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<p>The seven unknown parameters in the Amphlett semi-empirical proton exchange membrane fuel cell (PEMFC) model are critical to accurate performance prediction, system design, and degradation diagnosis. Gradient-based methods are often unreliable in this context because the sum-of-squared-errors (SSE) objective is highly nonlinear and multimodal, while existing population-based approaches tend to exhibit substantial run-to-run variability. To address these challenges, this paper proposes the Enhanced Fourier Transform Optimizer (EFTO), a hybrid adaptive algorithm that combines a success-history differential evolution branch with elite-guided mutation and a covariance-adaptive sampling branch, dynamically balanced through an online branch-selection mechanism. On the IEEE CEC 2017 benchmark suite (28 functions, D = 50, 30 independent runs), EFTO achieved a Friedman rank of one with an average rank of 1.607 and a Wilcoxon <i>p</i> ≤ 1.17 × 10⁻<sup>3</sup> against six competing algorithms. A supplementary comparison with three recognized state-of-the-art solvers found no statistically significant performance differences relative to two of the three solvers (<i>p</i> &gt; 0.05), while EFTO recorded the lowest average runtime of 8.653&#xa0;s. When applied to three commercially validated PEMFC stacks, EFTO achieved machine-precision reproducibility, with a standard deviation below 10⁻<sup>14</sup> V<sup>2</sup> across 30 independent runs and best SSE values of 2.0656 V<sup>2</sup> (NedStack PS6), 1.0564 V<sup>2</sup> (AVISTA SR-12), and 0.8139 V<sup>2</sup> (Ballard Mark V). These results were statistically confirmed by Wilcoxon signed-rank tests (R⁺ = 465, <i>p</i> = 1.73 × 10⁻⁶). Component wise ablation showed that the covariance-adaptive sampling mechanism was the most influential component, with removal of the covariance-adaptive sampling mechanism causing a 98.7% degradation in SSE (<i>p</i> = 1.09 × 10⁻<sup>24</sup>). Stack-specific sensitivity analysis further demonstrated that the identified parameters remain physically consistent with the electrochemical operating regime of each stack, establishing EFTO as a competitive and consistent tool for PEMFC parameters identification on the evaluated benchmark configurations.</p>

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Parameter estimation of proton exchange membrane fuel cells using enhanced Fourier transform optimizer with adaptive learning mechanisms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月8日

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  • Ramakrishna Raghutu,
  • Tummala S. L. V. Ayyarao,
  • G. Sasikumar,
  • U. Siddaraj

摘要

The seven unknown parameters in the Amphlett semi-empirical proton exchange membrane fuel cell (PEMFC) model are critical to accurate performance prediction, system design, and degradation diagnosis. Gradient-based methods are often unreliable in this context because the sum-of-squared-errors (SSE) objective is highly nonlinear and multimodal, while existing population-based approaches tend to exhibit substantial run-to-run variability. To address these challenges, this paper proposes the Enhanced Fourier Transform Optimizer (EFTO), a hybrid adaptive algorithm that combines a success-history differential evolution branch with elite-guided mutation and a covariance-adaptive sampling branch, dynamically balanced through an online branch-selection mechanism. On the IEEE CEC 2017 benchmark suite (28 functions, D = 50, 30 independent runs), EFTO achieved a Friedman rank of one with an average rank of 1.607 and a Wilcoxon p ≤ 1.17 × 10⁻3 against six competing algorithms. A supplementary comparison with three recognized state-of-the-art solvers found no statistically significant performance differences relative to two of the three solvers (p > 0.05), while EFTO recorded the lowest average runtime of 8.653 s. When applied to three commercially validated PEMFC stacks, EFTO achieved machine-precision reproducibility, with a standard deviation below 10⁻14 V2 across 30 independent runs and best SSE values of 2.0656 V2 (NedStack PS6), 1.0564 V2 (AVISTA SR-12), and 0.8139 V2 (Ballard Mark V). These results were statistically confirmed by Wilcoxon signed-rank tests (R⁺ = 465, p = 1.73 × 10⁻⁶). Component wise ablation showed that the covariance-adaptive sampling mechanism was the most influential component, with removal of the covariance-adaptive sampling mechanism causing a 98.7% degradation in SSE (p = 1.09 × 10⁻24). Stack-specific sensitivity analysis further demonstrated that the identified parameters remain physically consistent with the electrochemical operating regime of each stack, establishing EFTO as a competitive and consistent tool for PEMFC parameters identification on the evaluated benchmark configurations.