Neuro Fuzzy and Gray Box Modeling of Supercritical ... - ISSF 2012

ABSTRACT
Neuro Fuzzy and Gray Box Modeling of Supercritical
Fluid Extraction of Pimpinella Anisum L. Seed
Meysam Davoody 1 , Gholamreza Zahedi 1 , Mazda Biglari *,2 , M. Angela A. Meireles 3
1 Process Systems Engineering Centre (PROSPECT), Faculty of Chemical Engineering
Universiti Teknologi Malaysia, UTM Skudai, 81310 Johor Bahru, Johor, Malaysia
2 Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
*Corresponding author: mbiglari@uwaterloo.ca
3 LASEFI/DEA/FEA (School of Food Engineering)/UNICAMP (University of Campinas)
Rua Monteiro Labato, 80; 13083-970 Campinas, São Paulo, Brazil
In the current study, a Neuro-Fuzzy model has been developed to predict the mass of extract in the process of
supercritical fluid extraction of Pimpinella anisum L. seed. The adaptive-network-based fuzzy inference system
(ANFIS) technique was trained with the recorded data from kinetic experiments of the mentioned process at
pressures of 8, 10, 14 and 18 MPa and constant temperature of 303.15 K which generated the membership
function and rules that excellently expounded the input/output correlations in the process. Great prediction with
Root Mean Square Error (RMSE) of 0.0235 was observed. In the next step, mass transfer coefficient in terms of
Sherwood number was estimated by a neuro-fuzzy network. Then, the estimated mass transfer coefficient was
introduced into the mathematical model. The proposed gray box (hybrid) model was validated with the
experimental data. Results confirmed that equipping mathematical model with neuro-fuzzy network to estimate
one of its variables, improved performance of the model significantly. Finally, all four models (including two
proposed models in this study) of the process were compared. It was concluded that neuro-fuzzy and gray box
models had the best performance.
INTRODUCTION
Anise belongs to the Umbelliferae family and originates from Asian countries, Egypt, and Greece. It is cultivated
in Turkey, Russia, South Africa, Latin America, and Brazil. In general, the essential oil is extracted from the
fruits, but the roots may also be used [1]. The phyto therapeutic applications of the plant include digestive,
carminative, diuretic, and expectorating actions. Anise infusions are largely used for problems in the intestinal
tract. Aniseed oil is used in food processing to impart flavor to cakes, alcoholic beverages such as liquors, sweet
snacks, and so on [1]. Anethole, the aniseed oil major compound, is largely used as a substrate for the synthesis
of various substances of pharmaceutical interest such as chloral, an anticonvulsion agent, and pentobarbital [2].
Pourgholami et al. [3] investigated the anticonvulsant effects of Pimpinella anisum essential oil. Boskabady and
Ramazani-Assari [4] reported the bronchodilatory effects of the essential oil, the aqueous extract, and the
ethanolic extract of Anis; the authors concluded that the relaxant effect of the plant is not due to an inhibitory
effect of histamine but instead due to inhibitory effects on muscarinic receptors.
Supercritical fluid extraction (SFE) has proven to be technically and economically feasible, presenting several
advantages when compared to traditional extraction methods [5]. The interest in SFE process is primarily due to
the ability to recover functional ingredients with high purity [6]. Carbon dioxide (CO2) has been the solvent of
choice for most SFE studies primarily because it has a relatively low critical temperature and pressure, low
toxicity, relatively high purity and low cost [7].
In order to reach the optimum operational condition for a SFE process, many authors model this process using
either mathematical modeling or artificial neural network (ANN) modeling. Meireles et al. [8] mathematically
modeled supercritical fluid extraction of oil from the vetiver root. Hatami et al. [9] also applied a mathematical
model on SFE of oil from clove buds to determine optimum temperature and pressure and also the effect of these
parameters on the mass of extract. In both cases CO2 was employed as the solvent. Hatami et al. [10] studied the
extraction of volatile oil from Khoa. The experiment was done with both presence and absence of the co-solvent
(ethanol). They then managed to apply a mathematical model on the process. Another popular approach for
modeling the SFE processes has been ANN. Izadifar and Abdollahi [11] employed a feed-forward multi-layer
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neural network to predict yield for the SFE of black pepper essential oil. Shokri et al. [12] have applied both
mathematical and ANN modeling on the SFE of Pimpinella anisum L. seed. They found the results of ANN
more accurate and reliable in comparison with those of mathematical modeling. In case of gray box, Azizi et al.
