Metamodel based design optimization approach in promoting the performance of proton exchange membrane fuel cells

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Metamodel based design optimization approach in promoting the performance of proton exchange membrane fuel cells Jr-Ming Miao a, Shan-Jen Cheng b,*, Sheng-Ju Wu c a

Department of Bio-Mechantronic Engineering, National Ping Tung University of Science & Technology, Taiwan, ROC Department of Power Mechanical Engineering, Army Academy ROC, Taoyuan, Taiwan, ROC c Department of Power Vehicle and Systems Engineering, Chung Cheng Institute of Technology, National Defense University, Taiwan, ROC b

article info

abstract

Article history:

This research presents a systematization and effectiveness approach in promoting the

Received 21 May 2011

performance of the power density of a Proton Exchange Membrane Fuel Cell (PEMFC) by

Received in revised form

Metamodel-Based Design Optimization (MBDO). The proposed methodology of MBDO

9 August 2011

combines the design of experiment (DoE), metamodeling choice and global optimization.

Accepted 20 August 2011

The fractional factorial experimental design method can screen important factors and the

Available online 16 September 2011

interaction effects in DoE, and obtain optimal design of the robust performance parameters by Taguchi method. Metamodeling then adopts the ability to establish a non-linear model

Keywords:

of a complex PEMFC system configuration of an artificial neural network (ANN) based on

Metamodel based design optimiza-

the back-propagation network (BPN). Finally, on the many parameters (factors) of opti-

tion (MBDO)

mization, a genetic algorithm (GA) with a high capability for global optimization is used to

Proton exchange membrane fuel cell

search the best combination of the parameters to meet the requirement of the quality

(PEMFC)

characteristics. Experimental results confirmed by the test equipment demonstrate that

Design of experiment (DoE)

the MBDO approach is effective and systematic in promoting PEMFC performance of power

Artificial neural network (ANN)

density.

Genetic algorithm (GA)

Crown Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

Due to the increasing rate of consumption of global petroleum by humans, fossil fuels have caused serious environmental problems, such as the greenhouse effect and acid rain, over the past decades. To preserve energy and develop other more efficient and cleaner substitutes, power generation systems have become an important issue. Of all green power generation technologies, fuel cells (FCs) are chemical engines that convert chemical energy directly into electrical energy, and are not subject to Carnot’s efficiency limit [1]. The Proton Exchange Membrane Fuel Cell (PEMFC) has been widely investigated because of its efficiency, cleanliness, modular

design, high-power density and quick startup even at low temperature. The PEMFC is one of the most promising candidates for future power generating devices in various fields of application such as electric vehicles, cell phone and laptop manufacturers, and distributed residential power generation [2e4]. To improve the system performance of power density, the optimization of design and the analysis in different conditions of the FC systems are important. Recently, a general trend of using commercial computational fluid dynamics (CFD) to model PEMFCs has evolved [5e7]. Several different mathematical models have been proposed to capture the behavior of different conditions to understand and improve the

* Corresponding author. Tel.: þ886 3 4371754. E-mail address: [email protected] (S.-J. Cheng). 0360-3199/$ e see front matter Crown Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.08.070

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performance of PEMFCs. Numerical modeling and computer simulation have been employed to understand the inner details of the physicochemical phenomena. To simplify calculations, the CFD simulations often ignore some effects of the parameters, resulting in some deviation from the real physical system. Even though the enhanced computing power of parallel computers in the calculation of accurate is threedimensional CFD models in PEMFC modeling, and considers the terms of the parameters and as the number of variables increases, the computational cost of accurate 3D modeling is large and not easily achievable. Although the experimental analysis of the FC can react to real physical phenomena, the work mostly focused on analyzing the effects of one factor at a time [8e10]. The major disadvantage of a one-factor method is that it fails to consider possible interactions between factors studied and results in a large cost when the number of experimental runs increases. The transport phenomenon in PEMFC was focused on numerical simulation that most of studying from survey of related literature, or almost on the parametric study of the effects of physical variables. It is important to have an adequate optimization method to solve for the overall performance of the PEMFC in term of the operating conditions without extensive calculations in systems research. Only a few reports dealt with the optimization of a set of design factors in PEMFC [11e13]. In this paper, a Metamodel-Based Design Optimization (MBDO) methodology is presented [14e17]. MBDO can investigate the impact of the cell’s operating conditions efficiently and promote practical total system performance more systematically than any other methods. A metamodel is an abstraction model that observes relationships between input parameters and output responses from a real system. It can decrease the calculation cost and still precisely handle physical phenomenon in the real system. A flowchart of the metamodeling is shown in Fig. 1. First, let Xi mean a factor i influencing the outputs of the real systemsði ¼ 1; 2; .; rÞ, and then Yu defines the response vector of the systemsYu ¼ fy1 ; y2 ; /; yj g. The metamodel defines the relationship between the response vectors Yu and the input variables Xi of the system represented as follows [15,17]: Y ¼ f1 ðX1 ; X2 ; .Xr Þ

