Algorithm selection for lithium-ion battery ECM parameterization: a comparative study of trust-region, Levenberg-Marquardt, Gauss-Newton, and BFGS for accuracy and physical consistency

This paper presents a comparative study of four optimization algorithms, namely Gauss-Newton (GN), Levenberg-Marquardt (LM), Trust-Region (TR) and (Broyden-Fletcher-Goldfarb-Shanno (BFGS), for parameter identification of a second-order (2RC) equivalent circuit model of lithium-ion batteries using INR21700-45E cell data over a 10%-100% state-of-charge range. The algorithms are evaluated in terms of fitting accuracy, computational efficiency, and parameter consistency. TR and BFGS achieved lower mean rmse values of 0.922 mV and 0.971 mV, respectively, with [Formula: see text] values above 0.988 across most SOC levels, while LM produced a mean rmse of 2.441 mV. The GN method showed poor convergence and unreliable parameter estimation under the tested conditions. Model validation under Hybrid Pulse Power Characterization and C/2 discharge tests showed that TR and BFGS maintained voltage prediction errors below 0.022 V and 0.065 V, respectively, whereas LM exhibited larger deviations in dynamic conditions. Computationally, LM was the fastest method (0.244 s), followed by BFGS (0.383 s) and TR (0.655 s). The results indicate that TR and BFGS provide improved estimation accuracy and robustness, while LM offers lower computational cost, providing useful guidance for optimization algorithm selection in battery modeling and battery management system applications.