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J. Biomedical Science and Engineering, 2010, 3, 430-438 JBiSE doi:10.4236/jbise.2010.34059 Published Online April 2010 (http://www.SciRP.org/journal/jbise/). Published Online April 2010 in SciRes. http://www.scirp.org/journal/jbise Fermentation process modeling of exopolysaccharide using neural networks and fuzzy systems with entropy criterion Zuo-Ping Tan1,2,3, Shi-Tong Wang1, Zhao-Hong Deng1, Guo-Cheng Du2 1School of Information Engineering, Jiangnan University, Wuxi, china; 2Key Laboratory of Industrial Biotechnology, Ministry of Education, Jiangnan University, Wuxi, China; 3Jiangsu Province Key Laboratory of Information Technology at Suzhou University, Suzhou, China. Email: wxwangst@yahoo.com.cn Received 17 December 2009; revised 28 December 2009; accepted 12 January 2010. . ABSTRACT The prediction accuracy and generalization of fer- mentation process modeling on exopolysaccharide (EPS) production from Lactobacillus are often dete- riorated by noise existing in the corresponding ex- perimental data. In order to circumvent this problem, a novel entropy-based criterion is proposed as the objective function of several commonly used model- ing methods, i.e. Multi-Layer Perceptron (MLP) net- work, Radial Basis Function (RBF) neural network, Takagi-Sugeno-Kang (TSK) fuzzy system, for fer- mentation process model in this study. Quite different from the traditional Mean Square Error (MSE) based criterion, the novel entropy-based criterion can be used to train the parameters of the adopted mod- eling methods from the whole distribution structure of the training data set, which results in the fact that the adopted modeling methods can have global ap- proximation capability. Compared with the MSE- criterion, the advantage of this novel criterion exists in that the parameter learning can effectively avoid the over-fitting phenomenon, therefore the proposed criterion based modeling methods have much better generalization ability and robustness. Our experi- mental results confirm the above virtues of the pro- posed entropy-criterion based modeling methods. Keywords: Relative Entropy; MSE-Criterion Based Modeling; Robustness; Parzen Window; TSK Fuzzy System 1. INTRODUCTION Polysaccharides are produced by plants, algae and bacte- ria, which are used in pharmaceutical, chemical, pesti- cide and oil exploitation. Some microorganisms such as the lactic acid producers are known to synthesize e xo po ly - saccharides (EPS), which can be used commercially as food additives and have health stimulating properties such as immunity stimulation, anti-ulcer activity and cholesterol reduction. However, as we may know well, EPS’s fermentation mechanism is very comp lex because it refers to the growth and reproduction of microorgan- isms [1]. In view of control, fermentation process con- tains high non-linearity, high time-varying and uncer- tainty. Meanwhile the lack of biosensor and the interac- tion of coupled parameters also bring much difficulty for the fermentation process modeling [2]. In the last decade, artificial neural networks (ANNs) have been proved to be able to model nonlinear systems and successfully applied in various chemical and biological models [3]. Especially they have emerged as an attractive tool for predicting and approximating the parameters in fermen- tation process [4], and demonstrated their powers in the factorial design [5]. More examples include one ANNs- based model for amino acid composition and optimum pH in G/11 xylanase [6], and another ANNs -ba sed mo del for optimization of fermentation media for exopolysac- charide production from Lactobacillus plantarum [7]. In recent years, fuzzy systems and/or fuzzy neural networks researchers have paid particular attention on industrial fermentation process modeling [8]. For instance, fuzzy neural network has been used for dissolved Oxygen pre- dictive control of fermentation process [9], and Takagi- Sugeno-Kang (TSK) fuzzy system has been used for biochemical variable estimation of fermentation process [10]. In addition, an application of fuzzy control in cit- ric acid fermentation process has been adopted to maxi- mize the biomass quantities [11]. However, when MSE- criterion based objective function is used for model pa- rameter