On neural network modeling to maximize the power output of PEMFCs

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Introduction
Fuel cells (FCs) can provide efficient energy conversion with a low impact on the environment and accordingly they are considered as a potential source of alternative energy.FCs are of interest in the production of independent commercial electricity, residential applications, and power plants.PEMFCs usually operate at low temperatures and may provide benefits like high energy density as well as safe operation etc. Due to the low operating temperature and good performance, PEMFCs are nowadays of great interest in providing power for the propulsion in the automotive field [1].
Nevertheless, there are several barriers that have to be overcome, e.g., high cost, weight, and volume, to make PEMFCs competitive to traditional engine power systems, i.e., internal combustion engines [2e4].Mathematical models and simulations are then needed to enable design and performance improvements and to optimize the operating conditions so that the output and efficiency of the fuel cell can be increased [5].The operating conditions play a significant role in the PEMFC performance [6,7].The performance optimization is a key approach to achieve a cost reduction in PEMFCs, as more compact stacks can be achieved featuring a reduced number of cells for a given power output.
The method of artificial neural network (ANN) is known to be a powerful tool in nonlinear modeling [8].Several different ANN models to optimize PEMFC operations [8e14] have been presented and these include static and dynamic states, see Table 1.
A model for the management of water was developed by Zhang et al. [15].Using a repeated neural network optimization (RNN), a prediction model control mechanism was proposed.The models were implemented in MATLAB and SIMULINK environments.The simulations revealed that by using this method, fluctuations in water concentration in the cathode could be avoided and accordingly the lifetime of the PEMFC stack could be prolonged.In another study, Lebreton et al. [16] approved a Fault Tolerance Control Strategy (FTCS) for PEMFC water management and validated it for a real PEMFC system.A combined method of the sequential neuralnetwork approximation and orthogonal arrays (SNAOA) to determine the performance parameters in the operation of PEMFCs was presented by Chang [17].
A number of articles have used other methods to optimize the operation of a single PEMFC [5,18e23].Salva et al. [5] conducted an optimization study to maximize the performance polarization curve with EES (solving the engineering equation).Mawardi et al. [18] suggested an optimization model maximize the power density of a PEMFC.The numerical model of the fuel cells was solved using simulated annealing and a simplex search algorithm.The Taguchi method was applied by Kaytakoglu and Akyalcin [19] to find the optimal operating conditions for maximum PEMFC power density.Askarzadeh and Rezazadeh [20] applied a modified particle swarm optimization (MPSO) method for a PEMFC.They proved that the MPSO can be regarded as a useful and reliable method to optimize the model parameters.They claimed that also it might be applicable for solving other complex problems of optimization of fuel cells.Meidanshahi and Karimi [21] considered a nonlinear dynamic model for a PEMFC analysis in one dimension.The operating conditions of the cell were optimized at steady-state conditions in order to obtain the most suitable parameters for achieving the highest and most uniform distribution of the current density.The differential evolution (DE) was used as an optimization algorithm.Zhang et al. [22] determined the optimum temperature of a hightemperature PEMFC in terms of performance and CO tolerance as well as durability.Kanani et al. [23] applied the response surface method (RSM) to find out the maximum power of a single PEMFC.
In addition, in other works ( [24,25]) parameter optimization of a PEMFC stack has been investigated.A niche hybrid genetic algorithm (HGA) was used by Mo et al. [24] to optimize a PEMFC.The input-output data used by them were output-voltage and demand current of the stack, cathode and anode pressures.Their genetic algorithm is a modified one and they found that it might be effective and reliable to optimize the model parameters of a PEMFC.Liu et al. [25] used an orthogonal experimental design for the optimization of the performance of a PEMFC stack.For this purpose, the operating parameters included operating temperature, stoichiometry in the cathode, relative humidity as well as backpressure.The results revealed that operating temperature and stoichiometry in the cathode side have a greater impact on the output voltage and efficiency of the stack compared to other parameters.
The ANN has advantages over other analytical methods.Among these, it is worthwhile to mention the use of fewer assumptions for modeling and excellent non-linear approximation ability.In addition, an incomplete database can be applied and it has a low sensitivity to noise [26].
In this paper, the artificial neural network is applied to find the operating conditions which maximize and/or minimize the power output.An analytical one-dimensional model introduced by Salva et al. [27] is used as a dataset for the ANN network (section 2).This model simulates the main phenomena occurring during the fuel cell operation, i.e., electrochemistry, mass transport (gas and liquid) and heat transfer.In addition, the analytical model has been thoroughly validated versus experimental data including cell voltage and water content inside the PEMFC (Tests were conducted in the previous work [5] for a 50 cm 2 fuel cell).Two parameters were used simultaneously in the validation process to ensure that the results are accurate.Validation was carried out for different operating conditions, i.e., temperature, cathode and anode stoichiometry, and relative humidity in the cathode and anode.The NeuroSolutions software [28] is used to simulate and analyze a PEMFC performance using an artificial neural network (ANN) approach.There are three basic steps in developing the neural network, namely network training on the data, network testing for accuracy, and creating predictions/classifications from new data.The NeuroSolutions Excel can handle this entirely automatically in one simple step [28].The main novelty of the current work is the analysis of a PEMFC with an MPL and maximizing the operating conditions for any current.The ANN model can simulate the system without using simplifying assumptions and to provide a powerful optimization tool.
where E 0 ðT; PÞrepresents the equilibrium open-circuit potential of the cell (V), h a;c and h a;a are the activation overpotentials in the cathode and anode (V), respectively, h r is the ohmic overpotential (V) while and h m;a are the concentration overpotentials in the cathode and anode (V), respectively.
where G 0 ðTÞ, R, F, P 0 , P sat , P anode=cathode are the Gibbs free energy (J), ideal gas constant (8.314J/moleK), Faraday constant (96,487C/ mole), reference pressure (Pa), saturation pressure (Pa), operating pressure in anode and cathode (Pa), respectively, n is the number of moles of electrons in a reaction (2 for anode side and 4 for cathode side), y i represents hydrogen mole fraction at the anode and water and oxygen mole fraction, respectively, at the cathode.

