t is a random 

process, the change in a very small time interval Δt 

is 

expressed as Δ z . If Δz 

satisfies that Δ z = ε Δ t where 

ε ∼ N ( 0,1) 

. For different time interval Δ t , Δz 

are 

independent, then call z = z() 

t follows Wiener process. 

Suppose the stock price follows ds = μsdt + σ sdz , 

where dz is the Standard Brown motion. In the practical 

^ 



application, more accurate simulation not starts from S, 

but log-price ln S . Monte Carlo simulation steps: 

(1) To generate sample paths for underlying asset, given 

the initial value 

i i i i 

S = t 1 

S + t 

μiS Δ t 

t + + 

σiS Δ t 

tεt 

(2)To calculate option price of each sample path. 

(3) To average option price for each sample path. 

IV.EMPIRICAL EXAMPLE 

In order to illustrate the features and applications of 

this model, we make a numerical example. For simple, 

we only consider two stocks. And there is a call and a put 

option based on each stock. Suppose that the investment 

horizon is T = 1year, including 20 trading days in each 

month, so there is 240 trading days in total. To divide 

T by daily, that is Δ t =1day, equals to 1 year. The 

240 

price of each stock is supposed to follow log-normal 

distribution, then the price of stock i,( i = 1,2) in 

t + 1day is: 

i i i i 

S S μ S t σ S tε 

ε ∼ N 0,1 

= + Δ + Δ , ( ) 

+ t 

t 1 t i t i t t 

i i i 

Generate a path S 0 

, S 1 

S 

240 

for stock i by Monte 

Carlo method. 

Each stock will only correspond to a European call 

option and a European put option, asset specific 

parameters are as follows: 

μ1 = 11%, σ1 = 26.86%; μ2 = 8.05%, σ2 

= 16.3% 

Other parameters are as shown in the following. 

The kind of option, underlying, market price, option 

price, time and strike price respectively are: 

For call option C 1 

whose underling is S with initial 

1 

value S 1 ( 0 ) =15.59, the option premium C 1 ( 0 ) =2.17, 

the strike price is K 

11 

=14.5, the expired time is 6 month. 

For call option P 1 

whose underling is S 1 

with initial 

P =1.87, 

value S ( ) =15.59, the option premium ( ) 

1 0 

1 0 

the strike price is K 12 

=16.5, the expired time is 12 

month. 

For call option C whose underling is 

2 

S 1 


value ( ) 2 

0 

C 

2 

0 =1.32, 

the strike price is K =13, the expired time is 3 month. 

21 

For call option P 2 

whose underling is S 2 


P =1.48 , 

S =13.71, the option premium ( ) 

value S ( ) =13.71, the option premium ( ) 

2 

0 

2 

0 

the strike price is K =15, the expired time is 9 month. 

22 

If the option j based on stock i is exercised on the 

l ( ≤ 240) 

day, the option value is 

i i i i 

( Srr 

01 2 

rl 

− Kij) 

max 0, 

,and in the rest of investment 

horizon, that is, in the following 240 − l days,the value 

is treated as risk free asset,so the total value of the 

option in the investment horizon is: 

i i i i 

r( 240 −l) 

/ 365 

max ( 0, Srr 

0 1 2rl 

− Kij) e , r= 

5% is the risk 

free interest rate. 

The European call option price before expiration day, 

for example, on the v− th day is 

i i i i −r l−v i 

max 0, Srr r − K e − c , v≤ 

l 

( ) 

( l ij) 0 1 2 0 

i 

where C is the option current price (option premium) 

0 

based on stock i. 

If v> l , then on the v− th day, the call option price 

is 

r 

⎛ ⎞ 

365 

i i i i 

⎜e −1⎟max( 0, S0r1r2 

rl 

−Kij) 

⎝ ⎠ 

Suppose that the portfolio assets real returns are 

μ = μ , μ , r 1 , r 1 , r 

2 , r 

2 , and the means of samples 

( 1 2 c p c p ) 

return are μ ( μ′ ) 

1 1 2 2 

1 

, μ ′ 

2 

, r ′ 

c 

, r ′ 

p 

, r ′ 

c 

, r ′ 

p 

′ = with investment 

share x = ( x , x , w , w , w , w ) . We construct the model: 

1 2 1 2 3 4 

μ x μ x r w r w r w r w 

1 1 2 1 

max 

1 1+ 2 2+ c 1+ p 2+ c 3+ 

p 4 

⎧ 

1 1 2 1 

μ′ 1 

x1+ μ ′ 

2 

x2 + r ′ 

c 

w1+ r ′ 

p 

w2 + r ′ 

c 

w3+ r ′ 

p 

w4 

≥0.001 

⎪ 

−1 

⎪ 

( I − L) 

wxβγ 

= C μa 

⎪ 

−1 −1 −1 2 

a= eC ′ μ, b= μ′ C μ, c= eC ′ e, 

d = bc−a 

⎪ 

⎪ ⎛b−aμ 

⎞ ⎛cμ−a⎞ 

−1 

⎪ μa = ⎜ ⎟, μc = ⎜ ⎟, 

L= 

C μcμ′ 

⎨ ⎝ d ⎠ ⎝ d ⎠ 

⎪x1+ x2 + w1+ w2 + w3+ w4 

= 1 

⎪ 

⎪μ′ x + μ ′ x + r ′ w + r ′ w + r ′ w + r ′ w −∑ 

sm ≥r 

⎪ 

⎪mi 

≥ xi 

⎪ 

⎩si 

≥ 0 

1 1 2 1 

1 1 2 2 c 1 p 2 c 3 p 4 i i p 

where C is the covariance matrix between the assets , 

the minimum return for an investor is 2%. 

By solving the above model, we obtain the optimal 

portfolio is (0.4,-0.04,-0.1,-0.3,-0.16), the objective 

is0.00682456. If it is set s 

i 

= 0 , that is there is no robust 

of return mean, the result is 0.0070175439. It is easy to 

understand that under robust, investment is more 

conservative. Because the advantage of combining option 

in portfolio is option could hedging with risk. In order to 

test it, we change the variance from small to large, for 

example, supposeσ 

1 

= 30%; σ 2 

= 25% , we find that the 

objective is 0.0052984, if there is without options, the 

objective is 0.000215. That is, options in portfolio could 

hedge risks. 

V. CONCLUSION 

This paper extents the general portfolio model in two 

aspects. The first is to combined option in the portfolio 

could hedge the risk, and the options can also considered 

as an asset in the portfolio, extending the general 

model.And we use Monte Carlo method to simulate the 



option prices. The second point is to propose the model 

of maximizing the return under constrains of variance 

efficiency and shortfall preference structure in the robust 

counterpart, taking account of uncertain inputs. It extends 

the general portfolio model, putting forward some 

feasible suggestions to investors. 


This research is supported by a Project Supported by 

Scientific Research Fund of Hunan Provincial Education 

Department (12C0749). 

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management with options. European Journal of 

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and robust portfolio optimization: A conic 

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Xing Yu was born in 1981. From 2000.9.1 to 2004,7.1, she 

studied at Department of mathematics and applied mathematics 

of Yangtze University, received Bachelor of Science Degree, 

From 2004.9.1 to 2007,1, she studied at Department of 

mathematics and applied mathematics of Huazhong University 

of science and technology, and earned a Master of Science 

Degree. From 2007,3, she is working at Hunan university of 

humanities Science and Technology, studying aim at financial 

mathematics, mathematical model. 



A Novel Water Quality Assessment Method 

Based on Combination BP Neural Network 

Model and Fuzzy System 


Chang Chun Institute of Technology 

Chang Chun, China,130012 

Email: xueming_net@sina.com 

Abstract—As the forefront of complex nonlinear science and 

artificial intelligence science, artificial neural network has 

began to be applied in the field of water quality control and 

planning step by step. According to the fuzzy feature of 

water quality information, this paper proposes a 

membership degree Back-Propagation network (MDBP) for 

water quality assessment with combining fuzzy mathematics 

and artificial neural network. The proposed MDBP model 

combines the merits of artificial neural network method and 

fuzzy evaluation method, which overcomes effectively the 

shortcoming of other assessment methods. With improving 

the accuracy and reliability of the assessment method, the 

method has a higher flexibility than other conventional 

approach and its programs have a better adaptability and 

more convenient application. The assessment method is 

closer to the reality with considering the continuity of the 

changes of water quality environment. 

Index Terms—Water Quality, Fuzzy Mathematics, Back- 

Propagation Neural Network, Assessment Method 


The water quality assessment is basic program to plan 

and manage water quality and important base of 

computing water environment capacity and controlling 

water pollutant, which shows the total information of 

water environment quality. In practice, there are many 

assessment methods used to water quality assessment. 

For example, the integrated index approach shows the 

uncertain characters of water quality changes, which 

holds the needs of water quality function classification. 

The practice shows that all of these used methods need to 

suppose subjective parameters and concrete assessment 

mode, so the assessment results always have obviously 

subjectivity and restrained applicability. In theory, the 

artificial neural network method with potentiality can 

solve the problem. As for the artificial neural theory, the 

function of learning and memorizing can provide the 

basic theory and methods for water quality assessment 

mode and classification problem. In the reference [1] the 

un-point pollutant sources drainage area is assessed by 

using the method of Bayesian concepts and combining 

artificial neutral network. In reference [2-4], the Back- 

Propagation network model with multi-input, multioutput 

and multi-layer is adopt to assess integrated water 

quality, and the qualitative description is used in water 

quality classification. But the shortcoming of this method 

is that the output mode must be obtained not by learning 

but artificially loading. Thus the assessment results can 

not be objective, direct and compact enough. 

In this paper, a new water quality assessment method 

is studied, which can be so much more effective and 

objective to overcome the shortcoming of the present 

artificial neural network method. A membership degree 

Back-Propagation network for water quality assessment 

with combining fuzzy mathematics and artificial neural 

network is proposed, which combines the merits of 

artificial neural network method and fuzzy evaluation 

method, and then the model overcomes effectively the 

shortcoming of other assessment methods. So the 

assessment method is closer to the reality with 

considering the continuity of the changes of water quality 

environment. The experiment and analysis show that the 

new water quality assessment method which combines 

BP neural network model and fuzzy system is effective. 

II. THE PRINCIPLE OF BACK PROPAGATION NEURAL 

NETWORK MODEL 

A. The Basic Structure of Back Propagation Network 

Model 

In 1985, Rumelhart and Meclelland proposed Back 

Propagation neural network model. Error Back 

Propagation usually called BP network in short, which is 

one of the most widely applied neural network model. 

[5]From the structure, BP network is typical multi-layer 

network which has not only input layer nodes and output 

layer nodes, but also one layer or multi-layer recessive 

nodes. In BP network, the consecutive layers are 

complete connected, but no connections in different 

nodes of same layer. [6] 

The structure of the BP neural network model with 

three layers is shown as fig.1. In the BP neural network 

model, the weigh coefficients between different layers 

can be adjusted automatically. Except for the input layer, 

the process units in other layers have nonlinear 

input/output connection. That is to say, the characteristic 


doi:10.4304/jcp.8.6.1587-1593


functions of the process units are differentiable, which are 

usually S type function (Sigmoid function) f ( x ), that is 

1 

f( x) 

= (1) 

x 

1 + e − 

The study process of BP neural network includes 

forward propagation and error back-propagation. If given 

some input mode, the BP network will study for every 

input mode in accordance with the followed methods. 

The input mode are transferred from input layers to the 

hidden layer units, by which the input mode can be 

processed, the new output mode will be transferred to 

output layer, that is called forward propagation. If the 

output mode is not expected, the error signals will return 

along the origin route, connection weights of neurons in 

every layer should be corrected to make the error signals 

least, that is error back-propagation. Forward propagation 

and back propagation repeatedly, until the expected 

output mode can be obtained 

The learning process of BP network begin from a set 

of random weights and thresholds, any selected samples 

can be input. The output can be computed by forwardback 

method. Usually this error is big, the new weights 

and thresholds of the mode must be computed over again 

by the back propagation. For all of the samples, the 

process should be done repeatedly again and again, to get 

the appointed accuracy. In the process of network 

operation, the system error and single mode error can be 

followed. If the network learning successfully, the system 

errors will decrease with increasing of iterative time, at 

last converge at a set of steady weights and thresholds. 

y1 

y2 

y3 

x1 

x2 

x3 

Figure 1. the BP network model structure with three layers 

B. The Mathematical Principle of Back Propagation 

Network Model 

The propagation formulas for BP network study are 

used to adjust the weights and thresholds. In fact, the 

network study process is a process in which weights and 

thresholds of network connection are revised repeatedly 

according to the propagation formula in the direction of 

least error. There are some symbol conventions: 

O : output of nodei ; 

i 

net : input of node 

j 

j ; 

w : connected weight from node i to node j ; 

ij 

θ : threshold of node 

j 

j ; 

y : actual output of node 

k 

k in output layer; 

t : expected output of node 

k 

k in output layer. 

Obviously, for hidden node j : 

net 

j 

= ∑ wijO 

⎫ 

i ⎪ ⎬ 

(2) 

Oj = f( netj −θ 

j) 

⎪⎭ 

In study process of BP algorithm, the errors of every 

output node can be computed according to the following 

formula: 

1 

2 

e= ∑ ( tk 

− yk) 

(3) 

2 k 

The connection weights can be corrected according to 

the following formula: 

w ( t+ 1) = w ( t) 

+Δ w 

(4) 

ij ij ij 

w 

In the formula, () ij 

t wij 

( t+ 1) 

and are separately 

connection weights from node j to node k at time t 

andt + 1 Δw 

; 

ij is variation of connection weights. 

In order to improve the connection weights in the 

Δwij 

gradient change direction of error E, can be 

computed: 

e 

Δ wij 

=−η ∂ 

(5) 

∂ w 

In the formula, η is gain factor, 

Thus 

Thus 

jk 

∂e 

∂w 

jk 

∂e 

∂e 

∂net 

= 

∂w ∂net ∂w 

∂net 

jk k jk 

∂ 

can be computed: 

k 

= ∑ wjkOj = O (6) 

j 

∂wjk 

∂wjk 

j 

∂ 

δk 

= ∂ net k 

∂e 

Δ w =− η =−ηδ 

O 

ij k j 

∂wjk 

When computingδ k 

, it is essential to distinguish the 

output layer nodes and hidden layer nodes. If node k lies 

in output layer, thus: 

∂e 

∂e 

∂yk 

δk 

= = 

∂netk ∂yk ∂netk 

Because of 

∂ e 

∂y 

=− ( t − 

k 

k 

yk) 

= f ′( netk 

) 

∂yk 

∂netk 

Thus 

δk =−( tk −yk) f′ 

( netk) 

⎫⎪ ⎬ (8) 

Δ wjk = η( tk − yk) f′ 

( netk) 

Oj⎪⎭ 

k 

(7) 



If node k is not the node in output layer, connection 

weights effect on hidden node, then δ k 

can be computed 

by the following formula: 

That is 

Thus 

∂e ∂e ∂Ok 

∂e δk 

= = = f ′( net 

k) 

∂net ∂O ∂net ∂O 

k k k k 

∂e 

(9) 

= ∑ δmw 

(10) 

km 

∂Ok 

δ = f ′( net ) ∑ δ w 

(11) 

k k m km 

m 

The formula shows that δ in low layer can be 

computed by δ in the upper layer. 

The learning process of BP network begin from a set 

of random weights and thresholds, any selected samples 

can be input. The output can be computed by forwardback 

method. Usually this error is big, the new weights 

and thresholds of the mode must be computed over again 

by the back propagation. For all of the samples, the 

process should be done repeatedly again and again, to get 

the appointed accuracy. In the process of network 

operation, the system error and single mode error can be 

followed. If the network learning successfully, the system 

errors will decrease with increasing of iterative time, at 

last converge at a set of steady weights and thresholds. [7] 

C. The Study Algorithm of Back Propagation Network 

In BP network model, the study algorithm of BP 

network can be described as the following rules. 

Step 1 Initializing study parameters and BP network 

parameters. That is to set random numbers in [ − 1,1] for 

Neuron threshold and connection weights in hidden 

layers and output layers. 

Step 2 Proposing the training mode of BP network. 

That is to select a training mode from the training mode 

set, and put the input mode and expected output mode to 

the BP network. 

Step 3 Forward propagation process. That is to 

compute the output mode of the network from the No.1 

hidden layer for the given input layer. If error energizing, 

executing the step 4, else returning to step 2, and 

providing next training mode for the algorithm. 

Step 4 Back propagation process. That is to correct the 

connection weight of every unit in different layer from 

output layer to the first hidden layer, and following the 

rules: 

1) Computing the error δ k 

of different units in the 

same layer. 

2) Correcting the connection weights and threshold. 

For connection weights, the correcting formula is: 

w ( t+ 1) = w ( t) 

+ ηδ O (12) 

jk jk k j 

For threshold, the correction method is same as the 

study method of connection weights. 

3) Repeating the Above-mentioned correcting process 

to get expected output mode. 

Step 5 Turn back to step 2, and doing step 2 to step 3 

for the every training mode of training mode set, until 

every training mode meet the expected output. 

III. THE PRINCIPLE OF BACK PROPAGATION NEURAL 

NETWORK MODEL 

A. The Basic Principle of Fuzzy Mathematics 

Assumed that X represents a set of some objects, 

which is called co domain. For a subset A in X , it can 

be expressed by its characteristic function, that is 

⎧1 

x ∈ A 

μA( x) 

= ⎨ 

(13) 

⎩0 

x ∈ A 

In this, μ A 

is a function defined in X , its values 

belong to{ 0,1 } ,which is called characteristic function of 

A . For x ∈ X , if μ ( x A 

) = 1, thus, x is element of A . 

But if μ ( x A 

) = 0, thus, x isn’t the element of A . So we 

can define fuzzy sets: 

In co domain X , for any element x ∈ X , if there is a 

formula corresponding real function μ A( x ) : 

μA( x): X → [0,1] 

(14) 

X → μA( x) 

Then all elements x meeting the formula assemble a 

set which is a fuzzy set A in set X . For x ∈ X , μ is 

A 

membership function of A . μ A ( x ) is called membership 

degree from x to A .[6] 

The Relationship that expresses uncertain relationship 

using fuzzy Sets is defined fuzzy relation. [8] Fuzzy 

relation R between set X andY is fuzzy subset defined 

in X × Y , its membership function is shown as: 

μ 

R 

: X × Y → [0,1] (15) 

If X is same asY , so R is called the fuzzy relation in X . 

If the co domain is product of n sets Xi 

( i = 1,2, , n) 

X × X × × X , its corresponding fuzzy relationship 

1 2 n 

R is called n dimensions fuzzy relation. 

If X and Y are both limited subsets, 

X = { x , x , , x m 

} , Y = { y1, y2, , y n 

} , thus the 

then 

1 2 

fuzzy relation in X 

R 

× Y can be expressed by : 

⎡ μR( x1, y1) μR( x1, y2) μR( x1, yn) 

⎤ 

⎢ 

μ ( x , y ) μ ( x , y ) μ ( x , y ) 

⎥ 

⎢ 

 

⎥ 

 

 

⎢ 

⎥ 

⎣μR( xm, y1) μR( xm, y2) μR( xm, yn) 

⎦ 

R 2 1 R 2 2 R 2 n 

= ⎢ ⎥ 

(16) 

The above matrix is called fuzzy matrix, its 

element μ ( x , y ) in the scope of 0 between 1. 

R i i 



B. The Design of Membership Degree BP Neural 

Network 

The paper adopted a three layers BP network to build 

the membership degree BP network for water quality 

assessment. In the structure, the network has one input 

layer one output layer and one hidden layer. The output 

layer can expressed water quality classification by one 

neuron, actual testing parameters are six, so input layer 

has six neurons, hidden layer has three neurons [9]. 

In order to make the assessment more objective and 

certain, this paper puts the membership degree of fuzzy 

mathematics into BP network. The membership degree 

BP network model is built on combining the fuzzy system 

and neural network in series. In the series connection, 

output of neural network is input of the fuzzy system. 

Membership degree can be computed, then the exact and 

concrete water quality classification can be put out. The 

membership degree BP network for water quality 

assessment is shown as fig. 2. 

In the formula, abstand , for the classification of 

neighboring two water quality samples, the membership 

degree to every standard water quality classification of 

test sample can be computed by the formula (17). 

