Using adaptive neuro-fuzzy inference system (ANFIS) for proton ...

Journal of Mechanical Science and Technology 26 (11) (2012) 3701~3709 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-0844-2

Using adaptive neuro-fuzzy inference system (ANFIS) for proton exchange membrane fuel cell (PEMFC) performance modeling† S. Rezazadeh1,*, M. Mehrabi2, T. Pashaee3 and I. Mirzaee1 1

Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran Department of Mechanical and Aeronautical Engineering, University of Pretoria Pretoria, South Africa 3 Department of Mechanical Engineering, Faculty of Engineering, Elm-o-Fan University, Urmia, Iran

2

(Manuscript Received December 9, 2011; Revised April 25, 2012; Accepted June 8, 2012) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract In this paper, an adaptive neuro-fuzzy inference system (ANFIS) is used for modeling proton exchange membrane fuel cell (PEMFC) performance using some numerically investigated and compared with those to experimental results for training and test data. In this way, current density I (A/cm2) is modeled to the variation of pressure at the cathode side PC (atm), voltage V (V), membrane thickness (mm), Anode transfer coefficient αan, relative humidity of inlet fuel RHa and relative humidity of inlet air RHc which are defined as input (design) variables. Then, we divided these data into train and test sections to do modeling. We instructed ANFIS network by 80% of numerical-validated data. 20% of primary data which had been considered for testing the appropriateness of the models was entered ANFIS network models and results were compared by three statistical criterions. Considering the results, it is obvious that our proposed modeling by ANFIS is efficient and valid and it can be expanded for more general states. Keywords: PEM fuel cells; ANFIS; Relative humidity; Fuel cell performance ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction The proton exchange membrane fuel cell (PEMFC) using very thin polymer membrane as electrolyte has been considered as a promising candidate of future power sources, especially for transportation applications and residential power. This type of fuel cell has many important advantages such as high efficiency, clean, quiet, low temperature operation, capable of quick start-up, no liquid electrolyte and simple cell design. However its performance and cost should be further optimized before this system becomes competitive with the traditional combustion power planets [1, 2]. In recent years, research and development in fuel cells and fuel cell systems have accelerated, but at present, the cost of fuel cell systems are still too high to become viable commercial product. In a fuel cell, fuel (e.g., hydrogen gas) and an oxidant (e.g., oxygen gas from the air) are used to generate electricity, while heat and water are typical products of the fuel cell operation. A fuel cell typically works on the following principle: the hydrogen gas as fuel flows into the anode gas channel. Platinum catalyst layer facilitates oxidation of the hydrogen gas which produces protons (hydrogen ions) and *

Corresponding author. Tel.: +989143437748 E-mail address: [email protected] † Recommended by Associate Editor Yong Tae Kim © KSME & Springer 2012

electrons. The hydrogen ions diffuse through the membrane (the membrane is located at the center of the fuel cell which is made of Nafion). The electrons, which cannot pass through the membrane, flow from the anode to the cathode through an external electrical circuit containing a motor or other electric load, which consumes the power generated by the cell. At the cathode catalyst layer, the hydrogen ions combine with oxygen and electrons. According to this electrochemical reaction, the water and heat are produced. The anode and the cathode (the electrodes) are porous and made of an electrically conductive material, typically carbon. As mentioned before, fuelcell half reactions, oxidation and reduction, take place in the anode and the cathode catalyst layer, respectively. The PEMFC electrodes are of gas-diffusion type and generally designed for maximum surface area per unit material volume (the specific surface area). In this way, the electrodes would be available for the reactants, and the resistance against the hydrogen and the oxygen transportation to the active layers, will decrease, and also there would be an easy removal of water from the cathodic active layer. Excellent reviews of hydrogen PEMFC research up to the mid-1990s were presented by Prater [3] and Gottesfeld [4]. Modeling and computer simulation of hydrogen fuel cells have been attempted by a number of groups with the common

