CycleDegrade: An Explicit Periodicity Modeling Approach for Long-Term Fuel Cell Voltage Degradation Forecasting

Proton exchange membrane fuel cells are pivotal for decarbonizing heavy-duty transportation. Stack durability bottlenecks and complex voltage degradation mechanisms constrain large-scale commercialization. Accurate prediction of voltage degradation trends is essential for health management and remaining useful life assessment. Under dynamic load conditions, the coupling of periodic fluctuations with long-term nonlinear degradation trends poses significant challenges for conventional deep learning models. To address this, this article proposes CycleDegrade, a voltage degradation prediction method combining residual cycle forecasting with a convolutional neural network-long short-term memory (LSTM) backbone. To enhance modeling efficiency, a hybrid periodicity analysis method integrating fast fourier transform with time-domain peak detection is introduced to identify the optimal cycle length. Then, periodic patterns are modeled through a learnable cycle template, decoupling periodic components from residual degradation trends to reduce modeling complexity. Furthermore, a patchwise structural loss is adopted to capture temporal structural features, and a simplified dynamic weighting strategy based on loss value reciprocals reduces training time by 34% with comparable prediction accuracy. Experimental results demonstrate that CycleDegrade achieves an average R$^{2}$of 0.9972 for 102-step prediction, outperforming existing models. Even for ultra-long-term predictions (up to 6800 steps), the model maintains high accuracy, demonstrating its superiority for long-term health prognostic tasks.