Handling Capacity Regeneration Effects for Accurate SOH Estimation in Lithium-Ion Batteries via Optimized Transformer

Non-linear changes and local fluctuations during lithium-ion battery capacity degradation complicate state of health (SOH) characterization. This study proposes a multiscale capacity reconstruction method combining complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), an improved sparrow search algorithm (ISSA), and a Transformer. CEEMDAN decomposes historical capacity sequences into modal components and a residual; ISSA selects the Transformer hyperparameters, and the network estimates these components from health indicators to reconstruct capacity. Records from eight NASA and CALCE cells at nominal ambient temperatures of 4, 24 and 43 °C are evaluated retrospectively using global capacity decomposition and chronological splitting. In the original experiments with all four indicators, the proposed method achieved SOH RMSE values of 0.00310–0.00946. Supplementary experiments independently reselected the hyperparameters for the complete-indicator and two-indicator groups and conducted three paired repeat fits. Removing HI3 and HI4 increased the mean RMSE and MAE for all eight cells; the mean RMSE increased from 0.001627 to 0.031010 for B0005 and from 0.002030 to 0.070238 for CS2_35. These results demonstrate the substantial influence of capacity-related inputs on reconstruction accuracy, with cell-dependent benefits from hyperparameter reselection. Parameter sensitivity analysis further quantified the effects of decomposition settings on SOH reconstruction errors and offline computational cost. This study characterizes the performance and input-information dependence of multiscale historical capacity reconstruction, providing experimental evidence to inform indicator selection, decomposition settings and subsequent temporal validation.