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goal of better understanding and hence optimizing fuel cell systems. Notable works have been done by Bernardi and Verbrugge [5, 6] and Springer et al. [7, 8] whose models are essentially one-dimensional. Fuller and Newman [9] Nguyen and White [10] Gurau et al. [11] and Yi and Nguyen [12, 13] developed pseudo two-dimensional models accounting for composition changes along the flow path. While such models are useful for small single cells, their applicability to largescale fuel cells, particularly under high fuel utilization conditions, is limited. The optimization of a PEMFC stack was conducted for maximizing the stack net power output, by Vargas et al. [14]. This procedure started with the construction of a mathematical model for fluid flow, mass and heat transfer in a PEMFC stack, which takes into account the spatial temperature and pressure gradients in a single PEMFC, pressure drops in the headers and all gas channels in the entire PEMFC stack. Khakpour and Vafai [15] investigated transport phenomena within PEM fuel cells. Their analysis includes both transverse and axial convective transport as well as transverse diffusive transport processes. Chemical reactions within the catalyst layers are also included. The methodology couples the transport within the fuel cell supply channels and the porous substrate. Their work provided the first comprehensive analytical solution representing fuel cell transport phenomena. The presented solution can be used to analyze fuel cell operation under different conditions. It also provides a benchmark for future works on PEM fuel cells field, especially those investigating transport characteristics. A three-dimensional model was presented by Carcadea et al. [16] in order to investigate the flow and mass concentration patterns in the entire fuel cell. The electrochemical kinetics, phase potential distribution, and multicomponent transport in the fuel cell are studied in order to understand the fuel cell operation and to improve the performance of a fuel cell systems. Among the various aspects of PEMFCs that affect cell performance, geometrical parameters play a major role. For example, performance of the fuel cell with smaller shoulder widths is better than those with larger shoulder widths [17]. In addition, the conventional cell (fuel cell with the rectangular or square channel cross-section) performance has been compared with the fuel cell with trapezoidal gas flow channels [18]. Ahmed et al. [19] performed simulations of PEMFCs with a new design for the channel shoulder geometry, in which the membrane electrode assembly (MEA) is deflected from shoulder to shoulder. In a few recent years, theoretical research about information processing develops to use it, in applied aspects, particularly for problems that are not soluble or easily solved. This interest specially displays much more in intelligent systems which are based on the empirical data. Artificial neural networks are among the systems which transfer the knowledge and rules beyond the empirical data into the network structure by their processing. Because artificial neural network does not con-

sider any presupposition about statistical distribution and characteristics of the data, they are practically more efficient than common statistical methods. But, they use a linear approach to create a model, so when encountered with the complicated and non-linear data, these networks may express such data much more accurately as a defined model. High learning abilities of artificial neural network has converted the method into a superior choice when combined with fuzzy systems. The combination of artificial neural network with fuzzy method can create an efficient approach for various modeling systems, so that each of these two methods may recover the weakness of another and raise the efficiency of the neurofuzzy system. A neuro-fuzzy system uses learning methods derived from artificial neural network to find the parameters of fuzzy system which includes appropriate membership functions and fuzzy rules. One of the neuro-fuzzy systems in which learning algorithm is coincided with integrates learning approaches, is adaptive neuro-fuzzy inference system (ANFIS) system. In recent years, many investigations perform to apply the ANFIS system for modeling engineering processes. Hayati et al. [20] applied an ANFIS model for prediction heat transfer rate of the wire-on-tube type heat exchanger. Mehrabi and Pesteei [21] provide a model for convection heat transfer of turbulent supercritical carbon dioxide flow in a vertical circular tube with a hydraulic diameter of 7.8 mm in inlet bulk temperature of 15°C and an 8 MPa constant pressure by using ANFIS. El-Sebakhy [22] investigated the capabilities of neuro-fuzzy Type I in identifying flow regimes and forecasting liquid holdup in horizontal multiphase flow. Ata and Kocyigit [23] introduced an adaptive neuro-fuzzy inference system (ANFIS) model to predict the tip speed ratio (TSR) and the power factor of a wind turbine. Mehrabi et al. [24] performed simulations of heat transfer and fluid flow characteristics of helicoidally double-pipe heat exchangers using ANFIS. In the present work, the performance of a proton exchange membrane fuel cell (PEMFC) is numerically studied and validation of the simulation is conducted by comparing the current density I (A/cm2) with those found in literatures. After that, we use these validated data for modeling performance of a proton exchange membrane fuel cell (PEMFC) using ANFIS network. In this model, current density I (A/cm2) selected for target variable (output parameter) and pressure at the cathode side PC (atm), voltage V (V), membrane thickness (mm), Anode transfer coefficient αan, relative humidity of inlet fuel RHa and relative humidity of inlet air RHc were chosen as designing variables (input parameters).