IV. THE PRINCIPLE OF BACK PROPAGATION NEURAL 

NETWORK MODEL 

A.. The Model of BP Neural Network Algorithm 

According to the point of mathematics, BP algorithm is 

a generalized function convergence numeric method, and 

it has training and testing processes. The whole training 

process includes forward and back propagation. After 

being built, the BP network model is tested by other 

samples to testify the effectiveness and validity of the 

model. The results show that the BP network model and 

its algorithm are effective. The algorithm of BP neural 

network is shown as in fig.3. 

Figure 2. The framework of BP neural network combining 

membership degree 

According to fuzzy mathematics theory, the standard 

water quality classification 1-5 as co domain can be 

defined. For n assessment parameters of some standard 

water quality classification, we suppose that the 

membership degree to itself is zero, so a fuzzy subset E 

can be gotten. We suppose that the membership degree to 

other is zero, subset F can also be gotten. In here, the 

membership degree to standard water quality 

classification for n assessment parameters of other water 

quality samples must belong to[0,1] , and building fuzzy 

subset A . Therefore, the problem of assessing water 

quality sample transforms into computing the 

membership degree to two neighboring standard water 

quality classification. In this paper, the membership 

function is built as following formula. 

⎧1 

x = a 

⎪ 

ux ( ) = ⎨1 − f( x) 

a< x< 

b 

⎪ 

⎩0 

x = b 

(17) 

Figure 3. The algorithm process of BP neural network 

B. The Training of BP Neural Network 

The whole network training process includes forward 

propagation and error back-propagation, the training 

process are shown as followed. 

1) Assignment the weighs w_ 

xh , w_ 

hy between 

nodes and need threshold u_ 

h, u_ 

y , the assigned 

values are Nonzero Random initial valuebetween (-1,1). 

2) Inputting input vector X of one training sample and 

target output vector T . 

3) Computing output vector Y . 

Computing output vector H of hidden layers: 



∑ 

neth = w _ xhih⋅X i 

−u _ hh 

⎫ 

⎪ 

i 

⎬ 

Hh = ( neth) = 1 1+ exp( −neth) 

⎪⎭ 

Computing output vector Y of output layers: 

net 

j 

= ∑ w _ hyhj ⋅Hh −u _ y ⎫ 

j 

⎪ 

h 

⎬ 

Yj = ( netj) = 1 (1 + exp( −netj)) 

⎪ ⎭ 

4) Computing the difference mountδ 

δ 

j 

(18) 

(19) 

Computing difference mount of output layers 

δ = Y (1 −Y )( T − Y ) (20) 

j j j j j 

δ 

Computing difference mount of hidden layers 

h : 

δ = H (1 −H ) ∑ w_ 

hy δ (21) 

h h h hj j 

j 

5) Computing correction mount of weigh dw , and 

correction mount of threshold du . 

Computing weigh correction mount of output layers 

dw _ hy , correction mount of threshold du _ y : 

dw _ hyhj = δ 

jH 

h ⎫⎪ ⎬ (22) 

du _ y 

j 

=−ηδ 

j ⎪⎭ 

Computing weigh correction mount of hidden layers 

dw , correction mount of threshold du : 

dw _ xhih = ηδh X 

i ⎫ 

⎬ (23) 

du _ H 

h 

=−ηδh 

⎭ 

6) Updating weigh mount w_ 

hy , and threshold 

u_ 

y. 

Updating weigh mount of output layer w_ 

hy and 

threshold u_ 

y: 

w _ hyhj = w _ hyhj + dw _ hyhj 

⎫⎪ ⎬ (24) 

u_ yj = u_ yj + du_ 

yj 

⎪⎭ 

Updating weigh mount of hidden layer w_ 

hy and 

threshold u_ 

y: 

w _ xhih = w _ xhih + dw _ xhih 

⎫ 

⎬ (25) 

u_ hh = u_ hh + du_ 

hh 

⎭ 

(c) The testing of BP neural network 

After being building, the character of model must be 

tested by using the samples which are not used in 

building the model, so that the Correctness and 

Practicality of the model can be verified. 

The computing format of the testing process is showed 

as followed. 

1) Adopted the stable Weight matrices after trained 

w_ 

xh, w_ 

hy and Threshold vector u_ 

h, u_ 

y. 

2)Input vector X of testing samples. 

3)Computing output vector Y . 

Computing the output vector of hidden layer H : 

∑ 

neth = w _ xhih⋅X i 

−u _ hh⎫ 

i 

⎪ 

1 ⎬ 

Hh = f( neth) 

= ⎪ 

−neth 

1+ exp ⎪⎭ 

(27) 

Computing the output vector of hidden layer Y : 

net 

j 

= ∑ w _ hyhj⋅H h 

−u _ y ⎫ 

j 

h 

⎪ 

1 ⎬ (28) 

Yj = f( netj) 

= 

−net 

⎪ 

j 

1+ exp ⎪⎭ 

V. THE EXPERIMENT AND ANALYSIS OF BP NEURAL 

NETWORK FOR WATER QUALITY ASSESSMENT 

In the learning process of network, some standard 

water quality classification is adopted in learning samples. 

With considering that the range of activation function 

is[0,1] , and water quality classification is from the first 

class to the fifth class, so the five water quality 

classifications are only part of the whole range, and no 

attaching the limited values 0 and 1. 

In this paper, target outputs are 0.1,0.3,0.5,0.7,0.9 , 

and the output represents No.1-5 water quality 

classifications. As the most important parameters in 

debugging the BP network, learning rate η = 0.68 , 

Impulse coefficient α = 0.5 , then the network can be 

trained after 1600 iterations. 

(a) Errors curve of learning process 

(b) Testing result curve of network for some samples 

Fig. 4 The learning process curve of the network 



Then the accuracy of the trained network can be 

accepted. The accuracy of the trained network is accepted, 

and the learning process curves are shown in fig 4. 

After being trained, the BP network has held the 

characters of water quality classification, which can 

recognize the samples effectively. In experiment, the 

testing results of membership degree BP network are 

shown as table1 & table 2. 

Sample 

Index 

Dissolved 

oxygen (mg/l) 

TABLE I. 

THE INTERMEDIATE RESULTS OF MEMBERSHIP DEGREE BP NETWORK 

BOD5 

COD Mn 

Total 

phosphorus 

Ammonia 

Nitrate 

Output of 

network 

Water quality 

classification 

1 5.02 2.86 4.61 0.81 0.023 4.39 0.41 Ⅱ~ Ⅲ, near Ⅲ 

2 8.91 0.77 1.17 0.18 0.015 0.13 0.093 Ⅰ 

3 6.78 3.42 3.32 0.23 0.07 0.93 0.17 Ⅰ~ Ⅱ, near Ⅰ 

4 7.56 0.71 0.71 0.19 0 0.1 0.096 Ⅰ 

5 3.54 6.15 8.05 1.36 0.05 1.00 0.62 Ⅲ~ Ⅳ, near Ⅳ 

6 4.13 1.33 1.24 0.46 0.02 1.1 0.22 Ⅰ~ Ⅱ, near Ⅱ 

7 10.22 1.33 1.26 0.17 0 0.06 0.092 Ⅰ 

8 6.32 4.57 5.56 0.78 0.19 0.97 0.42 Ⅱ~ Ⅲ, near Ⅲ 

9 9.67 1.57 3.16 0.21 0 0.31 0.1 Ⅰ~ Ⅱ, near Ⅰ 

10 4.96 6.58 6.55 1.1 0 0.23 0.56 Ⅲ~ Ⅳ, near Ⅲ 

TABLE II. 

THE MEMBERSHIP DEGREE TESTING RESULTS OF SAMPLES TO STANDARD WATER QUALITY 

Sample 

1 2 3 4 5 6 7 8 9 10 

Classification 

Ⅰ 0 0.939 0.696 0.971 0 0.393 0.997 0 0.92 0 

Ⅱ 0.425 0.061 0.304 0.029 0 0.607 0.003 0.45 0.08 0.729 

Ⅲ 0.575 0 0 0 0.403 0 00 0.55 0 0.271 

Ⅳ 0 0 0 0 0.597 0 0 0 0 0 

Ⅴ 0 0 0 0 0 0 0 0 0 0 

Fig.7 the Software structure of the prediction and warning system 



VI. THE NEW WATER QUALITY ASSESSMENT METHOD 

APPLIED IN THE PREDICTION AND WARNING SYSTEM 

In the paper, the automatic prediction and warning 

system based on the new water quality assessment 

methods, which is a whole information system integrating 

computer hardware technique, communication technique, 

and software Intelligent analysis technology. The system 

includes monitoring terminal, user terminal, data 

transmission channel and data management center. The 

prediction and warning system can provide some water 

quality information for the department to making some 

decision. In the system, the water quality can be predicted 

based on hydrology and water quality data, natural and 

geographical environment, by the methods of software 

technology and theory of mathematical model. The water 

quality parameters predicted by the system include 

dissolved oxygen, total phosphorus, ammonia nitrogen, 

nitrate nitrogen, permanganate index and BOD 5. The 

software structure of system is shown as fig.7, which can 

be divided into water quality database module, integrated 

information analysis module, assessment report 

generation module, water quality trend analysis module. 

The water quality database system includes both water 

quality database and geography information database. 

According to the above database, water quality data can 

be counted and evaluated. The water quality database 

covers monitoring network information, all kinds of 

water data and water composition for example total 

phosphorus, ammonia nitrogen, nitrate nitrogen, 

permanganate index and BOD 5 etc. The geography 

information database mainly includes all kinds of 

geographical zoning maps. Based on web, the statistics 

and evaluation reports can be archived, queried and 

published automatically. In the system, the water quality 

trends can be predicted base on the BP model. 


The new water quality assessment method proposed in 

this paper integrates the fuzzy mathematics theory and 

artificial neural network. The theoretical analysis shows 

that the assessment method has theoretical feasibility and 

great practical utility. The new ideal and method in the 

paper propose a new way of water quality assessment and 

develop the application of artificial neural network. The 

experimental results and research demonstrate that the 

water quality assessment method has good prospects for 

further application and development. 

VIII. ACKNOWLEDGMENT 

This research was supported in part by JiLin province 

science and technology development plan project 

(No.20110421) and foundation of Jilin province 

educational committee (No.20110232). All the authors 

would like to thank the sponsors and the colleagues who 

give us good suggestions and helps during the research. 

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768. 

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Technology and Applications 

Ming Xue born in Jilin, China, in 1970, received the B.S., M.S. 

degrees from Jilin University, China, in 1990, 1995, 

respectively, all in Computer Science and Technology. And 

now she is currently a associate professor in department of 

electrical and information, Chang Chun Institute of Technology. 

Her current research interests include computer technology, 

software engineering. 



An Isolated Dual-Input Converter for 

Grid/PV Hybrid Power Systems 

Yu-Lin Juan 

National Changhua University of Education Department of Electrical Engineering, Changhua City, Taiwan 

Email: yljuan0815@cc.ncue.edu.tw 

Hsin-Ying Yang, Peng-Lai Chen 

National Changhua University of Education Department of Electrical Engineering, Changhua City, Taiwan 

Email: a13816@abc.ncue.edu.tw 

Abstract—An isolated dual-input power converter for a 

grid/photovoltaic (PV) hybrid power indoor lighting system 

is proposed in this paper. The proposed converter can be 

operated in single power supply mode or hybrid power 

supply mode. While the available PV power is insufficient 

for the load demand, the proposed dual-input converter will 

automatically deliver the complement power from the grid. 

The power complementing is achieved by two independent 

control loops of the PV power and the grid power. Finally, a 

prototype for a 36W LED lighting module is constructed to 

verify the validity of the proposed converter. From the 

experimental results, it can be seen that a smooth 24V/1.5A 

output power for the LED lighting module can be provided 

even while the PV power is insufficient or unavailable. 

Index Terms—hybrid power system, dual-input converter, 

PV array 


Renewable energy systems have attracted a lot of 

attention due to the global warming and fuel crisis [1]-[6]. 

It is seen that the power consumption of office lighting 

systems may take 20% to 60% of total energy 

consumption in daily life [7]. Among the renewable 

energy resources, PV power has been considered as a 

more stable and reliable power source [8]. In most of PV 

power systems, the battery storage device is required to 

provide smoother electricity. However, the costs of 

installing PV arrays and maintaining battery pack are still 

considerable for consumers. In recent studies, reducing 

the consumption of grid power by combining renewable 

resources is one of the major trends. To reduce the system 

cost and provide a stable power supply, several types of 

multi-input converters with renewable energy resources 

and grid power hybrid have been proposed [9]-[18]. The 

dependence on grid power can then be reduced and the 

output power quality is also remained. 

Basically, these multi-input converters can be 

classified into three types of topology. In first type, a 

multi-winding transformer is used to integrate the multi 

input power sources with single core [12]-[14]. In second 

type of converter, a pulsating voltage source cell (PVSC) 

is used as the power coupling component [9],[15]-[18]. 

Because the inductor is the main component in the PVSC, 

the major design criteria of the PVSC-type converter are 

the continuity of inductor current and the copper loss of 

inductor winding. In the last type converter, a pulsating 

current source cell (PCSC) is adopted as the power 

coupling component [17],[18]. The copper loss is 

relatively much lower because the multi-input power 

sources are coupled by capacitors [18]. 

Figure 1. Grid/PV hybrid power system with proposed dual-input converter 


doi:10.4304/jcp.8.6.1594-1601


Figure 2. Power supply modes of the grid/PV hybrid power system 

The circuit diagram of the grid/PV hybrid power 

system with proposed dual-input converter is shown in 

Fig. 1. The system can be operated in single power 

supply mode or hybrid power supply mode as shown in 

Fig. 2. While the PV power is unavailable, the converter 

would be operated in single power supply mode, namely, 

the grid supply mode. If the PV power can only provide 

part of the load, the converter will be operated in hybrid 

power supply mode for delivering the rest part of power 

from the grid to the load side. As a result, the commonly 

required battery pack in the stand-alone system can then 

be replaced by the grid to provide smooth electricity. The 

PV array installation capacity can also be reduced 

because additional capacity for presorting in the battery 

pack is not required. Therefore, resulted system 

installation and maintenance costs can both be reduced. It 

would be very helpful to encourage consumers to 

purchase a PV power system as an alternative electricity 

system. 

II. OPERATION PRINCIPLE OF THE PRPOSED CONVERTER 

For the proposed converter shown in Fig. 1, the active 

switch S 1 is adopted to control the power flow from the 

grid to the load through the coupling capacitor C 1 . The 

other input terminal is connected to the PV array and the 

PV output power is controlled by the active switch S 2 . 

The PV power is delivered to the load side through the 

coupling capacitor C 1 as well. Once the available power 

from PV array is lower than the load demand, the 

proposed converter would deliver the complement power 

from the grid to the load side according to the feedback 

information about the load current. Based on the 

supplying power sources, there are three power supply 

modes of the proposed converter as shown in Fig. 2. First, 

if the PV power is unavailable, the converter is operated 

in the grid supply mode. Then the converter would be 

changed into the PV supply mode while the available PV 

power is higher than the load demand. Finally, if the PV 

power is available but not enough for the load, the 

converter would be operated in the third mode, namely 

the hybrid supply mode. 

While the two sources are simultaneously delivering 

power, i.e. in the hybrid supply mode, there would be six 

operation modes in one switching cycle as shown in Fig. 

3. The relative waveforms in one switching cycle are 

shown in Fig. 4. It can be seen that the two active 

switches are controlled with interleave phase shift 

technique to reduce the voltage and current ripple of the 

coupled capacitor. The corresponding operation 

principles are described as follows: 

Mode1—(t 0 ≦t


(a) Mode 1 

(b) Mode 2 

(c) Mode 3 

(d) Mode 4 



(e) Mode 5 

(f) Mode 6 

Figure 3. Equivalent circuits of the proposed converter in different operation modes 

Figure 4. Relative waveforms in one switching cycle 

III. POWER COMPLEMENT CONTROLLER 

From section II, it is seen that the power drawn from 

the grid is controlled by the active switch S 1 and firstly 

buffered in the coupling capacitor. Then, it would be 

transmitted to the load side through the inductor L 2 . The 

other input power, i.e. the PV power, is controlled by the 

active switch S 2 . The power processes are similar to an 

isolated Cuk converter. The PV power would be 

delivered to the load side through the transformer T 2 and 

coupling capacitor C 1 . Obviously, the two power flows 

are both unidirectional and transferred to the load side 

individually. Therefore, the two active switches can be 

independently used to control the power from each input 

source. To achieve automatically delivering the 

complement power part from the grid to provide smooth 

electricity for the load, a power complement controller 

for the proposed converter is shown in Fig. 5. It is seen 

that the power complement controller is composed of two 

independent control loops for grid power and PV power 

respectively. 

Usually, a maximum power point tracking (MPPT) 

would be adopted to fully utilize the renewable PV power. 

Hence, the gating signal of the active switch S 2 is 

provided according to the adopted MPPT strategy. The 

MPPT strategy is out of the scope of this study and would 

not be further described. Basically, either one of the wellknown 

current-controlled type MPPT strategies can be 

directly applied to this controller. And the gating signal 

of the active switch S 1 is then decided according to the 

amount of the complement power for the load. In this 

paper, a well-known hill-climbing searching MPPT 

strategy is adopted in the prototype lighting system. For 

the control loop of PV power, the PV current is regulated 

to the current command for extracting maximum PV 

power. 



Figure 5. Power complement controller diagram 

The active switch S 2 is driven by gating signal V GS2 to 

control the input current from PV array. For the control 

loop of grid power, the main object is to deliver the 

complement power for remaining smooth current to the 

LED lighting module. Therefore, the load current I o is fed 

back and needs to be regulated to the load current 

command I o * which is decided by the normal operating 

current of LED module. Then the active switch S 1 will be 

driven by the gating signal V GS1 to control the input grid 

power for complementing the power demand. 

IV. EXPERIMENT RESULTS 

To evaluate the performance and validity of proposed 

converter, a prototype with a 45W PV array for a 36W 

LED lighting module is constructed as shown in Fig. 6. 

The controlled is implemented by a microprocessor, 

HT46R23, and relative electrical parameters are shown in 

Table I. The input current from PV array and load current 

are sampled by hall sensors. Fig. 7 shows the waveforms 

of the grid input current, PV input power and the load 

condition. In Fig. 7(a), it can be seen that firstly the load 

demand is only provided by the grid because the PV 

power is unavailable. Then, the PV power is started to 

provide its maximum power, but the available PV power 

is still not enough for the load. 

Therefore, the converter is automatically changed into 

hybrid supply mode for delivering the complement power 

from the grid. Once, the maximum PV power is higher 

than the load demand, there is no complement power 

required from grid. As a result, the output power for the 

LED module as shown in Fig. 7(b) can then be wellcontrolled 

at 36W/24V/1.5A. Fig. 8 shows the waveforms 

of the capacitor C 1 while the converter is operated in 

hybrid supply mode with 50% PV power and 50% grid 

power. It can be seen that the current ripple and peak 

current are reduced because of adopting the interleave 

phase shift technique. Fig. 9 shows the efficiency of the 

proposed converter in single power supply mode with PV 

power or Grid power input. The efficiency in hybrid 

power supply mode is measured and shown in Fig. 10, 

and the definition of the efficiency η is given as 

following: 

PO 

η = 

(1) 

P + P 

PV 

Grid 

Table I. PARAMETERS OF PROTOTYPE SYSTEM 

Input - 

V Grid =110VACrms, 60 Hz 

V MPPT ≈45 V, I MPPT ≈1 A 

Output - V O =24 V, I O =1.5 A 

Frequency - 38.4 kHz 

Ferrite core 

Transformer 

Component 

- 

- 

EI-33 

L T1P /L T1S =425μH / 35.8μH 

A gip ≈ 0.29 mm 

N T2P /N T2S =32N / 16N 

Inductance 

L 1 =460μH 

- 

Component 

L 2 =525μH 

C 1 =6μF 

Capacitor 

Component 

- C 2 =1μF 

C 3 =220μF 

Figure 6. Prototype of proposed dual-input power converter 



(a) grid input current I GRID 

Figure 10. Measured Efficiency of the proposed converter in hybrid 

power supply mode 

(b) output voltage V o , output current I o and output power P o 

Figure 7. Measured waveforms in hybrid power supply mode 

The comparison of system cost between stand-alone 

PV power system and the proposed hybrid power system 

is shown in Table II. For a 36W office lighting power 

system with 85% efficiency works 8 hours a day, the 

minimum required power capacity is 340Wh. However, 

the rated power of PV array is only available in 2~3 hours 

a day [19]. The minimum PV array installed capacity for 

a 36W stand-alone power system is 120W. Compared 

with the stand-alone system, the required capacity of PV 

array in the proposed system is only 36W. Moreover, the 

energy storage device is not required neither. It is seen 

that the installing and maintenance cost can then be 

greatly reduced. 

