Enhanced manta ray foraging optimization algorithm involving fuzzy-based fitness-distance balance method for estimation of unidentified parameters of PEMFC model

Estimating the parameters for proton exchange membrane fuel cells (PEMFC) is critical for optimizing this technology; yet, difficulties emerge due to inadequate data and the nonlinear characteristics of PEMFCs. To guarantee an accurate and dependable model, it is important to carefully identify the optimal values of unknown parameters and develop an appropriate method particular to the problem's features. In this study, two novel methods were proposed regarding meta-heuristic search algorithms. Firstly, the fuzzy-based fitness-distance balance (FFDB) method was introduced to enhance the classical fitness-distance balance (FDB) method. Secondly, the FFDB method was applied to the manta ray foraging optimization (MRFO) algorithm, and the FFDB-MRFO algorithm was proposed in the literature. To validate the efficacy of the proposed algorithm, two experimental studies were performed on benchmark and PEMFC parameter estimation problems. In the first experimental study, FFDB-MRFO outperformed other MRFO variations on classic and CEC2020 benchmark problems, achieving the highest rank with a score of 2.2678 based on the Friedman test results. The second experimental study examined sixteen case studies utilizing four commercial PEMFC stacks and four objective functions. To assess the efficacy of the FFDB-MRFO, the results obtained from the sixteen case studies were compared with seven up-to-date MHS algorithms utilizing statistical analysis methods and various performance metrics. The FFDB-MRFO achieved the best optimal solutions in all cases, demonstrating an enhancement of up to 80.7235% compared to other methods and ranking first with a mean score of 1.3167 in the Friedman test. The critical point is that an assessment was conducted utilizing the relative error values of the objective functions for each case study to identify the most appropriate objective function for the PEMFC stack types. Furthermore, stability analysis demonstrated that FFDB-MRFO achieved a 100% mean success rate, markedly outperforming other MRFO variants. Overall, the results indicate the superiority and reliability of the FFDB-MRFO algorithm in precisely estimating PEMFC parameters.