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Equivalent circuit models for batteries are commonly used in electric vehicle battery management systems to estimate state of charge and other important latent variables. They are computationally inexpensive, but suffer from a loss of accuracy over the full range of conditions that may be experienced in real-life. One reason for this is that the model parameters, such as internal resistance, change over the lifetime of the battery due to degradation. However, estimating long term changes is challenging, because parameters also change with state of charge and other variables. To address this, we modelled the internal resistance parameter as a function of state of charge and degradation using a Gaussian process (GP). This was performed computationally efficiently using an algorithm [1] that interprets a GP to be the solution of a linear time-invariant stochastic differential equation. As a result, inference of the posterior distribution of the GP scales as 𝒪(n) and can be implemented recursively using a Kalman filter.

This paper presents a Bayesian parameter estimation approach and identifiability analysis for a lithium-ion battery model, to determine the uniqueness, evaluate the sensitivity and quantify the uncertainty of a subset of the model parameters. The analysis was based on the single particle model with electrolyte dynamics, rigorously derived from the Doyle-Fuller-Newman model using asymptotic analysis including electrode-average terms. The Bayesian approach allows complex target distributions to be estimated, which enables a global analysis of the parameter space. The analysis focuses on the identification problem (i) locally, under a set of discrete quasi-steady states of charge, and in comparison (ii) globally with a continuous excursion of state of charge. The performance of the methodology was evaluated using synthetic data from multiple numerical simulations under diverse types of current excitation. We show that various diffusivities as well as the transference number may be estimated with small variances in the global case, but with much larger uncertainty in the local estimation case. This also has significant implications for estimation where parameters might vary as a function of state of charge or other latent variables.