Physics-Informed SP-LSTM for State of Health Estimation of Lithium-Ion Batteries with Macro and Physical Feature Fusion

Accurately estimating the state of health (SOH) of lithium-ion batteries remains challenging for battery management systems. Traditional data-driven methods, such as long short-term memory (LSTM), lack physical interpretability and often fail to generalize across varying operating conditions. To address this, a physics-informed SP-LSTM framework is proposed that integrates the single particle model (SPM) with a bidirectional LSTM network. A hybrid optimization strategy combining particle swarm optimization and the limited-memory Broyden–Fletcher–Goldfarb–Shanno with bounds (L-BFGS-B) is first used to identify key SPM parameters, which are then combined with macro external features (charging time, discharge energy, IC peak) to form a seven-dimensional fusion vector. A dual-stream Bi-LSTM architecture separately models fast-varying macro trends and slow-varying physical parameters, achieving robust SOH mapping. Validated on the NASA PCoE dataset, the proposed SP-LSTM achieves a root mean square error (RMSE) of 0.0136 and a mean absolute error (MAE) of 0.0089 on an independent test set (B0018), outperforming the baseline LSTM by 38.2% in RMSE. Noise robustness tests (0–3% voltage noise) and Sobol global sensitivity analysis further confirm its stability and interpretability. By embedding electrochemical priors into the data-driven pipeline, this work provides a practical physics-data collaborative framework for accurate and trustworthy battery SOH estimation.