Robust parameter estimation of a PEMFC via optimization based on probabilistic model building

Abstract

In this work, we approximated a set of unknown physical parameters for a semi-empirical mathematical model of a PEMFC. We used an Estimation of Distribution Algorithm (EDA) known as UMDAG to find the tuple that best reproduces the experimental polarization curve. We tackled non-derivable objective functions to perform robust parameter estimation. We compared the sum of the squared error with published results, and the sum and the median of the absolute error values were used to diminish or remove the effect of possible noise or outliers. Since the UMDAG requires a single user-given parameter (the population size) and presents a natural reduction of the variance, it was possible to introduce a variance-based stopping criterion. The obtained results were compared with the most up-to-date evolutionary algorithms, demonstrating that this proposal is competitive. We used four previously reported experimental datasets to get the parameters or validate them. Two of them were used to test the method and to compare it with reported results of recent bio-inspired metaheuristics. Then, we used the identified parameters to simulate the cases of the remaining data sets validating the correct estimation. Finally, we introduced a posterior statistical analysis (hypothesis test), which provided further information about dependencies and the impact of each parameter on the cell performance.