2. CFD model description and validation In this research a fully two dimensional, single phase and single domain model is implemented into a CFD code. Fig. 1 shows a schematic of a single cell of a PEM fuel cell. It is made of two porous electrodes, a polymer electrolyte membrane, two very thin catalyst layers and two gas diffusion layers. The channels walls are straight, humidified oxidant gases

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enter the cathode channel while humidified fuel enters the anode channel. The oxidant and fuel transport through the porous gas diffusion layers (GDL) to the catalyst layers, where the electrochemical reactions occur. The concentration of fuel and oxidant varies along the channel due to their consumption in the electrochemical reactions. Both gaseous reactant flows in the cathode and anode channels are subject to fluid suction or injection over the porous electrode surface. 2.1 Model Assumptions The proposed model includes the following assumptions: (1) The system operates under a steady-state condition. (2) The incoming gas mixtures are considered as an incompressible fluid. (3) The fluid flow in the channels is supposed to be laminar because of low velocities gradient and eventually low Reynolds number. (4) The gas diffusion layers, catalyst layers and membrane are isotropic and homogeneous porous media, which asserts that the porosity is a constant in the whole region of the gas diffusers, and the volume fraction of Nafion in the catalyst layer is constant too. (5) The membrane is considered impermeable for reactant gases. (6) The water in the pores of diffusion layer is separated from the gases in the diffusion layers, i.e. no interaction between the gases and the liquid water exists.

Table 1. Cell operating conditions. Parameter

Symbol

Value

Cell temperature (°C)

Tcell

80

Pressure at the anode (atm)

Pa

3

Relative humidity of inlet fuel

RHa

1

Pressure at the cathode (atm)

Pc

5

Relative humidity of inlet air

RHc

1

Anode stoichiometry

ζa

2.8

Cathode stoichiometry

ζc

3

Reference current density (A/cm2)

Iref

1

Anode transfer coefficient

αan

2

Cathode transfer coefficient

αcat

2

Fig. 1. Two dimensional proton exchange membrane fuel cell [9].

2.2 Boundary conditions The computational domain is divided into 21000 cells. Boundary conditions are set as follows: constant mass flow rate at the channel inlet and constant pressure condition at the channel outlet. The inlet mass fractions are determined by the inlet pressure and humidity according to the ideal gas law. Gradients at the channel exits are set to zero. In this study, the performance curves of voltage and current density compared with the experimental data of Ticianelli et al. [25].Validation is performed in these situations: cathode pressure PC = 5 atm, membrane thickness = 0.23294 mm, anode transfer coefficient αan = 2, relative humidity of inlet fuel RHa = 1 and relative humidity of inlet air RHc = 1. Fuel cell operating conditions are shown in Table 1. Fig. 2 shows the numerical results in comparison with experimental data. The computed polarization curve is in favorable agreement with the experimental polarization curve but at high current density, the discrepancy between the computational results and experimental data is slightly large, and the model always under predicted the current density in the high current density region. In the high current density region, the low current density of the numerical results may be caused by the presence of liquid water in the catalyst layers and the gas diffusion layers. In presence of liquid water, effective porosity of gas diffusion layers and catalyst layers decreased, and mass

