Remaining Useful Life Prediction of Retired Lithium-Ion Batteries Under Second-Life Energy Storage Conditions Using Wavelet Packet Energy Entropy

Retired lithium-ion batteries retain considerable residual value for second-life energy storage applications, but significant variations in health conditions and complex operating scenarios make accurate remaining useful life (RUL) prediction challenging. To address the limited availability of capacity measurements and the poor adaptability of conventional models to dynamically fluctuating degradation trajectories, a hybrid RUL prediction framework integrating Wavelet Packet Energy Entropy (WPEE), a Fractional-Order Grey Model (FGM), and an Unscented Kalman Filter (UKF) is proposed. WPEE extracted from discharge voltage signals is employed as a degradation indicator, while a Box–Cox transformation enhances its correlation with capacity. An Adaptive Mutation Particle Swarm Optimization (AMPSO) algorithm is used to determine the optimal fractional-order parameter, and the optimized FGM is incorporated into the UKF state-transition process for recursive state correction. Validation was conducted using four retired lithium-ion cells and two series-connected battery packs with different health conditions at prediction starting points of 20, 25, and 30 cycles. The results show that the proposed method effectively tracks degradation evolution, with RUL prediction errors within 7 cycles for retired cells and within 6 cycles for battery packs. Across all 18 prediction cases, FGM–UKF achieved an overall mean AE of 3.111 cycles, lower than those of FGM (5.111 cycles), GM(1, 1) (4.000 cycles), and LR (4.278 cycles). These results demonstrate the effectiveness and robustness of the proposed framework for lifetime assessment in second-life battery energy storage systems.