A closed-loop estimation method for lithium battery SOH based on data-driven integration model and error compensation mechanism

Battery State of Health (SOH) estimation is a fundamental and challenging problem in battery management systems (BMS), particularly for lithium-ion batteries widely used in electric vehicles and energy storage systems. Accurate SOH estimation is crucial, as it not only ensures the safe operation of battery systems but also contributes significantly to extending their service life and improving overall energy efficiency. Traditional model-based approaches often require detailed knowledge of battery internal mechanisms, which are complex and highly nonlinear, making it difficult to construct accurate physical models. To address these limitations, this paper proposes a novel SOH estimation method based on a data-driven integrated model combined with an error compensation mechanism, offering both high accuracy and robustness in practical applications. The proposed method begins with the extraction of health features based on energy-related information, which serve as quantitative indicators reflecting the aging state of the battery. By systematically analyzing the temporal variation patterns of these energy indicators, the method captures the degradation trend of battery performance over long-term usage. This step provides a reliable quantitative basis for battery health assessment and ensures that the subsequent modeling and prediction stages are grounded in meaningful physical and operational characteristics. Following feature extraction, a data-driven approach based on Gaussian Process Regression (GPR) is employed to construct a dynamic integrated model. GPR is particularly suitable for this task because it can flexibly describe the nonlinear relationship between battery capacity degradation and health features without requiring an explicit analytical model, which is often difficult to derive due to the complex electrochemical processes inside the battery. In the proposed framework, GPR predicts future capacity using historical capacity sequences, thereby achieving recursive estimation and formulating a state equation for SOH evolution. Simultaneously, the relationship between the extracted health features and battery capacity is mapped to form a measurement equation, enabling the model to relate observable indicators to the underlying battery health state. To further enhance estimation accuracy, the particle filter (PF) algorithm is incorporated into the framework. By using the extracted health features as observations and combining them with the integrated GPR model, the PF algorithm enables feedback correction of SOH predictions, forming a closed-loop estimation process. This approach effectively accounts for measurement noise and system uncertainties, improving the robustness of the SOH estimation under real operating conditions. In addition, an error compensation mechanism based on the Extreme Learning Machine (ELM) is introduced. This mechanism learns and corrects residual errors between the predicted SOH and the actual measurements, further refining the estimation results and reducing overall prediction error. Finally, the effectiveness of the proposed method is validated using experimental data from a dataset containing four aged lithium-ion batteries. The results demonstrate that the extracted health features exhibit a high correlation with actual battery degradation, with an average correlation coefficient of 0.85, indicating strong reliability of the chosen features. The proposed SOH estimation method achieves an average mean absolute error (MAE) of 0.29% and a root mean square error (RMSE) of 0.38%, highlighting both high accuracy and robustness. Overall, the proposed data-driven integrated approach, enhanced by feedback correction and error compensation, provides a comprehensive and reliable solution for battery SOH estimation, offering significant potential for practical applications in battery management systems.