Fig. 2. Comparison between experimental [25] and numerical data (PC = 5 (atm), membrane thickness = 2.3294 (mm), αan = 2, RHa = 1 and RHc = 1).

transfer resistance increased. In order to determine the inlet gas composition as a function of temperature, the following relation between the temperature and the saturation pressure of water has been used: log10 psat = −2.1794 + 0.02953v − 9.1837e − 5 × v 2 + 1.4454e − 7 × v 3

(1)

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Fig. 4. Cathode pressure effect on cell performance.

Fig. 3. Inlet gas composition for different pressures.

where υ is the temperature (°C). The molar fraction of water vapor in the incoming gas stream is simply the ratio of the saturation pressure and the total pressure: xH 2O ,in =

psat . pin

(2)

Since the ratio of nitrogen and oxygen in dry air is known to be 79:21, the inlet oxygen fraction can be found via: xO 2, in =

1 − xH 2O ,in

1 + 79 / 21

.

(3)

The resulting inlet gas composition for different pressures is shown in Fig. 3. 2.3 Effect of cathode pressure Since the saturation pressure for water is only a function of temperature, it remains constant for a variation of the inlet pressure, and the molar fraction of water in the incoming cathode gas stream is given by the Eqs. (1), (2). The molar oxygen fraction results then out of Eq. (3). It was already noted in Fig. 3 above 3 atm, the composition changes only slightly with the pressure. The polarization curves shown in Fig. 4 reveal a significant change in the initial drop-off, when the pressure is changed. This can be attributed to the change in the equilibrium potential that goes along with a decrease in the reactant pressure (Nernst equation). To a much lesser extent, the decrease in the exchange current density with decreasing pressure also contributes to this effect. 2.4 Effect of anode transfer coefficient αan Transfer coefficients are important and effecting parameter on current density. In this work the effect of reducing the transport coefficient on cell performance was investigated.

Fig. 5. Anode transfer coefficient effect on cell performance.

The default coefficient is intended as 2. Decreasing the coefficient leads to reduction of current density and power density in the cell. The reason can be explained by Butler-Volmer equations (Eqs. (4), (5)). According to this equation by reducing the transfer coefficient of anode, the rate of current density corresponding to each voltage and consequently the power density decreases. The Fig. 5 shows current and power density of base model for transfer coefficient. In present work the coefficient was reduced from 2 to respectively 0.4 and 0.2, and for each coefficient the curves of current density and power density are plotted and compared.  [H2 ] Ran = janref   [H2 ]ref 

 [O2 ] Rcat = j   [O2 ]ref  ref an

janref

γ an

   

(e

αamFηan / RT

γ cat

   

( −e

−αcat Fη an

−e

α amFηcat / RT

+e

RT

)

−α cat Fη cat

(4)

RT

)

(5)

is volumetric reference exchange current density (A/m3), γ is concentration dependence (dimensionless), α is transfer coefficient (dimensionless), F is faraday constant (9.5*107 C/Kgmol).

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Fig. 7. Effect of membrane thickness on fuel cell performance. Fig. 6. Relative humidity effect on cell performance.