Calculation of activation overpotentials
The activation overpotentials are calculated by using the Tafel simplification [6,7] and are given by Eqs. ( 3) and (4).
where T and i represent operating temperature ( o C) and current density (A/m 2 ), respectively, a c and a a are the charge transfer coefficients at the cathode and anode, respectively, while i 0;c and i 0;a are exchange current densities in the cathode and anode (A/m 2 ), respectively.Eqs. ( 5) and ( 6) are used to calculate the exchange current densities, [6].
where i ref ;a and i ref ;c are the reference values of the exchange current densities without concentration losses and at a certain reference temperature for the anode or cathode (A/m 2 ), respectively.C c;GDLÀCL and C a;GDLÀCL represent the oxygen or hydrogen concentration at the cathode and anode side (mol/m 3 ), respectively.The activation energies, E a;a and E a;c , are valid at the anode and cathode electrodes (J/mol), respectively.C ref is a reference concentration (mol/m 3 ), and g i means the reaction order of the elementary charge transfer step.

Calculation of the ohmic overpotential
The electrical conductivity and thickness of the bipolar plates, GDLs, CLs, MPLs and the membrane affect the ohmic overpotential.In addition, as the contact resistance at the interface between the GDL and bipolar plate affects the performance of the fuel cell, it is included in the ohmic overpotential [31].
where t i and s i are thickness (m) and electrical conductivity (1/ Um), respectively, of the BP (bipolar plate), GDLs, MPLs, CLs and the MEA (membrane electrode assembly).R contact is the contact resistance at the interface between the GDL and bipolar plate (Um 2 ).The electrical conductivities were picked up in available datasheets for each material [33e35].The membrane protonic conductivity is a function of the water content and is calculated by Eq. ( 8) [36].
where C mem H2O;a and C mem H2O;c , respectively, represent the water concentrations at the anode and cathode sides (mol/m 3 ) of the membrane.
where n i is the number moles of electrons in the reactions (2 for anode side and 4 for cathode side) and i lim;i is the limiting current density at the cathode or anode sides.The limiting current densities can be found, e.g., experimentally.