learning, the above methods have the so-called over-fitting drawback, that is t o say, M SE- cri ter ion ba sed modeling methods may over-fit each training sample such that the whole distribution of the training set is er- rously estimated and the generalization ability can not b e assured. In this study, in order to overcome the weaknesses Z. P. Tan et al. / J. Biomedical Science and Engineering 3 (2010) 430-438 Copyright © 2010 SciRes. JBiSE 431 mentioned above, the new criterion is proposed as the objective function for fermentation process modeling. This new criterion, called the entropy criterion, is based on the probability density estimation for the whole train- ing set and relative entropy [12]. And then the proposed criterion is used in the classical Multi- Layer Percep tron (MLP) network modeling, Radial Basis Function (RBF) neural network modeling and Takagi-Sugeno-Kang (TSK) fuzzy system modeling, for the EPS fermentation proc- ess modeling. 2. MATERIALS AND METHODS The data we used in this study wa s derived from the ref- erence [7]. This project was conducted in 2004-2006 by Mumbai University of Food Engineering, in Mumbai, India. 2.1. Bacterial Strain Lactobacilli strain is isolated from the Indian fermented food ragi. This isolation is characterized as Lactobacillus plantarum using biochemical tests. 2.2. Medium The medium contain lactose, casine hydrolysate, triam- monium citrate, beef extract and proteose peptone, along with sodium acetate: 1 g/l, Mg-sulfate: 1 g/l, manganese sulfate: 0.5 g/l and calcium chloride: 0.25 g/l. The me- dium are autoclaved at 110℃ for 10 min; lactose is autoclaved separately. 2.3. Fermentation Conditions The batch fermentation is carried in a 250 ml shake flask for 24 h at 150 rpm and 35℃. The pH of the fermenta- tion medium is adjusted to 6.5 ± 0.3 with the addition of 1N NaOH/1N HCL. Flasks at the end of fermentation are analyzed for EPS productio n. 2.4. Analysis The cells are separated by centrifugation(10,000 rpm, 10℃, 15 min) and the crude EPS is precipitated from the broth at 4 by the addition of two volumes of col d ethanol (95﹪). The resulting precipitate is collected by centrifugation and re-dissolved in water. The crude EPS solution is dialyzed at 4℃ to estimate the yield. 2.5. MSE-Criterion Based Fermentation Process Modeling In most of current modeling methods, the MSE-criterion based objective function is often used for training model parameters. The MSE-criterion can be formulated as 2 11 1() 2 N idi i Eyy N (1) where , idi yy are the predicted and desired outpu t for ith sample , respectively. From Eq.1, we can see that the MSE-criterion based model parameter learning is just a local approximation process and does not consider the whole distribution of the training set [13,14], thus the generalization and ro- bustness of the model will not be ensured and the over-fitting often occurs, espe cially when there are no ises in the training data. 3. ENTROPY-CRITERION BASED FERMENTATION PROCESS MODELING 3.1. Relative Entropy and Jeffreys-Divergence Entropy Entropy is a measurement of uncertainty in information theory, which is a function of the probability density distribution. The concept of relative entropy can be in- troduced to measure the difference between certain probability density distribution 1i f x and a given prob- ability density distribu tion 2i f x, which may be written as follows [12,15], 1211 2 (,)( )log[( )/( )]0 iii Vfffxfxf x (2) where the smaller value of relative entropy is, the larger difference between the two density distributions is. Meanwhile, when certain p robability dens ity distribution is equal to the given distribution, the relative entropy will reach its maximum (equal to zero). It is well known that relative entropy is additive an d non-symmetrical. To obtain a symmetrical measure, Jeffreys-divergence en- tropy (J-divergence entrop y) can be used. I t is also called symmetrical relative entropy which can measure the difference between two densities 1i f xand 2i f x. 1212 21 112 221 112 2 12 21 (, )(, )(,) ()log[()/()] ()log[()/ ()] ()log[()]()log[()] ()log[()] ()log[()] iii iii iiii ii ii Wf fVf fVff fxfxfx fxfx fx f xfx fxfx f xfx fxfx (3) According to the above J-divergence entropy, a novel objective function based on entropy-criterion will be illus- trated in the next subsection. 