2.4 Effect of anode and cathode relative humidity (RH) If the incoming gas is completely humidified, the fuel cell performance will increase with increasing temperature. If the humidity is less than necessary amount, drying the membrane reduces the membrane protonic conductivity and the result is reducing cell performance. It is essential to humidify the anode inlet gas in low current density, but it is not necessary in high current densities. The reason for this is that in high current density water is produced in cathode catalyst and necessary humidity easily reaches to the membrane, so as what is said humidification is not essential in high densities. Because drying the membrane may occur at the anode and water flooding phenomena may take place in cathode side. In many cases it can be seen that increasing the humidity of gases into cathode leads to cell performance reduction. In this study the humidity of anode and cathode decrease from level RH = 1 simultaneously to RH = 0.5, and RH = 0.25 and performance of cell was investigated at these levels. It can be seen when the humidity of both anode and cathode side decrease simultaneously the performance of cell decreases too. Because by this process the water level in the membrane diminishes and the membrane ionic conductivity and consequently the performance reduces. The Fig. 6. shows that the current density loss is more for RH = 0.25. The reason is severe drying of membrane and tense decline of ionic conductivity in this humidity. According to the obtained numerical results for different operating conditions, this study suggests that how we may use ANFIS network for modeling proton exchange membrane fuel cell (PEMFC) performance. 2.5 Effect of membrane thickness In Fig. 7 we investigate the effects of membrane thickness on the fuel cell potential and current density. As we know, ion conductivity resistance decreases as the membrane thickness decreases and it has no effect on the cell open circuit potential.

The membrane thickness increases from 0.23294 to 0.23994 mm. It can be obtaied from Fig. 7 that fuel cell potential clearly decreases while membrane thickness increasing. The membrane thickness effect is significant in the high electrical potential.

3. Neural and Neuro-Fuzzy networks Artificial neural network is a calculation tool which is used to test the data and to create a model by these data. When neural network applies the training data for learning latent patterns in the data, it may use them to access to the outputs. On the researcher’s objectives, various kinds of artificial neural networks may be used. One of the most well-known artificial neural networks is multilayer feed forward neural network which is a neural network instructed by supervisor. This neural network is useful for solving the problems that include learning the relationship between input and output sets. In fact, this is a method of instructing by a supervisor to learn the relationships between data by training data sets. In the error back propagation algorithm, the network creates an output (or an output set) for the provided input criterion and compares the reaction with proper reaction of each neuron. Then, the weights of network are corrected to reduce the error and the next criterion is emerged. The weights will be corrected continuously, until the total errors are less than the authorized error value. Since, this algorithm has descending gradient in the error function, so the inputs correction gradually reduces mean square error [26, 27]. As moving forward, the neuro-fuzzy networks normally calculate the nodes outputs up to last layer in every period of instruction. So, the resulted parameters are calculated by least square error method. After calculation of error in returning backward route, the error ratios are distributed on condition parameters and their values are corrected by error descending gradient method. Various structures suggest establishing a fuzzy system by neural networks. One of the most powerful structures which have been developed by Jang [28] is known

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In which x is input value of the node and Ci and σ i are membership function parameters of this set which explain Gaussian membership function center and Gaussian membership function width respectively. Layer 2: In this layer input signals values into each node are multiplied by each other and a rule firing strength is calculated. Oi2 = ωi = µ Ai ( x) µ Bi ( y ),

i = 1, 2

(7)

In which µAi is the membership grade of x in Ai fuzzy set and µBi is the membership of y in fuzzy set of Bi. Layer 3: This layer nodes calculate rules relative weight, in which ωin is the normalized firing strength of ith rule. Fig. 8. Architecture of ANFIS.

Oi3 = ωin =

as adaptive neuro fuzzy inference system (ANFIS). The main instruction approach in this structure is error back propagation which scatters the error value toward inputs by algorithm of the steepest gradient descent and corrects the parameters [28].

ANFIS system uses two neural network and fuzzy logic approaches. When these two systems are combined, they may qualitatively and quantitatively achieve a proper result that will include either fuzzy intellect or calculative abilities of neural network. As other fuzzy systems, the ANFIS structure is organized of two introductory and concluding parts which are linked together by a set of rules. We may recognize five distinct layers in the structure of ANFIS network which makes it as a multi-layer network. A kind of this network, which is a Sugeno type fuzzy system with two inputs and one output, is shown in Fig. 8. As shown in Fig. 8, this system contains two inputs x and y and an output or f which is associated with the following rules: Rule 1 If (x is A1) and (y is B1) then f1 = p1x + q1y + r1 Rule 2 If (x is A2) and (y is B2) then f2 = p2x + q2y + r2 In this system, Ai, Bi and fi are fuzzy sets and system’s output respectively. pi , qi and ri are designing parameters which are got during the learning process. If we consider the output of each layer in the ANFIS network as Oij (ith node output in jth layer) then we may explain the various layers functions of this network as follows: Layer 1: In this layer, each node is equal to a fuzzy set and output of a node in the respective fuzzy set is equal to the input variable membership grade. The parameters of each node determine the membership function form. Because we used the Gaussian membership function in this study, so we will have: 1 x − ci 2 − ( ) 2 σi

