Evaluation of a hybrid battery digital twin for joint SOC-SOE estimation under real driving conditions

Reliable estimation of battery state of charge (SOC) and state of energy (SOE) under real world dynamic driving conditions is essential for battery management systems. However, traditional physics-based models and purely data-driven models struggle to adapt and generalize. This work proposes Closed-Loop Hybrid Digital Twin (CL-HDT) that synergizes adaptive physics twin, recurrent residual learning, physics guided optimization, and recursive state feedback for joint SOC-SOE estimation. Adaptive physics twin generates physically consistent reference estimate and residual from closed-loop recurrent model recursively corrects it. The proposed CL-HDT was developed with a dataset containing 30 real-world electric cycle driving trips, split with leakage-safe strategy into training, validation, and locked holdout test set. To analyze generalizability, leave-one-trip-out cross-validation (LOTO-CV) was applied within training set. The proposed architecture was benchmarked against five baselines including Extended Kalman Filter (EKF), Gated Recurrent Unit (GRU), Feature-Fusion Recurrent estimator (FFR), Residual-Guided Hybrid estimator (RGH), and Adaptive Physics Twin (APT). All the baselines and CL-HDT were trained and evaluated under identical pipeline to ensure fair comparison. CL-HDT attained strongest generalization in LOTO-CV with mean RMSE values of 0.7078% and 0.6883% for SOC and SOE respectively, while maintaining competitive performance in locked holdout test. Apart from aggregate metrics, CL-HDT was further evaluated using residual correction analysis, tracking curves, drift curves, component-wise ablation, error distribution, and ambient condition analysis to demonstrate its robustness and ability to mitigate accumulation of error over longer real-world trips. This approach offers a physically consistent solution for next-generation battery management systems under realistic driving conditions to support safety and battery life.