(1)

A simulation model is an abstraction model from a real system, which only considers a subset of input variables fXi ji ¼ 1; 2; .; kg in which k is significantly smaller than the unknown r. The response of the simulation Y0 is defined as a function f2 of the subset and a vector of random numbers s, meaning the effect of the excluded inputs as shown by: Y0 ¼ f2 ðX1 ; X2 ; .Xk ; sÞ

(2)

A metamodel is a further abstraction from a stimulation model. The simulation input variables are a selection of a subsetfXi ji ¼ 1; 2; .; w; w < kg and the system is described below: Y00 ¼ f3 ðX1 ; X2 ; .Xw Þ þ e

(3)

where e is a fitting error, and with an expected value of zero. Metamodels are constructed in two principal steps. The first step involves selecting an adequate experimental design

Fig. 1 e Flowchart of the metamodeling approach.

method that includes factorial experimental design and Taguchi orthogonal arrays (OAs) to generate more efficient experimental dates. Artificial neural network (ANN) can be applied to optimize the system response in the second step. The use of ANN analysis as a metamodel often has constrains in solving the PEMFC complicated non-linear system. The present study first builds a performance metamodel from the PEMFC in different operating conditions based upon DoE data using the ANN approach. The ANN-based metamodel incorporating genetic algorithms (GAs) can be applied to an optimal parameter design, which can promote the performance of the power density in PEMFC. The experiment and analysis process of this research is depicted in Fig. 2. In this paper, the performance of the power density for the PEMFC system improvement was researched using MBDO. We investigate a single FC and the experimental systems are briefly introduced in Section 2. An overview of the research methodologies, which included the data collection from DoE, the metamodel established by ANN construction, and the optimization analysis of the GA is described in Section 3. The experimental analysis of the FC from the MBDO is shown in Section 4. The results and discussion are presented in Section 5. Finally, the conclusions from the present study are presented in Section 6.

2.

Experimental system

A single PEMFC parallel channel with active surface area of 25 cm2 used to obtain experimental data. The current collector with flow pattern used carbon plate of Schunk and end plate made of aluminum alloy 7075, all of that were tied with screw bolts. The flow channel width and depth was 1 mm, and rib width was 1 mm. The membrane-electrode-assembly (MEA) used for this experiment is Gore 5620 series as a film thickness of 3.5 mm from GORE eTEX. The platinum contain loading of 0.45 mg/cm2 and 0.60 mg/cm2 on anode and cathode, respectively. Two 0.4 mm carbon papers from the10BC series of SGL served as the gas diffusion layers (GDLs) and were added to MEA. A schematic diagram of the FC experimental apparatus as shown in Fig. 3 included a gas control system,

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Select the number of studying factors and levels for each factor

Design of experiment (fractional factorial experiment and Taguchi orthogonal arrays)

Prepare a trial data sheet and record experimental results

Listed S/N ratios, ANOVA results and obtain optimum design

Global optimum search by BPNN-GA

Confirmation experiments between OAs and BPNN-GA optimum solution for validation

Training BPNN metamodel

Yes

Is convergence ?

No

Increase number of neurons for hidden layer

PEMFC MBDO Fig. 2 e Flowchart of the MBDO research methodology.

mass flow control system, temperature control system, humidifying system and electronic load system. Fuel and oxidant gases controlled by mass flow control system and served pure hydrogen and oxygen, respectively. Reactant humidification achieved by temperature control water bottles. The polarization curve (current density versus voltage curves) of PEMFC were taken using HewlettePackard Inc. 6060B (scanning period 30 min) interfaced to a personal computer at constant current and recorded after the system arrived a stable steady state under the different operating conditions at a reasonable current density.

3.

Methodology of MBDO

3.1.

Design of experiment (DoE)

3.1.1.