3.2. Relative Entropy Based Objective Function For a given training sample set ,1,2,..., d idiidi yRyRi Nxx，，, we can re- construct two new sets, i.e., one contains the sample inputs and the sample outputs,'' 1{(,)} iii di Syzz x, Z. P. Tan et al. / J. Biomedical Science and Engineering 3 (2010) 430-438 Copyright © 2010 SciRes. JBiSE 432 ''d iRz ('1dd), and the other contains the sample inputs and the model predicted outputs, 2 S '' '' {(,)} iii i y zz x, '''d iRz. For the above sample set 1,2,..., d ii RiNxx ，, its probability density can be estimated with the follow- ing parzen win dow density estimator, 2 2 1 1 (,)( 2)i Nd i fe N xx x (4) where represents the window width. For a given data, it is constant and can be used to effectively esti- mate the corresponding density distribution. Here with maximum likelihood estimation (MLE), it is determined through cross-validation (CV) method, and the value resulting in the max magnitude is chosen [16]. For the above two data sets 1 Sand 2 S, their probabi- lity density distribu tion functions, 1(, )fz and 2(, )fz , can be formulated as ' '2 2 11 1 (,)( 2) i d N i fe N zz z (5) '' '2 2 21 1 (,)( 2) i d N i fe N zz z (6) Suppose ' 2 '2 2 (,) i Ge zz zz , then we get, ' 1 '2 11 (2 ) (, )(,) dN t fG N zzz (7) ' 2 '' 2 21 (2 ) (, )(,) dN t fG N zzz (8) By using the properties of relative entropy, the bigger the value of relative entropy is, the smaller the difference between two probability densities is, as aforementioned. When the relative entropy reaches its maximal v alue, the two density functions will absolutely be the same, i.e., 2(, )fz is equal to1(, )fz . In other words, in this case the predicted outputi y of the model approximates the sample output di y in the training set well. Conse- quently the novel objective function may be defined as 212 12 21 1122 21 11 2 22 1 , ,, log log log log log log EWff VffVf f f ffdzf ffdz ff f ff fd zzzzzz zz z zz zz (9) From Eq.4-Eq.6, we can see that f(z) is obtained by Parzen window estimator , thus its value ranges from 0 to 1. According to the properties of Taylor’s expansion, when fz is small, we can just keep the linear parts of log fz, that is to say, log fzcan be simplified as follows, loglog 111fff zzz (10) Therefore, submitting Eq.10 into Eq.9, we get, Please note, Erhan and Jose [17] have strictly inferred the following formulas, 12 12 22 1211 22 ,2zzz z d NN tt tt fd G N (12) 12 12 22 2211 22 ,2zzz z d NN tt tt fd G N (13) 12 12 2 12 211 22 ,2zzz zz d NN tt tt ffd G N (14) Thus, submitting Eqs.12,13, and 14 into Eq.11, we can immediately derive the novel objective function as follows 12 12 12 12 12 12 2 2211 22 11 11 22 ,2 ,2 2,2 zz zz zz d NN tt tt NN NN tt tt tt tt EG N GG (15) Since Eq.15 actually originates from the Parzen win- dow desity estimator and relative entropy for the sam- pling set and roots at the whole distribution of the train- ing sample set, this novel objective function has the fol- lowing virtues: since the new criterion is based on the density probability and not the local data points, this corresponding model parameter learning can effectively avoid the over-fitting drawback an d show a less sensitiv - ity to noise in the noisy environment. Our experimental results in this study will confirm these virtues. 3.3. Entr op y-Criteri on Base d Paramete r Lear ning For a given modeling model, with the commonly used gradient descent procedure [18], we can easily get the following model parameter’s learning rule, 2 1E ptptr p (16) where p denotes the model parameter; t denotes the it- eration number and ris the learning rate. Z. P. Tan et al. / J. Biomedical Science and Engineering 3 (2010) 430-438 Copyright © 2010 SciRes. JBiSE 433 4. RESULTS In this section, we will illustrate the performance of the proposed entropy-criterion based fermentation process modeling on EPS production from Lactobacillus. 4.1. Performance Index In order to do the comparative study for the perform- ances of different modeling methods with MSE-criterion and entropy-criterion, we adopt the following perform- ance index to evaluate different modeling methods [19,20]. 