Optimum parameters extraction of proton exchange membrane fuel cells using Fractional‐Order Whale Optimization Algorithm

Abstract

This study proposes a novel metaheuristic-based technique for optimum parameters' estimation of the proton exchange membrane fuel cells (PEMFCs).To provide better results with more reliability and accuracy, a Fractional Order-based design of the Whale Optimizer Algorithm (FO-WOA) is designed.A validation test showed that the proposed method provides a good trade-off between accuracy and convergence speed. Performing the algorithm for multiple independent runs also shows that the proposed method delivers reliable results toward some other comparative metaheuristic algorithms. This algorithm is then used for the minimization of the sum of square deviation between the experimental voltage-current polarization and the optimal achieved results by the model based on FO-WOA. The method is validated by considering two practical case studies, which are the Nexa PEMFC and 250 W PEM system, and its achievements are put in comparison with some approaches to indicate the higher effectiveness of the proposed method toward the others. The experimental results on the Nexa PEMFC indicate that the proposed FO-WOA-based method with 12 sum square errors (SSE) provided the minimum error toward the other. Also, the experiments on the 250 W PEM Stack indicated that for 250 W PEM Stack with 3/5 bar and 80°C, the proposed method with 0.01 SSE provides the fittest profile with the experimental data, and finally, the experiments on the same stack with 3/5 bar and 80°C showed the higher accuracy of the proposed method with the least SSE value (0.16) toward the others.

An interpretable BRB model with interval optimization strategy for lithium battery capacity prediction

“…Each whale was randomly sprinkled, 42 and the $$i$$th whale can be described as: $$${X}_{{\rm{i}}}=f\times (ub-lb)+lb,$$$ $$$lb=[Ek-{\rm{I}}\times 0.01],$$$ $$$ub=[Ek+{\rm{I}}\times 0.01],$$$where $$f$$ is a random number whose value range is $$[0,1]$$. The range of $${X}_{i}$$ is $$[lb,ub]$$.…”

“…Therefore, this paper proposes an interval optimization strategy to achieve optimization and adopts the modified WOA with interpretability constraints, as shown in Figure 3. The WOA is a new metaheuristic optimization method inspired by nature, 42 and it can construct a bubble net search strategy by simulating the hunting behavior of humpback whales. 27 As shown in Figure 4, the interval optimization strategy proposed in this paper can fully cover the entire feasible region, and diffusion starts from expert knowledge.…”

“…Step 2: Sprinkle operation. Each whale was randomly sprinkled, 42 and the ith whale can be described as:…”