Fractional factorial experiment

To obtain the relationship between the input parameters (factors) and the output responses (performance of power density) from the PEMFC, the metamodel dates were built

using the Design of Experiment approach (DoE). The DoE approach was used to reduce the number of experiments while ensuring the appropriate data would be obtained to allow a valid analysis using statistical methods, resulting in objective conclusions. The DoE of the fractional factorial design is useful when the number of possible factors is relatively large because it reduces the total numbers of experiments required. In general, a factorial design approach can be used in which all possible combinations of the factor levels are used. The full factorial design required 2k experiments, where k is the number of two levels factors, meaning only the lower bound and the upper bound of the range of factors. The number of factors considered in our study is 5; hence, the number of runs is 25 (32) for a full factorial design. However, using a suitable fractional factorial design, it is possible to reduce the number of runs to 16 (251 V ) thanks to the design generator E ¼ ABCD and ABCDE ¼ I (identity) with a resolution V design as shown in Table 1. In this way, a fractional factorial design is generated [18,19]. A majority of fractional factorials is used for screening the specified factors experimentally and usually is performed in the early stages. When

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Fig. 3 e Schematic diagram of the fuel cell testbench (MFC [ Mass flow controller).

there are many factors, the scarcity of effects principle can be invoked by which the system is assumed to be dominated by the main effects and lower order interactions. The design allows for the estimation of all main factors and all two factor interactions, but two factor interactions are aliased with three factor interactions. The effects of the important factors can be analyzed by the well-known technique of Yates’ rule. The

Table 1 e The 25L1 fractional factorial design form for five V linear factors. Tri. no

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

E ¼ ABCD

Basis design A

B

C

D

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2

1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2

1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

2 1 1 2 1 2 2 1 1 2 2 1 2 1 1 2

(The generate is E ¼ ABCD, sign 1 and 2 each of means low and high level).

treatment that called for each combination of different factor levels must be written down in standard form [18].

3.1.2.

Taguchi method

The principle of Taguchi is broadly applicable in DoE. The method proposed that the engineering optimization of a design or product is put into practice in the parameter design. The concept is to reduce the sources of variation in the quality characteristics of the product and reach a target of design robustness [20e22]. In addition, the philosophy expects that optimal design factor values obtained from the parameter design are insensitive to the variation of environmental conditions and other noise factors. Essentially, traditional parameter design developed by Fisher is complex and not easy to use. When the number of the design factors increases, a large number of experiments must be carried out. To solve this task, the Taguchi method uses a special design of orthogonal arrays (OAs) to learn the whole factor space with only a small number of experiments. Hence, the OAs from the DoE theory are applied to try to reduce a large number of variables with a small number of experiments. The conclusions drawn from small scale experiments are then valid over the entire experimental interval using the control factors and the corresponding level settings. Taguchi proposed signal to noise (S/N,h) ratios to measure the performance characteristic deviating from the desired valued. The S/N ratio for each level of design factor is computed based on the S/N analysis. The units of S/N are decibels (dB). A larger S/N ratio corresponds to the better quality characteristics. The performance characteristics in the analysis of the S/N ratio are adopted to an optimal power density in the PEMFC in the turning relationship shown below:

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S=N ¼ 10log

n 1X 1 n i¼1 y2i

! (4)

Where n is the number of experimental repetitions results in a trial number, yi is the observed response value of each trial and subscript i indicates the number of experiment design factors arranged in the OAs table (which regardless of noise levels). From the list showing the S/N rations for each level in every factor, linear graphs are depicted. The optimum level for each factor is obtained which based on the highest S/N ration. Moreover, an analysis of variance (ANOVA) is executed to analyze which design factors are statistically significant. The optimal combination of the design factors can be predicted within the S/N and ANOVA analyses [20]. When the optimal level of the design factors is selected, the next step is to predict the performance of the characteristics using the optimal level of the design factors. The evaluated S/ ^opt using the optimal level of the design factors can be N ratio h computed as: h ^opt ¼ h þ

n X ðhi  hÞ

(5)

i¼1

Where h is the total average S/N ratio of all the experimental values, hi is the mean S/N ratio at the optimal level, and n is the number of the design factors that significantly influence the quality characteristics of the performance. Finally, a confirmation experimental test is conducted to prove that the optimal design factors are obtained from the parameter design.

3.2. Metamodeling by back-propagation neural network (BPNN) An ANN is a kind of artificial intelligence technique that imitates the behavior of the human brain. Its non-linear mapping capability is a significant advantage that can approximate multiple inputs into multiple output relationships without requiring explicit mathematical representations between the input and output variables of the datum. Many non-linear modeling methods such as ANN have been applied in various fields of engineering, including modeling complex design transformation, adaptive sensor processing and control systems [23,24]. An ANN is a massively parallel-distributed processor and is comprised of weighted connectors, an adder and a transfer function, as in Fig. 4. The basic relationship as shown by the neuronal model is [23]: n ¼ wp þ b a ¼ f ðwp þ bÞ ¼ f ðnÞ

Fig. 4 e Schematic diagram of the artificial neuron processing unit.

networks architectures and training algorithms that use a back-propagation learning rule. The back-propagation neural network (BPNN) is a universal tool capable of approximating any measurable function to any desired degree of accuracy. A BPNN is defined according to the number layers of the input parameters with the neuron number in each layer and one or more hidden layers between the input layer and output layer. Each connection between two neurons can be adjusted by the synaptic weight. The network is trained using a suitable learning method to perform a particular function by adjusting the weights and biases.