2 1 2 1 Nd ll lNd l l yy J yy (17) where 1 1Nd l l yy N ; N denotes the number of the testing samples; d l y is the l th desired output in the testing set; l y is the predicted output of the model in testing set. Here, the smaller the value of J is, the better the performance of the corresponding training model is. 4.2. Results In our experiments, we take three modeling methods: MLP network model, RBF network model and TSK fuzzy system model. All three models have four input nodes representing the four influential process variables (concentrations of lactose, casein hydrolysate and tri- ammonium citrate, and inoculum size) and one output node representing the EPS yield (g/l) at the end of batch. The process data for modeling are generated by carrying out a number of fermentation runs under various input conditions. Here we collect 54 sample data as shown in Table 1, each sample data represents a pair of model inputs (fermentation conditions) and a single output (EPS concentration). For MLP network model, RBF neural network model and TSK fuzzy system model, these 54 sample data will be partitioned into a training set (45 samples) and a testing set (9 samples) [7]. The training set is utilized to adjust the parameters of all three models and the testing set is used to evaluate the prediction ac- curacy. The EPS yield comparisons of the sample data and predicted ones in the testing set obtained by using MSE-criterion based models and entropy-criterion based models are illustrated in Figures 2-4. a L, T, C and I in the table represented for Lactose/(g/l), Triammonium citrate/(g/l), Ca sei n hydrolysate/(g/l), Inocul um size/(vol%), respectively. In fact, due to the extremely complexity of both the fermentation mechanism and the limitation of the ex- perimental condition, experimental data may inevitably contain noise. Hence, how to enhance robustness of the fermentation process modeling is very important. In or- der to compare the robustness between MSE-criterion based models and entropy-criterion based models, we add Gaussian white noise (G(0, 1 )) to the training sample set, where 1(0,0.20) [8]. In Tables 2-4, we list the corresponding performance index for the testing set with 1 1 dif f erent Gaussian white noises. 4.3. MLP Network Modeling Multi-Layer Perceptron (MLP) network [21] is one of the most widely utilized paradigms in the fermentation process modeling, because it is very simple, general and matured. In the network training procedure, the tangent sigmoid activation function and linear combination function are used for computing the outputs of the hid- den and output nodes, respectively. When developing an appropriate MLP model, we must carefully select the number of hidden nodes and then use Back- propagation procedure (BP procedure) [22] to adjust the model pa- rameters. Here the MLP network model contains 15 hidden nodes, and its architectu re is illustrated in Figure 1(a). The experimental results about EPS fermentation data from Lactobacillus are illustrated in Table 2. 4.4. RBF Network Modeling Another widely utilized modeling method is Radial Ba- sis Function (RBF) neural network [23], Just like MLP network, RBF network is essentially a feed-forward network. However, RBF network utilizes radial basis functions as its activation functions in the hidden layer. In our experiments, the number of hidden nodes is fixed to be 13, and the RBF network’s architecture can be seen in Figure 1(b). The experimental results about EPS fer- mentation data are illustrated in Table 3. 4.5. TSK Fuzzy System Modeling Takagi-Sugeno-Kang (TSK) fuzzy system [24] has been widely applied, due to its strong capability in learning, universal approximation and handling with matural lin- guistics with fuzzy ru les acquried fro m the skilled wo rk er and/or experts. In our experiments, the number of the fuzzy rules is fixed to be 8, and the architecture of the TSK fuzzy system can be seen in Figure 1(c). The ex- perimental results about EPS fermentation data are illus- trated in Table 4. As it can be seen from Ta bl es 2, 3 and 4, the predic- tion accuracies of these three modeling methods with the proposed entropy-criterion based objective function are obviously higher than these methods with MSE-criterion based objective function. This fact means that the pro- posed objective function is very suitable for the EPS ferment ation process modeling. Z. P. Tan et al. / J. Biomedical Science and Engineering 3 (2010) 430-438 Copyright © 2010 SciRes. JBiSE 434 Figures 5-7 are generated from Tables 2-4. In Fig- ures 5-7, X-axis denotes the added noise corresponded (see the second column in Tables 2-4), and Y-axis de- notes the testing performance index. Dotted lines corre- spond to the testing performance indices of MSE-based criterion (see the third column in Tables 2-4), while real lines correspond to the testing performance indices of these modeling methods with entropy-based criterion (see the fourth column in Tables 2-4). (a) (b) (c) Figure 1. (a) Architecture of MLP network; (b) Architecture of RBF neural µnetwork; (c) Architecture of TSK fuzzy system. Figure 2. Comparison of EPS yield prediction using MLP network model. Figure 3. Comparison of EPS yield prediction using RBF model. Figure 4. Comparison of EPS yield prediction using fuzzy system model. Z. P. Tan et al. / J. Biomedical Science and Engineering 3 (2010) 430-438 Copyright © 2010 SciRes. JBiSE 435 Table 1. EPS fermentation data. Factors and levels Factors and levels No. L T C I EPS No. L T C I EPS 1 8 0 2 1.5 2.29 0.41 28 20 0.3 5 1 1.90 0.44 2 8 0.2 8 3.5 3.43 0.12 29 8 0.2 4 3.5 2.68 0.42 3 25 0 4 1.5 5.16 0.73 30 8 0 4 2 2.65 0.45 4 8 0.2 2 2 2.38 0.62 31 8 0.2 2 1.5 2.51 0.66 5 25 0.2 2 2 4.51 0.37 32 4 0.2 8 2 1.99 0.07 6 25 0.2 8 2 5.32 0.12 33 25 0 4 3.5 5.04 0.16 7 20 0.2 8 1 1.64 0.18 34 40 0.2 4 1 1.88 0.05 8 4 0.2 4 1.5 1.54 0.04 35 2 0.2 4 1 0.65 0.46 9 25 0.2 4 2 5.20 0.24 36 8 0.2 8 2 3.55 0.40 10 25 0 8 1.5 5.66 0.76 37 8 0.2 4 1 1.20 0.05 11 8 0 4 1.5 2.80 0.01 38 20 0.2 4 1 1.70 0.18 12 20 0.1 5 1 1.80 0.50 39 25 0 2 3.5 4.61 0.73 13 10 0.2 4 1 1.35 0.64 40 4 0 8 1.5 2.26 0.48 14 4 0 4 1.5 1.43 0.15 41 4 0.2 8 3.5 2.17 0.39 15 25 0.2 4 1.5 5.22 0.57 42 20 0.2 1 1 0.80 0.69 16 4 0 2 2 0.98 0.58 43 4 0 2 3.5 1.02 0.34 17 8 0.2 4 1.5 2.91 0.32 44 25 0 2 2 4.90 0.57 18 8 0.2 8 1.5 3.79 0.53 45 4 0.2 2 3.5 1.11 0.21 19 4 0.2 2 1.5 1.08 0.42 46 20 0.2 5 1 1.95 0.26 20 4 0.2 4 1 0.80 0.51 47 20 0.2 3 1 1.40 0.13 21 25 0 4 2 5.40 0.12 48 4 0.2 8 1.5 1.98 0.79 22 4 0 4 2 1.59 0.34 49 4 0.2 4 2 1.60 0.73 23 25 0 8 3.5 5.13 0.30 50 4 0.2 4 3.5 2.53 0.28 24 8 0 2 2 2.59 0.59 51 25 0.2 2 3.5 5.04 0.69 25 8 0 4 3.5 2.87 0.47 52 4 0 8 3.5 2.25 0.12 26 8 0 8 3.5 3.78 0.52 53 20 0.4 5 1 1.86 0.26 27 4 0 8 2 2.21 0.71 54 25 0 8 2 5.64 0.66 Table 2. The results about MLP network modeling with MSE-criterion and entropy-criterion. Performance index J No. Noise MSE-criterion Entropy-criterion 1 0.00 0.8621 0.7730 2 0.02 0.9101 0.8160 3 0.04 0.9940 0.7988 4 0.06 1.1855 0.8487 5 0.08 1.0616 0.8502 6 0.10 1.2130 0.8501 7 0.12 1.3540 0.8511 8 0.14 1.4107 0.8565 9 0.16 1.3558 0.8676 10 0.18 1.5425 0.9117 11 0.20 1.5924 0.9188 Table 3. The results about RBF network modeling with MSE-criterion and entropy-criterion. Performance index J No. Noise MSE-criterion Entropy-criterion 1 0.00 0.8724 0.7223 2 0.02 0.9279 0.7291 3 0.04 0.9375 0.7441 4 0.06 0.9637 0.7572 5 0.08 0.9970 0.7522 6 0.10 0.9718 0.7779 7 0.12 1.0933 0.7753 8 0.14 1.1369 0.7868 9 0.16 1.1793 0.7914 10 0.18 1.2189 0.7999 11 0.20 1.2413 0.8051 Z. P. Tan et al. / J. Biomedical Science and Engineering 3 (2010) 430-438 Copyright © 2010 SciRes. JBiSE 436 Table 4. The results about fuzzy system modeling with MSE-criterion and entropy-criterion. Performance index J No. Noise MSE-criterion Entropy-criterion 1 0.00 0.8810 0.6889 2 0.02 1.0852 0.7446 3 0.04 1.1616 0.7641 4 0.06 1.2195 0.8051 5 0.08 1.2237 0.8170 6 0.10 1.2531 0.8124 7 0.12 1.2330 0.8235 8 0.14 1.2689 0.8201 9 0.16 1.2680 0.8390 10 0.18 1.2798 0.8771 11 0.20 1.3141 0.8733 From Figures 5-7, it is easy to observe that the three curves corresponding to these three modeling methods with MSE-criterion objective function are always re- spectively over the curves of these three modeling methods with entropy-criterion based objective function. In addition, with the increases of the noise, the curves of predicted performance indices in Figures 5-7, corre- sponding to the MSE-criterion based modeling methods, have dramatic changes, which mean that the prediction accuracy is deteriorated greatly with the increasing of noise, while the curves corresponding to entropy-criterion based modeling methods in these figures are very smooth. Therefore the experimental results obviously demonstrate that the entropy-criterion based modeling Figure 5. Comparison of testing performance indices of MSE-criterion and entropy-criterion based MLP network mod- eling method. Figure 6. Comparison of testing performance indices of MSE-criterion and entropy-criterion based RBF modeling method. Figure 7. Comparison of testing performance indices of MSE-criterion and entropy-criterion based fuzzy system mod- eling method. methods have a better generalization and robustness than the MSE-criterion based modeling methods in the EPS ferment ation process modeling. 