State-of-charge estimation of LiFePO4 batteries by voltage-expansion force fusion

The flat voltage plateau of LiFePO4 batteries limits the accuracy of voltage-based State of Charge (SOC) estimation. To address this, a method integrating voltage and expansion force is proposed. Experimental data under different preload forces (1000 N, 2000 N) and dynamic conditions (DST, FUDS, UDDS) show that expansion force effectively reflects SOC variations. A voltage observation model and a GPR-based expansion force model with SE-ARD kernel are constructed, where GPR automatically optimizes parameters to relate expansion force to current and SOC across operating conditions. Signal fusion is realized via a series-connected double-layer untraceable Kalman filter (DLUKF), achieving RMSE ≤ 0.66%, MAE ≤ 0.48%, and MAX ≤ 2%, outperforming single-observation methods. With initial errors of ±20%, OCV-based correction accelerates DLUKF convergence while keeping MAX within 2%. SOC estimation can be computed within 5 ms per step, meeting BMS real-time requirements and demonstrating strong practical potential.