Fractional-Order Circuit Model-Based SOC Estimation for Lithium-Ion Batteries with LSTM Residual Correction

A fractional-order equivalent circuit model (FOECM) provides a compact and physically interpretable representation of the memory-dependent polarization behavior of lithium-ion batteries. Leveraging this property, a fractional order model-guided residual-correction framework is proposed for state-of-charge (SOC) estimation, in which the FOECM, unscented Kalman filter (UKF), and long short-term memory (LSTM) residual learner are integrated into a unified estimation chain rather than treated as separate modules. In this framework, the FOECM is parameterized using Dynamic Stress Test (DST) data and incorporated into the UKF to construct the FOECM + UKF estimator. The LSTM learns the history-dependent SOC residual from sequences of measured operating signals and FOECM + UKF SOC estimates, and its output is added to the UKF estimate without replacing the fractional-order physical model. The proposed hybrid estimator is trained and configured using the available DST, Supplemental Federal Test Procedure (US06), and Federal Urban Driving Schedule (FUDS) data, and is independently evaluated on the US06 and FUDS profiles of Cell 008. Compared with the FOECM + UKF estimator, the proposed hybrid estimator reduces the SOC root mean square error (RMSE) from 2.70% to 0.90% on US06 and from 2.93% to 1.20% on FUDS, with mean absolute error (MAE) values of 0.66% and 1.03%, respectively. These results demonstrate the effectiveness of coupling fractional-order memory modeling with sequence-based residual correction under the tested dynamic operating profiles.