Semi-supervised learning with physicochemical health indicators using an Encoder-Gaussian process framework for battery state of health estimation under dynamic discharge conditions

Reliable estimation of the State of Health (SoH) of lithium-ion batteries is essential for ensuring safety, performance, and longevity in electric vehicles (EVs). Existing approaches, ranging from physicochemical and circuit-based models to fully supervised deep learning, encounter limitations in real-world applications due to high data requirements, modeling assumptions, or lack of generalizability under dynamic operating conditions. In this study, a semisupervised deep kernel learning (SSDKL) framework is proposed for the first time to estimate battery SoH using dynamic discharge data with limited labeled samples. The new architecture combines an Encoder-T + GRU with Gaussian process regression (GPR) to exploit both temporal dependencies and probabilistic uncertainty. 15% of the training data are labeled, with the remaining 75% utilized as unlabeled input to guide model generalization. The method is evaluated on the NASA randomized battery usage dataset, following a comprehensive data preprocessing pipeline that includes anomaly detection, normalization, and the extraction of physicochemical and statistical health indicators. The proposed model achieves an MAPE of 1.396% and an RMSPE of 2.029%, surpassing the current state-of-the-art benchmark by over 24%. To enhance interpretability, the internal behavior of the model is analyzed using SHAP values, saliency maps, and GRU gate weight dynamics, identifying key features and timesteps that influence predictions. The results demonstrate that semi-supervised learning can significantly improve SoH estimation accuracy while reducing dependence on extensive labeled datasets, offering a data-driven framework validated under dynamic discharge conditions, with potential applicability to battery management systems. The paper’s validated source codes are available in Appendix A.