Table II. THE POWER SUPPLY SYSTEM COST COMPARISON 

(8HOURS/DAY AT 36W) 

Stand-Alone 

Proposed system 

PV System 

Loading 36W 36W 

PV Array 120W 36W 

Battery bank 720Wh — 

Cost High Low 

Figure 8. Waveforms in different supply modes (V GS1&GS2 : 20V/DIV, 

V C1 : 5V/DIV, I C1 :4A/DIV) 

Figure 9. Measured Efficiency of the proposed converter in single 

power supply modes 

V. CONCLUSION 

This paper proposed an isolated dual-input power 

converter for grid/PV hybrid power conversion systems 

which can be operated in single power supply mode or 

hybrid power supply mode. The power complement 

controller composed of two independent control loops for 

the grid and the PV power. Once the available PV power 

is insufficient for the load demand, the power flow from 

the grid would automatically be controlled to complement 

the output power. Finally, a prototype for a 36W LED 

lighting module is constructed to evaluate the validity and 

performance of the proposed converter. From the 

experimental results, it is seen that even while the PV 

power is unstable, the proposed converter can provide a 

smooth 24V/1.5A output power for the LED module. 



a prototype with a 45W PV array for a 36W LED 

lighting module is constructed as shown in Fig. 6. 

Figure 11. Prototype of the 36W LED lighting module 

Figure 12. Prototype of the 45W PV array 

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Converter Based on the Multi-winding Transformer for 

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2002. 

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Designed ZVS Multi-Input Converter, IEEE Trans. Ind. 

Electr., vol. 58 no. 2, pp. 555-566, February 2011. 

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Based on H-Bridge Cells: Derivation, Small-Signal 

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Convers., vol. 24, no.2, pp.511-519, 2009 

Yu-Lin Juan (S’08) was born in 

Kaohsiung, Taiwan, in 1979. He 

received the B.S. degree in electrical 

engineering from National Cheng Kung 

University, Tainan, Taiwan, in 2001 

and the M.S. degree in electrical 

engineering in 2003 from National 

Tsing Hua University, Hsinchu, Taiwan. 

His current research interests include 

power electronics, renewable energy 

systems, and ac motor drives. 



Hsin-Ying Yang was born in Taichung 

Taiwan, R.O.C. in 1982. He received 

the B. S. degree in electrical 

engineering from National Formosa 

University, Yunlin, Taiwan, in 2005 

and was conferred the Master of 

Electrical Degree by National 

Changhua University of Education, 

Changhua City, Taiwan, R.O.C. in 2007. 

He is currently working toward the 

Ph.D. degree in electrical engineering. His research interests are 

power electronics, electronic circuit design, battery charge and 

microprocessor application. 

Peng-Lai Chen is currently working 

toward the Ph.D. degree in electrical 

engineering. His research interests are 

power electronics, design and 

application. 



Deformed Kernel Based Extreme Learning 

Machine 

Zhang Chen 

School of Computer Science and Technology,China University of Mining and Technology, XuZhou,221116,China 

Email: zc@cumt.edu.cn 

Xia Shi Xiong and Liu Bing 

School of Computer Science and Technology,China University of Mining and Technology, XuZhou,221116,China 

Email: xiasx@cumt.edu.cn, liubing@cumt.edu.cn 

Abstract—The extreme learning machine (ELM) is a newly 

emerging supervised learning method. In order to use the 

information provided by unlabeled samples and improve the 

performance of the ELM, we deformed the kernel in the 

ELM by modeling the marginal distribution with the graph 

Laplacian, which is built with both labeled and unlabeled 

samples. We further approximated the deformed kernel by 

means of random feature mapping. The experimental 

results showed that the proposed semi-supervised extreme 

learning machine tends to achieve outstanding 

generalization performance at a relatively faster learning 

speed than traditional semi-supervised learning algorithms. 

Index Terms—extreme learning machine (ELM); random 

feature mapping; semi-supervised learning; Reproducing 

Kernel Hilbert Spaces (RKHS). 


Lately, extreme learning machine ELM has been 

attracting a lot of attention from an increasing number of 

researchers [1]-[5]. It was originally developed for the 

single-hidden layer feedforward neural networks (SLFN) 

[6]-[8], which was extended to the “generalized” SLFNs, 

i.e., may not be neuron alike [9, 10]. ELM has three main 

learning features: (1) ELM was originally proposed to 

apply random computational nodes in the hidden layer. 

Thus, the hidden layer of the ELM does not need be 

tuned. (2) ELM incorporates the smallest training error 

and the norm of output weights into the objective 

function. Hence, it controls the complexity of decision 

functions by means of regularization. (3) Unlike LS-SVM 

and SVM that only provide one type of computational 

need, ELM provides a unified solution to different 

practical applications (e.g., regression, binary, and 

multiclass classifications). 

ELM is a supervised learning method. In many 

applications, however, there are little labeled data and a 

large amount of unlabeled data available. Semi- 

Supervised Learning (SSL) methods are proposed to 

solve this problem. ELM can be naturally extended to the 

unsupervised scenario, where the “cluster” and “manifold” 

assumptions are used to learn input-output mapping 

functions. The “cluster” assumption refers to that points 

in a data cluster have similar labels. The “manifold” 

assumption corresponds to high-dimensional data 

distributed on a low-dimensional manifold and the 

samples in each local region have similar labels. There 

are many approaches based on the “cluster” assumption, 

which uses techniques such as local combinatorial 

searches[12], branch-and-bound algorithms[13,14], 

gradient descent[15], semi-definite programming [16-19], 

continuation techniques[20], non-differentiable 

methods[21], concave-convex procedures[22,23], and 

deterministic annealing[24]. However, the time 

complexity of these methods scales at least quadratically 

with the dataset size, which makes them inapplicable to 

large-scale datasets. In [25], a cutting plane semisupervised 

support vector machine algorithm (CutS3VM) 

was proposed to reduce the number of iterations, but it 

still takes time O(sn) to converge with guaranteed 

accuracy in the linear case, where n is the total number of 

samples in the dataset and s is the average number of 

non-zero features. Sindhwani et al.[26] proposed two 

kinds of large-scale semi-supervised linear SVMs: the 

transductive modified finite newton linear L 2 -SVM (L 2 - 

TSVM-MFN) and the deterministic annealing L 2 -SVM- 

MFN method (DA L 2 -SVM-MFN). L 2 -TSVM-MFN is 

converged after having been switched many times and 

DA L 2 -SVM-MFN needs a number of iterations to 

compute the corresponding parameters of unlabeled data. 

Besides the “cluster” assumption, many regularization 

frameworks based on the “manifold” assumption have 

been designed by adding a manifold regularization term. 

In [27], Belkin et al. proposed a general Manifold 

Regularization (MR) framework for a full range of 

learning problems from unsupervised and semisupervised, 

to supervised. The MR framework adds an 

additional penalty term to the traditional regularization, 

from which the Laplacian Regularization Least Square 

Classification (LapRLSC) and the Laplacian SVM 

(LapSVM) methods are derived and have been shown to 

be efficient in semi-supervised learning problems. 

Additionally, the Discriminatively Regularization Least 

Square Classification (DRLSC) method and the Sparse 

Regularized Least Square Classification (S-RLSC) 

algorithm[29] were proposed, which improves the MR 

framework further. Although these frameworks can 

handle semi-supervised learning problems and the 

analytic solutions can also be derived, they still involve 


doi:10.4304/jcp.8.6.1602-1609


expensive computation when training large-scale data 

sets. 

To improve the performance of the ELM, it is essential 

to use the information provided by both labeled and 

unlabeled samples. We construct the deformed kernel for 

the ELM, which is adapted to the geometry of the 

underlying distribution. Based on the deformed kernel, 

we propose a deformed kernel-based extreme learning 

machine (DKELM) to provide a unified solution for 

regression, binary, and multiclass classifications (like 

ELM). To address large-scale data training, we 

approximate the deformed kernel by random feature 

mapping, so that the proposed DKELM does not need 

parameter tuning and has less computational complexity, 

as well as a natural out-of-sample extension for novel 

examples. We demonstrate the relationship between the 

traditional kernel-based learning approach and ELM, and 

our approach can be used by other kernel-based methods 

and a sequence of fast learning algorithms can be derived. 

The rest of this paper is organized as follows. Some 

previous works are introduced in Section II. The method 

of constructing and approximating the deformed kernel is 

discussed in Section III. In Section IV, we first 

demonstrate the relationship between the traditional 

kernel-based learning approach and ELM, and propose 

the deformed kernel based extreme learning machine. 

The experiments using benchmark real-world data sets 

are reported in Section V. Finally, we conclude this paper 

in Section VI. 

II. BRIEF OF THE EXTREME LEARNING MACHINE 

The output function of ELM for generalized SLFNs in 

the case of one output node case is 

(1) 

where 

is the vector of the weights 

between a hidden layer of L nodes and the output node. 

Note that 

is the output (row) 

vector of the hidden layer with respect to the input x. In 

fact, maps the data from the d-dimensional input 

space to the L-dimensional hidden-layer feature space 

(ELM feature space) H. Different from traditional 

learning algorithms [11], ELM is meant to minimize the 

training error as well as the norm of the output weights [7] 

Minimize: and (2) 

where H is the hidden-layer output matrix, which is 

denoted by 

where , and is a 

kernel function. 

If a feature mapping h(x) is known, we have 

(5) 

where is a nonlinear piecewise continuous 

function satisfying ELM universal approximation 

capability theorems [7],[30] and are 

randomly generated according to any continuous 

probability distribution. The output function of ELM 

classifier is 

or 

where 

classes. 

(4) 

, (6) 

, (7) 

and m is the number of 

III. DEFORMING THE KERNEL BY WARPING AN RKHS 

For a Mercer kernel K: X X , there is an 

associated RKHS of functions X with the 

corresponding norm . Given a set of l labeled 

examples and a set of u unlabeled examples 

, where and , the classical 

kernel-based learning approach is based on solving the 

regularization problem given by 

, (8) 

where V is some loss function, such as the squared loss 

for RLS and the hinge loss function 

for SVM; is the norm of the 

classification function in the reproducing kernel Hilbert 

space , and controls the complexity of function . 

The Representer Theorem [27] states that a solution can 

be found in the form 

. In order to 

avoid confusion, we list main notations of this paper in 

Table I. 

TABLE I. 

. (3) 

As with SVM for the binary classification, to minimize 

the norm of the output weights is actually used to 

maximize the distance of the separating margins of the 

two different classes in the ELM feature space: . 

The norm controls the complexity of the function in the 

ambient space, which will be elaborated later. 

If a feature mapping h(x) is unknown to users, the 

output function of ELM classifier is 

Notation 

m 

NOTATIONS 

Explanation 

The input d-dimensional Euclidean space 

is the 

training data matrix. are labeled points, 

and are unlabeled points. 

The number of classes that the samples belong 

to 

is the 0-1 label matrix. 

is the label vector of , and all 

components of are s except one being . 

is the discriminative 

vector function. The index of the class which x 



belongs to is that of the component with the 

maximum value. 

Kernel function of variables and 

Kernel matrix 

. Its columns are the 

coefficients of the kernel function to represent 

the discriminative function . 

Norm in the Hilbert space 

Inner product in the Hilbert space 

tr(M) 

The trace of the matrix M , that is, the sum of 

the diagonal elements of the matrix M. 

span{ } subspace expanded by 

In the implementation of this kernel-based learning 

approach, we often use the Radial Basis Function or 

Gaussian (RBF) as kernel, and the kernel k defines a 

unique RKHS. Since the Gaussian kernel is isotropic, it 

has a spherical symmetry. That is, it generally does not 

conform to the particular geometry of the underlying 

classes. In other words, the underlying data structure is 

obviated. Finally, it is unable to provide an accurate 

decision surface. To address these limitations, it is crucial 

to define a new kernel that is adapted to the geometry of 

the data distribution well. 

Instead of solving (8) like a traditional kernel-based 

learning approach, we modify (or deform) the original 

kernel in order to adapt it to the underlying distribution 

geometry. Defining a new deformed kernel , the new 

problem to be solved becomes 

, (9) 

(8) and (9) solved with different kernels, and thus in 

different . 

The solution of (9) is 

, (10) 

that should be appropriate for real setting. 

To “deform” the original kernel and adapt it to the 

geometry of the underlying distribution, let be a linear 

space with positive semi-definite inner product, and let 

be a bounded linear operator. Defining 

to be the space with the same functions as and its 

inner product defines 

, (11) 

It is proved in [27] that is a valid . In this 

specific problem, it is required that and should 

depend on the data. Therefore, let be , and define 

as the evaluation map 

.Using a symmetric positive semidefinite 

matrix , the semi-norm on can be written 

as 

. With such a norm, the regularization 

problem in (9) becomes 

(12) 

where includes both labeled and unlabeled data 

and the matrix encodes smoothness w.r.t. the graph or 

manifold. 

Let 

and substitute it into (12), we have 

(13) 

where 

is a free parameter that controls 

the “deformation” of the original kernel. Thus, Equation 

(13), in fact, is a graph-based semi-supervised learning 

problem based on the manifold assumption; it can be 

indirectly set out using (12) and solved using (10). 

To utilize the geometry information of the data 

distribution, a graph can be constructed using labeled 

and unlabeled pixels. The graph Laplacian of is a 

matrix defined as , where is the 

adjacency matrix. The elements are measures of the 

similarity between pixels and , and the diagonal 

matrix D is given by 

. The graph 

Laplacian L measures the variation of the function 

along the graph built upon all labeled and unlabeled 

samples. By fixing , the original (undeformed) 

kernel is obtained. 

Next, we discuss the computation of the deformed 

kernel . In [27], the resulting new kernel was computed 

explicitly in terms of labeled and unlabeled data. It is 

proved that 

and 

(14) 

Thus, the two spans are same and we have 

where the coefficients depend on x, let 

. 

We can compute at x: 

(17) 

(15) 

(16) 

Where 

and g is the 

vector given by components 

. Therefore, it can be derived from (17) 

that 

(I+MK) (18) 

where K is the kernel matrix 

, = and is the 

identity matrix. Finally, we obtain the following explicit 

form for 

(19) 

where 

. It satisfies the Mercer’s 

conditions, being a valid kernel. If 

, the 

deformed kernel is degenerated into the original 



(undeformed) kernel. When is singular, one adds a 

small ridge term to and uses a continuity argument. 

IV. ELM BASED ON DEFORMED KERNEL 

In regularization problem (8), if yi is an m-dimensional 

label vector with the elements 0 or 1, where m is the 

number of classes, and xi belongs to the k-th class, then 

the k-th component of yi takes the value 1 and the rest 

components take the value 0. The corresponding vector 

function is defined as 

. Then 

the extended regularization problem estimates an 

unknown vector function by minimizing 

where. 

(20) 

Next, we discuss the computation of the deformed 

kernel , according to 

, 

where 

is the kernel 

matrix over labeled and unlabeled samples, we have to 

compute a matrix inversion of size . 

Note that this inversion scales exponentially with the 

number of samples. If the number of labeled and 

unlabeled samples is huge, it is difficult to compute. So 

we further approximate the kernel matrix K, letting 

and 

, then , 

and 

, so we achieve 

In (20), if we introduce a deformed kernel 

problem to be solved becomes 

, the 

(21) 

where 

, . 

The solution of (21) is 

, where 

Based on what is introduced above, the regularization 

problem for DKELM with multioutput nodes can be 

formulated as 

(22) 

The solution of the optimization problem (22) is given 

by 

, 

where is the identity matrix. . 

Let 

and 

and 

, so 

,where 

is the deformed kernel 

matrix over labeled points. 

If the number of labeled samples is not huge, the 

output function is 

, (23) 

if the number of labeled samples is huge, according to 

the Sherman-Morrison-Woodbury(SMW) formula for 

matrix inversion, we have 

, (24) 

where 

is the label matrix 

with elements or , and ( ) is an m- 

dimensional label vector with the elements 0 or 1. In a 

semi-supervised case, the number of labeled samples is 

small, so (40) should be used to compute the output 

function. 

, (25) 

where , . 

Correspondingly, in a semi-supervised case, the output 

function of DKELM with a single output is 

(26) 

where is an l dimensional label vector given by: 

. 

The formula (25) and (26) all involve the inversion of 

a matrix of order , as long as L is large enough, the 

generalization performance of DKELM is not sensitive to 

the dimensionality of the feature space (L) and good 

performance can be reached, which will be verified later 

in Section 5. The DKELM algorithm is summarized in 

the Table II. 

TABLE II. 

THE DESCRIPTION OF DKELM ALGORITHM BASED ON DEFORMED 

KERNEL 

DKELM Algorithm based on deformed kernel 

Input: l labeled examples , u unlabeled examples . 

Output: Estimated function . 

Step 1: Construct data adjacency graph with (l+u) nodes using k nearest 

neighbors or a graph kernel. Choose edge weights Wij, for 

example, for binary weights or heat kernel weights 

. 

Step 2: Compute graph Laplacian matrix: , where is a 

diagonal matrix given by 

. 

Step 3: Choose a kernel function . Choose , C and L (the 

number of sample points), randomly generate . 

Step 4: if the number of the training data sets is very large , 

compute , 

, select (25) for 

computing the deformed kernel; Otherwise, use (19) . 

Step 5: Select (23) for computing the output function of DKELM 



with multioutputs or select (26) for computing the output 

function of DKELM with single output (m=1). 

Step 6: Output . 

Like ELM, DKELM has the unified solutions for 

regression, binary and multiclass classification. But we 

mainly discuss DKELM for the classification problems in 

this paper. 

A DKELM classifier with a single-output node (m = 1): 

For multiclass problems, among all the multiclass labels, 

the predicted class label of a given testing sample is 

closest to the output of a DKELM classifier. The decision 

function of the DKELM classifier is 

. (27) 

For the binary classification, the decision function of 

DKELM classifier is 

. (28) 

A DKELM classifier with multioutput nodes (m > 1) is: 

For multiclass cases, the predicted class label of a given 

testing sample is the index number of the output node, 

which has the highest output value for the given testing 

sample. The decision function of the DKELM classifier is 

. (29) 

The predicted class label of sample x is 

* 

label( x) arg max fi 

( x) 

i{1,..., m} 

. (30) 

The deformed kernel in both cases is computed by 

, 

which is applied to moderate scale training samples, or 

, 

(31) 

which is applied to large scale training samples, where 

, . 

V. EXPERIMENTS 

In this section, we will validate the performance of the 

proposed DKELM algorithm on a number of real-world 

data sets. In particular, we studied the sensitivity of 

DKELM to the number of labeled samples. All the 

experiments are performed with MATLAB 7.0.1 

environment on a 3.10GHZ Intel CoreTM i5-2400 with 

3-GB RAM. 

A. Data Sets 

We used different scale data sets from the UCI 

machine learning repository (satellite, Ionosphere), and 

another benchmark repository (Extended Yale B, USPS). 

For the satellite data sets, there are multiple class labels; 

we used their first two classes only. For USPS, we 

randomly selected 250 data points from each class for our 

experiments. The basic information about these data sets 

is summarized in Table III. 

TABLE III. 

DESCRIPTION OF THE DATA SETS 

Data Size (n) Feature (d) Class 

SatelliteC1-C2 2236 36 2 

Ionosphere 351 34 2 

Extended Yale B 2114 1024 38 

USPS 2500 256 10 

B. Parameter selection and experimental settings 

Comparisons are made with four important 

classification methods: CutS 3 VM[25], L 2 -TSVM- 

MFN[26], DA L 2 -SVM-MFN[26] and S-RLSC 

algorithm[29]. In our experiments, binary edge weights 

are chosen and the neighborhood size k is set to be 12 for 

all the data sets. DKELM algorithm needs to choose the 

feature mapping, the cost parameter C and the number of 

hidden nodes L, since ELM algorithm achieves good 

generalization performance as long as L and C are large 

enough[30]. Thus we let C =500. The regularization 

parameters and are split into the ratio 1:9, and we 

let , , which is 

set in the same way as in [27]. We select Gaussian 

functions as the hidden-node output functions. 

We test L 2 -TSVM-MFN with multiple switchings and 

DA L 2 -SVM-MFN with parameter and 

on all datasets. We also test CutS3VM with parameters 

, and set in the balancing constraint to the 

true ratio of the positive points in the unlabeled set. The 

S-RLSC methods also have regularization parameters 

and . Let , , and also use the 

Gaussian kernel function. In our experiments, we also set 

CA=0.005, CI=0.01 and for all data sets, which 

is set in the same way as in [29]. 

