Lithium-ion battery SOH estimation based on degradation physics constraints and cross-attention Transformer-GRU

Accurate estimation of lithium-ion battery state of health (SOH) is essential for battery management systems in safety warning, lifetime management, and energy scheduling. To address the difficulty of simultaneously capturing global feature coupling and local degradation memory with a single deep learning model, as well as the lack of degradation-physics constraints in purely data-driven prediction, this paper proposes an SOH estimation method that integrates degradation physics constraints with cross-attention Transformer-GRU, denoted as PI-CTG. First, five health features are extracted from the constant-current/constant-voltage charging-voltage curve and the incremental-capacity (IC) curve, including constant-current charging time, constant-current average voltage, IC peak value, IC peak voltage, and IC average value. Subsequently, the Transformer branch is used to learn the global coupling relationships among health features, the GRU branch is used to capture local degradation memory along the cycle dimension, and the cross-attention module is used to adaptively fuse the two types of representations. Furthermore, the SOH degradation rate is expressed as an implicit function of cycle index and health features, and degradation-dynamics residual and weak monotonicity constraints are incorporated into the training objective. Results on three datasets, namely Oxford, CALCE, and NASA, show that PI-CTG achieves an average RMSE of 0.0072 and an average $$R^2$$ of 0.9730 over six batteries, outperforming the comparison models GRU, Transformer, and CTG without physics constraints. Battery-wise SHAP analysis further shows that constant-current charging time, IC average value, and IC peak value are the major contributing features for SOH estimation, while highly correlated features may exhibit different marginal contributions because of redundancy caused by collinearity.