A reliable degradation prediction method for proton exchange membrane fuel cells based on uncertainty Bayesian self-attention

Abstract

Health state prediction of Proton Exchange Membrane Fuel Cells (PEMFCs) is a critical technology to ensure their long-term reliable operation. Prediction accuracy directly influences the effectiveness of maintenance strategies and risk management. However, existing PEMFC degradation prediction methods based on Recurrent Neural Networks (RNNs) or Transformer architectures mostly focus on point estimation while neglecting uncertainty quantification. This limitation makes it difficult to assess the confidence level of predictions in practical engineering applications, reducing the models' reliability in decision support. To address this issue, this paper proposes a novel Bayesian Patch Time Series Transformer (B-PatchTST) method. By deeply integrating Bayesian variational inference with time series patch modeling, the method enables probabilistic prediction of PEMFC degradation trajectories and disentangled analysis of uncertainty sources. Unlike traditional Bayesian Neural Networks (BNNs) that primarily apply Bayesian modeling to fully connected layers, B-PatchTST introduces a Bayesian Self-Attention Mechanism, which models epistemic uncertainty in three stages: patch embedding, uncertainty-aware self-attention computation, and adaptive regularization. This design significantly enhances the credibility of the model. Extensive experiments on the fuel cell datasets demonstrate the proposed method's outstanding performance. It achieves an average reduction of 36.31 % in root mean square error and an average compression of 83.39 % in the 95 % confidence interval, significantly outperforming existing methods. This approach offers a trustworthy basis for predictive maintenance in PEMFC systems, promoting a shift from “experience-based maintenance” to “reliable prognostics” in hydrogen energy applications.