For each data set , 15% of the data points are left for 

out-of-sample extension experiment. We denote by the 

rest data points of the data set . In each class of , we 

randomly label l data points to train every algorithm. For 

DKELM, S-RLSC, L 2 -TSVM-MFN, DA L 2 -SVM-MFN 

and CutS 3 VM, the training set consists of the whole , 

including the labeled and the unlabeled data points. For 

L 2 -TSVM-MFN, DA L 2 -SVM-MFN and CutS 3 VM, 

multiclass datasets are learned using a one-versus-rest 

approach. 

C. Experimental results 

For simplicity, we used DKELM with a single output 

and 800 hidden nodes; the recognition result of all the 

algorithms is shown in Table 4–6, respectively. For each 

dataset, classification accuracy and training time 

averaged over 20 independent trials. The number of l (in 

each class) of the labeled data points varies from 5 to 250 

for the Satellite data set, from 5 to 150 for the Ionosphere 

and from 5 to 40 for the Extended Yale B data set. 

In Tables 4–6, for several values of m, the best 

classification results are in boldface for each fixed value 

of m. As can be seen from the tables, the classification 

accuracy is lower for all algorithms when l is small. With 

the increase of labeled data, the discriminative ability of 

the DKELM algorithm is much better than the other 

algorithms, since it utilizes the manifold structure of 

labeled and unlabeled samples. The recognition result of 

the S-RLSC algorithm is very close to that of the 



DKELM algorithm, but it runs much slower than our 

algorithm. For the Satellite and Ionosphere data sets, the 

performance of the DKELM algorithm is worse than that 

of Extended Yale B data set, since the manifold structure 

is less salient than that of face images. As can be seen 

from Table 6, the recognition accuracy of the L2-TSVM- 

MFN, DA L 2 -SVM-MFN and CutS3VM classifiers 

decreases with the increase of the number of classes, 

since these classifiers are constructed with a one-versusrest 

approach, which has a great influence on the 

accuracy. Moreover, this kind of multiclass classification 

approach also increases the running time of these 

algorithms. With the increase of the number of the feature 

dimensions of data sets, the running time of the 

CutS3VM increases dramatically, since its time 

complexity depends on the average number of non-zero 

features. In contrast, as can be seen from Table IVandVI, 

the speed of the DKELM algorithm is not sensitive to the 

number of classes and the feature dimensions of data sets. 

It can perform well by means of the intrinsic geometry of 

data distribution. 

TABLE IV. 

PERFORMANCE COMPARISON OF ALL T 

Numb 

er of 

labele 

d 

data 

points 

l 

DKELM 

Accuracy 

(%) 

SATELLITE DATA SET 

S-RLSC 

Accurac 

y(%) 

L 2-TSVM- 

MFN 

Accuracy 

(%) 

HE ALGORITHMS FOR THE 

DA L 2- 

SVM- 

MFN 

Accuracy 

(%) 

CutS 3 VM 

Accuracy 

(%) 

l =5 57.62 62.78 56.48 61.02 73.59 

l =10 78.45 79.79 69.83 70.73 74.46 

l =50 85.68 83.47 71.95 75.28 82.85 

l =250 89.21 87.86 75.82 76.29 84.46 

Numb 

er of 

labele 

d 

data 


l 

DKELM 

Training 

Time(s) 

S-RLSC 


Time(s) 

L 2-TSVM- 

MFN 


Time(s) 

DA L 2- 

SVM- 

MFN 


Time(s) 

CutS 3 VM 


Time(s) 

l =5 52.782 328.579 3.782 12.652 1.190 

l =10 55.273 328.647 3.894 11.676 0.976 

l =50 54.374 330.152 2.957 10.016 0.620 

l =250 52.962 322.674 2.365 5.625 0.569 

Numb 

er of 

labele 

d 

data 


l 

DKELM 


Time(s) 

S-RLSC 


Time(s) 

L 2-TSVM- 

MFN 


Time(s) 

DA L 2- 

SVM- 

MFN 


Time(s) 

CutS 3 VM 


Time(s) 

l =5 21.704 168.579 0.618 5.724 0.554 

l =10 25.753 168.647 0.772 5.676 0.377 

l =50 23.176 170.152 0.252 4.534 0.324 

l =250 22.802 162.674 0.246 3.165 0.232 

Number 

of 

labeled 

data 

points l 

TABLEVI 

PERFORMANCE COMPARISON OF ALL THE ALGORITHMS FOR THE 

EXTENDED YALE B DATA SET 

DKELM 

Accura 

cy(%) 

S-RLSC 

Accurac 

y(%) 

L 2-TSVM- 

MFN 

Accuracy 

(%) 

DA L 2- 

SVM- 

MFN 

Accuracy 

(%) 

CutS 3 VM 

Accuracy 

(%) 

l =5 61.25 64.41 55.17 38.47 63.93 

l =10 82.05 83.18 62.76 58.71 69.82 

l =20 94.52 93.10 67.72 68.49 75.91 

l =30 95.42 95.24 71.35 73.59 79.56 

l =40 97.44 97.12 75.25 76.84 80.13 

Number 

of 

labeled 

data 

points l 

DKELM 

Trainin 

g 

Time(s) 

S-RLSC 

TrainingTi 

me(s) 

L 2-TSVM- 

MFN 


Time(s) 

DA L 2- 

SVM- 

MFN 


Time(s) 

CutS 3 VM 


Time(s) 

l =5 87.589 452.644 60.427 361.928 75.249 

l =10 88.670 455.972 58.958 273.536 69.162 

l =20 86.465 452.177 49.514 247.923 65.368 

l =30 87.259 454.921 42.943 190.380 58.532 

l =40 89.694 452.228 35.519 163.476 54.348 

The out-of-sample extension result of the algorithms 

on larger USPS data sets is shown in Fig. 1. We perform 

the DKELM algorithm using 500 hidden nodes. As can 

be seen from Fig.1, the DKELM algorithm has best 

recognition results over any other algorithm. So our 

proposed DKELM algorithm tends to have better 

scalability and achieve best generalization performance at 

a relatively faster learning speed. 

TABLEV. 

PERFORMANCE COMPARISON OF ALL THE ALGORITHMS FOR THE 

IONOSPHERE DATA SET 

Numb 

er of 

labele 

d 

data 


l 

DKELM 

Accuracy 

(%) 

S-RLSC 

Accurac 

y(%) 

L 2-TSVM- 

MFN 

Accuracy 

(%) 

DA L 2- 

SVM- 

MFN 

Accuracy 

(%) 

CutS 3 VM 

Accuracy 

(%) 

l =5 57.62 72.78 66.52 60.81 73.89 

l =10 74.79 73.45 69.42 71.67 74.56 

l =50 87.68 83.47 81.14 77.21 85.25 

l =250 90.21 87.86 85.73 86.39 86.43 

Figure 1. Out-of-sample extension classification results on the USPS 

data set 

VI CONCLUSIONS 



In this paper, we first extended the traditional kernelbased 

learning problem to multiclass cases in an Extreme 

Learning Machine context. To enhance the performance 

of ELM, a deformed kernel was proposed, which can 

make use of underlying information from both labeled 

and unlabeled samples. To speed up our algorithm, we 

further approximated the deformed kernel by means of 

random feature mapping. Our algorithm does not need 

kernel parameter tuning. The experimental results have 

shown that the DKELM algorithm achieves better 

generalization performance at a relatively faster learning 

speed than traditional semi-supervised classification 

algorithms. In the future, we will further optimize our 

proposed framework and study the sparse regularization 

problems in our framework. 

ACKNOWLEDGMENTS 

This work was supported by the National Natural 

Science Foundation of China under Grant Nos. 50674086. 

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Cybernetics. pp:107–122,2011. 



Zhang Chen is current a Ph.D 

candidate at China University of 

Mining and Technology(CUMT), 

China. She received her MS degree 

in Computer Application 

Technology from CUMT in 2004, 

and her BS degree in Computer 

Science from CUMT in 2001. She 

is currently a lecture at school of Computer Science and 

Technology, CUMT. Her research interest is computation 

intelligence and machine learning et al. 

Xia Shi Xiong is born in 1962, 

Ph.D. He is a professor at school 

of Computer Science and 

Technology in CUMT. He has 

published more than 60 research 

papers in journals and 

international conferences. His 

research interest is Wireless sensor 

networks and intelligent 

information processing et al. 

Liu Bing is current a Ph.D 

candidate at China University of 

Mining and Technology(CUMT), 

China. She received her MS degree 

in Computer Application 

Technology from CUMT in 2005, 

and her BS degree in Computer 

Science from CUMT in 2002. She is 

currently a lecture at school of Computer Science and 

Technology, CUMT. His research interest is computation 

intelligence and machine learning et al. 



Optimal Sleep Scheduling Scheme for Wireless 

Sensor Networks Based on Balanced Energy 

Consumption 

Shan-shan Ma 

College of Computer Science and Technology, China University of Mining and Technology, Xuzhou, 221116, China 

Email: ssma@cumt.edu.cn 

Jian-sheng Qian, Yan-jing Sun 

College of Information and Electrical Engineer, China University of Mining and Technology, Xuzhou, 221116, China 

Abstract—Node scheduling scheme of sensor nodes is one of 

the most important method to solve the energy-constrained 

wireless sensor networks. Because there are the defects that 

high computational complexity of exact location information 

and the energy consumption unbalance of location-unaware 

in traditional schemes. Aiming at these problems, an optimal 

sleep scheduling scheme based on balanced energy 

consumption (ECBS) was proposed in this paper. 

Accounting the residual energy, the precision for node 

redundancy evaluating was improved by using the distance 

information between the sensor and its neighbors. The 

numerical experiments results illustrate that our scheduling 

scheme may improve the energy efficiency and extends the 

network lifetime while ensure the coverage requirement. 

Index Terms—wireless sensor networks; node scheduling 

algorithm; energy balance; Location-Unaware 


Rapid advances in micro-electro-mechanical systems 

and wireless communication have led to the deployment 

of large scale wireless sensor networks (WSNs). The 

potential applications of sensor networks are highly 

varied, such as environmental monitoring like 

temperature, humidity, seismic events, vibrations, and so 

on. But the energy source of WSNs often consists of a 

battery with a limited energy budget; and it is difficult or 

impossible to replace the power supplies for sensor nodes 

after deployed .So lifetime is the key performance 

measure for WSNs [1]. Sensors are usually deployed 

densely to prolong the network lifetime. But a 

high-density network will waste a lot of energy and 

cause severe problems such as redundancy, radio 

channel contention. A broadly-used method is to 

place nodes in sleep mode by scheduling sensor nodes to 

work alternatively. But selecting the optimal sensing 

ranges for all the sensors is a well-known NP-hard 

problem [2]. Random putting nodes to sleep mode for 

fixed time interval [3 and 4] would cause the network to 

synchronize and may generate some blind points that 

cannot be monitored by any sensors [5,6] . Based on the 

location of sensor nodes, some schedule schemes are 

known as GAF [7], PEAS [8], SSC [9], etc. Using the 

geography (location, direction, or distance) with global 

position system (GPS) or the directional antenna 

technology may ensure the coverage and connectivity 

effectively. But the costs of GPS or other complicated 

hardware devices are too high for tiny sensors. Due to 

the limited processing and memory capabilities, it is not 

realistic to take the sensor nodes equipped with 

specialized hardware components such as GPS into mass 

production [10]. Furthermore, most applications may not 

suit equip with GPS, such as underground, etc. Nodes 

scheduling schemes without location information are 

more valuable in practical. 

Without accurate geography information, however, it is 

very hard to check whether a sensor’s sensing area can be 

completely covered by other sensors. Fortunately, most 

applications may not require complete coverage of the 

monitored area. Fewer researchers have proposed the 

node scheduling schemes without the accurate location 

information. Gao et al [11] propose a mathematical model 

to describe the redundancy in randomly deployed sensor 

networks. The results indicate that: a sensor requires 

about 11 neighbors to get a 90% probability of being a 

complete redundant sensor. If we only require a sensor’s 

90% sensing area to be covered by its neighbors, 5 

neighbors are necessary. Based on this theoretical 

analysis, a Lightweight Deployment-Aware Scheduling 

(LDAS) scheme to turn off redundant sensors has been 

proposed [12]. LDAS uses a weighted random voting 

method to decide who will be eligible to fall asleep. But 

LDAS only consider a sensor’s 1-hop neighbors which 

can cause larger redundancy coverage. Younis proposed 

two distributed protocols (LUC-I and LUC-P) rely on 

distance between one-hop neighbors along with 

advertised tow-hop neighborhood information [13]. In 

[14], Li-Hsing et al presented range-based sleep 

scheduling (RBSS) protocol, an optimal sensor selection 

patter to ensure the coverage quality. These methods can 

effectively reduce network energy consumption without 

any location or directional information. But none of them 

take the balance of energy consumption into account. The 


doi:10.4304/jcp.8.6.1610-1617


unbalanced energy consumption means that the nodes 

inequality sleeps. It leads to the number of nodes 

premature death, and then speed up those nodes died in 

this region, called as “funneling effect”. Thus the “energy 

hole” are formed and the network lifetime is reduced 

[15~18] . Ideally, all of the nodes deployed in the region 

should be consumed their energy at the same time as 

possible. The residual energy of the entire network is 

almost zero when the network is death. 

In this paper, we propose an optimal sleep scheduling 

scheme (ECBS) which relies on approximate neighbor 

distances and two-hop neighbors’ information but no 

location information. Simulation results indicate that our 

scheme not only prolongs the network lifetime, but also 

improves energy efficiency. The reset of the paper is 

organized as follows. Section II introduces the system 

model and problem statement. Section III presents and 

analyzes the algorithm. In section IV, we present our 

experimental results for performance evaluation. Finally, 

section V gives a summary and conclusion. 

the wireless communication module to send the data is on 

the transmitting circuit and the power amplifying circuit. 

And the mainly energy consumption to receive the data 

focus on the receiving circuit. Under the reasonable SNR 

condition, the transmission energy consumption to send k 

bit data is: 

ET 

( k, d) 

= ⎨ 

⎪⎩ 

2 

⎧ ⎪ Eelec × k+ ε 

fs 

× k× d d < dcross over 

4 

Eelec × k+ ε 

mp 

× k× d d ≥dcross over 

and the reception energy consumption is 

E = E × k . 

R 

elec 

Among the formulas, E elec is the energy consumption 

coefficient for the radio electronics, ε fs and ε mp are the 

energy consumption coefficients for a power amplifier 

under different condition. Radio parameters are set as 

tableⅠ. We only consider the data aggregation, while 

ignore other processing energy consumption. The energy 

for performing data aggregation is 5nJ/bit/signal. 

II. SYSTEM MODEL AND PROBLEM STATEMENT 

A. System Model 

We consider sensor nodes for which r t is the 

transmission range and r s is the sensing range. And our 

analysis is based on the following assumes: (1) sensors 

are stationary and are deployed randomly within an area; 

(2) A sensor’s sensing range is a circle area; (3) all 

sensors are supposed to have the same sensing range and 

no two sensors can be deployed exactly at a same 

location; (4) no geography information is available; (5) a 

node can estimate the approximately distance between 

itself and a neighbor based on the received signal 

strength[19],and fusion, conflict and retransmission are 

not taken into account when data transmitting; (6) 

r t ≥2r s , under this condition, coverage implies 

connectivity[20]. 

Definition 1 (Neighbor nodes): the neighbor set of sensor 

i is defined as 

Ni () = { j∈ℵ| di (, j) ≤2 rs 

, i∈ℵ, j≠i } . Where 

ℵ represents the sensor set in the deployment region. 

d(i,j) denotes the distance between sensor i and j. 

Definition 2 1-hop neighbor of sensor i: 

N1 () i = { j∈N()| i d(, i j) ≤rs 

, i∈ℵ }. 

Definition 3 Half-hop neighbor of sensor i: 

ND( i) = { j ∈N( i) | d( i, j) ≤0.5 rs 

, i ∈ℵ} 

. 

Definition 4 Network lifetime: the running time of the 

network meeting the required coverage. 

B. Energy Dissipation 

In our simulations, we use the same energy parameters 

and radio model as discussed in [21] which are used 

widely. In the model, the mainly energy consumption of 

TABLE I. 

RADIO PARAMETERS 

Parameter 

Value 

Threshold distance(dcrossover)(m) 87 

E elec (nJ/bit) 50 

ε fs (pJ/bit/m 2 ) 10 

ε mp (pJ/bit/m 4 ) 0.0013 

Initial energy(J) 0.05 

Data packet size(bits) 4000 

C. Problem Statement 

Assume that N nodes are distributed in a field, and 

the number of the active nodes is N A . Then the sleep ratio 

of the network is defined as: 

N − N 

A 

Q = (1) 

N 

The sleep ratio is one of the standards for measuring 

the efficiency of energy consumption. When the total 

number of nodes in the network is fixed, the higher the 

sleep ratio, the better the energy can be saved. If θ is the 

desired coverage rate of the network, the objective of 

sleep scheduling scheme is to maximize the lifetime and 

the sleep ratio of the network while ensue the coverage 

rate of active nodes meet the θ requirement. 

III. OPTIMAL SLEEP SCHEDULING SCHEME 

A. Coverage Redundancy Determines 



Figure 1. 

Supposed that sensor i has a neighbor sensor j. S i and 

S j denote the circle sensing area covered by node i and j 

respectively. d ij is the distance between node i and j. And 

S denotes the sensing area that is covered by node i 

i∩ j 

and j, as shown in Figure 1. Refer to [22], we can get 

that: 

⎧ 

2 

d 

2 

ij 

dij 

⎪2rs arccos −dijrs 1− d ≤2 

2 ij 

rs 

Si∩ 

j 

= 

(2) 

⎨ 2rs 4rs 

⎪⎩ 

0 

otherwise 

So from formula (2), we can get that when the distance 

between node i and j is less than or equal to 0.5r, the 

redundant coverage area S 

i∩ 

j 

is more than about 68.5% 

of S i . When the distance of node i and node j is more than 

1.75r, the area S i∩ 

j 

is very small, about 0.052 S i. 

These results can be used in our nodes scheduling. If 

d ij ≥1.75r, the effects that node i to node j will be ignored 

in this paper. 

If θ is the percentage of the redundant area covered by 

all the neighbors of node i. Refer to paper [22, 23], θ can 

be expressed as 

∪ 

θ = 

S ∩ S 

S 

= 

Si 

= 1 − 

m 

Si 

j 

(1 − ) 

S 

− S 

S 

S i∩j 

j i 

j∈N() i i N() 

i 

j= 

1 

i 

i 

∏ ∩ (3) 

S 

N() 

i 

is the area that covered by sensor i but not 

covered by its neighbors. Then, if node i has a neighbor 

node k and d ik ≤0.5r. Based on formula (2) and (3), the θ 

of node i can be expressed as 

m 

Si 

j 

θ ≥1− 0.32 • ∏(1 − 

∩ ) 

(4) 

S 

j= 

1 

j≠k 

Suppose node j is a neighbor node of node i. Based 

on the above definition, the distance between node i and j 

satisfy the condition: 0


the condition to sleep, it enters the pre-sleep state with a 

random short time T w. If the node received other 

sensor’s sleep-message at the pre-sleep state, it will 

return the active state. Otherwise, it broadcasts itself 

sleep-message after waiting T w time and then goes to 

sleep state; fall asleep for a period of time Ts. 

Based on the classic LEACH cluster protocol, time is 

divided into fixed-length time periods called rounds. 

Each round begins with a competition phase, in which 

every node determines whether it can be active or sleep. 

Then those active sensors enter into clustering and 

sensing. We detail the steps as follows. 

Step1: Networks initialization. We assumed that all 

sensors are active initially. Each sensor broadcasts 

messages to estimate the distance between itself and its 

every neighbor and then record these information. 

According to the QoS demand (the coverage rate θ) of 

network, sink broadcasts the system message including 

the two parameters HT and AT. Where HT is the 

minimum number of active neighbors with one half-hop 

neighbor and AT is the minimum number of neighbor 

nodes that have no half-hop neighbor. For example, the 

network coverage (θ) is required to 85%. According to 

tableⅡ, we can set HT = 5 and AT = 8. While the 

coverage rateθis more than 90%, we can set HT = 6 

and AT = 9. 

Start 

cluster heads broadcast hello messages and other active 

nodes select the closest head to join. 

Step 4: Sensing. 

Step 5: The current round end and return step 2. 

