Physics-informed adaptive estimation framework for estimating subdiffusion characteristics of lithium-ion batteries

Subdiffusive electrochemical transport arising from electrode heterogeneity and degradation introduces dynamics that are poorly represented by conventional integer-order equivalent circuit models (ECMs) for lithium-ion battery (LIB) models. This paper presents a physics-informed adaptive estimation framework with digital twin capability that integrates fractional-order impedance modeling with nonlinear state estimation to enable estimation of battery states and physically interpretable subdiffusion characteristics beyond conventional ECM-extended Kalman filter (EKF) methods. A reduced-order equivalent circuit incorporating a fractional Warburg impedance element is combined with an EKF to estimate state-of-charge (SoC), internal electrochemical states, and fractional diffusion parameters under dynamic loading conditions. The fractional-order dynamics are approximated by a computationally efficient state-space representation, while HPPC-based parameter identification enables adaptive updating of diffusion characteristics from measured pulse-response data. Validation using NMC811 21700 and BAK 18650 datasets demonstrates voltage prediction errors below 6 mV, SoC estimation RMSE below 4%, and improved estimation accuracy relative to conventional integer-order ECM-based approaches. The identified subdiffusion parameters correlate strongly with degradation indicators including SEI growth, resistance increase, polarization, and capacity fade. The proposed framework augments conventional ECM-EKF estimation with physics-informed subdiffusion modeling, providing a scalable approach for real-time, health-aware estimation with digital twin capability for advanced battery management, diagnostics, and prognostics.