[13] have employed Neuro-Fuzzy network to design a gray box for estimating the yield of nimbin extraction
from neem seeds. Agreement with the experimental data was the best feature of their designed network outputs.
PROBLEM STATEMENT
Neuro-Fuzzy has not been widely employed on chemical engineering case studies. Mehrabi and Pesteei [14]
applied Neuro-Fuzzy approach for modeling of heat transfer convection by a turbulent supercritical carbon
dioxide flow. They found the designed model efficient and valid. KaanYetilmezsoy et al. [15] stated that
utilizing Adaptive Neuro-Fuzzy Inference Systems (ANFIS) approach has a superior predictive performance on
forecasting water-in-oil emulsions stability. In the field of SFE, all referred literatures have applied classical
methods and statistical techniques on SFE case studies, but this paper employs a new approach (Neuro-Fuzzy) in
order to achieve more accurate predictions.
In the current study, supercritical fluid extraction of Pimpinella Anisum L. seed is modeled by ANFIS
methodology in order to design a reliable network for estimation. Therefore, the development of an artificial
intelligence modeling scheme using the ANFIS methodology was described. The proposed neuro-fuzzy model
considered pressure, mass flow rate, feed mass, and time data as the input variables which are readily available
for most of the extractions. In the next part, a network was designed (by Neuro-Fuzzy approach) to estimate
Sherwood number (Sh) which served as a black box. The designed black box was combined by the mathematical
model proposed by Shokri et al. [12] (which serves as the white box) in order to make a powerful gray box with
an acceptable performance. Their proposed mathematical model was designed based on specific variables such
as external mass transfer coefficient (kf) which is highly dependent on Sh. They then calculated Sh by a
correlation given by Zahedi et al. [16]. In the current study we show that replacing the mentioned correlation by
neuro-fuzzy approach would result in more reliable Sh numbers which positively can affect the model
performance. Based on the discussed facts, the objectives of this study were (1) to develop an ANFIS-based
neuro-fuzzy network for modeling the process of SFE of Pimpinella Anisum L. seed, (2) to design a gray box
model by using neuro-fuzzy approach, and (3) to compare the performance of our proposed approache with the
previous ones.
MATERIALS AND METHODS
Neuro-Fuzzy approach
Neuro-Fuzzy is a combination of two approaches: ANN and fuzzy logic, summarized below.
Artificial Neural Networks
The history of ANN began with the pioneering work of McCulloch and Pitss [17] who first introduced the idea
of ANN as computing machines. Ability to find nonlinear and complex relationships has been the main reason
for the popularity of ANN application in various branches of science and also in industrial managements [18,
19]. Image processing [20], document analysis [21], engineering tasks [22, 23], financial modeling[24],
biomedical [25] and optimization [26] could be perfect examples of the various applications of ANN in different
branches of science.
One of the serious problems with ANN is lack of interpretation. Wieland et al. [27] claimed that ANN fails to
improve the explicit knowledge of the user. Limitations in catching casual relationships between major system
components were mentioned as the main reason. Another fact to notice is that ANN reasoning is from the inputs
to the outputs, therefore in cases that the opposite is demanded (input based on the given output), it won’t be a
suitable choice. There are also specific issues regarding fuzzy inference system (FIS) which demand a better
understanding [28].
ANFIS
The idea of ANFIS arises from the limitations and problems of ANN and FIS which tries to design more reliable
approach by combining them. ANFIS, which used to stand for adaptive network-based fuzzy inference system,
was proposed by Jang [28]. ANFIS was changed to “adaptive neuro-fuzzy inference systems” when Jang and
Sun [29] found no difference between the aim of this expression with the other one.