.

i = 1, 2

(6)

(8)

Layer 4: This layer is named rules layer which is got from multiplication of normalized firing strength (has been resulted in the previous layer) by first order of Sugeno fuzzy rule. Oi4 = ωin f i = ωin ( pi x + qi y + ri ),

4. Architecture of ANFIS

µ Ai ( x ) = e

ωi , ω1 + ω 2

i = 1, 2

(9)

Layer 5: This layer is the last layer of network and is composed of one node and adds up all inputs of the node. 2

O15 = ∑ ωin fi = i =1

ω1 f1 + ω2 f 2 , ω1 + ω2

i = 1, 2

(10)

Briefly, the first layer in ANFIS structure performs fuzzy formation and second layer performs fuzzy AND and fuzzy rules. The third layer performs normalization of membership functions and the fourth layer is the conclusive part of fuzzy rules and the last layer calculates network output. According to these, it is obvious that the first and fourth layers in ANFIS structure are adaptive layers in which Ci and σi in layer 1 are known as premise parameters relating to membership function of fuzzy input. In layer 4, ri , qi and pi are adaptive parameters of the layer and called consequent parameters [29, 30]. There are adaptive and consequent parameters sets in ANFISstructure. In fact, when the simulation has been conducted correctly, providing that both sets of parameters are estimated so as the model error function has the lowest value in training and experimental sections. These parameters are obtained two passes: In first pass, we assume that the adaptive parameter sets are constant and the consequent parameter sets are calculated by least square error algorithm; this pass is called forward pass. In the second pass which is named backward pass, the consequent parameters are assumed to be constant and the adaptive parameters set is obtained by gradient descent algorithm. When we obtained the parameters sets of the model, we can calculate the value of the model output for each orderly pair of training data and compare them with values that have been anticipated by the model. Consequently, the error func-

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Table 2. Parameters of membership functions for current density I (A/cm2) modeling. Input 1 PC (atm)

Membership function

Input 2 Voltage (V)

Input 3 membrane thickness (mm)

Input 4 αan

Input 5 RHa

Input 6 RHc

N

m

n

m

n

M

n

m

n

m

n

m

MF1

0.8491

3

0.1853

0.4829

0.0299

2.3290

0.7658

0.1955

0.3169

0.2484

0.3169

0.2484

MF2

0.8491

5

0.2206

1.3460

0.0214

2.4020

0.7888

1.9840

0.3196

0.9986

0.3196

0.9986

n represents Gaussian MFs width, m determines Gaussian MFs center

tion of the model's instruction is determined. After considering the appropriative of this error function, the training process is stopped and the final model is achieved.

Table 3. Statistical result for current density I (A/cm2) modeling.

current density I (A/cm2) modeling

5. Results and discussion

MAE

RMSE

IA

0.02301

0.03224

0.99769

Grid partition method of fuzzy inference systems was tried to generate the fuzzy rule base sets. The performance of proposed model tested by using mean absolute error (MAE), root mean square error (RMSE) and Index of Agreement (IA) values. If Q1 , Q2 , Q3 , …, Qn are n observed values, P1 , P2 , P3 , …, Pn are n predicted values and Qm represent the average value of observed values then the mean absolute error (MAE), root mean square error (RMSE) and Index of Agreement (IA) values are as follows [31]: MAE =

1 n ∑ Qi − Pi n i=1

(11)

2 1 n ∑ ( Qi − Pi ) n i=1

RMSE =

n

IA = 1 −

∑(Q − P ) i

(12) Fig. 9. Comparison between numerical-validated data and ANFIS model for current density, I (A/cm2), modeling. (PC = 5 (atm), membrane thickness = 0.23294 (mm), αan = 2, RHa = 1 and RHc = 1).

