A semi-supervised learning strategy for lithium-ion battery capacity estimation with limited impedance data

Lithium-ion battery capacity inevitably degrades over charge-discharge cycles, necessitating precise capacity estimation for health monitoring, operational safety, and timely replacement. Despite significant advancements, most existing data-driven methods rely on supervised learning approaches, requiring extensive labeled data, which limits practical applicability. To overcome this challenge, we propose a semi-supervised battery capacity estimation method using limited impedance data. The distribution of relaxation times is employed to decouple impedance across different operational stages, linking its features to underlying electrochemical degradation processes while proposing temperature-adaptive health indicators with physical significance. An ensemble semi-supervised learning framework is then developed, where two heterogeneous models with joint training alternately generate and exchange pseudo-labels to enhance model performance, while the extracted features are leveraged for accurate capacity estimation. Extensive comparative experiments across various label rates, models, and ensemble strategies demonstrate superior accuracy, generalization, and interpretability. Notably, with only 5 % labeled data, the method achieves an average root mean square error of 0.51 mAh, a mean absolute error of 0.39 mAh, and a coefficient of determination of 96.31 %, providing an effective solution to data scarcity and feature generalization challenges in battery capacity estimation.