Operations in ANFIS are similar to those in FFBP (feed forward back propagated) ANN. Fuzzy rules connect
the antecedent and conclusion parts to each other. Hybrid learning method and back propagation are the main
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choices for learning methods. In fuzzy section, only zero or first-order Sugeno inference system or Tsukamoto
inference system can be used, and output variables are achieved by applying fuzzy rules to fuzzy sets of input
variables [30, 28, 31, 32]:
Rule 1: if x is A1 and y is B1, then f1 = p1x + q1y + r1 (1)
Rule 2: if x is A2 and y is B2 , then f2 = p2x + q2y + r2 (2)
where p1, p2, q1 and q2 are linear parameters and A1, A2, B1 and B2 nonlinear. Figure 1 shows architecture of a two
input first-order Sugeno FIS model with two inputs and rules. Architecture includes five layers: fuzzy layer,
product layer, normalized layer, defuzzy layer, and a total output layer.
.
Figure 1. ANFIS architecture of a two input model with two rules.
Each node in this Figure represents a node function which has an adjustable parameter, and nodes in the same
layers follow samilar functions. The learning algorithm of neural network seeks for the best values of model
parameters, and performance of the network is evaluated based on training and testing data. The main task of the
mentioned learning algorithms (back propagation and hybrid learning) is to reach the minimized amount of
errors like in the Root Mean Square Error (RMSE) methodology. The next section discusses the procedure of
transforming input to output in ANFIS based on the five mentioned layers.
As seen in Figure 1, fuzzy layer consists of nodes A1, A2, B1 and B2, which receive the inputs x and y,
respectively. A1, A2, B1 and B2 represent linguistic labels or fuzzy sets (like fast, big, etc), which apply fuzzy
membership functions, and determine to which degree each input belongs to the sets. This mapping can be
shown as:
Q1,i = µAi(x), for i = 1, 2 or (3)
Q1,i = µBj(y), for j = 1, 2 (4)
in which x (or y) is the input to node i and Ai (or Bj) is the fuzzy set. Q1,i determines the degree to which the input
belongs to the set. µAi(x) or µBj(y) usually denotes the Guassian curve or the generalized bell-shaped membership
functions with a maximum equal to 1 and minimum equal to 0, such as [28, 33]:
1
µ A ( x)
=
(5)
i 2
⎛⎛ ci
⎞⎞
1+
⎜⎜
⎜⎜ x − bi
a ⎟⎟
⎟⎟
⎝⎝ i ⎠⎠
µ (x) = e Ai − x−ci $
# ai "
2
%
'
&
3
(6)

where {ai, bi, ci} is the parameter set. The bell-shaped functions change based on changes of these parameters,
resulting in different forms of membership functions.
There are two nodes labeled “П” in the product layer. As they receive the signals, they multiply it and make the
layer outputs (w1 and w2) which will be the weight functions of the next layer. The output of this layer can be
expressed as [28, 30, 34]:
Q2, i i Ai Bj
= w = µ ( x)
µ ( y)
for i = 1, 2 and j = 1, 2 (7)
where Q2,i stands for the product layer output.
The layer with nodes labeled “N” is the normalized layer. The outputs of the previous layer’s nodes represented
the firing strength of a rule [28, 33]. The ith node calculates the ratio of the ith rules firing strength to the sum of
all rule’s firing strengths [15]. The weight function gets normalized by [28, 30, 33, 34]:
Q
3,
i
wi
= wi
=
for i = 1,2 (8)
w + w
1
2
Therefore, the output of this layer (Q3,i) is called the normalized firing strengths.
The fourth layer with adaptive nodes is the defuzzy layer. In fact, the signals which have been fuzzified at the
beginning of the process get defuzzifed and return to normal form. The relationship in this layer can be written
as [28, 30, 33-34]:
Q = w f = w ( p x + q y + r ) for i = 1,2 (9)
4, i i i i i i i
The output of layer four is Q4,i while i w stands for normalized firing strength from layer 3, and {pix + qiy + ri}
represents the parameter set.
