Load-Aware Stochastic Degradation Modeling and Lifetime Characterization for PEM Fuel Cells

Abstract

The degradation of proton exchange membrane fuel cells (PEMFCs) is strongly dependent on load history and presents significant variability across nominally identical stacks. This paper proposes a physics-based, load-aware stochastic degradation framework for PEMFCs, with the objective of characterizing lifetime under static and dynamic operating profiles and providing a modeling basis for future Prognostics and Health Management (PHM) applications. The cell voltage is described through a polarization model parameterized by degradation-sensitive quantities, namely the normalized electrochemically active surface area (ECSA), the membrane ohmic resistance, and the hydrogen crossover current. Catalyst degradation is represented by a simplified ECSA state driven by platinum dissolution--oxidation kinetics, while membrane ageing is described through a stochastic cumulative damage state modeled as a non-homogeneous Gamma process whose mean evolution is matched to a semi-empirical membrane degradation law. Membrane thickness and conductivity are reconstructed consistently from this damage state, and the resulting ohmic resistance and crossover current are fed back into the voltage model. Load dependence is enforced through the coupling between mission demand, operating-point computation, and voltage-driven degradation dynamics. The resulting framework captures both intra-stack stochasticity, through the membrane damage process, and inter-stack variability, through dispersion in selected model parameters. A Health Index (HI) is defined as the normalized virtual rated-point voltage. Simulation studies under static and dynamic load profiles illustrate the influence of load level, load cycling, and parameter variability on degradation trajectories and lifetime distributions. Although state estimation and remaining useful life prediction are not addressed here, the proposed framework is intended to serve as a compact modeling basis for such future PHM developments.