Parameter characterization of PEM fuel cell mathematical models using an orthogonal learning-based GOOSE algorithm

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In this paper, a new method is designed to effectively determine the parameters of proton exchange membrane fuel cells (PEMFCs), i.e., ξ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\xi }_{1}$$\\end{document}, ξ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\xi }_{2}$$\\end{document}, ξ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\xi }_{3}$$\\end{document}, ξ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\xi }_{4}$$\\end{document}, RC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{\ ext{C}}$$\\end{document}, λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}, and b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b$$\\end{document}. The fuel cells (FCs) involve multiple variable quantities with complex non-linear behaviours, demanding accurate modelling to ensure optimal operation. An accurate model of these FCs is essential to evaluate their performance accurately. Furthermore, the design of the FCs significantly impacts simulation studies, which are crucial for various technological applications. This study proposed an improved parameter estimation procedure for PEMFCs by using the GOOSE algorithm, which was inspired by the adaptive behaviours found in geese during their relaxing and foraging times. The orthogonal learning mechanism improves the performance of the original GOOSE algorithm. This FC model uses the root mean squared error as the objective function for optimizing the unknown parameters. In order to validate the proposed algorithm, a number of experiments using various datasets were conducted and compared the outcomes with different state-of-the-art algorithms. The outcomes indicate that the proposed GOOSE algorithm not only produced promising results but also exhibited superior performance in comparison to other similar algorithms. This approach demonstrates the ability of the GOOSE algorithm to simulate complex systems and enhances the robustness and adaptability of the simulation tool by integrating essential behaviours into the computational framework. The proposed strategy facilitates the development of more accurate and effective advancements in the utilization of FCs.