Effective Parameterization of PEM Fuel Cell Models—Part I: Sensitivity Analysis and Parameter Identifiability

This two-part series develops a framework for effective parameterization of polymer electrolyte membrane (PEM) fuel cell models with limited and non-invasive measurements. In the first part, a systematic procedure for identifiability analysis is presented, where a recently developed model is analyzed for the sensitivity of its output predictions to a variety of structural and fitting parameters. This is achieved by conducting local analyses about several points in the parameter space to obtain sensitivities that are more representative of the entire space than the local values estimated at a single point, which are commonly used in the literature. Three output predictions are studied, namely, cell voltage, resistance, and membrane water crossover. It is found that the cell voltage is sensitive to many of the model parameters, whereas the other model predictions demonstrate a sparser sensitivity pattern. The results are further analyzed from the perspective of collinearity of parameter pairs and it is shown that many of the parameters have similar impact on voltage predictions, which diminishes their identifiability prospects. Lastly, the sensitivity results are utilized to analyze parameter identifiability. The least squares cost Hessian is shown to have an eigenvalue spectrum evenly spanned over many decades and the resulting identifiability challenges are discussed.