Artificial neural network (ANN)
An artificial neural network (ANN) is built up of a number of elementary processing units, called neurons, which are connected together into a neural network.The relationship between two neurons is handled by weight functions [11].
With an available set of input and output data, the ANN is able to learn and construct non-linear mappings providing incentive solutions for modeling complex systems, especially those that are known to be without variable relationships.Concerning the structure of neural networks, two basic topologies exist, namely feed-forward networks and recurrent networks.In the feed-forward network, outputs of a certain layer are inputs of the following adjacent layer.The so-called hidden layers are situated between the input nodes and the output layer [38].
Among the different ANNs, the MLP (Multi-Layer Perceptron) type is the most common one used in PEMFC modeling [39].The MLP has three sections: the input layer, the output layer, and the intermediate or hidden layer.Any section can have several layers.Each unit performs a biased weighted sum of the inputs and sends this information to a transfer function.The output is given by the activation level of this transfer function.The organization of neurons is a set of parallel layers [11].
When the numbers of layers and neurons within these layers are fixed, training algorithms are applied to determine the network weights.The main purpose is to minimize the deviation between the calculated output from the neural network and an experiment.There are many techniques for training a neural network.The two main techniques employed by neural networks are known as supervised learning and unsupervised learning.The most common supervised training algorithm is known as back-propagation [39].Network training with back-propagation algorithms requires the steps described below: A set of examples is assembled for the network training.Each item includes inputs into the network and the corresponding solution which represents the desired output from the network.The network output is calculated.The deviation between the output of the network and the target vector of the learning pair is calculated.The network weights are set in a way that minimizes the error.Steps 1e4 are repeated for each vector in the instruction class to reduce the error for the entire class in a way that is acceptable.
By providing each set of information to the network, weights are corrected.Once the entire data set has been given to the network, an epoch has been completed.Another issue addressed in the learning algorithm is when the training should end.To do this, one of the following three methods can be used: A constant value for the number of times (epoch) is to provide the total data to the network.If the results are not satisfactory at the end of the training, the steps will be repeated again.During the training, after every round of data provided to the network, training is temporarily stopped and the network performance is measured.Network performance measurement can be conducted against a training series or a Cross-Validation Data series.The two above methods as graduation criteria can be combined.
Generally, the performance of a neural network is tested against a cross-validation data series to judge the future outcome of the network and prevent over-network training.
A suitable learning algorithm for training MLPs is the Genetic Algorithm (GA).GA imitates natural evolution.A population of chromosomes is a better solution due to different selection, crossover, and mutation.A uniform distribution of the population is randomly assigned primarily and the number of chromosomes contained is described by the population size.The chromosomes include optimized parameters and evaluation of the value of the solution is done using a fit function.This method is repeated many times and a parameter named "number of generations" is defined [40].Genetic algorithms are generally applied in four procedures [28]: Best inputs to the neural network are chosen; Neural network parameters are optimized; Training of actual network weights; Choose/modify neural network architecture.
In this study, the procedure to design the networks was implemented by the NeuroSolutions software [28].Users can train a neural network and test its performance directly in this software.In addition, this software has powerful built-in features which can be used to genetically optimize the network parameters.The software combines a neural network and a genetic algorithm to obtain the optimal network size and parameters [41].

Application of NeuroSolutions for excel
The NeuroSolutions software is used as it has powerful built-in features that can find the optimal neural network for a problem.These are genetically optimization of the network parameters, ability to train a neural network multiple times, and changing each neural network parameter in several implementations.Neuro-Solutions for Excel is broken down into five major modules that are used to create and train a network.These modules are shown in Fig. 1 [42] and described below.

