Joint Estimation of Lithium Battery States Based on Improved Fuzzy Entropy Fusion Weighting Method with Regulation Factors
Zhang Cheng1,2, Lu Wanlin1, Zhang Dongqing1, Lin Jinping1
1. School of Electronic Electrical and Physics Fujian University of Technology Fuzhou 350118 China; 2. Fujian Provincal University Engineering Research Center for Simulation Analysis and Integrated Control of Smart Grid Fuzhou 350118 China
Abstract：The state of charge (SOC) and state of health (SOH) of lithium-ion batteries are key parameters that determine the performance, safety, and service life of battery-powered systems. To improve the accuracy of SOC and SOH estimation, this paper presents the regulation factor improved fuzzy entropy fusion weighting (AFFEWF) method. This method integrates multiple Kalman joint estimation algorithms with a regulation factor and a fuzzy entropy-based dynamic weighting mechanism to combine the advantages of various estimation techniques. Firstly, based on a second-order RC battery model, four distinct Kalman joint estimators are employed to independently calculate SOC, SOH, and terminal voltage residuals. These estimators, which include variants of the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), generate outputs that differ due to variations in algorithm structure and underlying assumptions. Such diversity provides complementary information that is utilized in the fusion process to compensate for the limitations inherent in any single estimator. Secondly, a regulation factor is applied to preprocess the terminal voltage residuals. This factor is used to eliminate data that deviate from expected values due to sensor inaccuracies or environmental disturbances, thereby improving the reliability of the inputs for the subsequent fusion process. Thirdly, a fuzzy entropy fusion weighting algorithm is applied to dynamically assign weights to each estimator’s output. The algorithm quantifies the uncertainty in each estimator’s output using fuzzy entropy. Estimators with lower fuzzy entropy, which indicate more stable outputs, are assigned higher weights during the fusion process. This dynamic weighting mechanism ensures that the final estimation of SOC and SOH predominantly reflects the contributions of models with more stable outputs while reducing the influence of those with greater uncertainty. The formulation of fuzzy entropy in this context is detailed in the paper, providing the rationale for its use as a weighting criterion.Finally, to validate the proposed AFFEWF method, comparative experiments were conducted under urban dynamometer driving schedule (UDDS) conditions, which simulate practical driving scenarios characterized by variable speeds, frequent acceleration and deceleration, and extended idling periods. During these experiments, detailed battery voltage and current data were collected under dynamic load conditions. In addition, the performance of the AFFEWF method was compared with that of a conventional fuzzy entropy weighted fusion method (FEWF) and a multi-model probabilities based weighted fusion method (MMPWF). Result: (1) Compared with individual Kalman joint estimation algorithms, the AFFEWF method improves the accuracy of both SOC and SOH estimation. (2) The regulation factor effectively mitigates the impact of erroneous data, making the improved fuzzy entropy fusion weighting method superior to both the version without the regulation factor and the multi-model probabilistic fusion weighting method in SOC and SOH estimation. (3) Running time tests show that the fuzzy entropy fusion weighting method, which uses four Kalman joint estimators, operates within the same order of magnitude as the Kalman joint estimation algorithms and is much smaller than the sampling time of 0.1 seconds. This indicates that the computational burden is relatively small and does not significantly affect overall system performance. The computational efficiency of this method ensures its feasibility for real-time applications while maintaining high estimation accuracy.
张程, 陆万林, 张东清, 林锦平. 基于调节因子改进模糊熵融合加权法的锂电池状态联合估计[J]. 电工技术学报, 2026, 41(3): 1062-1074.
Zhang Cheng, Lu Wanlin, Zhang Dongqing, Lin Jinping. Joint Estimation of Lithium Battery States Based on Improved Fuzzy Entropy Fusion Weighting Method with Regulation Factors. Transactions of China Electrotechnical Society, 2026, 41(3): 1062-1074.
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2026, Vol. 41 
