Learning battery model parameter dynamics from data with recursive Gaussian process regression

TL;DR

The paper tackles the challenge of estimating battery SOH under real-world usage, where purely model-driven or data-driven methods struggle. It introduces a hybrid approach that uses Gaussian process regression to model equivalent circuit parameters as functions of state, operating conditions, and lifetime, embedded in a recursive, EKF-based joint state–parameter estimator. Key contributions include a non-stationary lifetime kernel and a separable kernel structure over SOC and current, a discretized GP representation for efficient recursion, and a two-phase hyperparameter estimation strategy validated on simulated and experimental data to enable accurate SOH forecasting with quantified uncertainty. The framework is chemistry- and construction-agnostic, scalable to field data, and offers a practical path toward more reliable online SOH estimation and future-life prediction in battery management systems.

Abstract

Estimating state of health is a critical function of a battery management system but remains challenging due to the variability of operating conditions and usage requirements of real applications. As a result, techniques based on fitting equivalent circuit models may exhibit inaccuracy at extremes of performance and over long-term ageing, or instability of parameter estimates. Pure data-driven techniques, on the other hand, suffer from lack of generality beyond their training dataset. In this paper, we propose a hybrid approach combining data- and model-driven techniques for battery health estimation. Specifically, we demonstrate a Bayesian data-driven method, Gaussian process regression, to estimate model parameters as functions of states, operating conditions, and lifetime. Computational efficiency is ensured through a recursive approach yielding a unified joint state-parameter estimator that learns parameter dynamics from data and is robust to gaps and varying operating conditions. Results show the efficacy of the method, on both simulated and measured data, including accurate estimates and forecasts of battery capacity and internal resistance. This opens up new opportunities to understand battery ageing in real applications.

Figures (9)

• Figure 1: Li-ion model with first-order RC electrical circuit and lumped thermal model. All electrical parameters are modelled as Gaussian processes.
• Figure 2: Input/output data for simulation
• Figure 3: Ground truth functions for $\alpha(z)$, $\beta(z)$, $R_{\mathrm{0}}(z,I)$ together with their GP estimates using 1 cycle of input/output data. Estimation errors are reported in Table \ref{['tab:sim_params']}.
• Figure 4: Current, voltage and temperature profiles for the drive cycle used in experimental set-up. To parameterise the thermal model, we estimated $R_{\mathrm{c}}$ from the thermal relaxation at the end of the drive cycle using least-squares.
• Figure 5: Projections of GP posteriors for $Q$, $R_{\mathrm{0}}$, $\alpha$ and $\beta$. The validation data for $Q$ and $R_{\mathrm{0}}$ (dots) show that the model accurately captures the evolution of SOH. The right three plots of $\alpha$, $\beta$ and $R_{\mathrm{0}}$ as a function of discharge capacity show the strong dependency of ECM parameters on SOC (confidence bounds omitted for clarity). The colours indicate battery age expressed as full equivalent cycles (FEC), defined as the ratio of total Ampere-hour throughput to nominal capacity, and the dashed lines denote extrapolated points in time equivalent to the $Q$ and $R_{\mathrm{0}}$ points to the right of the vertical dashed lines.