Preprocess data
This module is used to apply different preprocessing techniques to the raw data to provide it as input into the neural network.Rows by percentages: The selection of this menu item provides a quick method for tagging multiple rows of data.Selection of this sub-menu item allows one to enter the percentages (of the total number of rows) to tag as Cross-Validation and Testing.The remaining part of the data will be tagged as Training.

Create/open network
This module is used to create a NeuroSolutions breadboard (neural network).

Training the network
This module is used to train a network using one of the several built-in training processes.This powerful module permits the user to easily find the optimum network for a particular problem.
Train Genetic: The selection of this option trains the active NeuroSolutions breadboard while genetically optimizing the network choice of inputs, step sizes, momentum values, and the number of processing elements in the hidden layer(s).Other parameters can also be optimized by setting them up manually within NeuroSolutions.The goal of the optimization is to find the parameter settings that result in a minimum error.If crossvalidation is used, the goal will be to minimize the crossvalidation error.Otherwise, the goal will be to minimize the training error.To perform genetic training, first, an initial population of networks is randomly created, each having a different set of parameters.Each of these networks is then trained and evaluated (to determine its fitness) based on the minimum error achieved.The characteristics of the good networks are then combined and mutated to create a new population of networks.Again, the networks in this population are evaluated and the characteristics of the best networks are passed along to the next generation of networks.This process is repeated until the maximum generations or maximum evolution time is reached or the user stops the evolution.Train: The selection of this menu item, the active Neuro-Solutions breadboard is trained one time and the best network weights are saved.

Tests of the network
This module is used to test the network after the optimum network has been found using the Train Network module.In testing the network, various performance measures are computed.

Analyze the network
This model aims to analyze the findings.

On designing the fuel cell artificial neural network
In this study, the process of designing the network is implemented by NeuroSolutions, where the MLP model of the neural network is constructed.The topology of the network is depicted in Fig. 2. As can be seen in this Figure, the network includes one input layer, two hidden layers, and one output layer.Network inputs are operation temperature, relative humidity, anode stoichiometry, cathode stoichiometry as well as current.The output of the network is the voltage.Table 2 shows the ranges of network input parameters.The hyperbolic tangent activation function (f ðxÞ ¼ tanhðxÞ ¼ e x Àe Àx e x þe Àx ) is used for the hidden and output layers.
To create the network, 1296 series of data, 1296 inputs (T, i, RH, anode stoichiometry and cathode stoichiometry) were used.For   each of these, there is one input, and accordingly we have 1296 outputs.The data were randomly divided into three independent subsets, namely 70% for training, 20% for cross-validation and 10% for tests.This division ensures that each subset contains the same amount of data from any operating mode as the initial dataset [11].
The number of neurons in the first and the second hidden layers of the network was 40 and 45, respectively.It should be noted that there is no precise method allowing the selection of the optimal neuron number in the hidden layers.In this work, a "trial-and-error" procedure is adopted.It starts from a small number of neurons and this number is successively increased until an acceptable compromise between complexity and performance of the model is achieved [11].Associated with this procedure, the mean square error of the difference between the response values of the experimental data and the model data was calculated.The LevenbergeMarquardt procedure is selected for the learning rule and the number of the maximum epoch was set to 1000.
The training algorithm used was GA (Train Genetic option as indicated in Section 4.4), which performs the training while genetically optimizing the network's choice of inputs, step sizes, momentum values, and the number of processing elements in the hidden layers.The goal of the optimization is to find the parameter settings that result in the minimum error (minimize the training error).The software creates first a random initial population of networks with each a different set of parameters.Each of these networks is then trained and evaluated to determine its fitness based on the minimum error achieved.The characteristics of the good networks are then combined and mutated to create a new population of networks.After a new evaluation, the characteristics of the best networks are passed along to the next generation of networks.The parameters of GA that were chosen were: Number of Epoch: 1000; Population size: 50; Maximum generations: 100; Maximum evaluation time: 60.
Table 3 reports the performance of networks 1 to 4 in terms of the mean square error (MSE), the root mean square error (RMSE), and the linear correlation coefficient (r) between model data and neural network outputs.The MSE and RMSE are defined in Eqs. ( 15) and ( 16) below.
6. Results and discussion

