Dynamic Neural-Network-Based Model-Predictive Control of an ...

IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 19, NO. 7, JULY 2008

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Dynamic Neural-Network-Based Model-Predictive Control of an Industrial Baker's Yeast Drying Process U˘gur Yüzgeç, Student Member, IEEE, Yas¸ar Becerikli, Member, IEEE, and Mustafa Türker

Abstract—This paper presents dynamic neural-network-based model-predictive control (MPC) structure for a baker’s yeast drying process. Mathematical model consists of two partial nonlinear differential equations that are obtained from heat and mass balances inside dried granules. The drying curves that are obtained from granule-based model were used as training data for neural network (NN) models. The target is to predict the moisture content and product activity, which are very important parameters in drying process, for different horizon values. Genetic-based search algorithm determines the optimal drying profile by solving optimization problem in MPC. As a result of the performance evaluation of the proposed control structure, which is compared with the model based on nonlinear partial differential equation (PDE) and with feedforward neural network (FFN) models, it is particularly satisfactory for the drying process of a baker’s yeast. Index Terms—Drying process, dynamic neural networks (NNs), genetic algorithm (GA), model-predictive control (MPC).

I. INTRODUCTION N a drying process, it is important to remove sufficient water to obtain stable product at reasonable production conditions. Thermal drying methods as, i.e., spray or fluidized bed drying process are suitable for the production of dried materials. On the other hand, thermal methods involve the risk of cell damage and deterioration in product quality [1], [2]. Among many factors affecting desired product quality, the most important are temperature and moisture content [3]. The drying process is basically simultaneous heat and mass transfer operations. A satisfactory model of the drying process should contain good estimates of drying rate, heat and mass transfer coefficient, coefficients defined in product quality, and so on. Some authors [4]–[6] have developed rigorous models for convective fixed bed dryers. Ratti and Mujumdar [4] proposed the four partial differential equations that are obtained from heat and mass balances for a differential element of a fixed bed. The mathematical model presented in [7] involves heat and mass transfer

I

Manuscript received October 4, 2006; revised May 25, 2007 and October 10, 2007; accepted December 30, 2007. First published April 11, 2008; last published July 7, 2008 (projected). U. Yüzgeç is with the Electronic and Telecommunications Engineering Department, Kocaeli University, 41040 Kocaeli, Turkey (e-mail: uyuzgec@kou. edu.tr). Y. Becerikli is with the Wireless Communications and Information Systems Research Unit (WINS) and Computer Engineering Department, Kocaeli University, 41040 Kocaeli, Turkey and also with the Department of Computer Engineering, and Electronics and Telecommunication Engineering, Halic University, Istanbul, Turkey (e-mail: [email protected]). M. Türker is with Pakmaya, International Yeast Company, 41001 Kocaeli, Turkey (e-mail: [email protected]). Digital Object Identifier 10.1109/TNN.2008.2000205

properties in both air and product for a nonsteady-state drying process. A drying model presented by [8] is based on the a the mass balance and heat transfer in a baker’s yeast drying process. However, for larger granules, the deviations between the measurements and the model outputs were observed and this was attributed to diffusive transport limitation of moisture content inside granules. For this reason, a new mathematical model was developed in [9], which describes spatial distribution of moisture and temperature inside the granules. An efficient control of a drying process depends on the energy requirements to reach the expected product quality. Model-based control, being a relatively recent development in process control, is particularly effective in controlling complex processes. Industry has widely accepted model-predictive control (MPC) as a powerful control strategy [10], [11]. MPC demands a dynamic process model that is sufficiently accurate and high-speed computing. Yüzgeç et al. [12] proposed a valid mathematical model describing the process dynamics and step ahead predictive model was used for control studies. However, as can be seen from this paper, increasing the prediction horizon requires a high computational time. Artificial neural networks (ANNs) have superiority as compared with other conventional modeling methods. The advantage of ANN is that it does not need any knowledge about the process. However, ANN needs a lot of data for the training procedure [13]. There are different types of ANNs used in both academic and industrial sectors. Some network structures are listed such as perceptrons [14], [15], feedforward neural networks (NNs), radial basis networks [16], [17], and dynamic NNs [17]–[20]. Dynamic NN models are more successful and superior than feedforward networks due to their structure [21], [22]. A number of studies were carried out on the optimization of drying processes. Dufour et al. [23] presented the MPC of a drying process described by nonlinear parabolic partial differential equations. Olmos et al. [24] developed a technique to determine the drying air temperature and relative humidity profiles that maximize the final head kernel yield of paddy rice. To solve the optimization problem, a sequential quadratic programming was proposed in their study. ANN models developed in [25] predict quality changes during osmo–convective drying of blueberries for process optimization. This multilayer NN models consist of three inputs (concentration, osmotic temperature, and contact time) and five outputs (air drying time, color, texture, hardness, and comprehensive index). Optimization problems are solved by either analytical or numerical solutions. The structure of the objective function is important. If it has a nondifferentiable and complex structure, analytical solution is very difficult, and moreover, sometimes there cannot

