Sensitivity Analysis Based on Monte Carlo Simulations of a 1D Accelerated Mechanistic Model of a Proton Exchange Membrane Fuel Cell

Abstract

Mathematical modelling of polymer electrolyte membrane fuel cells (PEMFCs) commenced with a one-dimensional (1D) model incorporating gas diffusion and chemical reaction mechanisms, movement at the membrane via electroosmotic drag and proton and water transport at the electrolyte membrane was developed. Subsequently more sophisticated two- and three-dimensional models incorporating the water and thermal management were established to improve the accuracy and thereby identify parameters that influence the performance of the PEMFCs. Recently, as the computational power improved, statistical analyses including sensitivity analyses of approximated models were carried out. However, employing a mechanistic model considering the conservation of charge, mass, momentum, species and energy, for sensitivity analysis is not trivial particularly because of the associated computational cost. In this study, a Monte Carlo based sensitivity analysis is carried out based on an accelerated, time-marched 1D mechanistic model of a PEMFC that captures the effects of dependent variables in all three dimensions. To achieve this, we investigate the effect of random, simultaneous, variation of over 30 normally distributed parameters (physical, geometric, operating electrochemical and fitting parameters) at different operating conditions of the PEMFC. Kolmogorov-Smirnov (KS) test is performed to ensure that the size of the drawn sample is reliable for stable results. An experimentally validated model is taken as the base case and all the parameters are varied with a standard deviation of 10%. The standard deviation in the current at different operating cell potentials is presented. Additionally, the contribution of each stochastic parameter to the current is ranked and quantified by multiple linear regression and sigma-normalized derivative method. Furthermore, a sample size of 10000 is chosen to generate enough variations to the model and identify optimal operating and physical parameters to improve the performance of PEMFC. Moreover, any artificial intelligence centered model predictor can estimate the best set of parameters by accessing the data generated from this study to fit an experimental curve at different operating cell potentials. This accelerated model prediction thereby enables improved accuracy of the predicted models, faster diagnosis and easier optimization of a PEMFC.