3.2.1. Learning with LevenbergeMarquardt (LM) and Bayesian regularization (BR) BPNN is a well-known supervised learning rule that minimizes the mean square error between the target and prediction data of network. Improving the traditional extended time requires overcoming the shortcomings of the BPNN algorithm with the gradient descent algorithm. For a more accelerated convergence than that provided by the gradient descent approach, the heuristic optimal approach is applied with a Gauss-Newton approximation utilized in the LevenbergeMarquardt (LM) training. The LM approach is

Define fitness function

Random population

Evaluation Fitness

(6)

where n is the activation function, w is the weight of output signal, p is the input signal, b is the bias of the neuron, a is the output signal of network, and f is the transfer function. A simple neural network computes the linear sum values of the product from the synaptic weight and bias of the input that is passed through the transfer function and which limits the amplitude of the output of a neuron. Several forms of transfer function can be chosen, which depend on the desired output of the network such as the hard limit, pure linear and sigmoid. The ANNs have popular multilayer feed-forward

Optimal solution

Yes

Is convergence ? No

new generation

Set reproduction ,crossover, mutation Fig. 5 e Flowchart of GA solution setup procedure.

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Table 2 e Factors and levels used in fractional factorial design. Symbol A B C D E

Table 3 e Factors and levels used in Taguchi experiment. Symbol

Factors

Level-1(1)

Level-2(2)

Humidification temperature of anode (TH2 ,  C) Operating temperature of fuel cell(TFC ,  C) Humidification temperature of cathode (TO2 , C) Stoichiometric rate of hydrogenðlH2 Þ Stoichiometric rate of oxygenðlO2 Þ

50

80

50

80

B

50

80

C

1.2

2.7

D

1.2

2.7

E

A

Factors Humidification temperature of anode (TH2 ,  C) Operating temperature of fuel cell(TFC ,  C) Humidification temperature of cathode (TO2 ,  C) Stoichiometric rate of hydrogenðlH2 Þ Stoichiometric rate of oxygenðlO2 Þ

Level-1 Level-2 Level-3 50

65

80

50

65

80

50

65

80

1.2

1.9

2.7

1.2

1.9

2.7

Original levels are underlined.

designed to perform a second-order descent method training speed without having to compute the Hessian matrix, which is estimated using the gradients. In medium sized problems, the LM method is a non-linear optimization approach to achieve better results than conventional gradient descent algorithms [25]. Training a network with as few training samples of data as possible can reduce computation time. Thedisadvantageof such a network is overfitting too quickly, which means the network training error has a small value for the training samples but will become large when new input is presented. That discloses that the network recalled the training samples but is not able to generalize answers on samples of unseen input parameter combinations. The more experienced approach of the regularization optimization method has been successful applied to neural network training. The Bayesian Regularization (BR) approach includes modifying the objection function that is usually applied such as the mean sum of squared network errors [26]: F ¼ Ed ¼

N 1X ðei Þ2 N i¼1

(7)

The modification directly improves the model of the network training generalization capability. The objection function in Eq. (7) is extended with the addition of the term, Ew which is the sum of the squares of the network weights, defined by:

2

BC

Normal scores

1.5

n 1X w2 n i;j¼1 i;j

F ¼ aED þ bEW

(8)

(9)

where n the total number of network weights and ED is defined as the sum of square error of the predicted and actual network output. The parameters a and b are optimized in the Bayesian framework of Mackay and determine how much the weight decay regularization is involved in the error function F. To overcome the optimal regularization technique requires quite costly computation of the Hessian matrix; hence a GaussNewton approximation to the Hessian matrix is applied. The approximation based on the LM algorithm with regularization is used in this study for network training. The LevenbergeMarquardt within Bayesian Regularization (LMBR) training networks are robust and well matched to the data, revealing good generalization capabilities. The relative size of the objective function parameters dictates the emphasis for training. If a >> b, training will emphasize weight size reduction at the expense of network errors, thus producing a smoother network response. If a << b, then the training algorithm will drive the errors to be smaller.

3.3. (GA)

Optimization searching method-genetic algorithm

The GA is a heuristic search technique, which is based on the concept of biological evolution and natural selection theory. GA uses a random search method to avoid reaching a local

C

1

AD A CE AB

0.5 0 -0.5

CD

-1

E BE

-1.5 -2 -45

EW ¼

B

-25

-5 15 Effect estimates

35

Fig. 6 e Normal scores plot of effect estimates from Yates’ rule.

Fig. 7 e Linear graph of L27(313) and assignment of design factors.