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Fig. 1. Batch fluidized bed drying process.

be a solution. Whereas traditional search techniques use characteristics of the problem to determine the next sampling point (gradients, Hessians, and linearity), stochastic search techniques make no such assumptions. Instead, the next point is determined by the stochastic decision rules. This study introduces a novel search technique based on a genetic algorithm (GA) to solve the optimization problem in MPC structure. GAs are based on the principles of natural genetics/selection and are thus able to evolve the solutions to real-world problems [26]. These algorithms maintain and manipulate a population of solutions and realize a “survival of the fittest gene” strategy in their search for better solutions. GA approach has recently been used for optimization of fed-batch bioreactors [27]–[29], selfadaptation of artificial recurrent NNs [30]–[33], and adaptive control applications using fuzzy logic [34], [35]. In this paper, a control method based on prediction is proposed for an industrial baker’s yeast drying process. ANN models have been used to predict moisture content and product activity. In addition, GA, a stochastic search algorithm, has been proposed for optimization procedure. II. MODELING OF THE BAKER’S YEAST DRYING PROCESS The fluidized-bed drying technique holds an important position among modern drying methods. It is used mainly for granular materials; nevertheless, it is applicable also in the drying

of solutions, pastes, and liquids sprayed onto the fluidized inert bed [36]. The fluidized-bed drying system is shown in Fig. 1. The drying method is based on passing hot air through the fluidized bed. Fluidized dryers can be either batch or continuous. In this study, fluidized bed drying process of a baker’s yeast was batch. Baker’s yeast cake was extruded into the dryer through a perforated plate of different diameter to get desired granule size. The fluid bed consisted of a centrifugal fan to supply air drawn from ambient air (Fig. 1). Air inlet temperature was maintained at 100 C during most of the drying process. The temperature and humidity values of air at inlet and outlet and its flow rate were measured online and registered on computer in order to establish continuous material and energy balances for the prediction of the moisture content and temperature of the product. The drying of a material can be described as the heat and mass transport. The moisture and heat gradients in each granule are modeled by moisture diffusion and heat convection inside the granule. The equations of the heat balance and the moisture diffusion for a granule with general geometry can be expressed by the following nonlinear partial differential equations [37], [3], [38], [39]: (1) (2)

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where is the temperature inside the granule; (m /s) is the moisture diffusion coefficient which is the function of the maand temperature represents terial’s moisture content geometry factor with slab, cylinder, and sphere; (kg water/kg dry solids) is the moisture concentrais the moisture concentration; is the dry solid contion; and are the heat capacicentration inside the granule; ties of the product and water; and is the thermal conductivity of the granule. Granule was considered in cylindrical and spherical forms. The internal diffusion depends on the moisture content and temperature of the granules as given by the following equation [40]–[42]: Fig. 2. MPC feedback system.

