Accurate optimizing proton exchange membrane fuel cell parameters using fitness deviation-based adaptive differential evolution

Proton exchange membrane fuel cells (PEMFCs) are complex, nonlinear systems whose performance depends on several interrelated parameters. Accurate estimation of these parameters is crucial for enhancing the efficiency and reliability of PEMFCs. In this paper, we used Fitness Deviation-based Differential Evolution (FD-DE) algorithm to optimally identify the unknown parameters of PEMFC models. An adaptive parameter control with wavelet basis function and Gaussian distribution, a hybrid trial vector generation strategy using t-distribution based perturbation, and a dimensional replacement mechanism for maintaining population diversity are introduced in the FD-DE algorithm. The innovations in these algorithms tackle the common problems in differential evolution algorithms, including premature convergence and loss of diversity. The proposed FD-DE algorithm is validated on twelve different PEMFC case studies under different operating conditions and compared with several state-of-the-art algorithms, including other DE variants and non-DE algorithms. For that purpose, the optimization targets seven parameters xi 1,xi 2,xi 3,xi 4,lambda,Rc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\xi }_{1}, {\xi }_{2}, {\xi }_{3}, {\xi }_{4}, \lambda , {R}_{c}$$\end{document} and B to closely match the polarization curves to those specified in the manufacturer datasheet, focusing initially on six primary stacks: BCS 500-W PEM, STD 250-W PEM, Nedstack PS6 PEM, 500W SR-12PEM, H-12 PEM, and HORIZON 500W PWM. The optimization approach is to minimize the sum of squared errors (SSE) between the predicted stack voltages of the model and the experimentally measured results. Absolute error (AE), relative error (RE), and mean bias error (MBE) are assessed across different datasheets. A comparative statistical analysis is made among several DE variants FD-DE, TDE, MadDE, LSHADE, LSHADE-cnEpSin, jSO, PaDE, and non-DE algorithms ACS, SSA, and TEO. The results show that the FD-DE algorithm performs consistently better than existing strategies in terms of accuracy, convergence speed and stability, and provides better parameter estimation with lower errors. The effectiveness of the FD-DE algorithm in solving complex optimization problems and its potential to enhance PEMFC modeling and analysis is shown in this work.