Empirical Approaches for Nonlinear Modeling of Hydrogen Fuel Cell Systems

Abstract

The paper presents a comprehensive methodology for the modeling and simulation of modern hydrogen fuel cells based on measured real-world data. The measured data are used to estimate optimal parameters of semi-parametric nonlinear mathematical models, which serve as a foundation for the design of control algorithms for air-cooled hydrogen fuel cells. Proton exchange membrane (PEM) hydrogen fuel cells are electrochemical devices with strongly nonlinear behavior, which poses a challenging problem for parameter identification and optimal structure design. The empirical modeling approaches presented in the paper are particularly suitable for capturing such complex dynamics without requiring detailed knowledge of the underlying physical or electrochemical processes. The paper proposes empirical mathematical models such as nonlinear Hammerstein–Wiener models (NLHW) and nonlinear autoregressive models with exogenous input (NARX), based on measured input–output data. The study demonstrates that these models enable rapid model development from measured data; however, their predictive capability may be limited when applied to datasets and operating conditions different from those used during model training. Using the MATLAB-Simulink software environment and the System Identification Toolbox, the paper demonstrates the modeling quality through numerical and graphical results and shows how these empirical models can reproduce the dynamic behavior of air-cooled PEM fuel cell systems. The proposed mathematical models are validated and compared with real measured data from an air-cooled PEM fuel cell system across various data types and datasets. The insights obtained from modeling and control of PEM fuel cells are generalizable and applicable in practice and in the development of new, modern PEM fuel cells. The paper provides an effective methodology for further practical applications in the design of optimal control algorithms and rapid prototyping.