The last layer with a single node labeled “Ʃ” is total output layer, which represents the final decision according
to [30, 28, 33, 34]:
Q5,i = overall output =
∑
∑
∑
=
i
i fi
i
Here Q5,i refers to the output of the last layer.
wi
fi
w (10)
w
i
i
ANFIS combines ANN and fuzzy-logic in order to benefit their advantages. It follows the ANN topology with
fuzzy-logic, and aims to remove the disadvantages of the both which makes this method to be able to deal with
complex and nonlinear cases. Even ANFIS can achieve acceptable results when it is not provided by the target
values. Unlike ANN, there is no vagueness in ANFIS [29, 31]. In addition, shorter time of learning duration in
ANFIS in comparison with ANN implies that ANFIS can achieve the demanded target faster. So, it can be
concluded that using ANFIS instead of ANN in sophisticated and complex systems can be more effective in
order to overcome the complexity of the problem [31].
In this study, ANFIS is employed to model the process of supercritical fluid extraction of Pimpinella Anisum L.
seed. Since the process has been modeled before using mathematical modeling and also ANN [12], it is expected
that applying ANFIS on this case can come up with a more accurate and reliable network. After evaluating the
designed ANFIS with experimental data, the performance of all four models including mathematical model,
ANN, ANFIS, and gray box (see the next section), were compared and the results are presented.
Gray box
Building mathematical models demand three approaches:
i. White box, where everything is considered to be known from physical laws
ii. Black box (system identification), where everything are driven from measurements
iii. Gray box, where both physical laws and observed measurements are used to design a model.
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Gray box assumes structure of the model is given from physical laws as a parameterized function [35]. Then, by
means of observed data, the model parameters are achieved. The ‘gray box’ is a term that describes the symbolic
approach to engineering computation that offers distinct benefits in education and research.
White box deals with investigating the equation model which works effectively in catching implementation
error. A black box investigates a running program by probing it with various inputs. While black box modeling
is found much easier to accomplish and demands less expertise, white box modeling is believed to be reliable in
case of knowledge detection of an equation. Gray box modeling aims to combine both techniques in the best
way. As a result, white box modeling analyzes the behavior of an equation statically and black box scans the
system across the networks.
Shokri et al. [12] have designed the mathematical model of the process and have reported the RMSE of this
model in different experiments. As discussed before, one of the serious problems of this model was related to
determining the amount of kf (mass transfer coefficient) which is highly dependent on Sherwood number (Sh).
Any mistake in calculating Sh can affect the performance of the whole network. The idea of this study is to
design a neuro-fuzzy network which is able to predict Sh based on the conditions of the problem. It is expected
that due to the excellent performance of ANFIS in similar cases, the estimated Sh has the least error, and
therefore, reduces the performance error of the network compared to mathematical modeling. Figure 2 illustrates
schematically the procedure of designing gray box.
RESULTS AND DISCUSSIONS
Figure 2. Gray box model to estimate mass of the extract.
ANFIS
The operational condition for four experiments are reported in Table 1 [12].
Table 1. Operational condition for four experiments.
Conditions Exp. 1 Exp. 2 Exp. 3 Exp. 4
T(K) 303.15 303.15 303.15 303.15
P(MPa) 8 10 14 18
Q (kgs -1 ) × 10 5 1.23-5.17 1.35-5.95 1.82-4.45 2.33-4.60
During the designing of an ANFIS network, data sets can be divided into two parts: “train” and “test” data. It is
obvious that train data are applied for training the network and teaching it how input/output data correlation
should be.
In this paper, 349 data set have been used to design the neuro-fuzzy network which can estimate mass of the
extract as the target variable with four variables (time, pressure, flow rate, and feed mass). These data were
adopted from M.A.A. Mireles’ work, one of the authors. 261 data sets (75% of the whole data) have been
selected for training the network and the remaining 88 data were used for testing the network to check whether
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the network can estimate unused inputs as well as training data or not. It was verified that the best type of
membership function was “Triangular-shaped built-in membership function” for the network.
In this section, mean square error (MSE), root mean square error (RMSE), and regression have been applied to
describe ability of the obtained network. Table 2 shows the statistical performance and the proposed ANFIS
model. Both of the error measurements (RMSE and MSE) are reasonably low and the results can be trusted as a
good estimation for further use. Since the network is designed based on the training data, it is reasonable that
errors in training are much lower than testing, as expected. Furthermore, the model reaches the test relative error
of 1.98 which confirms the outputs of the network are in excellent agreement with the real/target data.
Table 2. Statistical performance of the ANFIS model.
