Lithium-ion battery parameter identification using a GRU-guided particle swarm optimization with SLSQP refinement for accurate state-of-charge estimation

Accurate identification of equivalent circuit model (ECM) parameters is a prerequisite for reliable state-of-charge (SOC) estimation in battery management systems (BMSs). This paper proposes GRU-PSO-SLSQP, a hybrid metaheuristic framework that integrates a Gated Recurrent Unit (GRU) neural network with Particle Swarm Optimization (PSO) and Sequential Least Squares Programming (SLSQP) for high-fidelity identification of second-order Thevenin model parameters. The GRU operates as an online meta-optimizer: it encodes the temporal evolution of a 32-dimensional swarm-state vector—capturing population diversity, fitness statistics, velocity trends, and improvement dynamics—and dynamically infers the optimal PSO control parameters (w, c_1, c₂) at each iteration through a driven online learning mechanism. The GRU-guided global search is followed by a deterministic SLSQP local refinement stage, forming a bilevel optimization structure that combines the robustness of population-based exploration with the precision of gradient-based convergence. Validation on the INR18650-20R cell across three operating temperatures (0°C, 25°C, and 45°C) demonstrates that GRU-PSO-SLSQP consistently achieves terminal voltage RMSE below 0.48% and R² above 0.991 under all thermal conditions, outperforming all three PSO benchmark variants, whose terminal voltage errors are consistently higher and degrade more sharply at extreme temperatures. The quality of the identified parameters is further confirmed through EKF-based SOC estimation, where the proposed framework yields an RMSE below 0.30% and a peak error within 1% across all thermal conditions, reflecting a closer tracking of the true SOC trajectory compared to the benchmark algorithms. These results confirm that accurate parameter identification directly translates into superior SOC tracking performance, and establish GRU-PSO-SLSQP as an effective, temperature-robust, and autonomous framework for battery characterization in electric vehicle (EV) BMS applications.