Physics-Guided Residual Learning for Battery Modeling Across Held-Out Routes of a Single Electric Vehicle Using BMS Signals

Accurate battery models must generalize to unseen operating routes while supporting terminal-voltage prediction and recursive state-of-charge (SOC) estimation. This study evaluates whether physics-guided residual learning improves complete-route generalization compared with increasing equivalent-circuit-model (ECM) order or using direct data-driven voltage predictors. Seven open-loop voltage models and five matched extended Kalman filter (EKF) observers were assessed using 82 real-world electric-vehicle routes (119,720 synchronized observations) and only electrical and thermal battery-management-system signals. Sixty-six routes were used for development, and 16 formed a held-out route set. The residual 1RC M6 model achieved the lowest test path root mean square error (RMSE) voltage (0.797 V), reducing the error of the 2RC M3 physical model by 20.6%, while M7 achieved the (0.797 V), reducing the error of the physical 2RC model M3 by 20.6%, while M7 achieved the lowest median absolute route-energy error (0.091%). Development-only repeated grouped cross-validation yielded lower mean fold RMSE for M6 and M7 than for M3 in all 15 repeat fold combinations. For SOC estimation, the 1RC-residual observer S4 achieved the lowest mean and median RMSE relative to BMS-reported SOC (0.797 and 0.660 percentage points, respectively). The observer-family effect was significant (Friedman χ2=14.15, p=0.0068), although no planned paired comparison remained significant after Holm correction. The results support physics-guided residual learning as a promising single-vehicle across-route strategy, with route-dependent benefits and increased computational cost.