Physics-constrained machine learning for real-time lithium-ion battery health estimation from constant voltage charging data

Reliable, real-time state-of-health (SOH) estimation is essential for energy storage devices. Existing approaches often rely on constant current (CC) charging or impedance spectroscopy, while the constant voltage (CV) phase is commonly overlooked, and physics-based models remain too computationally intensive for real-time application. To address this gap, this work proposes a physics-constrained machine learning (PCML) framework that integrates a second-order RC equivalent circuit model-serving as a reduced-order surrogate of electrical processes-within a recurrent neural network architecture. By embedding discrete state equations into the learning process, the framework achieves both interpretable parameter identification and real-time SOH prediction from CV data. Simulation and experimental validation demonstrate superior accuracy compared with particle swarm optimization, recursive least squares, and first-order RC-based PCNN. A strong correlation (–0.9362) between estimated internal resistance and capacity-defined SOH underscores the practical value of this approach. The results highlight how combining mechanistic electrochemical models with machine learning advances predictive electrochemistry and strengthen the design of robust battery management systems.