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

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.