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

Abstract

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.

A Mathematical Model toward Real-Time Monitoring of Automotive PEM Fuel Cells

“…Nevertheless, we note that during model parameterization, we were able to find several parameter combinations that yield reasonable model predictions as compared to available voltage measurements. This further signifies the structural identifiability issues that are common for physics-based fuel cell models and are studied in separate publications [82,88].…”

“…Therefore, adding the HFR data to the identification process can considerably increase the confidence in parameter estimates. These issues are extensively studied in separate publications [82,88] and are not pursued here any further.…”

Electrochemiluminescence Mechanisms Investigated with Smartphone‐Based Sensor Data Modeling, Parameter Estimation and Sensitivity Analysis

“…(1) and 2, respectively, α is the charge transfer coefficient taken as 0.5, f = F/RT (38.92 V À 1 ), E is the applied potential (1.2 V vs. Ag/Ag + ), and E 0 is the standard potential taken as 1.06 V vs. Ag/Ag + for Eqs. (21) and (22) and 0.9 V vs. Ag/Ag + for Eqs. (23) and (24).…”

“…The problem of parameter identifiability can be addressed using sensitivity analysis (SA). [21] This type of analysis can provide relevant information on the sensitivity of the model outputs for a range of variation of the parameters. Recent literature shows that SA is being used as part of modeling tools in different fields of electrochemistry.…”

“…Recent literature shows that SA is being used as part of modeling tools in different fields of electrochemistry. [21][22][23][24] However, to the best of the authors' knowledge, just as the optimization algorithms, the formal sensitivity analysis applied to mechanistic models describing the ECL mechanism has not been reported in the literature. A common approach to sensitivity analysis of mechanistic model parameters is the one-at-a-time (OAT) approach (mathematically it is expressed using partial derivatives), in which only one parameter is changed at a time keeping others fixed at their nominal values.…”