Reliable estimation of battery remaining useful life (RUL) becomes difficult when the capacity trajectory contains regenerative rebounds, short-term oscillations, and long-range temporal dependence. To address this problem, an adaptive decomposition and hybrid deep-learning framework is proposed. First, the phototropic growth algorithm (PGA) is used to tune variational mode decomposition (VMD), allowing the capacity series to be separated into low-frequency trend information and high-frequency fluctuation information so that the influence of regeneration and noise is weakened. Next, a component-level predictor combining a temporal convolutional network (TCN), an attention mechanism (AM), and a Transformer is constructed. In this architecture, TCN learns multi-scale local features, AM enhances salient degradation cues, and the Transformer captures global long-horizon dependencies. To deduce the future capacity degradation path and the associated RUL, these estimated elements are synthesized. Results on the NASA, CALCE, and BIT datasets verify the effectiveness of the proposed framework. On NASA dataset, the average root mean square error (RMSE), mean absolute error (MAE), and absolute error (AE) reach 0.0123 Ah, 0.0073 Ah, and 0.5 cycles, respectively, improving on the strongest baseline by 11.9%, 19.7%, and 50.0%. On CALCE dataset, the corresponding values are 0.00695 Ah, 0.00499 Ah, and 1.75 cycles, and all R2 values are higher than 0.9989, indicating strong accuracy and robustness in the presence of complex regeneration behavior. Supplementary BIT validation on three higher-capacity cells further achieves average RMSE, MAE, and AE of 0.01201 Ah, 0.00771 Ah, and 1.0 cycle, respectively.
Wang et al. (2026) studied this question.