4.6. Statistical Results for the Obtained Performance Indices In view of the mean and standard variance of EPS pro- duction obtained from the above experiments as the output of the training samples, we can see from Ta ble 1 that the standard variance is not little, therefore, it is necessary for us to observe the performance of the above three modeling methods from the statistical viewpoint. Z. P. Tan et al. / J. Biomedical Science and Engineering 3 (2010) 430-438 Copyright © 2010 SciRes. JBiSE 437 In this experiment, we keep the same inputs in the train- ing set as above, however, add noise to the correspond- ing outputs. The added noise has the mean zero and the same standard variance as derived from the experimental data. In order to keep the experimental results fair, we run each sample data 50 times, and then take their means and standard variances of the performance indices J for the corresponding modeling methods. Table 5 lists the obtained re sults. We can clearly see from Ta ble 5 that, both the means and standard variances of the outputs of these three modeling methods with entropy-criterion are always lower than the ones with MSE-criterion. This fact con- firms our claims again that the proposed entropy- criterion based modeling methods possess the favorable capability in approximation, generalization and robustness. 5. DISCUSSION When studying fermentation process modeling of EPS from Lactobacillus, we must consider two factors. One is the collected data corrupted by noise, due to the shortage of apparatus and the limitation of experimental condi- tions. The other is the comparatively weak generaliza- tion and robustness capability of current MSE-criterion based modeling methods. In this work, the EPS fermen- tation process modeling methods with entropy-criterion based objective function are addressed. When it is used in MLP network modeling, RBF modeling and TSK fuzzy system modeling for EPS fermentation from Lac- tobacillus, our experimental results demonstrate that th ree modeling methods with entropy-criterion are less sensi- tive to noise and have better generalization abilities and robustnesses than three modeling methods with MSE- criterion. Because the proposed objective function is de- rived from the Parzen window desity estimator and rela- tive entropy, and considers the whole distribution struc- ture of the training set in the parameter’s learning proc- ess, which is different from previous study. The results obtained in this study are very useful in modeling EPS fermentation process, and the entropy- criterion based modeling methods can also be efficiently applied to other fermentation processes. Table 5. Statistical results of the performance index J of three modeling methods. Modeling meth- ods J of MLP net- work J of RBF net- work J of TSK fuzzy system MSE-criterion 1.3663 ± 0.2577 1.3893 ± 0.1684 1.1197 ± 0.1807 Entropy-criterion 1.1 165 ± 0.1363 0.9998 ± 0.1119 0.9240 ± 0.1210 6. ACKNOWLEDGEMENTS This work wa s supp orte d by 863 pr ojec t o f chi na (gra nt No. 2007AA1Z 158, 2006AA10Z313), National Science Foundation of China (grant No. 60773206/F020106，60704047/F030304), The Project Innovation of Graduate Students of Jiangsu Province of China 2008, New century Outstanding Young Scholar Grant of Ministry of Education of China (NCET-04-0496), 2006 Outstanding Young Scholar Grant at JiangSu Province, Grants from the National KeySoft Lab. at Nanjing Univer- sity and from Jiangsu Province Key Lab. of Information Technologies at Suzhou univers ity. REFERENCES [1] Du, F., Lei, M. and Liu, Q. (2004) Advanced control in fermentation process. Chinese Journal of Information Technology in Construction, 33, 314-317. 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