Experimental validation
To find the fuel cell polarization curve, three experiments were performed.These were conducted in previous work [5] for a 50 cm 2 fuel cell.The operating conditions for these three experiments are provided in Table 4.The validation of the model [27] is presented in Fig. 3.The polarization curves obtained by the model correspond well with the experimental data.Average absolute relative errors (AARE) are used to compare the experimental data with the results from the model and are calculated by Eq. ( 17).
The results show that Test 1, Test 2 and Test 3 achieved 3.68%, 2.80% and 2.01% of the AARE, respectively, indicating that good matching between the model and experimental data has been reached.

Optimization results
The output results of the neural network trained by the genetic algorithm in comparison with the model results suggested by Salva et al. [27] are presented in Fig. 4. According to this Fig. and 1.95% of AARE, the network training is deemed successful by the genetic algorithm and good agreement between network results and model results is found.
According to the results obtained from the neural network, the operating conditions offering maximum power output and the cell voltage corresponding to these conditions are shown in Table 5.The polarization curve with the best performance appears due to a combination of four different polarization curves.
Differences between the different sets confirm the importance of choosing appropriate operating conditions for various currents.The polarization curves, as well as the maximum performance of the PEMFC for the four different operating conditions, are shown in Fig. 5.
It is observed that for low currents, the optimal operating conditions appear at high temperatures, high relative humidity, high stoichiometry at the cathode and anode sides.If the current is increased, the outputs of the network recommend a reduction of the temperature from 70 C to 60 C. In addition, cathode stoichiometry should be reduced from 5 to 2, but anode stoichiometry is at the maximum value.This is because an increase in the temperature also increases the limiting current density [43].Hydrogen is transferred from the flow channels at a much faster rate at high currents, but within the air cathode, excessive water is produced in the form of liquid.This creates a gas-liquid two-phase flow in the porous cathode electrode.Transport of two-phase gaseous reactants to the reaction surface, i.e., the cathode-membrane interface, then becomes a mass transfer limiting mechanism [44].In Fig. 5, the set 4 shows an abnormal behavior at a current around 13 A. A similar thing is also reflected in Fig. 6.This might be due the  fact that the relative humidity has its minimum value at this current.At a certain limited range of the operating parameters, besides the operating conditions offering maximum power output and corresponding cell voltages, there are some operating conditions offering minimum power and corresponding cell voltages.Those conditions are shown in Table 6 for various currents (based on network results).These results clearly show that selecting operating conditions is important to increase the output power of a specific PEM fuel cell [5].The polarization curve with the worst performance is found by combining three different polarization curves.
Set 5: The polarization curves corresponding to these three operating conditions and the minimum performance of the PEMFC are shown in Fig. 6.It is observed that at low currents, high stoichiometry at the cathode, low temperature, and relative humidity, as well as low stoichiometry at the anode provide the lowest power and worst performance.On the other hand, under these conditions, the activation losses are the highest [5].By increasing the current, the network results show only a change with temperature and the PEMFC performance will change.An increase of the temperature from 50 C to 60 C increases the ohmic losses and dry-out of the membrane takes place [5].
At a current of 13 A, the cell shows the lowest power.The operating condition at this current shows the maximum value of relative humidity.This result is according to the literature because humidification is not important at high currents.The reason is that dehydration may occur at the anode side and flooding at the

Table 5
Operating conditions for the maximum power.cathode side.Accordingly, the humidifying of the cathode gas stream is not meaningful [45].
The polarization curve and the power curve for maximum and minimum performance are presented in Fig. 7.This figure confirms the very good agreement between the network and the model.The network results of the output power indicate that for the operating conditions of maximum performance, the power value reaches 9.78 W at 15 A. On the other hand, the maximum output power with minimum operating conditions is about 4.07 W at 13 A. A comparison between the operating condition of maximum performance with the operating condition of minimum performance, at a reference current of 12 A, shows 23.6% (8.02 W versus 6.49 W) and 28.9% (8.16 W versus 6.33 W) increase of the power by the model and the network, respectively.