During Training During Test
RMSE MSE R RMSE MSE R
0.0179 0.0003 0.9994 0.0353 0.0012 0.9998
Gray box results
After designing a neuro-fuzzy network with acceptable results (train RMSE = 0.0000998, test RMSE= 0.00048),
the estimated Sh replaced the previous one calculated by Zahedi et al. correlation [16]. A new kf was calculated
and the approach continued until convergence. Table 3 shows the statistical performance of the designed gray
box. As predicted before, performance of the model has been much improved. In addition, the model outputs
were compared with the real four experimental data.
Table 3. Statistical performance of the gray box.
During Training During Test
RMSE MSE R RMSE MSE R
0.0458 0.0021 0.9994 0.0583 0.0034 0.9998
Incorporation of neuro-fuzzy network into the gray box resulted in more accurate predictions. Obviously the
model benefited from more accurate Shs resulting in more accurate modeling of the process main variables.
Comparison between all models
Table 4 presents the RMSE comparison between the results of our two models and two model results from [12].
In Table 4, RMSE 1, 2, 3, and 4 refer to RMSE of the mathematical model, ANN, Gray Box, and ANFIS,
respectively. It is concluded that ANFIS has the best and the mathematical model has the worst performance.
The proposed grey box presented the second accurate predictions while ANN provided results only better than
the mathematical model.
CONCLUSIONS
Two new approaches were employed to model the process of SFE of Pimpinella Anisum L. seed. ANFIS and
Gray Box were utilized to accurately model SFE experimental data. There was also a comparison with other
modeling approaches. The errors involved in ANFIS were insignificatn while the errors of the gray box
modeling was satisfactorily small. Lastly, RMSE of four models were compared with each other concluding that
the ANFIS model is the best. In general the modeling approach presented in this study improved predictions.
Critical point to notice is the significant statistical difference between the neuro-fuzzy and the gray box networks
when used to calculate Sh number. Although the results of the gray box were founded acceptable, they are
weaker than those of proposed by ANFIS modeling (black box). It is concluded that in addition to Sh, there are
other parameters which are not estimated properly (e.g. dispersion coefficient). The authors encourage further
use of artificial intelligence instead of using specific correlations in estimating other critical parameters.
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Regarding the process modeling this study showed that ANFIS provides quite accurate results. It also indicated
that the neuro-fuzzy networks performance could be improved by designing gray boxes when few experimental
data are available.
ACKNOWLEDGEMENT
The authors would like to thank Prof. M.A.A. Meireles, Professor of Food Engineering, University of Campinas,
São Paulo, Brazil, for the experimental data of Anise extraction. Financial support of Ministry of Higher
Education (MOHE) Malaysia under RUG, QJ130000.2525.00H81 is gratefully acknowledged.
REFERENCE
Table 4. Statistical performance of all four models.
Experiment P(Mpa) Q RMSE 1 RMSE 2 RMSE 3 RMSE 4
1 8 1.23 0.0321 0.0279 0.0269 0.0024
8 2.58 0.0357 0.0581 0.0387 0.0115
8 3.35 0.0578 0.0414 0.0329 0.0029
8 3.42 0.0666 0.0298 0.0308 0.0027
8 5.17 0.0703 0.0502 0.0439 0.0162
2 10 1.35 0.0221 0.0305 0.0209 0.0049
10 1.88 0.0716 0.0243 0.0221 0.0163
10 2.38 0.0998 0.0404 0.0398 0.0187
10 3.47 0.1266 0.0573 0.0489 0.0294
10 3.55 0.1188 0.0760 0.0599 0.0586
10 5.95 0.0958 0.1283 0.0756 0.0329
3 14 1.82 0.0670 0.0350 0.0490 0.0032
14 2.35 0.0926 0.0355 0.0348 0.0162
14 3.27 0.0753 0.0276 0.0208 0.0109
14 3.57 0.0642 0.0413 0.0453 0.0067
14 4.45 0.1033 0.0137 0.0122 0.0075
4 18 2.33 0.0649 0.0206 0.0107 0.0046
18 3.32 0.1141 0.0480 0.0413 0.0471
18 3.45 0.0773 0.0323 0.0132 0.005
18 4.6 0.0841 0.03 0.0193 0.0016
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