(3)

(4) represents the activation energy for diffusion; is where the power in concentration dependence of diffusion coefficient; 8.314 J/mol K (gas constant); and 323 K. The initial conditions for both equations are given by

(5) At the center of the granule, the boundary conditions are given as the following equation for heat and moisture diffusion transfer:

(6) The boundary conditions at the surface of the granule can be described by

in which is the concentration of the active product, the quality is the specific rate of product acindex of the material, and tivity [9], [41], [43]. The temperature and the moisture content dependencies of the specific rate of the product activity can be described according to [43]

(11) and are the parameter values in the equation. where The other parameters in the drying model have been represented in [9] and [44]. III. MODEL-PREDICTIVE CONTROL MPC is an open-loop control design procedure based on obtaining nonlinear model outputs of a drying process and predicting future outputs [11]. This is done at each sampling time. A typical MPC feedback system is shown in Fig. 2. In this and represent references, process outputs, configure, trol variables, and predicted outputs, respectively; is the disturbance inputs; is the error that is between the process and is the step delay operator. the prediction model; and The prediction values are used to compute control moves by minimizing or maximizing an objective function , defined over a prediction horizon as follows:

(7) (8) (12)

(9) where represents the moisture flux at the interface; is the is liquid film mass transfer coefficient around the granule; is the the water vapor concentration at the interface and water vapor concentration in the bulk air; is the heat flux is the inlet at the interface; is the heat transfer coefficient; is the evaporation enthalpy of water. air temperature; and One of the important indicators in drying process of bioproducts is the product quality and it is usually described by first-order reaction kinetics (10)

subject to (13) (14) (15) (16) is the reference; is the predicted output; is where and are the weighting matrices; the control variable; and represent minimum, maximum prediction horizon, and control prediction horizon, respectively; is the number of decision variables; and is the number of control

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variables. In this study, control variables were used as air and air humidity for the drying process. temperature were taken as moisture content Again, predicted variables and product activity . If (12) is rearranged, then optimization problem can be obtained in the following form:

(17) (18) and represent the desired values. The following where constrains on the manipulated input and output variables can be enforced in the framework of MPC: Constraint on control variables and 0.005 kg water vapor/kg dry air Constraint on predicted outputs kg water/kg dry solid and

(19)

NN to both detect and generate time-varying patterns. On the other hand, a recurrent network takes its current and previous outputs as its partial inputs. In this study, two ANN predictive models were developed. In the first model, an RN structure was developed to predict the moisture content. Three layers were used in this prediction model. Logarithmic sigmoid (logsig) function was chosen as an activation function . There are three inputs, namely, inlet air temperature , , and moisture content . The time inlet air humidity delay operators (TDLs) have been used in the input and hidden layers. preThe outputs of all the layers of the moisture content dictive model based on the RN model are given by (21) (22) (23) where

(20)

The objective function described in (17) is a nondifferentiable and complex structure. Whereas traditional search techniques use characteristics of the problem to determine the next sampling point, stochastic search techniques make no such assumptions. Instead, the next point is determined by the stochastic decision rules. In this study, GA is proposed for solving optimization problem of MPC. GA is a probabilistic search technique based on the principles of genetics [45]. The details about how this search algorithm is used will be presented in the following sections. MPC demands that a dynamic prediction process model be sufficiently accurate and high-speed computing, though the feedback mechanism of MPC tolerates some model mismatch in the plant. ANN was considered as a prediction model for control purposes because of the superiority in comparison with other conventional modeling methods [21]. IV. DYNAMIC NN-BASED PREDICTION MODELS ANN consists of simple components (neurons) working with the parallel connections. A neuron is an information processing unit that is fundamental to the operation of an NN. A network can have several layers. Each layer has a weight matrix, a bias vector, and an output vector. The different layers can have different neuron numbers and the outputs of each intermediate layer are the inputs to the following layer. ANN model is trained by setting the weighting values of connections between its components [17]. In the training algorithm, ANN output and reference are compared and then weighting values are updated to minimize the error step by step. In the literature, there are many methods used for training the ANN models: Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton [17], [46], gradient descent [15], Levenberg–Marquardt [47]–[49], and conjugate gradient [17]. In this study, recurrent networks (RN) were proposed for the prediction of moisture and product activity . In dynamic RN, comcontent monly, there is a feedback from the hidden layer output to the hidden layer input. This recurrent connection allows the