IV. SIMULATION RESULTS 

We focus on the construction of one cover and assume 

that 1000 nodes are deployed randomly in a 100 

meter×100 meter square. Each sensor has a sensing range 

of 15 meters. The transmitting, receiving (idling), and 

sleeping power consumption ratio is 20:4:0.01[21]. We 

conducted simulations with matlab simulator for 

comparing among two sleep scheduling methods: LDAS 

and our proposed scheme (ECBS). 

A. Coverage Effectiveness 

Set θ≥90%. Run LDAS and ECBS at the same 

condition to compare. We sampled on the No.100 round 

respectively as shown in Figure 4 (only active sensors are 

marked to see clearly). Only 58 nodes are active in 

our algorithm, but 150 nodes are on-duty by LDAS 

algorithm. And Figure 5 shows the coverage condition 

with the active nodes on No.100 round by different 

algorithm. It can be easy to see that the fewer numbers of 

active nodes are needed in our algorithm to meet the 

same coverage required and the sensors distribute more 

uniform in Figure 4(b). However, there is more 

redundancy coverage in Figure 5(a). 

Ni>HT 

N 

Keep active 

Y 

Ndi>0 

N 

Y 

Ni>AT 

N 

The maximal residual 

energy of sensor in ND 

> Ei 

N 

Y 

Sensor i sleep 

Y 

Sensor j with the 

minimum residual 

energy in ND sleep 

100 

90 

(a) 

LDAS 

80 

End 

70 

60 

Figure 3 

The scheduling process of an active sensor i 

Step 2: Nodes-scheduling. At the beginning of each 

round, each active node determines whether it is a 

redundancy sensor or not. The scheduling scheme is 

detailed in Figure 3. Where N i is the number of sensor 

i ’s active neighbors, and N di is the number of sensor i’s 

half-hop neighbors, ND is the set of sensor i’s half-hop 

neighbors, E i is the residual energy of sensor i. 

Step 3: Clustering. Active nodes randomly select nodes 

as cluster heads based on LEACH algorithm. Then the 

50 

40 

30 

20 

10 

0 

0 10 20 30 40 50 60 70 80 90 100 

(b) ECBS 

Figure 4 The distribution of active nodes on No.100 round 



covered by those active nodes at some time. 

As shown in Figure 6, the network coverage is 

reducing with the network running using both the two 

algorithms. The higher the network coverage required, 

the shorter survival time of the network. During the initial 

operation, the two algorithms have maintained a higher 

coverage rate. But with the operation of network, more 

and more nodes exhausted their energy, the network 

coverage also decreased. Furthermore, the coverage rate 

of ECBS is always higher than LDAS at the same round 

during the whole running time. 

100 

80 

(a) 

LDAS 

the number of active nodes 

160 

140 

120 

100 

80 

60 

40 

θ=90%,LDAS 

θ=85%,LDAS 

θ=90%,ECBS 

θ=85%,ECBS 

60 

20 

network coverage 

1 

0.95 

0.9 

0.85 

0.8 

0.75 

0.7 

0.65 

40 

20 

0 

-20 0 20 40 60 80 100 120 

(b) 

ECBS 

Figure 5 The coverage condition on No.100 round 

0.6 

θ=90%,LDAS 

θ=85%,LDAS 

0.55 

θ=90%,ECBS 

θ=85%,ECBS 

0.5 

0 200 400 600 800 1000 1200 1400 1600 1800 

running rounds 

Figure 6 Comparisons of network coverage ratio 

The network coverage (η) is the ratio of the area 

covered by those active nodes to the whole monitoring 

area during the nodes scheduling scheme running 

process. 

Aactive 

∩ A 

η () t = 

(5) 

A 

A is the whole monitoring area, and A active is the area 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 

running round 

Figure 7 Comparisons of active nodes 

Figure 7 shows the number of active nodes during the 

network running. As can be seen from Figure 7 and 

Figure 6, the number of active nodes by ECBS is always 

less than the number that used by LDAS when the 

coverage ratio meeting the requirement. Because there 

are more active nodes in the early operation by LDAS, 

too much energy were consumed. The active nodes 

decreased with more and more nodes run out of their 

energy. And the coverage percentage dropped from 98% 

to 50% quickly. But the number of active nodes used by 

ECBS algorithm is kept stability in the whole running 

process. Using the less active nodes to meet a high 

coverage, thus the energy has been saved and the lifetime 

has been prolonged. 

B. Network Lifetime 

According to the definition 4 in this paper, network 

lifetime is the running time of the network meeting the 

required coverage. As illustrated in Figure 8, the network 

lifetime is only 70 rounds with no scheduling scheme. Set 

θ≥90%, using LDAS scheduling scheme the lifetime is 

850 rounds and the first dead node occurred on No.104 

round. But by ECBS scheduling scheme, the lifetime 

extends to 1520 rounds and the first dead node occurred 

on No.382 round. Set θ≥85%, the lifetime is 1020 rounds 

and the first dead node occurred on No.117 round by 

LDAS. But by ECBS algorithm, the lifetime extends to 

1750 rounds and the first dead node occurred on No.402 

round. ECBS algorithm can prolong the network lifetime 

efficiently. And the lower required coverage, the longer 

the network lifetime. 



∑ N 

Ei 

() t 

i= 

1 

mE 

() t = 

N 

(6) 

The energy variance function is: 

= 

D () t = 

E 

∑ N i E 

i 1 

[ E () t − m () t ] 2 

N 

(7) 

C. Energy Efficiency 

Figure 8 Comparison of network lifetime 

The average energy 

0.05 

0.045 

0.04 

0.035 

0.03 

0.025 

0.02 

0.015 

0.01 

θ=90%,LDAS 

θ=85%,LDAS 

θ=90%,ECBS 

θ=85%,ECBS 

0.005 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 


Figure 10 comparison of the average residual energy 

×10 -5 Figure 11 comparison of the energy Variance 

30 

25 

θ=90%,LDAS 

θ=85%,LDAS 

θ=90%,ECBS 

θ=85%,ECBS 

Figure 9 Comparison of sleep ratio 

As mentioned above, the sleep ratio is an important 

parameter to describe the situation of saving energy 

during the operation. When meeting the coverage 

requirement, the higher the sleep ratio, the better the 

energy can be saved. Figure 9 shows that the sleep ratios 

of ECBS are always higher than that of LDAS algorithm 

and maintain stability in the whole running time. 

Moreover with different coverage requirement, the sleep 

ratios of LDAS are also much different. The higher the 

network coverage requires the lower sleep ratio. But the 

sleep ratios of our algorithm have a little change. 

Figure10 shows the average residual energy of network 

during operation. It confirms that the residual energy of 

ECBS is always higher than that of LDAS on the same 

round. 

Sleep ratio can only demonstrate the total condition of 

energy consumed, but not measure the balance of energy 

consumed. In this paper, the average residual energy and 

the energy variance function are used to measure that the 

energy consumed is balanced or not at some time [25]. 

Considering the two values, the larger the average 

residual energy and the smaller the energy variance, the 

better balance of the energy consumed in the network. 

The average residual energy function is: 

Energy variance 

20 

15 

10 

5 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 


From Figure 10 and Figure 11, it can be seen that the 

ECBS algorithm has a better balance of energy consumed. 

By LDAS algorithm, the m E (t) decreased more rapidly 

and the D E (t) were larger. The experiment data shows that 

using LDAS algorithm some nodes still remained more 

than 90% energy even when the network died. But using 

ECBS algorithm, the maximal ratio of the residual energy 

to the initial energy was about 40% when the network 

died. It also indicates that LDAS algorithm exits the 

problem that energy consumes uneven. Thus it will lead 

to some nodes run out their energy earlier. And then 

energy hole are formed so as to make the network dying 

prematurely. Ideally each node in a network running out 

its energy at the same time will obtain the optimal energy 

efficiency. 



V. CONCLUSION 

Energy saving in WSNs has attracted a lot of attention 

in the recent years. Extensive research has been 

conducted to address these limitations by developing 

schemes that can improve resource efficiency. In this 

paper, we have introduced an optimal energy-efficient 

sleep scheduling scheme for WSNs. Without accurate 

geography information, the two-hop neighbors are 

considered. Simulation results show that our scheduling 

scheme has improved the sleep ratio and extended the 

network lifetime. But in the simulation experiments, we 

discovered that there is approximately 17% residual 

energy when the network died. Considering the death 

spread from the border of the monitor region to the 

central, we believe that there is still space to improve. So, 

one of our future works is to find a solution to alleviate 

the inequality sleep of the boundary nodes. 

ACKNOWLEDGMENTS 

This work was supported under the National Science 

Foundation of China (50904070, 51104157); The China 

Postdoctoral Science Foundation (20100471412). 

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Shan-shan Ma, was born in 1978, is 

currently a lecturer in China University 

of Mining and Technology. She received 

the B.S. in Electronic and Information 

Technology from China University of 

Mining and Technology, Xuzhou, China, 

in 2000 and the M.S. in Communication 

and Information Engineering from China 

University of Mining and Technology, 

Xuzhou, China, in 2003. She is currently pursuing the Ph. D. 

degree at Computer Application Technology in College of 

Computer Science and Technology, University of Mining and 

Technology, from 2007. Her research interests include wireless 

sensor network and information processing. 

Yan-Jing Sun, was born in 1977, is 

currently a professor in China University 

of Mining and Technology. He received 

his Ph.D. degree in Communication and 

Information System from China 

University of Mining and Technology in 

2007. His research interest includes 

wireless sensor network and embedded 

real-time system. 

Jian-sheng Qian, was born in 1964, is a 

professor and Ph.D. candidate tutor in 

China University of Mining and 

Technology currently. He received the 

Ph. D degree in Control Theory and 

Control Engineering from China 

University of Mining and Technology, 

China, in 2003. His research interest 

includes mine communication and 

wireless sensor network. 



Identity Based Proxy Re-encryption From BB1 

IBE 

Jindan Zhang 1 , Xu An Wang 2 and Xiaoyuan Yang 2 

1 Department of Electronic Information 

Xianyang Vocational Technical College, 712000, P. R. China 

2 Key Laboratory of Information and Network Security 

Engineering University of Chinese Armed Police Force, 710086, P. R. China 

wangxahq@yahoo.com.cn 

Abstract— In 1998, Blaze, Bleumer, and Strauss proposed a 

kind of cryptographic primitive called proxy re-encryption. 

In proxy re-encryption, a proxy can transform a ciphertext 

computed under Alice’s public key into one that can 

be opened under Bob’s decryption key. In 2007, Matsuo 

proposed the concept of four types of proxy re-encryption 

schemes: CBE (Certificate Based Public Key Encryption) 

to IBE (Identity Based Encryption) (type 1), IBE to IBE 

(type 2), IBE to CBE (type 3), CBE to CBE (type 4). In this 

paper, we find that if we allow the PKG to use its masterkey 

in the process of generating re-encryption key for proxy 

re-encryption in identity based setting, many open problems 

can be solved. We give the new security models for proxy reencryption 

in identity based setting, especially considering 

PKG’s involving in the re-encryption key generation process 

and PKG’s master-key’s security. We construct the new 

IND-ID-CPA and the first IND-ID-CCA2 secure proxy reencryption 

schemes based on BB1 IBE. We also prove their 

security by introducing some new techniques which maybe 

have independent interest. At last, we compare our new 

schemes with existing ones, the results show that our scheme 

can achieve high security levels and are very efficient for 

re-encryption and, which are very important for practical 

applications. 

Index Terms— Cryptography, Identity based proxy reencryption, 

PKG, BB1 IBE, Security proof. 


The concept of proxy re-encryption(PRE) comes from 

the work of Blaze, Bleumer, and Strauss in 1998[2]. 

The goal of proxy re-encryption is to securely enable 

the re-encryption of ciphertexts from one key to another, 

without relying on trusted parties. In 2005, Ateniese et 

al proposed a few new PRE schemes and discussed its 

several potential applications such as e-mail forwarding, 

law enforcement, cryptographic operations on storagelimited 

devices, distributed secure file systems and outsourced 

filtering of encrypted spam [1]. Since then, many 

excellent schemes have been proposed[10], [25], [20], 

[26], [15], [27], [11], [29]. In ACNS’07, Green et al. 

proposed the first identity based proxy re-encryption 

schemes(IDPRE) [15]. In ISC’07, Chu et al. proposed 

The second author is the corresponding author. This paper is an 

extended work of [34], [35] and supported by the National Natural 

Science Foundation of China under contract no. 61103230, 61103231, 

61272492, 61202492, Natural Science Foundation of Shaanxi Province 

and Natural Science Foundation of Engineering University of Chinese 

Armed Police Force. 

the first IND-ID-CCA2 IDPRE schemes in the standard 

model, they constructed their scheme based on Water’s 

IBE. But unfortunately Shao et al. found a flaw in their 

scheme and they fixed this flaw by proposing an improved 

scheme [29]. In Pairing’07, Matsuo proposed another 

few more PRE schemes in identity based setting [27]. 

Interestingly, they proposed the concept of four types of 

PRE: CBE(Certificate Based Public Key Encryption) to 

IBE(Identity Based Encryption)(type 1), IBE to IBE(type 

2), IBE to CBE (type 3), CBE to CBE (type 4)[27], which 

can help the ciphertext [33], [24] circulate smoothly in 

the network. They constructed two PRE schemes: one 

is the hybrid PRE from CBE to IBE, the other is the 

PRE from IBE to IBE. Both of the schemes are now 

being standardized by P1363.3 workgroup [28]. Recently, 

Tang et al. extended the concept of identity based proxy 

re-encryption, they proposed a concept of inter-domain 

identity based proxy re-encryption which aimed to constructing 

proxy re-encryption scheme between different 

domains in identity based setting [31]. 

A. Main Idea and Contribution 

Our contributions are mainly as following: If we follow 

the principal that all the work PKG can do is just 

generating private keys for IBE users, it is indeed difficult 

for constructing PRE based on BB 1 IBE. But if we allow 

PKG generating re-encryption keys for PRE by using its 

master − key, we can easily construct PRE based on a 

variant of BB 1 IBE. 

On the Role of PKG in IBPRE and Related Primitives. 

We challenge the traditional idea of PKG is only 

responsible to generate private keys. Traditionally when 

cryptographers design IBE and other related schemes, they 

assume the PKG can only generate the private keys to 

the users. The idea situation is that after PKG generating 

private keys for the whole users, the PKG is shut up 

to avoid “single-point failure” problem. But we remark 

that this idea situation can not work in the practical 

application, we can not predicate all the future users 

of the system when it was set up. Furthermore, in the 

IBE systems, there are also requirements of revocation 

of the identity, which will necessary involved the PKG. 

Thus many usable IBE systems let their PKG be online 


doi:10.4304/jcp.8.6.1618-1626


24/7/365. From a practical point, for PRE in the identity 

based setting, involving PKG in generating re-encryption 

key can generically help the proxy improve its efficiency, 

which is very important for practical IBPRE systems, 

after all, re-encryption is the main operation in the PRE 

systems. More importantly, involving PKG in generating 

some “valued ephemeral” maybe bring unexpected benefits 

to existing identity based primitives. For example, 

in identity based broadcast encryption, some “valued 

ephemeral” given by the PKG maybe be very useful 

for the receivers for decryption, Note the length of this 

“valued ephemeral” is just constant, instead of linear with 

the receivers, thus improve the efficiency greatly. Also 

note this feature can not be shared with the normal public 

key broadcast encryption schemes. 

B. Organization 

We organize our paper as following. In Section I- 

I, we give some preliminaries which are necessary to 

understand our paper. We propose our new proxy reencryption 

scheme based on a variant of BB 1 IBE and 

prove its security in SectionIII. In Section IV, we give 

the comparison results with previous IBPRE schemes. We 

give our conclusions in the last Section V. 

II. PRELIMINARIES 

In the following, we sometimes use notations described 

in this section without notice. We denote the concatenation 

of a and b by a||b, denote random choice from a set 

S by R ←− S. 

A. Bilinear groups 

Let G and G 1 be multiplicative cyclic groups of prime 

order p, and g be generator of G. We say that G 1 has an 

admissible bilinear map e : G×G → G 1 . if the following 

conditions hold. 

1) e(g a , g b ) = e(g, g) ab for all a, b. 

2) e(g, g) ≠ 1. 

3) There is an efficient algorithm to compute e(g a , g b ) 

for all a, b and g. 

B. Assumptions 

Definition 1: For randomly chosen integers a, b, c R ←− 

Z ∗ p, a random generator g R ←− G, and an element R R ←− G, 

we define the advantage of an algorithm A in solving 

the Decision Bilinear Diffie-Hellman(DBDH) problem as 

follows: 

Adv G dbdh (A) =| P r[A(g, g a , g b , g c , e(g, g) abc ) = 0] 

−P r[A(g, g a , g b , g c , R) = 0] | 

where the probability is over the random choice of generator 

g ∈ G, the randomly chosen integers a, b, c, the 

random choice of R ∈ G, and the random bits used by 

A. We say that the (k, t, ɛ)-DBDH assumption holds in G 

if no t-time algorithm has advantage at least ɛ in solving 

the DBDH problem in G under a security parameter k. 

C. Identity Based Encryption 

An Identity Based Encryption(IBE) system consists of 

the following algorithms. 

1) SetUp IBE (k). Given a security parameter k, PKG 

generate a pair (parms, mk), where parms denotes 

the public parameters and mk is the master − key. 

2) KeyGen IBE (mk, parms, ID). Given the 

master − key mk and an identity ID with parms, 

generate a secret key sk ID for ID. 

3) Enc IBE (ID, parms, M). Given a message M and the 

identity ID with parms, compute the encryption of 

M, C ID for ID. 

4) Dec IBE (sk, parms, C ID ). Given the secret key sk, 

decrypt the ciphertext C ID . 

III. IBPRE BASED ON A VARIANT OF BB 1 IBE 

A. Our Definition for IBPRE 

In this section, we give our definition and security 

model for identity based PRE scheme, which is based 

on [15], [31]. 

Definition 2: An identity based PRE scheme is tuple 

of algorithms (Setup, KeyGen, Encrypt, Decrypt, RK- 

Gen, Reencrypt): 

• Setup(1 k ). On input a security parameter, the algorithm 

outputs both the master public parameters 

which are distributed to users, and the master secret 

key (msk) which is kept private. 

• KeyGen(params, msk, ID). On input an identity 

ID ∈ {0, 1} ∗ and the master secret key, outputs a 

decryption key sk ID corresponding to that identity. 

• Encrypt(params, ID, m). On input a set of public 

parameters, an identity ID ∈ {0, 1} ∗ and a plaintext 

m ∈ M, output c ID , the encryption of m under the 

specified identity. 

• RKGen(params, msk, sk ID1 , sk ID2 , ID 1 , ID 2 ). 

On input secret keys msk, sk ID1 , sk ID2 , and i- 

dentities ID ∈ {0, 1} ∗ , PKG, the delegator and the 

delegatee interactively generat the re-encryption key 

rk ID1→ID 2 

, the algorithm output it. 

• Reencrypt(params, rk ID1→ID 2 

, c ID1 ). On input 

a ciphertext c ID1 under identity ID 1 , and a reencryption 

key rk ID1→ID 2 

, outputs a re-encrypted 

ciphertext c ID2 . 

• Decrypt(params, sk ID , c ID ). Decrypts the ciphertext 

c ID using the secret key sk ID , and outputs m 

or ⊥. 

Remark 1: This definition is different from the Definition 

of IBPRE in the work of [27]. We insist this is a 

more natural and general Definition for PRE from IBE to 

IBE. This definition is consistent with the work of [15], 

[31]. 

B. Our Security Models for IBPRE 

In PRE from IBE to IBE, there is no necessary to 

consider the malicious PKG attack, so we omit PKG in 

our security model when considering delegator security 



and delegatee security. 

Delegator Security. 

In PRE from IBE to IBE, we consider the case that proxy 

and delegatee are corrupted. 

