Application of a TimeXer Model Incorporating ECM Based Features in Battery Remaining Useful Life Prediction

Accurate prediction of the remaining useful life (RUL) of lithium-ion batteries is critical for ensuring the safe and reliable operation of energy storage systems. Although existing data-driven methods demonstrate strong nonlinear modeling capabilities, they often suffer from a “black-box” nature and lack physical mechanism constraints, resulting in limited interpretability and generalization performance. To address these issues, this study proposes a TimeXer-based deep learning framework that integrates an equivalent circuit model (ECM) with an improved whale optimization algorithm (IWOA).First, a first-order RC equivalent circuit model is established, and recursive least squares is employed to achieve online parameter identification. Based on the identified physical parameters, six high-order health indicators with clear physical significance are constructed. Through correlation analysis, five key indicators are selected as exogenous inputs to the TimeXer model. Second, the dual-path attention mechanism of TimeXer is utilized to model battery degradation. Endogenous self-attention captures the temporal dependencies of the capacity degradation sequence, while exogenous–endogenous cross-attention effectively fuses physical health information, enabling accurate characterization of degradation trajectories. Subsequently, the IWOA algorithm is introduced to globally optimize the hyperparameters of the TimeXer model. By incorporating an improved nonlinear convergence factor and an adaptive perturbation strategy, IWOA effectively mitigates the tendency of the standard whale optimization algorithm to become trapped in local optima. Finally, experiments conducted on the Oxford battery dataset demonstrate that the proposed IWOA-TimeXer model achieves consistently superior prediction performance, with an average mean absolute error (MAE) of 0.00268. Compared with WOA-TimeXer, TimeXer, CNN + LSTM, and Transformer models, the MAE is reduced by 26.96%, 54.47%, 59.24%, and 58.28%, respectively.Overall, this study establishes a physics–data-driven hybrid framework that achieves both high prediction accuracy and strong interpretability, providing an effective solution for lithium-ion battery health management and offering valuable insights into the application of physics-informed neural networks in energy systems.