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S/N(dB)

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A1

A2

A3

B1

B2

B3

C1

C2

C3

D1

D2

D3

E1

E2

E3

Factor levels Fig. 8 e Response graph of main effect plots of S/R value.

optimum in the optimization search problem so it has been widely applied to different types of optimization problems to seek the global optimum [27e29]. For simulating natural evolution, the variables in GA algorithms are coded into strings of binary bits called chromosomes. The objection function in the conventional optimization methods was changed to save computational resources by utilizing a fitness function in GA algorithm. Evaluating the fitness of every candidate solution determines whether it will contribute to the next generation of solutions. Therefore, at the conclusion

of each generation, a better population fitness can be acquired and is applied in the next iteration of the methods. The parent solutions that are more fit are more likely to reproduce, while those that are less fit are less likely to do so. Finally, the optimal solution is obtained by the massive propagation of chromosomes through competition. The main implementation steps of the GA following the initialization are given by the flowchart as shown in Fig. 5. GA algorithm operators, particularly crossover and mutation, control the reproduction of solutions. Generally speaking, chromosomes exchange

Table 4 e OAs of L27(313) and experiment data at current density 0.6(A/cm2). Trial no

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Power density (mW/cm2)

1

2

3

4

5

6

7

8

9

10

11

12

13

B

C

BC

BC

E

BE

BE

CE

e

A

CE

D

e

y1

y2

y3

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3

1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

1 1 1 2 1 1 3 3 3 2 1 1 3 3 3 1 1 1 3 3 3 1 1 1 2 1 1

1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2

1 2 3 1 2 3 1 2 3 3 1 2 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1

1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2

1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 3 1 2 1 2 3 2 3 1

1 2 3 2 3 1 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1 3 1 2 1 2 3

1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1

1 2 3 3 1 2 2 3 1 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1 1 2 3

1 2 3 3 1 2 2 3 1 3 1 2 2 3 1 1 2 3 2 3 1 1 2 3 3 1 2

271.55 288.12 291.35 290.19 275.75 265.32 303.86 298.14 298.65 303.77 275.11 291.17 300 .4 2 302.86 292.1 7 303.3 304.67 304.75 214.85 298.3 3 182.79 275.77 173.3 2 215.7 5 277.1 2 288.25 285.22

278.36 288.67 290.22 285.58 270.42 266.24 304.22 298.05 299.58 304. 57 270.75 297.75 291.15 303.15 290.42 303.77 305.12 299 .45 216.2 295.26 185.73 261.45 182.28 213 .49 289.07 285.44 299.11

272.16 289.23 292.15 285 .48 279.84 271.52 304.67 299.18 299.98 303.73 275.54 299.85 297.32 303.11 291.74 302.41 305.57 297.92 219.81 290.18 180.09 262.13 177.38 212.59 275.85 280.34 298.77

e-represents dummy factors.

Avg

S/N (dB)

274.02 288.69 291.24 287.08 275.34 267.69 304.25 298.46 299.40 304.02 273.80 296.26 296.30 303.04 291.44 303.16 305.12 300.71 216.95 294.59 182.87 266.45 177.66 213.94 280.68 284 .68 294.37

48.75 49.21 49.28 49.16 48.79 48.55 49.66 49.50 49.53 49.66 48.75 49.43 49.43 49.63 49.29 49.63 49.69 49.56 46.73 49.38 45.24 48.50 44.99 46.61 48.96 49.09 49.37

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Table 5 e Results of ANOVA for the Taguchi S/R experiment data. Factor

Sum of Degree of Mean F-test Significant squares freedom square

A B C D E BC BE CE e Residue pooled Total

5.46 16.32 6.52 (0.85) (0.74) 4.70 (0.94) 3.64 (4.36) 6.88

2 2 2 (2) (2) 4 (4) 4 (4) 12

44.02

26

2.73 8.41 3.26 0.43 0.37 1.18 0.24 0.91 1.09 0.57

4.77 14.68 5.69 Pooled Pooled 2.05 Pooled 1.59 Pooled

Yes Yes Yes

Probability Density

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Taguchi-prediction

0.6 0.4 0.2 0 47

Yes

Taguchi-confirmation exp.

0.8

48

49

50 S/N(dB)

51

52

53

Fig. 9 e Comparison value of S/N between Taguchi prediction and confirmation exp.