Definition 3: (DGA-IBE-IND-ID-CPA) A PRE 

scheme from IBE to IBE is DGA 1 -IBE-IND-ID-CPA 

secure if the probability 

P r[{(ID ⋆ , sk ID ⋆) ← KeyGen(·)} 

{(ID x , sk IDx ) ← KeyGen(·)}, 

{(ID h , sk IDh ) ← KeyGen(·)}, 

{R hx ← RKGen(msk, sk IDh , sk IDx , ·)}, 

{R xh ← RKGen(msk, sk IDx , sk IDh , ·)}, 

{R hh ← RKGen(msk, sk IDh , sk IDh , ·)}, 

{R xx ← RKGen(msk, sk IDx , sk IDx , ·)}, 

{R ⋆h ← RKGen(msk, sk ID ⋆, sk IDh , ·)}, 

{R ⋆x ← RKGen(msk, sk ID ⋆, sk IDx , ·)}, 

(m 0 , m 1 , St) ← A Orenc (ID ⋆ , {sk IDx }, 

{R xh }, {R hx }, {R hh }, {R xx }, {R ⋆h }, {R ⋆x }), 

d ⋆ R 

←− {0, 1}, C ⋆ = Encrypt(m d ⋆, ID ⋆ ), 

d ′ ← A Ørenc (C ⋆ , St) : d ′ = d ⋆ ] 

is negligibly close to 1/2 for any PPT adversary A. In 

our notation, St is a state information maintained by A 

while (ID ⋆ , sk ID ⋆) is the target user’s pubic and private 

key pair generated by the challenger which also chooses 

other keys for corrupt and honest parties. For other honest 

parties, keys are subscripted by h and we subscript corrupt 

keys by x. Oracles O renc proceeds as follows: 

• Re-encryption O renc : on input (pk i , ID j , C pki ), 

where C pki is the ciphertext under the public key pk i 

, pk i were produced by Keygen CBE , ID j were produced 

by Keygen IBE , this oracle responds with ‘invalid’ 

if C pki is not properly shaped w.r.t. pk i . Otherwise 

the re-encrypted first level ciphertext C ID = 

ReEnc(KeyGen P RO (sk i , ID j , mk, parms), ID j , 

parms, C pki ) is returned to A. 

Delegatee Security. 

In PRE from IBE to IBE, we consider the case that proxy 

and delegator are corrupted. 

Definition 4: (DGE-IBE-IND-ID-CPA) A PRE 

scheme from IBE to IBE is DGE 2 -IBE-IND-ID-CPA 

1 DGA means Delegator 

2 DGE means Delegatee. 

secure if the probability 

P r[{(ID ⋆ , sk ID ⋆) ← KeyGen(·)} 

{(ID x , sk IDx ) ← KeyGen(·)}, 






{R h⋆ ← RKGen(msk, sk IDh , sk ID ⋆, ·)}, 

{R x⋆ ← RKGen(msk, sk IDx , sk ID ⋆, ·)}, 

(m 0 , m 1 , St) ← A Orenc (ID ⋆ , {sk IDx }, {R xh }, 

{R hx }, {R hh }, {R xx }, {R h⋆ }, {R x⋆ }), 

d ⋆ R 

←− {0, 1}, C ⋆ = Encrypt(m d ⋆, ID ⋆ ), 

d ′ ← A Ørenc (C ⋆ , St) : d ′ = d ⋆ ] 

is negligibly close to 1/2 for any PPT adversary A. The 

notations in this game are same as Definition 3. 

PKG Security. 

In PRE from IBE and IBE, PKG’s master key can not 

leverage even if the delegator, the delegatee and proxy 

collude. 

Definition 5: (PKG-OW) A PRE scheme from IBE to 

IBE is one way secure for PKG if the probability 

P r[{(ID x , sk IDx ) ← KeyGen(·)}, 






mk ′ ← A Orenc ({sk IDx }, {sk IDh }, {R xh }, 

{R hx }, {R hh }, {R xx }, {parms}) : mk = mk ′ ] 

is negligibly close to 0 for any PPT adversary A. The 

notations in this game are same as Definition 3. 

C. Our Proposed IND-Pr-sID-CPA Secure IBPRE 

Scheme Based on a Variant of BB 1 IBE 

• The underlying IBE scheme: We give a variant of 

BB 1 -IBE scheme as follows: 

Let G be a bilinear group of prime order p (the 

security parameter determines the size of G). Let 

e : G × G → G 1 be the bilinear map. For now, we 

assume public keys (ID) is element in Zp. ∗ We later 

extend the construction to public keys over {0, 1} ∗ 

by first hashing ID using a collision resistant hash 

H : {0, 1} ∗ → Z p . We also assume messages to be 

encrypted are elements in G. The IBE system works 

as follows: 

1) SetUp IBE (k). Given a security parameter k, 

select a random generator g ∈ G and random 

elements g 2 = g t1 , h = g t2 ∈ G. Pick a random 

α ∈ Zp. ∗ Set g 1 = g α ,mk = g2 α , and params = 



(g, g 1 , g 2 , h). Let mk be the master-secret key 

and let params be the public parameters. 

KeyGen IBE (mk, params, ID). Given 

mk = g2 α and ID with params, the 

PKG picks random s 0 , s 1 ∈ Zp, ∗ choose 

a hash function ˜H : Zp ∗ × {0, 1} ∗ → Zp 

∗ 

and computes u 0 = ˜H(s0 , ID), 

u 1 = ˜H(s 1 , ID). Set sk ID = (d 0 , d 1 , d ′ 0) = 

(g2 α (g1 ID h) u0 , g u0 , (g2 α (g1 ID h) u1 )). The PKG 

preserves (s 0 , s 1 ). 

Enc IBE (ID, params, M). To encrypt a message 

M ∈ G 1 under the public key ID ∈ Zp, 

∗ 

pick a random r ∈ Zp ∗ and compute C ID = 

(g r , (g1 ID h) r , Me(g 1 , g 2 ) r ). 

Dec IBE (sk ID , params, C ID ). Given ciphertext 

C ID = (C 1 , C 2 , C 3 ) and the secret key 

sk ID = (d 0 , d 1 ) with prams, compute M = 

C 3e(d 1,C 2) 

e(d . 

0,C 1) 

delegation scheme: 

KeyGen PRO (sk R , params, ID, ID ′ ). The 

PKG computes u ′ 1 = ˜H(s 1 , ID ′ ) and randomly 

selects k 1 , k 2 , k 3 ∈ Zp ∗ and sets 

rk ID→ID ′ = (rk 1 , rk 2 , rk 3 , rk 4 ) = 

( αID′ +t 2+k 1 

k 3(αID+t 2) 

+ k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ) and 

sends them to the proxy via secure channel. 

We must note that the PKG computes a different 

(k 1 , k 2 , k 3 ) for every different user pair 

(ID, ID ′ ). 

Check(params, C ID , ID). Given the delegator’s 

identity ID and C ID = (C 1 , C 2 , C 3 ) 

with params, compute v 0 = e(C 1 , g1 ID h) and 

v 1 = e(C 2 , g). If v 0 = v 1 then output 1. 

Otherwise output 0. 

ReEnc(rk ID→ID ′, params, C ID , ID ′ ). 

Given the identities ID, ID ′ , rk ID→ID ′ = 

(rk 1 , rk 2 , rk 3 , rk 4 ) = ( αID′ +t 2+k 1 

k 3(αID+t 2) 

+ 

k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ) with params, the 

proxy re-encrypt the ciphertext C ID into 

C ID ′ as follows. First it runs “Check”, if 

output 0, then return “Reject”. Else computes 

C 2ID ′ = (C 1, ′ C 2, ′ C 3, ′ C 4, ′ C 5, ′ C 6, ′ C 7) ′ = 

αID ′ +t 2 +k 1 

k 

(C 1 , C 2 , C 3 , C 

(αID+t 2 ) +k2 

2 , rk 2 , rk 3 , rk 4 ). 

Dec1 IBE (sk ID ′, params, C 2ID ′). Given 

a re-encrypted ciphertext C 2ID ′ = 

(C 1, ′ C 2, ′ C 3, ′ C 4, ′ C 5, ′ C 6, ′ C 7) ′ and the secret key 

sk ID = (d 0 , d 1 , d ′ 0) with params, computes 

C 

M = 

3e(C ′ 5, ′ C 4) 

′ 

e(C 2 ′ , C′ 6 )e(C′ 1 , C′ 7 )e(d′ 0 , C′ 1 ) 

C 

= 

3e(rk ′ 2 , C 4) 

′ 

e(C 2 ′ , rk 3)e(C 1 ′ , rk 4)e(d ′ 0 , C′ 1 ) 

Dec2 IBE (sk ID ′, params, C 1ID ′). Given a 

normal ciphertext C ID ′ = (C 1 , C 2 , C 3 ) and the 

secret key sk ID ′ = (d 0 , d 1 , d ′ 0) with prams, 

compute M = C3e(d1,C2) 

e(d . 0,C 1) 

We 

Remark 

computes 

pair 

+t 2+k 

3(αID+t 

same 

not secure 

Security 

Theorem 

our 

IND-sID-CPA 

colluding. 

Proof: 

construct 

On 

output 

= g 

interacting 

Initialization. 

with 

intends 

Setup.To 

rithm 

h 

params 

ing 

g2 a 

Phase 

• 

• 

can verify its correctness as following 

C 3e(rk ′ 2 , C 4) 

′ 

e(C 2 ′ , rk 3)e(C 1 ′ , rk 4)e(d ′ 0 , C′ 1 ) 

Me(g 1 , g 2 ) r e(g k3u′ 1 , (g 

ID 

= 

1 h) r( αID′ +t 2 +k 1 

k 3 (αID+t 2 ) +k2) ) 

e((g1 IDh)r 

, g u′ 1 k2k3 )e(g r , g k1u′ 1)e(g2 α(gID′ 

1 h) u′ 1, g r ) 

= Me(g 1, g 2 ) r e(g k3u′ 1 , (g 

ID 

1 h) k2r )e(g k3u′ 1 , (g 

ID ′ 

1 h) r 

e((g1 IDh)r 

, g u′ 1 k2k3 )e(g r , g k1u′ 1)e(g2 α(gID′ 

= Me(g 1, g 2 ) r 

e(g2 α, = M 

gr ) 

2: In our scheme, we must note that the P- 

a different (k 1 , k 2 , k 3 ) for every different 

(ID, ID ′ ). Otherwise, if the adversary knows 

1 

2) 2 for five different pairs (ID, ID ′ ) but 

k 1 , k 2 , k 3 , α, t 2 , he can compute (α, t 2 ), which 

at all. 

Analysis 

1: Suppose the DBDH assumption holds, 

scheme proposed in Section III-C is DGA-IBEsecure 

for the proxy and the delegatee’s 

Suppose A can attack our scheme, we 

an algorithm B solves the DBDH problem in 

input (g, g a , g a2 , g b , g c , T ), algorithm B’s goal 

1 if T = e(g, g) abc and 0 otherwise. Let 

, g 2 = g b , g 3 = g c . Algorithm B works by 

with A in a selective identity game as follows: 

The selective identity game begins 

A first outputting an identity ID ∗ that it 

to attack. 

generate the system’s parameters, algo- 

B picks α ′ ∈ Z p at random and defines 

= g1 −ID∗ g α′ ∈ G. It gives A the parameters 

= (g, g 1 , g 2 , h). Note that the correspond- 

master − key, which is unknown to B, is 

= g ab ∈ G ∗ . 

1 

“A issues up to private key queries on 

ID i ”. B selects randomly r i , r ′ ∗ 

i ∈ Z p 

and k ′ ∈ Z p , sets sk IDi = (d 0 , d 1 , d ′ 0) = 

−α ′ 

ID 

(g i −ID ∗ 

2 (g (IDi−ID∗ ) 

1 g a ) ri −1 

ID 

, g i −ID ∗ 

2 g ri , 

−α ′ 

ID 

g i −ID ∗ 

2 (g (IDi−ID∗ ) 

1 g a ) r′ i). We claim sk IDi 

is a valid random private key for ID i . 

b 

To see this, let ˜r i = r i − 

ID−ID 

and 

∗ 

˜r i ′ = r′ i − b 

ID−ID 

. Then we have that 

∗ 

−α ′ 

ID 

d 0 = g i −ID ∗ 

2 (g (IDi−ID∗ ) 

1 g α′ ) ri = 

g2(g a (IDi−ID∗ ) 

1 g α′ ) ri− b 

ID−ID∗ 

= g2(g a IDi 

1 h) ˜ri . 

−1 

ID 

d 1 = g i −ID ∗ 

2 g ri = g ˜ri . 

−α ′ 

d ′ ID 

0 = g i −ID ∗ 

2 (g (IDi−ID∗ ) 

1 g α′ ) r′ i 

= 

g2(g a (IDi−ID∗ ) 

1 g α′ ) r′ i − b 

ID−ID∗ 

= g2(g a IDi 

1 h) ˜r i ′ . 

“A issues up to rekey generation queries on 

(ID, ID ′ )”. 

The challenge B chooses a randomly x ∈ Zp, 

∗ 

2) 

KG 

3) 

αID ′ 

k 

the 

is 

4) 

D. 

• The then 

1) 

G. 

is to 

g a 1 

1) 

2) 

2) 

3) 

3) 

4) 

5) 

k 3 )e(g k3u′ 1 , g 

k 1 r 

1 h) u′ 1, g r ) 

k 3 ) 



sets rk ID→ID ′ = x and returns it to A. He 

computes w = (gH 1 (ID) h) x 

and sends it to the 

(g H 1 (ID) h) 

proxy. We observe that 

rk 1 = αID′ + t 2 + k 1 

k 3 (αID + t 2 ) + k 2 

but from the simulation, α = a and t 2 = α ′ − 

aID ∗ , so we can get 

rk 1 = aID′ + α ′ − aID ∗ + k 1 

k 3 (aID + α ′ − aID ∗ ) + k 2 

Let rk 1 = x, we can get 

k 1 = k 3 (aID + α ′ − aID ∗ )(x − k 2 ) 

−(aID ′ + α ′ − aID ∗ ) 

= [k 3 (x − k 2 )a(ID − ID ∗ ) 

−a(ID ′ − ID ∗ )] + k 3 α ′ (x − k 2 ) − α ′ 

So the challenge B simulates as follows. He 

chooses a randomly k 2 , k 3 ∈ Z ∗ p, sets 

x = 

ID′ − ID ∗ 

k 3 (ID − ID ∗ ) + k 2, 

k 1 = α ′ ( ID′ − ID ∗ 

ID − ID ∗ ) − α′ 

searches in User-key-list 

for item (ID ′ , α ′ , r, r ′ )(we assume 

sk ID ′ = (d 0 , d 1 , d ′ 0) = 

−α ′ 

−1 

ID ′ −ID ∗ 

ID 

(g 

′ −ID ∗ 

2 (g (ID′ −ID ∗ ) 

1 g a ) r , g2 g r , 

−α ′ 

ID 

g 

′ −ID ∗ 

2 (g (ID′ −ID ∗ ) 

1 g a ) r′ ) and computes 

rk 1 = 

rk 2 = g 

ID ′ − ID ∗ 

k 3 (ID − ID ∗ ) + k 2, 

−k 3 

ID ′ −ID ∗ 

2 g k3r′ 

−k 2 k 3 

ID ′ −ID ∗ 

rk 3 = g2 g k2k3r′ , 

α ′ ( ID′ −ID ∗ 

ID−ID ∗ )−α′ 

ID 

rk 4 = g 

′ −ID ∗ 

2 g (α′ ( ID′ −ID ∗ 

ID−ID ∗ )−α ′ )r ′ 

returns them to A. We can see 

C ′ 3e(rk 2 , C ′ 4) 

e(C ′ 2 , rk 3)e(C ′ 1 , rk 4)e(d ′ 0 , C′ 1 ) 

can be reduced to 

Me(g 1 , g 2 ) r 

e(g α 2 , gr ) 

= M 

Thus our simulation is indistinguishable from 

the real algorithm running. Thus our simulation 

is indistinguishable from the real algorithm 

running. 

• “A issues up to re-encryption queries on 

(C ID , ID, ID ′ )”. The challenge B runs 

ReEnc(rk ID→ID ′, C ID , ID, ID ′ ) and returns 

the results. 

4) Challenge When A decides that Phase1 is over, 

it outputs two messages M 0 , M 1 ∈ G. Algorithm 

B picks a random bit b and responds with the 

ciphertext C = (g c , (g α′ ) c , M b · T ). Hence if T = 

e(g, g) abc = e(g 1 , g 2 ) c , then C is a valid encryption 

of M b under ID ∗ . Otherwise, C is independent of 

b in the adversary’s view. 

5) Phase2 A issues queries as he does in Phase 1 

except natural constraints. 

6) Guess Finally, A outputs a guess b ′ ∈ {0, 1}. 

Algorithm B concludes its own game by outputting 

a guess as follows. If b = b ′ , then B outputs 1 

meaning T = e(g, g) abc . Otherwise it outputs 0 

meaning T ≠ e(g, g) abc . 

When T = e(g, g) abc then A’s advantage for breaking 

the scheme is same as B’s advantage for solving DBDH 

problem. 

Theorem 2: Suppose the DBDH assumption holds, 

then our scheme proposed in Section III-C is DGE- 

IBE-IND-sID-CPA secure for the delegator and proxy’s 


Proof: The security proof is same as the above 

theorem except that it does not allow “A issues up to 

rekey generation queries on (ID, ID ∗ )”, for B does not 

know the private key corresponding to ID ∗ . 


then our scheme proposed in Section III-C is PKG-OW 

secure for the delegator, delegatee and proxy’s colluding. 

Proof: We just give the intuition for this 

theorem. The master-key is g2 α , and delegator’s private 

key is sk ID = (g2 α (g1 ID h) u0 , g u0 , (g2 α (g1 ID h) u1 )), 

the delegatee’s private key is sk ID ′ = 

(g2 α (g1 ID′ h) u0 , g u0 , (g2 α (g1 ID′ h) u1 )) , the proxy reencryption 

key is rk ID→ID ′ = ( αID′ +t 2+k 1 

k 3(αID+t 2) 

+ 

k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ). Because the re-encryption key 

rk ID→ID ′ is uniformly distributed in (Zp, ∗ G, G, G), and 

the original BB 1 IBE is secure, we can conclude that 

g2 

α can not be disclosed by the proxy, delegatee and 

delegator’s colluding. 

E. Toward Chosen Ciphertext Security 

As we all know, just considering IND-sID-CPA security 

is not enough for many applications. We consider 

construct IND-Pr-ID-CCA secure IBPRE based on a 

variant of BB 1 IBE. There are two ways to construct 

IND-Pr-ID-CCA secure IBPRE. One way is considering 

CHK transformation to hierarchal variant of BB 1 IBE 

to get IND-Pr-sID-CCA secure IBPRE or get IND-Pr- 

IDKEM-CCA secure IBPRE. The other way is considering 

variant of BB 1 IBE in the random oracle model. 

From a practical viewpoint, we construct an IND-Pr-ID- 

CCA secure IBPRE based on a variant of BB 1 IBE in 

the random oracle model. 

F. Our Proposed IND-Pr-ID-CCA Secure IBPRE Scheme 

Based on a Variant of BB 1 IBE 

Let G be a bilinear group of prime order p(the security 

parameter determines the size of G). Let e : G × G → 

G 1 be the bilinear map. Identities are represented using 

distinct arbitrary bit strings in {0, 1} l . The messages (or 



session keys) are bit strings in {0, 1} l of some fixed length 

l. We require the availability of five hash functions viewed 

as random oracles: 

• A hash function H 1 : {0, 1} ∗ → Z ∗ q ; 

• A hash function H 2 : G 1 × {0, 1} l → G; 

• A hash function H 3 : G 1 → {0, 1} l ; 

• A hash function H 4 : {0, 1} ∗ ×G×G×G×{0, 1} l → 

G; 

1) SetUp. To generate IBE system parameters, first 

select three integers α, β, γ ∈ Z p at random. Set 

g 1 = g α , g 2 = g t1 and h = g t2 in G, and 

compute v 0 = e(g, g) αβ . The public system parameters 

params and the masterkey are given by: 

params = (g, g 1 , g 3 , v 0 ), masterkey = (α, β, γ). 

Strictly speaking, the generator need not be kept 

secret, but since it will be used exclusively by the 

authority, it can be retained in masterkey rather 

than published in params. 

2) Extract. To generate a private key d ID for an 

identity ID ∈ {0, 1} ∗ , using the masterkey, the 

PKG picks random s 0 , s 1 ∈ Zp, ∗ choose a hash 

function ˜H : Zp ∗ × {0, 1} ∗ → Zp ∗ and computes 

u 0 = ˜H(s 0 , ID), u 1 = ˜H(s 1 , ID). It outputs: 

d ID = (d 0 , d 1 ) = (g2 α (g H2(ID) 

1 h) u0 , g u0 , 

g2 α (g H2(ID) 

1 h) u1 ). The PKG preserves (s 0 , s 1 ). 