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In this notation, upper subscripts indicate relevant layer, the indicate the row indices on the elements of weight matrix destination neuron of the weight, and the column indices indicate which source is the input for that weight. represents the activation function. The second predictive model based on ANN was designed for the product activity. In this step, an external recurrent network (ERN) structure was used. This model consists of five layers and numbers of neurons in the layers are 6, 4, 16, 5, and 1, respectively. There are two input vector: first input

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Fig. 3. MPC structure based on NN for the baker’s yeast drying process.

vector is the current, the previous values of the air temper, and the air humidity ; and the other one is ature the current values of the moisture content and product ac. Note that the third-order TDLs have been used in the tivity third input layer. preThe outputs of all the layers of the product activity dictive model based on the ERN model are given by (24) (25) (26) (27) (28) where

The NN model output (predicted product quality) has been used as the inputs with TDL in the first layer. NNs require the same order of magnitude for their input and output. If the input and the output data are not of the same order of magnitude, some data may appear to have more significance than they actually do [50]. The training data need to be scaled to be the superior training; so, each input and output parameter . In both predictive models, was normalized to the range the network weights are adjusted by the training algorithm such as Levenberg–Marquardt method, which was preferred because of the training speed. The Levenberg–Marquardt algorithm was designed to approach the second-order training speed without having to compute the Hessian matrix. This algorithm updates of the network as given in the weights values (29) where is the Jacobian matrix that contains first derivatives of the network errors with respect to the weights and biases; is the identity matrix; is the adaptive value; and is the vector of the network errors. V. CONTROL STRUCTURE The developed MPC structure based on dynamic NN for the drying process is shown in Fig. 3. The control structure consists of three main parts: predictive model based on dynamic NN, calculating of cost function, and genetic search algorithm. In and are mutation probability, crossover this figure, probability, and population size respectively. NPM and NPM blocks represent the neural predictive models used to predict moisture content and the product quality, respectively.

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T

Fig. 4. Sample of training data set which is used for training process: (a) air temperature ( activity ( ).

Q

The use of a genetic search algorithm consists of five fundamental parts: chromosome representation, selection method, genetic operators, termination criteria, and evaluation function. A chromosome representation is to describe each individual in the population. Chromosome is made up as a gene sequence from a certain alphabet. In this GA approach, each chromosome is considered as the binary strings. Chromosomes consist of three different parts: first part denotes air temperature value from the first to the tenth bit, second part denotes air humidity value from the eleventh to the seventeenth bit, and the last bit denotes the value of fitness of chromosome. The selection method is used to clean the individuals who have bad fitness values in the population. The tournament procedure was preferred in this study due to the accomplishment in solving the minimization problems [51]. Genetic operators have two basic types: mutation and crossover. These operators generate new individuals with changing to digits in selected chromosomes. Crossover is a unique GA operator that combines two

Y

), (b) air humidity (

X ), and (d) product

), (c) moisture content (

parent chromosomes to produce offspring containing subparts from both parents [52]. The basic mathematical expression of crossover operator is given in if i < r otherwise if i < r otherwise

(30)

where and represent parent chromosomes, and represent new (offspring) chromosomes, and is the cutting point. Mutation is an operator that introduces variations into the chromosomes and thus adds the property of a random search to the GA. The binary mutation is applied in each bit in every indias given vidual in the population with mutation probability in if otherwise

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TABLE I GA RUN PARAMETERS AND INITIAL CONDITION OF A DRYING PROCESS

Fig. 5. Variation of mse during training procedure for (a) moisture content and (b) product activity predictive model based on the dynamic NN.

