Interpretable Grey-Box Residual Learning Framework for State-of-Health Prognostics in Electric Vehicle Batteries Using Real-World Data

Conventional black-box models for electric vehicle (EV) battery State-of-Health (SOH) prediction achieve high accuracy but lack interpretability, limiting their practical deployment in Battery Management Systems (BMSs). To circumvent these limitations, this study proposes a novel Grey-Box Residual-Driven Framework (GBRDF) that synergizes Deep Symbolic Regression (DSR) with a residual-learning BiLSTM network with two contributions: (1) the DSR component derives explicit, interpretable mathematical expressions governing global degradation trajectories based on electrochemical features, and (2) the BiLSTM network models the residual errors to capture high-frequency nonlinearities and complex sequential dependencies not addressed by the symbolic baseline. By fusing the physics-informed transparency of DSR with the data-driven refinement of BiLSTM, the GBRDF significantly enhances forecasting precision. Experimental validation across four independent EV datasets shows that the GBRDF achieves the highest coefficient of determination (R2) of 0.982, and the lowest mean absolute error (MAE) of 0.1398 and root mean square error (RMSE) of 0.3176, significantly outperforming existing methods. Furthermore, the DSR-derived SOH equation shows that battery degradation is primarily driven by high voltage exposure and charging time, with mathematical transformations reflecting how degradation accelerates initially then slows, matching real-world aging patterns where voltage stress dominates over temperature and usage variations.