3) Encrypt. To encrypt a message M ∈ {0, 1} l for 

a recipient {0, 1} ∗ , the sender chooses a randomly 

δ ∈ G and computes s = H 2 (δ, M), k = v0, s C 1 = 

g s , C 2 = h s g H1(ID)s 

1 , C 3 = δ·k, C 4 = M ⊕H 3 (δ), 

C 5 = H 4 (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 ) s , and then 

outputs C = (C 1 , C 2 , C 3 , C 4 , C 5 ). 

4) ReKeyGen. The PKG computes u ′ 1 = ˜H(s 1 , ID ′ ) 

and randomly selects k 1 , k 2 , k 3 ∈ Zp, 

∗ 

sets rk ID→ID ′ = ( αH1(ID′ )+t 2+k 1 

k 3(αH 1(ID)+t 2) 

+ 

k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ) and sends it to the 

proxy via secure channel. We must note that the 

PKG computes a different (k 1 , k 2 , k 3 ) for every 

different user pair (ID, ID ′ ). 

5) ReEnc. Given the identities (ID, ID ′ ), 

rk ID→ID ′ = (rk 1 , rk 2 , rk 3 , rk 4 ) = 

( αH1(ID′ )+t 2+k 1 

k 3(αH 1(ID)+t 2) 

+ k 2 , g u′ 1 k3 , g u′ 1 k2k3 , g u′ 1 k1 ), 

C ID = (C 1 , C 2 , C 3 , C 4 , C 5 ) with params, the 

proxy re-encrypts the ciphertext C ID into C ID ′ as 

follows. 

a) First it computes v 0 = e(C 5 , g) and v 1 = 

e(H 4 (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 ), C 1 ). If 

v 0 ≠ v 1 , the ciphertext is rejected. 

b) Else computes C ID ′ = 

(C ′ 1, C ′ 2, C ′ 3, C ′ 4, C ′ 5, C ′ 6, C ′ 7, C ′ 8) = 

(C 1 , C 2 , C 3 , C rk1 

2 , rk 2 , rk 3 , rk 4 , C 4 ). 

6) Decrypt. 

a) To decrypt a normal ciphertext C = 

(C 1 , C 2 , C 3 , C 4 , C 5 ) using the private key 

d ID = (d 0 , d 1 , d ′ 0), it computes v 0 = e(C 5 , g) 

and v 1 = e(H 4 (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ 

C 4 ), C 1 ). If v 0 ≠ v 1 , the ciphertext is rejected. 

The recipient computes k = e(C1,d0) 

e(C 2,d 1) 

. It then 

computes δ = 

C3 

k , M = H 4(δ) ⊕ C 4 . It 

computes s ′ = H 2 (δ, M) and verifies that 

C 1 = g s′ , C 2 = h s′ g H1(ID)s′ 

1 , if either checks 

fails, returns ⊥, otherwise returns M. 

b) To decrypt a re-encrypted ciphertext C ID ′ = 

(C 1, ′ C 2, ′ C 3, ′ C 4, ′ C 5, ′ C 6, ′ C 7, ′ C 8) ′ using the 

private key d ID = (d 0 , d 1 , d ′ 0), the recipient 

computes k = 

C ′ 3 e(rk2,C′ 4 ) 

e(C 2 ′ ,rk3)e(C′ 1 ,rk4)e(d′ 0 ,C′ C3 

1 

C ′ 3 e(C′ 5 ,C′ 4 ) 

e(C ′ 2 ,C′ 6 )e(C′ 1 ,C′ 7 )e(d′ 0 ,C′ 1 ) = 

). It then computes 

δ = 

k , M = H 3(δ) ⊕ C 8. ′ It computes 

s ′ = H(δ, M) and verifies that C 1 = g s′ , 

C 2 = h s′ g H1(ID)s′ 

1 , if either check fails, 

returns ⊥, otherwise returns M. 

G. Security Analysis 


then our scheme proposed in Section III-F is DGA- 

IBE-IND-ID-CCA secure for the proxy and delegatee’s 


Proof: Let A be a p.p.t. algorithm that has nonnegligible 

advantage in attacking the scheme proposed in 

Section III-F. We use A in order to construct a second algorithm 

B which has non-negligible advantage at solving 

the DBDH problem in G. Algorithm B accepts as input 

a properly-distributed tuple (g, g a , g b , g c , R) and outputs 

1 if R = e(g, g) abc . We now describe the algorithm B, 

which interacts with algorithm A as following. 

B simulates the random oracles H 1 , H 2 , H 3 , H 4 as 

follows. 

1) H 1 : {0, 1} ∗ → Zq ∗ . On receipt of a new query for 

ID ≠ ID ∗ , return t ← R Zq 

∗ and record (ID, t); 

On receipt of a new query for ID ∗ , select randomly 

T ∈ Zq ∗ , return T and record (ID ∗ , T ). 

2) H 2 : G 1 × {0, 1} l :→ Zq ∗ . On a new query (δ, M), 

returns s ← R G and record (δ, M, s). 

3) H 3 : G 1 :→ {0, 1} l . On receipt of a new query δ, 

select p ← {0, 1} l and return p. Record the tuple 

(δ, p). 

4) H 4 : {0, 1} ∗ × G × G × G × {0, 1} l :→ G. On 

receipt of a new query (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 ), 

select z ∈ Zq ∗ and return g z ∈ G, record (ID ‖ 

C 1 ‖ C 2 ‖ C 3 ‖ C 4 , z, g z ). 

Our simulation proceeds as follows: 

1) Setup. B generates the scheme’s master parameter 

as following. First it lets g 1 = g a , g 2 = 

g b , g 3 = g c , algorithm B picks α ∈ Z p at 

random and defines h = g −T 

1 g α′ ∈ G B lets 

params = (G 1 , H 1 , H 2 , H 3 , H 4 , g, g 1 , g 2 , g 3 , h) 

and gives params to A. 

2) Find/Guess. During the Find stage, there are 

no restrictions on which queries A may issue. 

The scheme permits only a single consecutive reencryption, 

therefore, during the GUESS stage, A 

is restricted from issuing the following queries: 

a) (extract, ID ∗ ) where ID ∗ is the challenge 

identity. 



b) (decrypt, ID ∗ , c ∗ ) where c ∗ is the challenge 

ciphertext. 

c) Any pair of queries (rkextract, ID ∗ , ID i ), 

(decrypt, ID i , c i ) 

where 

c i =Reencrypt(rk ID∗ →ID i 

, c ∗ ). 

In the Guess stage, let ID ∗ be the target i- 

dentity, and parse the challenge ciphertext c ∗ as 

(C1 ∗ , C2 ∗ , C3 ∗ , C4 ∗ , C5 ∗ ). In both phases, B responds 

to A’s queries as follows. 

• On (extract, ID), where(in the Guess)stage 

ID ≠ ID ∗ , B selects randomly 

r i ∈ Zp, ∗ sets sk IDi = (d 0 , d 1 ) = 

−α ′ 

H 

(g 1 (ID i )−T 

1 g α′ ) ri , g2 g ri ). 

We claim sk IDi is a valid random private key 

b 

for ID i . To see this, let ˜r i = r i − 

H . 

1(ID i)−T 

Then we have that 

2 (g (H1(IDi)−T ) 

d 0 = g 

−α ′ 

H 1 (ID i )−T 

2 (g (H1(IDi)−T ) 

g2(g a (H1(IDi)−T ) 

1 g α′ ) ri− b 

H 1 (ID i )−T 

g2(g a H1(IDi) 

1 h) ˜ri . 

−1 

H(ID 

d 1 = g i )−T 

2 g ri = g ˜ri . 

−1 

d ′ H(ID 

0 = g i )−T 

2 g ri = g ˜ri . 

−1 

H 1 (ID i )−T 

1 g α′ ) ri = 

• On (rkextract, ID, ID ′ ), do the same as A 

handling re-encryption key query in Phase 13 

in the above theorem. 

• On (decrypt, ID, c) where (in the Guess stage) 

(ID, c) ≠ (ID ∗ , c ∗ ), check whether c is 

a level-1 (non re-encrypted) or level-2 (reencrypted) 

ciphertext. In the Guess stage, parse 

c ∗ as (C1 ∗ , C2 ∗ , C3 ∗ , C4 ∗ , C5 ∗ ). 

For a level-1 ciphertext, B parses c as 

(C 1 , C 2 , C 3 , C 4 , C 5 ) and: 

a) Looks up the value (ID ‖ C 1 ‖ C 2 ‖ 

C 3 ‖ C 4 ) in the H 4 table, to obtain the 

tuple (ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 , z, g z ). If 

(ID ‖ C 1 ‖ C 2 ‖ C 3 ‖ C 4 ) is not in the 

table, or if (in the Guess stage) C 5 = C5 ∗ , 

then B returns ⊥ to A. 

b) Looks up the value (δ, M, s) in the H 2 

table. Checks whether there exist an item 

of (δ, M, s) such that S = g zs . If not, B 

returns ⊥ to A. 

c) Computes k = e(C1,d0) 

e(C , checks that δ = C 2,d 1) k . 

If not, B returns ⊥ to A. 

d) Checks that C 4 = H 3 (δ) ⊕ M. If not, B 

returns ⊥ to A. 

e) Otherwise, B returns M to A. 

For a level-2 ciphertext, B parses c as 

(C 1, ′ C 2, ′ C 3, ′ C 4, ′ C 5, ′ C 6, ′ C 7, ′ C 8) ′ and: 

a) Computes 

k = 

= 

C ′ 3e(C ′ 5, C ′ 4) 

e(C ′ 2 , C′ 6 )e(C′ 1 , C′ 7 )e(d′ 0 , C′ 1 ) 

C ′ 3e(rk 2 , C ′ 4) 

e(C ′ 2 , rk 3)e(C ′ 1 , rk 4)e(d ′ 0 , C′ 1 ) 

= 

b) Checks that δ = C k 

. If not, B returns ⊥ to 

A. 

c) Checks that C 2 = h s g H1(ID)s 

1 . If so, return 

M. Otherwise, return ⊥. 

• On (reencrypt, C ID , ID, ID ′ ). B runs 

ReEnc(rk ID→ID ′, C ID , ID, ID ′ ) and returns 

the results. 

At the end of the Find phase, A outputs 

(ID ∗ , M 0 , M 1 ), with the condition that A has not 

previously issued (extract, ID ∗ ). At the end of the 

Guess stage, A outputs its guess bit i ′ . 

3) Choice and Challenge. At the end of the Find 

phase, A outputs (ID ∗ , M 0 , M 1 ). B forms the 

challenge ciphertext as follows: 

a) Choose δ ∈ G 1 and p ∈ {0, 1} n randomly, 

and insert (δ, p) in H 3 table. 

b) Insert (δ, M b , , g 3 , δ · R, M b ⊕ p) to H 2 table. 

c) Choose z ∈ Z p randomly, and insert 

((g 3 , g3 α′ , δ ·R, M b ⊕p), z, g z ) in the H 4 table. 

B outputs the challenge ciphertext 

(C1 ∗ , C2 ∗ , C3 ∗ , C4 ∗ , C5 ∗ ) = (g 3 , g3 α′ , δ · R, M b ⊕ p, g3) 

z 

to A and begins the GUESS stage. 

4) Forgeries and Abort conditions The adversary 

may forge C 5 on (C 1 , C 2 , C 3 , C 4 ), but from the 

security of BLS short signature [7], this probability 

is negligible. 


then our scheme proposed in Section III-F is DGE- 

IBE-IND-ID-CCA secure for the delegator and proxy’s 


Proof: The security proof is same as the above 

theorem except that it does not allow “A issues up to 

rekey generation queries on (ID, ID ∗ )”, for B does not 

know the private key corresponding to ID ∗ . 


then our scheme proposed in Section III-F is PKG-OW 

secure for the delegator, proxy and delegatee’s colluding. 

Proof: The security proof is same as the proof for 

Theorem 3. 

IV. COMPARISON 

In this section, we give our comparison results with 

other identity based proxy re-encryption schemes[15], 

[11], [27], [29]. We compare our schemes with other 

schemes from two ways. First we concern about schemes’ 

security, then we concern about schemes’ efficiency. 

Notations: In Table I, we denote with/without random 

oracle as W/O RO, assumption as Assum, security model 

as SecMod, colluding attackers as Colluding, underlying 

IBE as UnderIBE, stand model as Std, , proxy as P, 

DGA as delegator, DGE as delegatee. P and DGA means 

that proxy colludes with delegator, P or DGA means that 

proxy or delegator is malicious adversary but they never 

collude. SymEnc-Sec means the security of symmetric 

encryption. 



TABLE I. 

IBPRE SECURITY COMPARISON 

Scheme Security W/O RO Assum SecMod Colluding UnderlyIBE Remark 

GA07A[15] IND-Pr-ID-CPA RO DBDH Sec.3.1[15] P and DGA BF IBE Weak 

or P and DGE 

GA07B[15] IND-Pr-ID-CCA RO DBDH Sec.3.1[15] P and DGA BF IBE Strong 

or P and DGE 

M07B [27] IND-Pr-sID-CPA Std DBDH Sec.4.2[27] P or DGA BB 1 IBE Weak 

or DGE 

CT07[11] IND-Pr-ID-CPA Std DBDH Sec.4.2[11] P and DGA Waters’ IBE Weak 

or P and DGE 

SXC08[29] IND-Pr-ID-CCA Std DBDH Sec.2.6[29] P and DGA Waters’ IBE Strong 

or P and DGE 

OursCIII-C IND-Pr-sID-CPA Std DBDH III-B P and DGA Variant of Weak 

or P and DGE BB 1 IBE 

OursDIII-F IND-Pr-ID-CCA RO DBDH III-B P and DGA Variant of Strong 

or P and DGE BB 1 IBE 

TABLE II. 

IBPRE EFFICIENCY COMPARISON 

Scheme Enc Check Reenc Dec Ciph-Len 

1stCiph 2-ndCiph 1stCiph 2-ndCiph 

GA07A[15] 1t e + 1t p 0 1t p 2t p 1t p 2|G| + 2|G e| 1|G| + 1|G e| 

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 | 

+2|m| + |id| +1|G e| + |m| 

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 | 

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 | 

+|vk| + |s| +|vk| + |s| 

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 | 

+2|vk| + 2|s| +1|vk| + 1|s| 

OursCIII-C 2t e + 1t p 2t p 1t e 4t p 2t p 6|G| + |G T | 2|G| + |G T | 

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 

From Table I, we can know that our IBPRE scheme 

based on a variant of BB 1 IBE scheme is the most 

secure IBPRE. M07B scheme is the weakest IBPRE for 

it can only achieve IND-Pr-sID-CPA under separated 

proxy or delegator or delegatee attack. 

In Table II, we denote encryption as Enc, reencryption 

as Reenc, decryption as Dec, ciphertext as 

Ciph and ciphertext length as Ciph-Len. t p , t e and t me 

represent the computational cost of a bilinear pairing, an 

exponentiation and a multi-exponentiation respectively, 

while t s and t v represent the computational cost of a 

one-time signature signing and verification respectively. 

|G|, |Z q |, |G e | and |G T | denote the bit -length of an 

element in groups G, Z q , G e and G T respectively. 

Here G and Z q denote the groups used in our scheme, 

while G e and G T are the bilinear groups used in GA07, 

CT07, SXC08 schemes, i.e., the bilinear pairing is 

e : G e × G e → G T . Finally, |vk| and |s| denote the 

bit length of the one-time signature’s public key and a 

one-time signature respectively. 

From Table II, Our schemes 3 , GA07 4 and M07B 

schemes are much more efficient than CT07 and SXC08 

scheme due to their underlying IBE is Waters’ IBE. 

And for the proxy, CT07 and SXC08 scheme are much 

3 Our first level ciphertext maps second level ciphertext and second 

level ciphertext maps first level ciphertext in [15], [11], [29]. Sometimes 

in our schemes we use e : G × G → G 1 or e : G 1 × G 1 → G T , in 

the former cases, G maps to G e, G 1 maps G T , in the latter case, G 1 

maps to G e, G T maps G T . 

4 GA07 and SXC08 are multi-hop IBPRE but we just consider their 

single-hop variant. 

more efficient than others for their special paradigm, our 

IBPRE scheme is more efficient than GA07B scheme 

and our other schemes, we think this is important for 

resisting DDos attack against the proxy. 

V. CONCLUSIONS AND OPEN PROBLEMS 

In 2007, Matsuo proposed the concept of four types 

of PRE schemes: CBE to CBE, IBE to CBE, CBE to 

IBE and IBE to IBE [27]. In Matsuo’s scheme, they 

allow the PKG to help the delegator and the delegatee 

to generate re-encryption key. We explore this feature 

further, if we allow PKG to generate re-encryption keys 

by directly using master − key, many open problems can 

be solved. Considering the standardization of BB 1 IBE 

and its broad applications, we give new identity based 

proxy re-encryption schemes based on BB 1 IBE, and 

prove its security in our new stronger security models. 

Furthermore, our schemes are very efficient for the reencryption 

process, which is the most heavy-load part of 

PRE. 

ACKNOWLEDGEMENT 

The authors would like to thank Dr. Jian Weng, Dr. Jun 

Shao, Dr. Licheng Wang, Dr. Fagen Li, Dr. Qiang Tang 

for many helpful discussions and the anonymous referees 

for helpful comments. 



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Jindan Zhang was born in April. 27th, 1983. She 

obtained her master degree from University of Shaanxi 

Science and Technology. Now she is a lecturer in Xianyang 

Vocational Technical College. Her main research 

interests includes cryptography, and information hiding. 

Xu An Wang was born in Feb. 23th, 1981. He obtained 

his master degree from University of Chinese Armed 

Police Force. Now he is an associate professor in the same 

University. His main research interests includes public key 

cryptography and information security. 

Xiaoyuan Yang was born in Nov. 12th, 1959. He 

obtained his master and bachelor degree from Xidian 

University. Now he is a professor in the Engineering 

University of Chinese Armed Police Force. 



Corn Moisture Measurement using a 

Capacitive Sensor 

Hongxia Zhang, Wei Liu*, Boxue Tan, Wenling Lu 

School of Electrical and Electronic Engineering, Shandong University of Technology, Zibo, China, 255049 

Abstract—Corn 

moisture content is the main factor of 

effecting corn safe transportation and storage, and is also an 

indispensable measurement part when it is 

used to feed, 

food and industry. Due to large particle size, corn will 

produce large gap during measuring moisture content. 

Because air has much influence on dielectric constant of the 

device, moisture content is not precision. In all kinds of corn 

moisture 

measurement 

methods, 

capacitance 

method 

becomes the main method with simple structure, low cost 

and online measurement. 

This paper designs a sensor for 

measuring the 

corn moisture 

that uses a capacitance 

detection circuit based on the relationship between the 

capacitance and the dielectric constant of the corn. In 

addition, different operating modes of the detection circuit 

are analyzed. The relationship between the moisture content 

of corn and the sensor capacitance is obtained through 

experiment and a binary cubic equation is obtained by the 

least squares fitting method. 

Index Terms—corn 

moisture 

sensor, detection circuit 

measurement, 

capacitive 


The moisture component of a corn cell is essential for 

maintaining its life activities. Furthermore, the moisture 

content must not be too high or too low. Higher moisture 

contents will cause corn mildew and other biochemical 

reactions. Lower moisture contents may destroy organic 

material and damage the dry matter. Hence, the 

measurement of moisture levels is important for the safe 

storage of corn [1,2] . 

The traditional method for measuring moisture content 

uses an oven which leads to high accuracy but because it 

is time-consuming and involves a complicated procedure, 

it is not suitable for field use. Various techniques for 

indirect testing methods have been studied for replacing 

the traditional oven method at home and abroad, e.g. the 

use of conductance, capacitance, X-rays, neutrons, and 

microwaves. These methods allow quick measurements 

and are easily applied under field conditions [3] . The most 

common method is the capacitive method which has 

advantages of low cost, small volume and fast detection, 

although it lacks high precision. 

Since the 1960s, many countries’ researchers attached 

great importance to the development of grain moisture 

measurement technology. Along with the measurement 

methods of grain moisture emerged, advanced grain 

moisture measurement methods and the instruments are 

being promotion at home and abroad. TABLE I and TABLE 

II show the company produced the measuring corn grain 

moisture instruments. 

