Disturbance-responsive online lithium-ion battery SOH estimation and analytical knee-point tracking with a Dual-Weibull Physics-Inspired Model

Accurate online estimation of lithium-ion battery state of health (SOH) and knee points remains challenging because feature-based estimators can be sensitive to changes in input-data quality, whereas conventional empirical models may lack the flexibility. Therefore, this study proposes an online SOH and knee-point estimation framework comprising a Transformer-adaptive Kalman filter (AKF) branch, a Dual-Weibull Physics-Inspired Model (DWPIM), and a disturbance-responsive multi-feature Multilayer Perceptron (MLP) gate. The residual-based AKF is adopted to recursively smooth the Transformer output and provide a posterior covariance state. Inspired by Weibull function in reliability engineering, DWPIM is introduced for capturing degradation trajectory and tracking the knee point online. Finally, the MLP gate dynamically fuses the Transformer-AKF and DWPIM estimates using the two current branch outputs, the AKF posterior covariance state, and the difference between the branches. Experimental evaluation was conducted on the CALCE battery dataset to assess the trajectory-representation capability, disturbance robustness, and online knee-point estimation performance of the proposed framework. The DWPIM achieved R 2 = 0.9911 on the source-cell trajectory. Under original data and simulated data disturbance, the observation-assisted framework achieved SOH RMSE values of 0.0125–0.0217. For CS2_36, CS2_37, and CS2_38, the final-100 pointwise knee-estimation MAEs were 84.39, 22.94, and 17.42 cycles, respectively; CS2_37 and CS2_38 achieved persistent ±10% accuracy lead times of 162 and 213 cycles. Extended strict closed-loop evaluation on six additional cells produced SOH RMSE values of 0.0214–0.0499.