where is a population size length vector, which consists of randomly selected binary numbers. The GA is terminated according to the population convergence criteria. The evaluation function determines the fitness of each chromosome string generated during the search in solution space. The control algorithm is summarized as follows. 1) Initialize drying model and genetic search algorithm. The initial chromosomes in population are randomly formed as a binary code. 2) The decoded values of each individual in population ( and ) carried out the NN models to predict values of moisture content and product activity. There is an important point that has to be noticed in this step. Consecutive inputs to the recurrent neural predictive models can change their internal state in detrimental way throughout GA procedure and GA fitness values can be calculated at fault due to this situation. In this way, the faulty fitness values cause the optimal control variables of a drying process to not be found. To avoid this problem, ERN and RN models returned the initial condition before each individual carried out the NN models. 3) Calculate the fitness (cost function) value of each individual in population using the moisture content values and the product activity values predicted by the recurrent structures, and difference between the decoded values of each individual and prior pairs of control variables of the process. 4) The chromosome which has the best fitness value is recorded. Perform the selection method based on the

5) 6)

7) 8)

9)

fitness of individuals in the population, and this way, the population has better individuals. Perform genetic operators (single-point crossover and mutation) to create new individuals in the population. Produce the prediction values for each new individual in the population and calculate their fitness values according to procedures in Steps 2) and 3). The best chromosome that has been recorded previously is located in the new generation instead of the chromosome that has the worst fitness value. Repeat Steps 4)–7) until a convergence criteria of the evaluation function are met. The best individuals ( and ) found by optimization procedure apply the model, and subsequent model outputs are obtained. Go to Step 2) and perform for outputs of the drying model. VI. APPLICATION AND DISCUSSION

The training results of two predictive models based on dynamic NN were presented and the performance of the proposed control structure for an industrial baker’s yeast drying process was evaluated. For training the NN and control studies, an Intel(R) Pentium(R) 4 CPU 2.80-GHz, 512-MB RAM computer was used. This study was run on Matlab® 6.5. Ten training and five test sets have been used for the training procedure of the dynamic NN models. The sampling time was 1 s. The initial conditions of the drying process were the same for all the 1.563 kg water/kg dry solid, training and test data sets: 289.90 K, 0.5 mm,

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TABLE II OPTIMIZATION WEIGHTS FOR MANIPULATED AND CONTROLLED VARIABLES, THE FINAL TIME, AND PRODUCT ACTIVITY (QUALITY) IN THE DRYING PROCESS

Fig. 6. Performance results of the moisture content predictive model based on RN for test Data#02. (o: test data; *: RN model).

Fig. 8. Comparison of the performance results of the FFN prediction model and the proposed RN and ERN prediction models.

Fig. 7. Performance results of the product activity predictive model based on ERN for test Data#04. (o: test data; *: ERN model).

m /s. All the of other parameters and initial condition values have been given in [44]. In preparing the training data set, especially, the air temperature and air humidity used as the inputs of the drying process were chosen randomly. Fig. 4 shows one sample of the training data sets. Table I shows the GA run parameters and initial conditions and the parameters of a baker’s yeast drying process. The computational time taken for one GA run was approximately 1 s. The total number of trials (fitness evaluations) for each run changed between 3 and 15. The number of trials was reduced gradually when GA converged to the solution of the optimization problem. , First, all of the data sets have been normalized to and then training procedure has been performed. During the training procedure, it was shown that training was successfully becoming small of mean square error (mse). If critic mse value is not reached or mse is continuously fixed for a long time,

then mse can be minimized in a better way by adapting the concerned parameters in training algorithm. The variation of mse is shown in Fig. 5. RN model reached the critical mse in shorter step numbers (502) than the ERN value model (921). The results of the RN and ERN prediction models are shown in Figs. 6 and 7 for some test data. In test condition, prediction is used as 1 min. As can be seen from these horizon figures, the performances of the proposed predictive models for the test sets are satisfactory. At the same time, these results show the success of the dynamic NN structures. One of the advantages of the prediction models based on recurrent NNs is the solution speed. These proposed models predict faster step prediction model presented by [12]. In step than prediction model, the drying model is used in each prediction step and it is operated for prediction horizon times, whereas this proposed model achieves this procedure in a short time. For instance, when prediction horizon is taken as 1 min, the prediction model based on NN proceeds in one processor clock cycle, but the other model spends 60 processor clock cycles for the same procedure. This is a very important criterion especially for online control applications. The product quality was measured with offline laboratory conditions as the amount of carbon dioxide produced upon introduction of the yeast into dough per unit time. This method is commonly used in yeast