TABLE I 

MOISTURE METER PRODUCED BY FOREIGN COMPANY 

Capacitance 

method 

Conductance 

method 

Decompression 

Infrared method 

Microwave method 

Carlfee Hugh 

method 

Capacitance 

method 

Conductance 

method 

Finland Humicoy company produced the 

WILE100 moisture meter [4] 

Japan KETT institute developed high frequency 

capacitive moisture meter 

European control company produced the CM - 4 

type moisture meter 

A Japanese enterprise produced VME type 

moisture meter 

British infrared engineering company produced 

the SM4 infrared moisture meter 

Japan QianYe institute produced the IR-AM300 

infrared moisture meter 

A Japan company produced the FD - 230, FD - 

310 and FD - 600 infrared moisture meter 

The battery motor manufacturing produced 

online microwave moisture meter 

A Germany company produced continuous 


Japan Kyoto electronic company produced the 

MKA - 3 type moisture meter 

TABLE II 

MOISTURE METER PRODUCED BY DOMESTIC COMPANY 

Infrared method 

East food inspection produced the SC – 5F corn 


Jinan detecting instrument company produced ly - 

8 capacitive moisture meter and LDS – 1G grain 


Shanghai Qingpu testing instrument company 

produced LDS-IF , LDS-2,LDS – IA and LDS - 

ID 

Tianjin science and technology company produced 

SFY-60 corn rapid moisture meter 

Beijing technology company produced high 

frequency capacitive grain moisture meter 

81W1PM-8188 and grain moisture meter BHC1 - 

PM818 

Beijing huatai instrument technology company 

produced JCY13 / SFY -60d moisture meter 

Wuhan electronic instrument produced LSKC - 4 

type grain moisture meter 

Hunan instrument factory balance instrument 

factory produced inserted link type moisture meter 

Hunan instrument factory balance instrument 

factory developed SCT - 3 moisture meter 

Xi’an light ministry of light industry developed 3 

YBSIA four beam infrared moisture meter 

Guangdong test analysis and wuhan combine 

automation instrument developed WSHT - 102 

type infrared moisture meter 

Tsinghua university developed near infrared 

moisture measurement instrument has completed 

the principle prototype 

*Corresponding Author: weikey@sdut.edu.cn 


doi:10.4304/jcp.8.6.1627-1631


Microwave 

method 

Neutron method 

Jilin province developed WSY - 100 microwave 

corn moisture meter 

Nanjing university developed SHD - 1 type of 

neutron moisture gauge 

II. THEORY 

The absolute permittivity divided by the permittivity of 

free space is small for samples because of the air gaps 

between particles in the container. Therefore, we adopt a 

coaxial cylinder arrangement in the design of the 

capacitive sensor to ensure the plates’ effective area is 

large enough. The electrodes of the sensor are 

asymmetrical in that the inner electrode is enveloped by 

the external one. This geometry is very effective in 

preventing human body induction. The design of the 

capacitive sensor is shown in Figure 1. 

The corn sample is placed in the media cavity between 

the two plate sensors. Changes in relative permittivity 

corresponding to different corn moisture contents cause 

variations in capacitance allowing the moisture content to 

be estimated. 

L 

R 1 

R 2 

external electrode 

media cavity 

inner electrode 

Figure 1. capacitive sensor schematic 

The cylinder height is L ; the external surface radius of 

inner cylinder is R 

1 

; the inner surface radius of external 

cylinder is R 

2 

. If L >> R2 − R1 

, the edge effect of 

cylindrical ends can be ignored. 

The capacitance of the sensor can be calculated from 

the formula [5] : 

C 

2πε 

L 

ln R R 

= (1) 

2 1 

Permittivity is understood to represent the relative 

complex permittivity. The permittivity relative to free 

space, or the absolute permittivity divided by the 

permittivity of free space [6] . 

ε 

r 

ε 

ε 

= (2) 

0 

After the sample is placed into the sensor the 

capacitance [7] is: 

C 

2πε ε L 

r 0 

= (3) 

R2 

It can be seen from the above formula that the changes 

of capacitance and relative dielectric constant of corn are 

linearly related. Since relative dielectric constant will 

change with corn moisture content, the latter can be 

obtained from the measured capacitance. 

When the corn relative dielectric constant changes 

capacitance changes 

∆ 

ε r 

Sensitivity for constant 

So 

∆C 

and ∆ε 

r 

ln 

R 

( ε 

r 

+ ∆ε 

r ) L 

−10 

∆ C = × 10 

R2 

1.8ln 

R 

ε 

rL 

− × 10 

R2 

1.8ln 

R 

1 

1 

1 

1 

−10 

∆ε 

rL 

× 10 

R2 

1.8ln 

∆C 

R1 

K = = 

∆ε 

∆ε 

r 

L 

= × 10 

R2 

1.8ln 

R 

r 

−10 

−10 

(4) 

(5) 

is linear relationship. For moisture 

content corn M , when the corn moisture content 

changes ∆ M , relative dielectric constant changes ∆ ε 

r 

, 

causes the capacitance change is ∆ C ,therefore 

is linear relationship. 

∆C 

also ∆M 

III. MEASUREMENT CIRCUIT 

Hardware structure diagram of corn moisture 

measurement system is shown in figure 2. The main parts 

are the main control circuit, capacitance detection circuit, 

temperature detection circuit and RS232 communication 

circuit. 

Capacitive sensor 

Temperature 

detection circuit 

Capacitance 

detection circuit 

M S P 4 3 0 F1 

3 5 

scre e n 

R S 232 

Communication 

circuit 

Figure2 Measuring system structure diagram 

Epistatic machine 



The working principle of moisture measurement 

system is: capacitance detection circuit and temperature 

detection circuit will set detected signal to the single-chip 

microcomputer. The single-chip microcomputer will 

received signal processing as shown on the screen. 

The capacitance and changes of capacitance are very 

small in the capacitive sensor. Hence, detection circuits 

are needed to measure the tiny capacitance increments. 

Usually we translate the tiny capacitance increments into 

a single value function of voltage, current or frequency. 

There are many transformed capacitance circuits, such as 

capacitance charging and discharging circuit, FM circuit, 

operational amplifiers circuit, common communication 

bridge method, diode double T ac electric bridge, pulse 

width modulation circuit and so on. 

In the present work we use charging and discharging of 

capacitance sensor and transforming capacitance into 

voltage. The capacitance of the sensor can be obtained 

according to the voltage 

The process of capacitance charge is 

VC 

= V ⎛ 

i ⎜1− 

e − 

⎝ 

t 

RC 

Where t denotes charging time, and RC denotes the 

time constant. The process of capacitance discharged: 

When C was charged until t 

1 

, C begin to discharging. 

The process of capacitance discharge is 

C 

⎞ 

⎟ 

⎠ 

(6) 

( = ) 

C t t 

1 

t 

RC 

V ′ = V e − 

(7) 

The measurement circuit uses the theory of capacitor 

charging and discharging which make the output signal 

change with the capacitance of the sensor. We can get the 

DC voltage signal corresponding to the changed sensor 

capacitor through difference amplifier, the same phase 

ratio amplifier and low-pass filter. Capacitive sensor 

detection circuit, equivalent detection circuit of the 

capacitance charging and equivalent detection circuit of 

the capacitance discharging can be seen from Figure 3 to 

Figure 5. 

C 

C 

Multiple 

s w itc h 

Periodic 

switch 

signals 

V C C 

R 

R 

Balance 

circuit 

Balance 

circuit 

R1 

R 1 

R 1 

- 

+ 

R1 

A 

Figure 3. Capacitive sensor detection circuit 

R1 

R 1 

R 1 

- 

+ 

R1 

A 

R1 

R1 

R1 

R1 

- 

+ 

- 

+ 

R1 

A 

R1 

A 

L o w -pass filter 


Output 

signal 

Output 

signal 

Figure 4. Equivalent detection circuit of the capacitance charging 

R 

C 

Balance 

circuit 

R1 

R 1 

R 1 

- 

+ 

R1 

A 

R1 

R1 

- 

+ 

R1 

A 


Output 

signal 

Figure 5. Equivalent detection circuit of the capacitance discharging 

VI. EXPERIMENT AND DATA ANALYSIS 

Configuration principle is important. If the default 

moisture content is lower than the original sample corn 

moisture content , we can dry corn gradually through the 

oven to reduce the corn moisture content. If the default 

moisture is higher than the original sample moisture, we 

can add water to improve corn grain moisture content. 

Calculation formula for about adding water weight [8] 

M = M 

1 

H2 − H1 

1− 

H 

Among formula, the M is added water weight. M1 is 

corn original sample weight. H1 is original sample 

moisture content. H2 is the default moisture content. 

During the process of corn sample preparation, if the 

default moisture value minus corn original sample 

moisture value is less than 10% [9] , the water can be onetime 

joined. TABLE III shows operation method of 

shaking jar of time and preparation. If greater than 10%, 

add water twice.Time about shaking jar and operation 

method such as shown in TABLE IV 

The first 

n day 

n=1 

TABLE III 

SHAKING TIME IF LESS Than 10% 

Wetting time(t/hour) 

one-time joined water 60 

t=1 15 

t=2 15 

t=3 15 

t=3~24 15 

n=2 15 

n=3 15 

n=4 15 

The first 

n day 

n=1 

n=2 

2 

Shaking time(s) 

TABLE IV 

SHAKING TIME IF GREATER THAN 10% 

Wetting time(t/hour) 

Half of total 60 

t=1 15 

t=2 15 

t=3 15 

t=3~24 15 

Another half of total 60 

t=1 15 

t=2 15 

t=3 15 

t=3~24 15 

Shaking time(s) 

(8) 



n=3 15 

n=4 15 

n=5 15 

x ′ − x ′ 

′ 2 1 

10 

= 

xn 

′ − x1 

′ 

r 

(10) 

Twelve corn samples were placed in jars of 1L. 

According to the above two kinds of operation methods 

prepared containing different moisture values of the corn 

samples. The sealed jars were stored in the laboratory of 

shady place. If the sample went bad, we must allocate the 

same corn samples to do the experiment. 

Place corn samples in the lab (laboratory temperature 

can be adjusted) and choose a temperature (through the 

temperature measurement circuit ). Using dry method 

measure a group of corn sample moisture content value, 

at the same time using the capacitive corn moisture 

measurement system collect capacitance value and 

voltage value related temperature. The data collection 

procedure as follows: 

1) Use dry method measure moisture content of a 

group of corn sample and record moisture value. 

2) At the same time a sample group will be placed in 

the cylinder of capacitive sensor. Press the reset 

button and start measuring. After a period of time, 

the results of voltage value about sensor capacitance 

and temperature will be recorded. 

3) Weigh the sample and then put into measurement, 

repeat steps 2 and record the results. 

4) Each group samples need to repeat measurement 5 

times. 

5) Another group of corn samples, repeat steps (1) - (4). 

Then configurate the same twelve groups of corn 

samples in lab (temperature changed) and repeat the 

above steps. Due to the limitation of the laboratory 

conditions, choose the five different temperatures. The 

measured data are saw in the appendix. 

In the process of data collection, the measurement of 

the personnel subjective reason, or the external condition 

of the objective causes, the results of each measurement 

can have individual measurement results and the real 

value a lot of deviation. For each group of corn samples 

more measured value, need to use some methods to 

remove or modify the deviation of measured value, the 

experiment using statistics discriminant method of Dixon 

(Dixon) criterion [10] get rid of deviation of measured 

value. 

Assuming there are normal measuring population 

x, x … x , arrangement for 

distribution of a sample 1 2 

, , 

n 

the sample x ′ , , 1 

x ′ 

2 

… x ′ 

n 

, by from big to small, 

according to the value of n can structure as shown below 

statistics, 

If n=3~7, 

x ′ 

n 

− x ′ 

n−1 

r10 

= 

x ′ − x ′ 

n 

1 

(9) 

If n=8~10, 

If n=11~13, 

If n=14~30, 

If rij r ′ 

ij 

x ′ 

n 

− x ′ 

n−1 

r11 

= 

x ′ − x ′ 

r ′ = 

11 

n 

2 

x ′ 

2 

− x ′ 

1 

x ′ − x ′ 

n−1 1 

x ′ 

n 

− x ′ 

n−2 

r21 

= 

x ′ − x ′ 

r ′ = 

r 

21 

22 

n 

2 

x ′ 

3 

− x ′ 

1 

x ′ − x ′ 

n−1 1 

x ′ 

n 

− x ′ 

n−2 

= 

x ′ − x ′ 

n 

x ′ 

3 

x ′ 

1 

r ′ 

− 

22 

= 

x ′ − x ′ 

3 

n−2 1 

> and r D ( a, 

n) 

x ′ 

n can be judged as abnormal value. 

r r ′ 

If 

ij ij 

ij 

< and r D ( a, 

n) 

ij 

(11) 

(12) 

(13) 

(14) 

(15) 

(16) 

> (Dixon coefficient), 

′ > , x ′ 

1 

can be judged as 

abnormal value. Otherwise, there is no abnormal value 

judgment. 

Experimental data obtained is discrete data, each set 

of data can not always avoid measurement error, need to 

use data fitting method to get data reflect the change 

trend of the whole of the approximate function. This 

paper collected the corn sample data based on the 

principle of least square fitting method, i.e., looking for a 

fitting curve y = s (x) to approximate show discrete data 

that coordinate relationship of function. 

All the experiments were carried out at room 

temperature and take no account of effects of 

temperature changes. Using the detection circuit to 

measure the capacitance of samples and the drying 

method to measure moisture content, we obtained the 



curve of moisture content versus capacitance as shown in 

Figure 6 . 

Using the least squares method we obtained the binary 

cubic equation linking the capacitance x(nF) and moisture 

content y(%) on the basis of the experimental data. The 

equation is shown as follow 

moisture content(%) 

32 

30 

28 

26 

24 

22 

20 

18 

16 

y x x x 

3 2 

= −0.000054149 − 0.0089798 + 0.63413 + 11.4539 (17) 

14 

0 10 20 30 40 50 60 70 80 

capacitance(nF) 

Figure 6. Plot of corn moisture content versus capacitance (the 

continuous line is the fitting curve) 

From Figure 6, we conclude that capacitance increases 

with increasing corn moisture content. 


The relationship between moisture content and 

capacitance was obtained in 8 groups of experiments. The 

moisture content of the samples can be determined on the 

basis of capacitance measured by the detection circuit. 

The error is smaller than in the drying method. We 

conclude that the accuracy in measuring moisture content 

by the capacitive sensor circuit is high and that the 

method is appropriate for accurate assessment of the 

moisture content in corn. 


The authors gratefully acknowledge assistance from Dr. 

Mike Hey from the University of Nottingham, and also 

give thanks to the Ministry of Shandong Education 

(J09LG17), who provided part of the research funding. 

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Bretterklieber. Capacitive sensing in process instrumentation, 

metrology and measurement systems, 2009; 557-568 

[10] WANG Zhaohua. Based on the active bridge of capacitive 

sensor and measuring system research. Beijing university 

of chemical, 2006:11 

[11] M.E.Casada, P.R.Armstrong. Wheat moisture measurement 

with a fringing field capacitive sensor.Transactions of 

the ASABE,vol.52(5):1785-1791 

[12] Measurement of Grain Moisture. Rice Quality Workshop, 

2003:1-5 

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measurement of moisture content and mass of single 

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ASAE, 1993, 36(1), 127-133 

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Call for Papers and Special Issues 

Aims and Scope. 

Journal of Computers (JCP, ISSN 1796-203X) is a scholarly peer-reviewed international scientific journal published monthly for researchers, 

developers, technical managers, and educators in the computer field. It provide a high profile, leading edge forum for academic researchers, industrial 

professionals, engineers, consultants, managers, educators and policy makers working in the field to contribute and disseminate innovative new work 

on all the areas of computers. 

JCP invites original, previously unpublished, research, survey and tutorial papers, plus case studies and short research notes, on both applied and 

theoretical aspects of computers. These areas include, but are not limited to, the following: 

• Computer Organizations and Architectures 

• Operating Systems, Software Systems, and Communication Protocols 

• Real-time Systems, Embedded Systems, and Distributed Systems 

• Digital Devices, Computer Components, and Interconnection Networks 

• Specification, Design, Prototyping, and Testing Methods and Tools 

• Artificial Intelligence, Algorithms, Computational Science 

• Performance, Fault Tolerance, Reliability, Security, and Testability 

• Case Studies and Experimental and Theoretical Evaluations 

• New and Important Applications and Trends 

Special Issue Guidelines 

Special issues feature specifically aimed and targeted topics of interest contributed by authors responding to a particular Call for Papers or by 

invitation, edited by guest editor(s). We encourage you to submit proposals for creating special issues in areas that are of interest to the Journal. 

Preference will be given to proposals that cover some unique aspect of the technology and ones that include subjects that are timely and useful to the 

readers of the Journal. A Special Issue is typically made of 10 to 15 papers, with each paper 8 to 12 pages of length. 

The following information should be included as part of the proposal: 

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• Name, contact, position, affiliation, and biography of the Guest Editor(s) 

• List of potential reviewers 

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If a proposal is accepted, the guest editor will be responsible for: 

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Special Issue for a Conference/Workshop 

A special issue for a Conference/Workshop is usually released in association with the committee members of the Conference/Workshop like 

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Guest Editors are involved in the following steps in guest-editing a Special Issue based on a Conference/Workshop: 

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Information about the Journal and Academy Publisher can be included in the Call for Papers. 

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• Writing a one- or two-page introductory editorial to be published in the Special Issue. 

More information is available on the web site at http://www.academypublisher.com/jcp/.

Deformed Kernel Based Extreme Learning Machine 

Chen Zhang, Shixiong Xia, and Bing Liu 

Optimal Sleep Scheduling Scheme for Wireless Sensor networks Based on Balanced Energy 

Consumption 

Shan-shan Ma, Jian-sheng Qian, and Yan-jing Sun 

Identity Based Proxy Re-encryption From BB1 IBE 

Jindan Zhang, Xu An Wang, and Xiaoyuan Yang 

Corn Moisture Measurement using a Capacitive Sensor 

Hongxia Zhang, Wei Liu, Boxue Tan, and Wenling Lu 

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(Contents Continued from Back Cover) 

Intrusion Detection Based on Improved SOM with Optimized GA 

Jian-Hua Zhao and Wei-Hua Li 

Fault Diagnosis System for NPC Inverter based on Multi-Layer Principal Component Neural Network 

Danjiang Chen, Yinzhong Ye, and Rong Hua 

Pulse Wave K Value Averaging Computation and Pathological Diagnosis 

Li Yang, Jinxue Sui, and Yunan Hu 

Multi-Step Prediction Algorithm of Traffic Flow Chaotic Time Series based on Volterra Neural 

Network 


Adaptive Tracking Control for Nonaffine Nonlinear Systems with Zero Dynamics 

Hui Hu and Peng Guo 

Improved Feasible SQP Algorithm for Nonlinear Programs with Equality Constrained Sub-Problems 

Zhijun Luo, Guohua Chen, Simei Luo, and Zhibin Zhu 

Finite Element Analysis Based Design of Mobile Robot for Removing Plug Oil Well 

Xiaojie Tian, Yonghong Liu, Rongju Lin, Baoping Cai, Zengkai Liu, and Rui Zhang 

Contour Error Coupled-Control Strategy based on Line Interpolation and Curve Interpolation 

Guoyong Zhao, Hongjing An, and Qingzhi Zhao 

Research of Leaf Quality Based on Snowflake Theory 

Lihui Zhou, Jiajia Sun, Juanjuan An, and Jun Long 

Oscillation Criteria for Second Order Nonlinear Neutral Perturbed Dynamic Equations on Time 

Scales 

Xiuping Yu, Hua Du, and Hongyu Yang 

Improved Quantum Ant Colony Algorithm based on Bloch Coordinates 

Xiaofeng Chen, Xingyou Xia, and Ruiyun Yu 

Image Fusion Method Based on Directional Contrast-Inspired Unit-Linking Pulse Coupled Neural 

Networks in Contourlet Domain 

Xi Cai, Guang Han, and Jinkuan Wang 

The Critical Legal Contention under the Challenge of Information Age and the Predominant Social 

Interests Concern for Developing Intelligent Vehicle Telematics in the United States 

Fa-Chang Cheng and Wen-Hsing Lai 

MPC Controller Performance Evaluation and Tuning of Single Inverted Pendulum Device 

Chao Cheng, Zhong Zhao, and Haixia Li 

A Metadata-driven Cloud Computing Application Virtualization Model 

Yunpeng Xiao, Guangxia Xu, Yanbing Liu, and Bai Wang 

Robust Portfolio Optimization with Options under VE Constraint using Monte Carlo 


A Novel Water Quality Assessment Method Based on Combination BP Neural Network Model and 

Fuzzy System 


An Isolated Dual-Input Converter for Grid/PV Hybrid Power Systems 

Yu-Lin Juan, Hsin-Ying Yang, and Peng-Lai Chen 

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