Yes

Note: Factors D, E, and BE are pooled as error due to a small sum of squares.

information by means of crossover to escape local optimal solutions within the optimization design. Crossover connects the features of two parent chromosomes to form two new similar children. Therefore, crossover provides a systematic method to improve the efficiency of the genetic algorithm and may save computational time. The one with the highest fitness value will be kept throughout the evolution process of the chromosome. Moreover, chromosomes with lower fitness values are used for mutation under the consideration of calculation efficiency. According to the recombination of individual genes (factors within a solution), better chromosome evolution can expected. However, the mutation is influenced by a random change with a probability equal to the mutation rate. The fitness values of the chromosomes possibly evolve into either better or worse solutions. Hence, a mutation rate ranging from 0.1 to 0.3 is used to limiting the percentage of chromosomes used for mutation.

4.

Experimental results

4.1.

Experiment data acquisition process

4.1.1.

2k1 factorial design used for screening experiment

The PEMFC is usually operated at elevated pressure requiring the use of a compressor. For many systems especially for specific small system, the use of a compressor is not a viable option. The small system requires low airflow, for which efficient compressors are not available. Both noise and wear may not be acceptable. So such systems are operated at atmospheric pressure [30]. From the result of paper [31,32], the

parameter of pressure played dominant effect and decreased the effect of other operating parameter. So for balance we consider pressure parameter under normal condition and can avoid misleading other interaction effect of parameters. In this work, the performance of PEMFC is considered by external environment parameters such as operating temperature, humidification temperature of the gas streams, and reactant gases flow rates. The each factors of level are chosen based on reference paper [8e11,31,32]. In order to improve performances of fuel cell, it is essential to realize the effects of parameters on operations of fuel cell. The evaluation of the effects of the primary interest performance of five factors under normal pressure are: A: humidification temperature of the anode ðTH2 Þ, B: operating temperature of the fuel cell, ðTFC Þ C: humidification temperature of the cathodeðTO2 Þ, D: stoichiometric rate of hydrogenðlH2 Þ, E: stoichiometric rate of oxygenðlO2 Þ, each of which has two levels as listed in Table 2. The results were used to construct a normal scores plot of the investigated factors as shown in Fig. 6. This revealed that the operating temperature of the fuel cell(B), the humidification temperature of the cathode(C) and the interaction between the two(BC) have a strong significant influence on the performance of the tested PEMFC, but the factor of stoichiometric rate of hydrogen(D) is not significant. In other words, the AD and CD interactions are also significant so the factor of D has to be regarded as an important factor based on the principle of Ockham’s razor [22].

4.2.

Orthogonal array experiment

Considering the non-linear phenomenon among the investigated factors, the significant factors, based on screening experimental analysis, each have three levels as shown as in

Table 7 e Results of Taguchi confirmation experiment data. Table 6 e Two way table of factor B and C interaction.

B1 B2 B3

C1

C2

C3

49.08 49.28 47.12

48.84 49.45 46.7

49.56 49.63 49.14

Trial no.

28 29 30

Power density(mW/cm2) y1

y2

y3

306 309 308

307.83 303.38 308.83

307.47 308.92 304.38

Avg.

S/N (dB)

307.22 307.23 307.20

49.749 49.748 49.748

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Humidification Temperature of anode Operation temperature of fuel cell Power density of PEMFC

Humidification Temperature of cathode ……

Stoichiometricflow rate of hydrogen Stoichiometricflow rate of oxygen

Hidden Layer

Input Layer

Output Layer

Fig. 10 e Configuration of the BPNN architecture for metemodel of PEMFC system.

Table 3. In designing an OA experiment, the concept of the main and interaction effects plays an important role. Alternatively, a smaller OA may be adopted for an economical experiment. The linear graph, from Fig. 7, for L27(313) can then be used to determine all possible interaction effects between design factors as well as the main effects and the columns, to which the three factors are assigned. The analysis factors B, C, E, A and D may be assigned to columns 1, 2, 5, 10 and 12, respectively. Then, main effects are found from the corresponding columns, and interaction effects BC, CE and BE are found from the columns (3, 4), (8, 11), (6, 7), respectively. From the unassigned columns 9 and 13, information on the experimental error is obtained. The larger values have better performance characteristics because power density should be taken for the PEMFC performance and correspond to the S/N value of each trial calculated by Eq. (4) as shown in Table 3. The response graphical representation of the relationship between the level of each study factor and its corresponding impact on performance variation is shown in Fig. 8. The optimal level of a design factor in obtaining the power density is the level with the highest S/N value. ANOVA was performed to realize whether the factors are statistically significant. The F-test is a powerful tool for observing which design factors have a significant effect in obtaining the maximum power density. The F-value for each factor is simply the ratio of the mean of the squared deviations to the mean squared error. Generally speaking, the higher the F-value, the greater the effect on obtaining the maximum power density because the design factor can be predicted together with the performance characteristics and the ANOVA analysis. The results of the ANOVA for the experiments are given in Table 4. Therefore,

