PEM fuel cells parameter estimation by solving constrained optimization problems with metaheuristic algorithms and multivariate analysis

Accurate parameter estimation for proton exchange membrane fuel cells (PEMFCs) is crucial for optimal performance, reducing costs, and safe operation. While the generalized steady-state electrochemical model (GSSEM) and optimization techniques are widely used, current research encounters data inconsistency from poor constraint handling and lacks crucial residual analyses like normality and heteroscedasticity tests, compromising model reliability and result validity. This study addresses these issues by introducing a reformulated stable constraint, integrating p-values for rigorous statistical validation, and implementing feasibility checks. A chaos-enhanced Arctic Puffin Optimization (C-APO) algorithm is proposed to improve global search and avoid local optima. Solution optimality is confirmed, with residuals satisfying normality and homogeneity criteria, ensuring reliability. Multivariate analysis (MVA) further validates results and explores decision variables, providing a thorough understanding of the solution space. Seven PEMFC cases and two optimization scenarios are examined to demonstrate the flexibility and adaptability of the proposed framework: (1) accuracy and consistency are achieved by enforcing a relative percent difference (RPD) of zero between two sources of the cathode charge transfer coefficient, and (2) reliability is enhanced by applying p-value constraints greater than 0.05 for normality and heteroscedasticity tests. Robustness is further supported through MVA, including correlation, key factor, and variable range analyses. Overall, the proposed methodology significantly improves the accuracy and reliability of PEMFC parameter estimation, thereby advancing optimization practices in this field.