A Statistical Analysis-Based PINN Framework for Joint SOC/SOE Estimation Across Multi-conditions

Accurate joint estimation of the state of charge (SOC) and the state of energy (SOE) is essential for reliable management of lithium-ion batteries (LIBs) under diverse operating conditions. However, robust estimation remains challenging because polarization induces pronounced variations in voltage response and internal dynamics, especially when only limited multi-condition data are available. In this work, a unified SPMe-based physics-informed neural network (PINN) framework is proposed for joint SOC/SOE estimation under small-sample, multi-condition settings. SPMe-derived physical constraints are embedded into the learning process, while a statistical representativeness analysis is conducted to justify the use of limited multi-condition data for cross-condition learning. An SOC fixed-point supervision (SOCFPS) strategy is further introduced to suppress cumulative SOC drift and improve the stability of joint estimation. Experimental results show that the proposed framework achieves an SOC RMSE below 1.2% in nearly all cases and an SOE RMSE consistently within 2% across 16 operating conditions. Compared with the SPMe-based particle filter (PF) method and representative data-driven baselines, including a gated recurrent unit (GRU) model, the proposed framework provides more accurate joint SOC/SOE estimation and stronger robustness. Moreover, under an unseen Dynamic Stress Test (DST) profile, the method still maintains clear advantages in terminal-voltage, SOC, and SOE estimation, indicating promising generalization beyond the constant-current training regime.