Battery State of Health Estimation Using a Hierarchical Gradient Algorithm Under Varying Temperature Conditions

Abstract

Accurate state-of-health (SOH) estimation of lithium-ion batteries under varying temperature conditions is essential for safe and efficient battery management systems (BMSs). However, conventional empirical SOH models often neglect temperature-dependent aging, while variable projection (VP)-based identification requires repeated projection and matrix-factorization operations. To address these issues, this paper proposes a temperature-coupled double-exponential SOH model and a hierarchical gradient (HG) algorithm for efficient parameter identification. An Arrhenius-type temperature factor is embedded in the degradation-rate terms to represent temperature-dependent electrochemical aging reflected by capacity fading. The HG algorithm alternately updates the linear and nonlinear parameter blocks through a Gauss--Seidel-type gradient scheme, thereby avoiding repeated projection calculations. Identification results under staircase temperature conditions show that HG achieves accuracy comparable to VP in terms of RMSE and the coefficient of determination, while substantially reducing computational time. The proposed method provides a lightweight temperature-aware SOH estimation scheme for resource-constrained BMS applications.