Physics-Informed Gaussian Process Regression for Battery Health Estimation Under Distribution Shift

Abstract

Accurate state-of-health (SOH) estimation is essential for safe, reliable battery management. Existing data-driven SOH estimation methods frequently exhibit limited operational coverage and lack calibrated predictive uncertainty under distribution shift. This study presents a physics-informed Gaussian process regression framework for SOH estimation from electrochemical impedance spectroscopy data. Equivalent circuit model parameters are extracted through a linear Kramers–Kronig validation and distribution of relaxation times deconvolution pipeline. These are combined with a Cumulative Stress Index (CSI), a scalar severity measure formed by integrating multiplicative stress factors over exposure and computable from operating history alone; it attains <inline-formula><tex-math notation="LaTeX">$R^{2}=0.938$</tex-math></inline-formula> on holdout and 0.709 on extrapolation, without any impedance measurement; its marginal contribution alongside the impedance features is 0.027 percentage points. A training set of 64 simulated cells is selected using a vertex-anchored maximum-projection space-filling design and evaluated using Leave-One-Battery-Out cross-validation. The method achieves a holdout Mean Absolute Percentage Error (MAPE) of 0.169% (<inline-formula><tex-math notation="LaTeX">$R^{2} = 0.995$</tex-math></inline-formula>) across 256 unseen simulated cells and 2.66% MAPE (<inline-formula><tex-math notation="LaTeX">$R^{2} = 0.752$</tex-math></inline-formula>) on a 94-cell extrapolation set beyond the training distribution, where the error is isolated to the sub-zero temperature tier. Scalar variance recalibration attains 94.3% to 96.1% prediction interval coverage.