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TABLE III CONTROLLED AND MANIPULATED VARIABLES FOR FOUR DIFFERENT PREDICTION HORIZON VALUES

industry to assess the performance of the baker’s yeast [53]. Relative activity is expressed as the ratio of activity of the product at time to the activity of yeast cake introduced into the dryer. It has been provided that the product activity was able to be observed online by the proposed external recurrent NN prediction model such as a neural soft sensor. In this study, the control structure was updated by adding two terms to introduce air temperature. Updated terms are given by (32) (33) In these equations, can be described as the crossing factor. The success of optimization methods depends on the determination of the weight values for the manipulated and controlled variables. Table II shows the performance of the drying process under the proposed control structure with different weights for the manipulated and controlled variables. In the first three tests, the weights for the controlled variables are changed and the other weights are fixed. In the last three tests, it is used in the opposite way. For all of the tests, singlestep-ahead prediction and control horizons have been used. As can be noted from the behavior of MPC with different weights

settings, the best optimization weight values have been obtained by test 3. We used many variations to find the best optimization weights. In this paper, only conspicuous test was presented. In Fig. 8, the proposed prediction models were compared with two FFN models developed by [44]. For predicting the moisture content, RN model reaches the desired value of moisture content in less time (12.4 min) than the FFN model does, and similarly, at the end of the drying process, the value of the product activity (0.926) obtained by the ERN model is better than the value (0.915) obtained by the FFN model. As a result of this comparison, we can conclude that the performances of the recurrent structures are more successful than the FFN models. The control results of the baker’s yeast drying process are given in Table III for different prediction horizon values. For all of the prediction horizons, the controlled variables have reached the desired values within short times. An important point can be noted from these figures that when the moisture content falls down, the product activity does not. It is desired that the product activity or quality is of high value at the end of the drying process. In comparison with the industrial baker’s yeast drying process conditions, it has been determined that there is approximately 5% increase in product activity and 26% decrease in drying time for the instant baker’s yeast. As can be seen from

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Fig. 9. (c) Moisture content and (d) product activity of the baker’s yeast drying process subjected to (a) air temperature and (b) air humidity feed profiles, under (e) different prediction horizons.

these figures, the best result was obtained with the prediction horizon of 3 min. Fig. 9 shows the performance of MPC based on ERN under different prediction horizons defined as 2 min 3 min 1 min

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The product activity increases from 94% to 96% in this illustration, but at the same time so does the drying time. This result is positive, acceptable, and satisfactory for the industrial baker’s yeast producer. Especially, in the last decade, medicine industry started to use the baker’s yeast, which has high quality. For this reason, the proposed control mechanism can be used in production of either the instant baker’s yeast or the medicines consisting of the baker’s yeast.

VII. CONCLUSION This paper presents an MPC structure based on the dynamic recurrent NNs for the industrial baker’s yeast drying process. The proposed control structure consists of two parts: developed models for predicting moisture content and product activity and optimization problem determined according to the control strategy.

Two prediction models have been realized using the NNs. The performances of RN and ERN models are far more successful than those of FFN models and nonlinear partial-differential-equations-based models. It is an advantage that the response time of these models is shorter than the response time of the mathematical models. Especially, in online control applications, solution speed is a very important criterion. Furthermore, instead of calculating the product activity as a result of analysis per hour in laboratory for the drying processes of biomass, using the proposed dynamic NN models, it is possible that product activity can be observed online. Genetic search algorithm, which is one of the numerical stochastic search methods, was presented to solve the optimization problem defined for our process. The controller determines air temperature and air humidity under different prediction horizons to use as an input of a drying process. The results demonstrate that this new developed controller is successful and can be easily used adapting in online control applications. ACKNOWLEDGMENT The authors would like to thank the editors and the reviewers for their constructive, valuable, and informative comments. REFERENCES [1] K. Zimmermann and W. Bauer, “Fluidized bed drying of mikroorganisms on carrier material,” in Proc. 5th Int. Congr. Eng. Food, 1990, vol. 2, pp. 666–678.

