Uncertainty assessment of a semi-empirical output voltage model for proton exchange membrane fuel cells

An accurate model of proton exchange membrane fuel cell (PEMFC) is essential for its characterization, performance analysis, and design of optimal control strategies. However, due to various disturbances and measurement noise in practical operation, a PEMFC presents high stochasticity and parameter uncertainty. Therefore, a semi-empirical output voltage model parameter estimation method based on variational Bayes (VB) PEMFC is proposed and combined with the Sobol sensitivity analysis method to analyze the relationship between the parameters of the model to be identified and the effect of the output voltage of the model under different noise and operating conditions. The numerical results show that the VB method is able to quantify the uncertainty of the parameter estimation results and has higher computational accuracy compared with the expectation maximization (EM) method. Compared with the Markov chain Monte Carlo (MCMC) method, the VB method is able to greatly reduce the computational effort and takes less time while satisfying the accuracy. Meanwhile, the sensitivity of the model parameters to be identified to the output voltage of the model under different noise and operating conditions is quantified using the Sobol method, which explains the variation of the posterior probability distribution results obtained using the VB method under different noise and operating conditions.