<p>An accurate model of a fuel cell (FC) is essential because it significantly impacts the transient and dynamic analysis of the FC in simulation studies. However, the mathematical model of FC consists of some unknown parameters and its identification is a challenging task. This article proposes a new implementation of the Ali Baba and forty thieves (ABFT) algorithm in extracting the values of unknown parameters to develop an accurate proton exchange membrane FC (PEMFC) model. The extraction process is expressed as an optimization challenge as well as solved based on the sum of squared error (between the experimental as well as estimated voltages) using the ABFT algorithm and aims to minimize the objective function with a set of inequality constraints. The accuracy of the proposed ABFT algorithm-based PEMFC model is evaluated by contrasting the achieved outcomes to the empirical outcomes of commonly available PEMFCs, including the NedStack PS6, Ballard Mark V, BCS 500 W, 250 W Stack, and obtained values of the objective functions are 2.303554E<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_814_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$+$</EquationSource> <EquationSource Format="MATHML"><math> <mo>+</mo> </math></EquationSource> </InlineEquation>00, 8.53608E−01, 1.1698E−02, and 3.31348E−01, respectively. Moreover, to prove the superiority of the proposed ABFT, its outcomes are compared to those obtained using well-established meta-heuristic (MH) techniques as well as that are reported in the literature. It is found that the ABFT algorithm is superior over these algorithms in terms of statistical analysis. It is elucidated that simulated I–V, I–P, as well as efficiency curves closely match the experimental curves in each of the examined cases. The analyses are conducted by taking into consider various operational conditions (temperature and pressure). In addition, a statistical analysis as well as box plot study are carried out to validate the accuracy as well as reliability of the ABFT algorithm. Furthermore, the Friedman as well as Wilcoxon tests have been performed and it is elucidated that the proposed ABFT algorithm achieved Ist rank and proved its robustness and effectiveness in all the case studies in identifying unknown parameters.</p>

Efficient parameter extraction for accurate modeling of PEM fuel cell using Ali-Baba and forty thieves algorithm

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发表日期：

2025年3月15日

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Rahul Khajuria,
Pankaj Sharma,
Rajesh Kumar,
Ravita Lamba,
Saravanakumar Raju

摘要

An accurate model of a fuel cell (FC) is essential because it significantly impacts the transient and dynamic analysis of the FC in simulation studies. However, the mathematical model of FC consists of some unknown parameters and its identification is a challenging task. This article proposes a new implementation of the Ali Baba and forty thieves (ABFT) algorithm in extracting the values of unknown parameters to develop an accurate proton exchange membrane FC (PEMFC) model. The extraction process is expressed as an optimization challenge as well as solved based on the sum of squared error (between the experimental as well as estimated voltages) using the ABFT algorithm and aims to minimize the objective function with a set of inequality constraints. The accuracy of the proposed ABFT algorithm-based PEMFC model is evaluated by contrasting the achieved outcomes to the empirical outcomes of commonly available PEMFCs, including the NedStack PS6, Ballard Mark V, BCS 500 W, 250 W Stack, and obtained values of the objective functions are 2.303554E $+$ $+$ 00, 8.53608E−01, 1.1698E−02, and 3.31348E−01, respectively. Moreover, to prove the superiority of the proposed ABFT, its outcomes are compared to those obtained using well-established meta-heuristic (MH) techniques as well as that are reported in the literature. It is found that the ABFT algorithm is superior over these algorithms in terms of statistical analysis. It is elucidated that simulated I–V, I–P, as well as efficiency curves closely match the experimental curves in each of the examined cases. The analyses are conducted by taking into consider various operational conditions (temperature and pressure). In addition, a statistical analysis as well as box plot study are carried out to validate the accuracy as well as reliability of the ABFT algorithm. Furthermore, the Friedman as well as Wilcoxon tests have been performed and it is elucidated that the proposed ABFT algorithm achieved Ist rank and proved its robustness and effectiveness in all the case studies in identifying unknown parameters.