Interpretable and uncertainty-quantified early remaining useful life prediction for lithium-ion batteries under fast charging protocols

Under fast-charging protocols, accurately and interpretably predicting the remaining useful life (RUL) of lithium-ion batteries during the initial cycling stage is of great significance for early fault warning and reliability assessment. To improve the interpretability of RUL prediction, this paper proposes a causal learning approach to conduct causal analysis on domain-specific features, identifying key causal variables and systematically uncovering their relationships with RUL. To enhance the model’s capacity to fit complex nonlinear relationships and generalize across various conditions, we propose a neural network based on Legendre polynomial orthogonal bases, termed LegendreNet. Its approximation ability and theoretical validity are rigorously demonstrated. The causally selected domain features are fed into LegendreNet for prediction. In parallel, the original features are fed into a causal convolutional neural network (CCNN) to extract deep representations, capturing both global spatiotemporal dependencies and local feature details. The outputs of LegendreNet and CCNN are then concatenated and fused via LegendreNet to generate the final RUL prediction. Based on this architecture, we propose a novel multimodal prediction framework for early RUL estimation of lithium-ion batteries, named LNCCNN. Finally, to adaptively adjust the bandwidth and quantify predictive uncertainty, we introduce curvature adjustment into the Bayesian bootstrap kernel density estimation (BB-KDE) framework and propose a novel method, called curvature-aware BB-KDE (CA-BB-KDE). Experimental results on two distinct batches from the same fast-charging dataset demonstrate improved early RUL prediction accuracy, reducing RMSE by 2.96% and 7.09% and MAPE by 1.32% and 8.16%, respectively, supporting lifetime monitoring and decision-making in battery management systems.