SHAP-Driven Fractional Long-Range Model for Degradation Trend Prediction of Proton Exchange Membrane Fuel Cells

Under dynamic loading conditions, the output voltage of proton exchange membrane fuel cells (PEMFCs) exhibits nonlinear degradation characterized by non-Gaussian fluctuations, abrupt changes, and long-range temporal dependence, which are difficult to model using conventional short-correlation or remaining useful life (RUL) prediction approaches. To capture both historical dependency and stochastic jump behavior, this study proposes a SHAP-driven mechanism–data fusion fractional stochastic degradation model based on fractional Brownian motion (fBm) and fractional Poisson process (fPp) for degradation trend forecasting. A terminal voltage mechanism model considering activation, ohmic, and concentration polarization losses is first established, and SHapley Additive exPlanations (SHAP) analysis is employed to quantify the contributions of multi-source operational variables and enhance interpretability. The Hurst exponent is then used to verify long-range dependence and jump characteristics in the voltage sequence. Subsequently, fBm is integrated with a fPp to construct a unified stochastic degradation framework capable of jointly describing continuous decay and discrete abrupt variations, enabling multi-step probabilistic prediction with confidence intervals. Validation on the publicly available FCLAB FC1 and FC2 datasets shows that the proposed model achieves superior overall performance under both steady and dynamic conditions, with MAPE/RMSE/R2 of 0.027%/0.00178/0.9895 and 0.056%/0.00259/0.9896, respectively, outperforming fBm, Wiener, WTD-RS-LSTM, and CNN-LSTM methods. The proposed approach provides accurate and interpretable degradation forecasting for PEMFC health management and maintenance decision support.