Physics-Informed Voltage Data Imputation for Robust Machine-Learning-Based Battery State of Charge Estimation

Machine learning (ML) estimators used for battery state of charge (SOC) prediction are vulnerable to missing measurement data and therefore require data imputation techniques to replace unavailable observations. However, most existing data imputation methods for SOC estimation rely primarily on statistical approaches rather than incorporating battery physics and dynamic behavior. Consequently, the estimation accuracy of such estimators degrades significantly during long periods of consecutive missing data. This study addresses this research gap by proposing a physics-informed (PI) data imputation method that reconstructs missing voltage measurements using a battery equivalent circuit model. The proposed PI data imputation technique is integrated with a long short-term memory (LSTM) architecture to develop the ML estimator. To evaluate the estimation performance, the developed model is compared with two other LSTM estimators that use conventional voltage imputation methods: last observation carried forward (LOCF) and extrapolation. The estimation errors of the three estimators are evaluated using experimental data obtained from a photovoltaic battery energy storage system (PV-BESS) equipped with lithium iron phosphate (LFP) batteries. Furthermore, the robustness of the estimators is analyzed by quantifying the confidence intervals using Bayesian approximation and Monte Carlo forward passes, providing a comprehensive assessment of estimation performance. The estimators are evaluated under different missing data ratios of 25%, 50%, and 75% in order to systematically compare their performance. The results demonstrate that the proposed PI-based estimator consistently achieves superior performance across all scenarios, and the performance gap between the PI-based approach and conventional imputation methods (LOCF and extrapolation) increases as the duration of missing data becomes longer.