Optimization of the operating conditions
In the following, the network results are used to predict the influence on the PEMFC performance based on changes in the operating conditions.As high temperature, high relative humidity, high stoichiometry at the cathode and anode sides provide the best performance (see section 4.2), these conditions (T ¼ 70 C, RH a/ c ¼ 100%, l a ¼ 5, l c ¼ 5) are selected as the fixed condition.At low current densities, an increase in temperature improves the cell performance.Nevertheless, at high currents, an increased temperature gives the opposite result.This is so because as the temperature increases, the membrane ion conductivity is increased as well, which improves the diffusion of the hydrogen protons in the membrane.In addition, as the electrochemical reaction becomes faster, the water production in the cathode is increased which results in better hydration of the membrane.Accordingly, the membrane ionic resistance is reduced [46].Then the performance of the cell is improved.At high current, an increased temperature imposes an increase in the water vapor partial pressure, which reduces the negative influence of flooding but it may also lead to membrane drying, which results in a decrease in ion conductivity.As a result, the performance of the cell decreases.
In Fig. 9, the influence of the relative humidity on the polarization curves of the PEMFC at a fixed operating condition (P ¼ 1 bar, T ¼ 70 C, l a ¼ 5, l c ¼ 5) is depicted for three relative humidities (50%, 80% and 100%).By increasing the RH of the reactants, improvement of the performance is achieved.This is so as a change in the water mole fraction, due to the higher relative humidity of the inlet gases, increases the amount of water in the membrane.Then a reduction of the ionic resistance occurs and the proton movement is enhanced and accordingly the outlet current is increased at a certain voltage.As membrane drying is greater at higher temperatures, a higher inlet RH is contributing to the membrane hydration.For low currents, a change in the relative humidity does not affect the performance.In contrast, at high currents, a higher relative humidity improves the performance, as a considerable drop in the ohmic resistance occurs.These results agree with those presented in Ref. [47e49].
Fig. 10 provides the influence of the anode stoichiometry on the polarization curves of the PEMFC at fixed operating conditions (P ¼ 1 bar, T ¼ 70 C, RH ¼ 100%, l c ¼ 5) for three anode stoichiometries (1.5, 3 and 5).It is observed that for all currents, increasing the anode stoichiometry improved cell performance, but the change is not so significant.Because this increase leads to increased hydrogen concentration, the electrochemical reaction rate is  increased as well.Fig. 11 provides the influence of cathode stoichiometry on the polarization curves of the PEMFC at fixed operating conditions (P ¼ 1 bar, T ¼ 70 C, RH ¼ 100%, l a ¼ 5) for three cathode stoichiometries (2, 3 and 5).At low currents, a change in the cathode stoichiometry does not affect the cell performance.However, at high currents, a decrease of the cathode stoichiometry results in improvement of the cell performance.At low current, the cell is influenced significantly by the activation losses and it is found that cell performance is almost independent of the cathode stoichiometry.Limitations of the mass transport or concentration overpotentials appear when the reactants cannot be supplied sufficiently fast for the chemical reaction to take place.This may happen at high currents when a lot of liquid water is produced at the cathode [50], so for high currents, decreasing the cathode stoichiometry improves the cell performance.In addition, in this situation, the concentration of water inside the duct increases faster and as a result, the membrane becomes humidified more quickly.
It must be noted that the conclusions of the proposed ANN model in this work may not be directly applicable in practice to any cell and operating conditions, as the properties and design of the cell components are obviously playing a fundamental influence on the operating conditions that lead to optimum performance.The analysis and discussions presented are corresponding to the range of operating conditions defined in Sections 6.2 and 6.3 together with the cell used (with components described in Salva et al. [27]).However, the methodology for the ANN model development presented in this work is applicable to any fuel cell and could be used to optimize the performance of the fuel cell being considered in each case.