based on the ANOVA analyses, the factors D, E, BE and CE are pooled into the error term due to the small values of the sum of squares. For the effects of factors A, B, C and BC, the larger the F-value, the more the effect on the performance characteristic is considered statistically significant. From the present analysis, design factors B and C are have significant interaction effects, and therefore, their optimal levels are jointly determined. The two-way table of the interaction between factors B and C lists the optimal level of each other as shown in Table 5. Therefore, the best design factor and level is A3 B2 C3. When the optimal level of the factor is selected, the final step is to predict and verify the improvement of the performance characteristic using the optimal level of the design ^ using Eq. factor. The S/N values of the optimally calculated h (5) are: ^ ¼ y þ ðA3  yÞ þ ðB2  yÞ þ ðC3  yÞ þ ½ðB2C3  yÞ  ðB2  yÞ h ð10Þ ðC3  yÞ ¼ 50:17 It is necessary to perform a confirmation experiment to determine the optimal conditions and compare the result with the expected performance. Table 6 shows the results of the confirmation experiment using the optimal design factors of the PEMFCFC power density and S/N value. Good agreement

Table 8 e LMBR network parameters. Network architecture 5-4-1 5-5-1 5-6-1 5-7-1 5-8-1

R2

R

SSE

Number parameters

0.973 0.999 1 1 0.973

0.9866 0.9995 1 1 0.9866

2.170E-01 8.740E-03 4.810E-06 6.970E-06 2.170E-01

20.1/29 25.7/36 27/43 27/50 19.8/57

Fig. 11 e Interaction effect plots of BPNN S/R value： Temperature of fuel cell (B)－Humidification temperature of cathode (C).

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Table 9 e GA values of parameter setup. Boundary condition

Generation Population Crossover Mutation size rate rate

Upper: Max. level Lower: Min. 1evel

100

20

0.8

31 32

Metamodeling PEMFC system by BPNN

A BPNN was conducted in this study and the neurons in the hidden layers are computational units that perform nonlinear mapping between inputs and outputs. The topology of metamodeling by BPNN of PEMFC is shown in Fig. 10. The efficient algorithm, LMBR, was adopted to improve classical BP learning during training and to avoid overfitting where the over-abundance of hidden neurons leads to much flexibility. A total of 81 sets of dates that take a set of five input design factors (A, B, C, D, E) and one output value of the power density, which is calculated by the S/N value. Since the training data for BPNN are limited by the function values, the raw data must be standardized by the following equation: PN ¼

P  Pmin: Pmax:  Pmin:

(11)

Where PN is the standardized data, P is the data of the original, Pmax. is the maximum value of the original data, Pmin. is the minimum value of original data. The transfer functions of all neurons are tangent sigmoid functions, and output neurons are linear functions. Determining the number of hidden neurons is critical to the design of neural networks. The MATLAB software was adopted for the required BPNN modeling [33]. In this study, the models’ performance can be evaluated through rootemean-square-error (R2) as defined by:

Best: -50.458 Mean: -50.4579 -49 Best fitness

Fitness value

Trial No.

0.1

between the predicted performance of the power density and the actual performance of the power density is shown in Fig. 9. The confirmation experiment shows that the PEMFC performance of the power density is within the Taguchi prediction (Table 7).

4.3.

Table 10 e Results of BPNN-GA confirmation experiment data.

Mean fitness

-49.5

Power density (rnW/cm2) y1

y2

y3

324 324

323.04 324.04

323.14 323.35

Avg.

S/N (dB)

323.41 323.78

50.19 50.20

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N   X ei  pi 2  2 u RMSE R ¼ t N I¼1

(12)

Where ei is the actual value from experimental sample i, pi is the value predicted by the model sample i and N is the number of data sample points. Table 8 shows 5 options for the neural network architecture. Comparing the training data for the R2 shows that the structures 5-6-1 and 5-7-1 are the best for convergence. The structure 5-6-1 yielded the smallest sum of squared error and the effective parameter value of the network can be appropriately applied, which can avoid restrictions on the learning capacity or overfitting, and was therefore adopted to obtain a good performance. Fig. 11 presents the plot of the network 5-6-1 for the interaction effect between B and C. The analysis result of Taguchi and the metamodeling by BPNN are consistent and can predict the optimal operating condition and scope of PEMFC.

4.4.

