Physics-Informed Transformer Using Degradation-Sensitive Indicators for Long-Term State-of-Health Estimation of Lithium-Ion Batteries

Accurate estimation of the State-of-Health (SOH) is essential for the reliable operation of lithium-ion batteries in electric vehicles and energy storage systems. However, conventional data-driven models often lack interpretability and show limited robustness under non-linear aging conditions. In this study, a physics-informed Transformer model is proposed for long-term SOH estimation by incorporating physically interpretable, degradation-sensitive indicators into a self-attention framework. Incremental Capacity Analysis (ICA)-derived features and thermal-gradient indicators are used as auxiliary inputs to provide physics-consistent inductive bias, enabling the model to focus on degradation-relevant regions of the charging trajectory. The proposed approach is validated using four lithium-ion battery cells exhibiting diverse aging behaviors, including severe non-linear capacity fade. Experimental results demonstrate that the proposed model consistently outperforms an LSTM baseline, achieving an RMSE below 1.5% even for the most degraded cell. Furthermore, attention map analysis reveals that the model autonomously emphasizes voltage regions associated with electrochemical phase transitions, providing clear physical interpretability. These results indicate that the proposed physics-informed Transformer offers a robust and explainable solution for battery health monitoring under practical aging conditions.