Conclusions
An artificial neural network (ANN) approach was applied to maximize the output power of a PEMFC for various currents.Various operating conditions were considered, i.e., operating temperature, relative humidity, stoichiometry at cathode and anode sides at a constant pressure of 1 bar.For this particular case, the comparison between the operating condition of maximum performance with the operating condition of minimum performance at a reference current of 12 A, shows 23.6% (8.02 W versus 6.49 W) and 28.9% (8.16 W versus 6.33 W) increase of the power outputs by the model and the network, respectively.
As the network results presented a very good agreement with model results, as AARE was 1.95%, the network results were used to study the influence of the operating conditions on the PEMFC performance.The main conclusions are as follows: 1.For low currents, an increase of the temperature improved the performance of the cell, but for higher currents, the cell performance decreased as the partial pressure of water vapor was increased due to the increased temperature and membrane drying.2. For low currents, the cell performance was relatively constant as the relative humidity was changed, but with increasing current, the cell performance was more perceptible to a change in relative humidity.Thus, as the relative humidity increases, due to the reduced charge transfer resistance, the cell performance was improved.3.For all currents, increasing the anode stoichiometry improved the cell performance, but the change was not so significant.This improvement resulted in increased hydrogen concentration and then the electrochemical reaction rate was improved.4. For low currents, a change of the cathode stoichiometry did not affect the cell performance.However, for high currents, the relative humidity was important.At high RH values, due to the mass transport limitations or concentration overpotentials, a decrease of the cathode stoichiometry improved cell performance.At low RH values, in general, it is better to increase the cathode stoichiometry as higher oxygen and water removal capability is achieved.
All the considered parameters in the model concerned the operating conditions of the PEM fuel cell, and therefore the power output was predicted only based on the optimum operating conditions.Optimization of the PEMFC performance based on design parameters will be in the scope of future investigations.The performance optimization is a key approach to achieve a cost reduction in PEMFCs, as more compact stacks can be achieved featuring a reduced number of cells for a given power output.The proposed ANN model revealed the maximum (or minimum) power output and the optimal operating conditions for any current, enabling the prediction of the optimal operation conditions for any current for achieving the maximum power output.The application of the ANN developed to the analysis of a PEMFC with MPL is also a novelty of this work.
This module is used to graphically tag portions of the data as Training Input, Training Desired, Cross-Validation Input, Cross-Validation Desired, Testing Input, and Testing Desired.Column(s) as Input: The selection of this menu item allows one to tag columns of data as Input.Column(s) as Desired: The selection of this menu item allows one to tag columns of data as Desired.

Fig. 3 .
Fig. 3. Validation of the model versus experiments in terms of polarization curves.

CurrentFig. 5 .
Fig. 5. Polarization curves for four different operating conditions and maximum performance.

Fig. 6 .
Fig. 6.Polarization curves for three operating conditions and the minimum performance.

Fig. 8
Fig. 8 depicts the effect of the operating temperature of the

Fig. 8 .
Fig. 8. Influence of operating temperature on the PEMFC performance.

Fig. 11 .
Fig. 11.Influence of cathode stoichiometry on the PEMFC performance.Fig. 9. Influence of relative humidity on the PEMFC performance.

Table 1
Applications of ANN for PEMFCs modeling.

Table 2
Ranges of network input parameters.

Table 3
Performance of GA-ANN model.

Table 4
Operating conditions in the three tests.

Table 6
Operating conditions for minimum power.
Fig. 7. Polarization power curves for maximum and minimum power.