A hybrid model with Gaussian process-based covariance matrix adaptation evolution strategy for state of charge estimation of lithium-ion batteries

With the widespread applications of lithium-ion batteries in high-end emerging industries, monitoring the state of charge (SOC) of lithium-ion batteries has attracted extensive attention and research. However, accurate SOC estimation is challenging due to the variability of lithium-ion batteries under different operating conditions. In this paper, a hybrid model is proposed for precise SOC estimation of lithium-ion batteries. The hybrid model combines a memory-enhanced gated recurrent unit (ME-GRU) network with an adaptive unscented Kalman filter (AUKF), and optimizes the hyperparameters of the ME-GRU network using a covariance matrix adaptation evolution strategy (CMAES). Specifically, the ME-GRU network serves as a deep learning-based method to produce preliminary SOC estimation results, avoiding the complex battery modeling process required by AUKF. In addition, AUKF corrects the preliminary SOC estimation results to mitigate the negative effect of inherent noise in the data. Moreover, during the optimization process, we introduce Gaussian process into CMAES, which effectively reduces the time required and enhances the real-time performance of the hybrid model in SOC estimation. This optimization process avoids the time-consuming hyperparameter design of the ME-GRU network, and helps the hybrid model yield accurate SOC estimation under different operating conditions. Experiments on an individual battery dataset and a battery pack dataset demonstrate that the hybrid model achieves satisfactory SOC estimation, with the root mean square error (RMSE) below 0.6% and the maximum error below 2.5% across both datasets. © 2025 Elsevier Ltd.