YÜZGEÇ et al.: DYNAMIC NEURAL-NETWORK-BASED MPC OF AN INDUSTRIAL BAKER'S YEAST DRYING PROCESS

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IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 19, NO. 7, JULY 2008

U˘gur Yüzgeç (S’05) was born in Adilcevaz, Bitlis, Turkey, in May 1974. He received the B.S. degree from the Electronics and Communication Engineering Department, Yıldız Technical University, Istanbul, Turkey, in 1995, and the M.S. and Ph.D. degrees from the Electronics and Communication Engineering Department, Kocaeli University, Kocaeli, Turkey, in 1999 and 2005, respectively. Since 1998, he has been a Research Assistant at Electronics and Communication Engineering Department, Kocaeli University. His research interest include modeling and control of drying and fermentation processes, intelligent systems and control, fuzzy, neuro-fuzzy systems, evolutionary algorithms, and numeric techniques in optimization problem.

Dr. Becerikli is an Associate Editor of the ICIC Express Letters and the International Journal of Research and Surveys (Innovative Computing, Information and Control), and he serves as a Reviewer for the IEEE TRANSACTIONS ON NEURAL NETWORKS, the IEEE TRANSACTIONS ON FUZZY SYSTEMS, the IEEE CONTROL SYSTEM TECHNOLOGY, the IEEE TRANSACTIONS ON SIGNAL PROCESSING, the IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICSPART C: APPLICATIONS AND REVIEW, ASME Journal of Dynamic Systems, Measurement, and Control, AIP Chaos, The Mediterranean Journal of Measurement and Control, Computers and Electrical Engineering (Elsevier), The Canadian Journal of Chemical Engineering, the IEE Proceedings of Vision, Image & Signal Processing, the ISA Transactions, the Advances in Engineering Software, the Journal of Intelligent & Fuzzy Systems, the Circuits, Systems & Signal Processing, the Digital Signal Processing, and the Mechanical Systems and Signal Processing.

Yas¸ar Becerikli (S’95–A’01–M’04) received the B.S. (honors) degree from the Electronics and Communication Engineering Department, Yıldız Technical University, Istanbul, Turkey, in 1991, the M.S. degree from the Electronics and Communication Engineering, Istanbul Technical University, Istanbul, Turkey, in 1994, and the Ph.D. degree from the Electrical and Electronics Engineering, Sakarya University, Sakarya, Turkey, in 1998. He was a Research Assistant at Sakarya University, from 1992 to 2000. Currently, he is an Assistant Professor of Computer Engineering at the Kocaeli University, Kocaeli, Turkey. He was also a Senior Researcher at Marmara Research Center (MRC), TUBITAK, Izmit, Turkey, from 2003 to 2004. His current research interests include intelligent systems and control, neurofuzzy systems, optimal control, computational intelligence, optimization theory, wavelet networks, stochastic process control, and signal and image processing.

Mustafa Türker He received the B.Sc. degree in chemical engineering from Selcuk University, Turkey, the M.Sc. degree in biochemical engineering from University of Wales, Swansea, U.K., and the Ph.D. degree in biochemical engineering from the Institute of Science and Technology, University of Manchester, Manchester, U.K. Currently, he is a Production Manager of Pakmaya, International Yeast Company in Turkey. His research interests focus on fermentation kinetics and modeling, drying, and environmental biotechnology. He has authored several papers in scientific journals as well as in national and international conferences. He also lectures on biological wastewater treatment, nutrient removal and anaerobic digestion at the Environmental Engineering Department, Gebze Institute of Technology, Turkey.