2

i

i =1

n

∑  Q − Q i

i =1

m

+ Qm − Pi 

2

.

(13)

There has been a total number of 180 input–output numerical-validated data considering five input parameters, namely pressure at the cathode side PC (atm), voltage V (V), membrane thickness (mm), Anode transfer coefficient αan, relative humidity of inlet fuel RHa and relative humidity of inlet air RHc that were obtained from previous studies were used for the model of current density I (A/cm2) in respect to their effective input parameter. This data set was divided randomly into two subsets as 80% for training and 20% for testing purposes. More data were used in the training phase because ANFIS is more adapted nonlinear functional dependency between input and output variables. Optimum ANFIS structure was obtained by trial and error of grid partition fuzzy inference system and the lowest RMSE values were obtained with grid partition system. Input variables were fuzzified with different membership functions, which were labeled MF1 and MF2 for current density I (A/cm2) model with Gaussian membership function. The parameters of these membership functions are given in Table 2.

The 64 rule base of this model that reflected the physical property of the system along with membership functions and optimum consequent parameters (Matrix a 64 × 6 with 64 rows and 6 columns) obtained after the ANFIS training process. 5.1 Model Validation Three statistical criterions were used to determine how well the FIS model could predict current density corresponding to various values of inlet variables. Fig. 9 shows plot of the numerical-validated data and ANFIS modeled utilizing of testing data. This diagram demonstrate that the predicted values are close to the numerical-validated values, as many of the data points fall very close to the diagonal (green) line in scatter plot. Clearly the model which is created by ANFIS has an agreement with the numerical-validated data. Statistical result for modeling is given in Table 3.

6. Conclusion This study suggests that how we can use ANFIS network

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for modeling proton exchange membrane fuel cell (PEMFC) performance. Result analysis and figure clearly demonstrate that this system is more effective for our proposed models. This study also indicates the high ability of ANFIS network for modeling more complicated engineering processes. Whereas the system does not require clear, definite and a large sample data, it is a more appropriate method than classical modeling approaches. However, whatever the effective parameters are identified and applied better in the modeling, surely improved results will be got.

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Sajad Rezazadeh was born in Urmia in 1984. He passed entrance exam of Technical University of Urmia in mechanical course in 2002. Immediately after finishing B.S, he was accepted in Master Degree of the same course (Energy conversion field). He finished his M.sc degree with his thesis about computational fluid dynamics modeling of proton exchange membrane Fuel cell. He was accepted in PhD and now he is studying in second year. During this nearly 8 years, he has presented several articles in internal and international seminars about main mechanical topics such as fuel cells and heat exchangers.

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Mehdi Mehrabi is from Iran. He passed entrance exam of Technical University of Urmia in mechanical course in 2007. He finished his M.sc degree in mechanical engineering (energy conversion field).

Tuhid Pashaee was born in Urmia in 1985. He passed entrance exam of Technical University of Urmia in mechanical course in 2002. Immediately after finishing B.S, he was accepted in Master Degree of the same course (energy conversion field). He finished his M.sc degree with his thesis about computational fluid dynamics modeling of helical heat exchangers. Iraj Mirzaee was born in 1960 in Ahar city in Iran. He received BS degree in Mechanical Engineering in Mashhad University in 1986. He started Msc. degree in mechanical engineering (energy conversion field) in Esfehan University in Iran and finally he received his Ph.D degree in mechanical engineering (energy conversion field) in 1997 at the Bath University in England. He is an associated professor in the mechanical engineering department at faculty of engineering of Urmia University. His professional interests are in the field of CFD, turbulent, fluid flow, energy conversion problems and turbine gas.