[Paper Review] Learning battery model parameter dynamics from data with recursive Gaussian process regression

Antti Aitio, Dominik Jöst+2 more|arXiv (Cornell University)|Apr 26, 2023

Advanced Battery Technologies Research5 citations

TL;DR

This paper proposes a recursive Gaussian process regression framework that learns battery model parameter dynamics from real-world data, enabling accurate, computationally efficient, and robust state and parameter estimation for battery state-of-health (SOH) monitoring. The method jointly estimates battery states and time-varying parameters (e.g., capacity, internal resistance) as functions of state of charge, current, and lifetime, achieving high accuracy and forecasting capability on both simulated and measured data.

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.

Motivation & Objective

• To address the challenge of inaccurate and unstable parameter estimates in model-based battery management systems under variable real-world operating conditions.
• To overcome the limitations of purely data-driven methods, which lack generalization beyond training data and struggle with data gaps and non-stationarity.
• To develop a hybrid model- and data-driven approach that captures time-varying parameter dynamics using Bayesian inference.
• To ensure computational efficiency for online applications by enabling recursive estimation with O(n) scaling instead of O(n³).
• To enable accurate long-term forecasting of battery capacity and internal resistance using real-world field data.

Proposed method

• The method models battery parameters (e.g., capacity, resistance) as Gaussian processes (GPs) that depend on state of charge, current, and battery lifetime.
• It employs a recursive GP regression formulation based on a linear stochastic differential equation representation, enabling online, real-time estimation.
• The approach uses a Kalman filter and Rauch-Tung-Striebel smoother to recursively update the posterior distribution over functions and hyperparameters.
• The kernel function is assumed to be separable in time and input space, allowing efficient implementation via state-space representation.
• Hyperparameters are optimized recursively using the log marginal likelihood, ensuring robustness to data gaps and varying operating conditions.
• The framework unifies state and parameter estimation into a single joint observer, improving consistency and reducing computational cost.

Experimental results

Research questions

• RQ1 Can a recursive Gaussian process regression framework accurately estimate time-varying battery model parameters from noisy, incomplete, and non-stationary real-world data?
• RQ2 How does the proposed method improve the accuracy and robustness of battery state-of-health (SOH) estimation compared to standard model-based or data-driven approaches?
• RQ3 To what extent can the method forecast future battery capacity and internal resistance over long-term ageing under variable operating conditions?
• RQ4 How does the recursive formulation maintain computational efficiency while preserving estimation accuracy compared to batch GP regression?
• RQ5 Can the method generalize across different cells and operating profiles without retraining, given its data-driven yet physically informed structure?

Key findings

• The recursive GP regression method achieves accurate and stable estimation of battery capacity and internal resistance across both simulated and measured data, even with data gaps and variable operating conditions.
• The method demonstrates robust performance in forecasting battery capacity and resistance over long-term ageing, outperforming traditional model-based observers.
• Computational complexity scales linearly with data size (O(n)), enabling real-time implementation, unlike standard GP regression which scales cubically (O(n³)).
• The joint state-parameter estimation framework reduces parameter estimation noise and improves convergence stability compared to standard recursive estimation techniques.
• The approach successfully captures complex, nonlinear parameter dynamics as functions of state of charge, current, and lifetime, enabling more accurate SOH tracking.
• The method provides uncertainty estimates for both states and parameters, enhancing reliability for safety-critical applications.