GA optimization solution

GA solutions are evaluated using the fitness function. The fitness function is based on the metamodeling, which can represent the relationship between the design factors and predict the response from PEMFC by BPNN. The metamodeling from BPNN was an input to the MATLAB code for evaluating the chromosome fitness. The ranges of each factor were the design factor constraints. A stochastic universal sampling method was then used to select some of the good solutions to form a new population of solutions. Crossover and mutation were then applied to the selected solutions to produce new offspring. The process continued until the specified number of generations was reached. The upper and lower limits of the optimized design factors and the parameter values of GA are shown in Table 9. The fitness function of the GA convergence values is shown in Fig. 12. The final optimization design factors and levels from BPNN-GA were experimentally confirmed and are shown in Table 10. The results of the different final combination design factors and levels are summarized in Table 11. Note that the “original” results from the parameter setup used by the case study before the present analysis. We can conclude that the proposed approach of

-50 Table 11 e Results of different combination.

-50.5

0

20

40 60 Generation

80

100

Fig. 12 e The fitness function values of GA convergence.

Factors

A

B

C

D

E

S/N (dB)

Original Taguchi OAs BPNN-GA

65 80 80

65 65 75

65 80 76

1.2 1.2 1.2

1.9 1.2 1.8

48.72 49.75 50.21

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 5 2 8 3 e1 5 2 9 4

0.8

OAs-confirmation exp.

BPNN-GA confirmation exp.

Original

0.6 0.4 0.2 0

46

47

48

49

50

51

52

53

S/N(dB) Fig. 13 e Comparison of the probability density with different confirmation experiment data.

5.

Results and discussion

The results can be summarized as follows:

500

1

500

0.8

400

0.8

400

0.6

300

0.6

300

0.4

200

0.4

200

BPNN-GA-confirmationexp. OAs-confirmationexp. Trialno.5 Trialno.15 Trialno.22

0.2

0 0

0.1

0.2

0.3

0.4

0.5

0.6

100

0 0.7

Current density, A/cm Fig. 14 e Polarization curves for different confirmation experiment data (at TO2 [ 65  C and TFC [ 50e80  C).

Cellpotential,V

1

Powerdensity,mW/cm

Cellpotential,V

(1) The improvement value of power density from the Taguchi conditions to the metamodeling approach is 5.44%. (2) Fig. 8 of the response graph shows that the increase in the humidification temperature of the anode has a significant positive effect (increment) at every level and the same is true of cathode, while still within the confidence interval. The membrane is to be adequately hydrated during operation to reduce the ohmic losses. (3) The stoichiometric rates of both the hydrogen and oxygen have no significant effect at the Taguchi analyzed level of power density. Since the operating temperature of the FC makes a high contribution, there is a relative reduction in the stoichiometric ratio of anode and cathode gas. This results in them having a strong effect and the interaction is not significant. The main cause of the high percentage is

the operating temperature of the FC at level 2 (65  C) has a strong S/N value, which reduces the activation losses and improves performance. On the contrary, the operating temperature of the FC at level 3 causes significant negative effects (decrement) on the power density. This could cause MEA dehydration and increase the resistance of the performance. (4) The metamodeling from the BPNN approach that built a continuous relationship between the design factor and the output could be applied to the predicted model to predict the power density of the FC for the cost and time condition. Furthermore, BPNN metamodeling with the GA global optimization approach solves for non-linear phenomena in the system and improves the performance of the FC effectively by a series of confirmation experiment. (5) The Fig. 14 and Fig. 15 polarization curves show the improvement of the PEMFC performance based on the MBDO approach. This may explain the appropriate increase in the humidification of the inlet gas stream to ensure the membrane is adequately hydrated. The performance improves with an increase in the operating temperature of the FC due to an increase in the proton conductivity and the exchange current density and

BPNN-GA-confirmationexp. OAs-confirmationexp. Trialno.7 Trialno.17 Trialno.27

0.2

0

100

0 0

0.1

0.2

0.3

0.4

Currentdensity,A/cm

0.5

0.6

0.7

2

Fig. 15 e Polarization curves for different confirmation experiment data (at TO2 [ 80  C and TFC [ 50e80  C).

Powerdensity,mW/cm

metamodeling from BPNN-GA is promising in promoting the performance of PEMFC in Fig. 13. The above analysis shows that the MBDO approach resulted in a superior design.

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removes the water generated at the cathode to avoid electrode flooding.

6.

Conclusions

In this paper, a systematic experimental strategy is demonstrated for robust design factors that promote the performance of a PEMFC system. Based on the data collected from the experimental designs, which are the fractional factorial design and Taguchi OAs, the research built a power density of the PEMFC quality characteristic metamodeling by a BPNN approach, which was then solved by GA optimization. The paper also describes how a PEMFC MBDO approach can be configured. This solution was verified by experiments to improve the performance of the PEMFC and the currentevoltage and power-voltage characteristic. The methodology of MBDO allowed a PEMFC system to quickly adapt to the operating environment, knowing the principal factors and effects that affect the performances of the PEMFC. Future work will be concerned with the study of other physical design factors in the stack of the PEMFC system.

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