Balancing accuracy and complexity when selecting battery models to fit data

This talk raises the challenge of selecting battery models to fit the experimental data and provides a solution. We find that popular metrics to evaluate the model fit, such as root-mean-square error and Bayesian information criterion, can lead to incorrect model selection. We study the possible causes of this using the simplest battery model, an equivalent circuit model, as a proof-of-concept. We show that misidentification occurs when the RC time constants are close to one another. We propose the concept of Bayesian model evidence as an alternative metric“;“ this works as Occam’s razor, balancing predictive accuracy and model complexity. However, computation of this is prohibitive because one must integrate out (average over) all possible parameters, needing hundreds of thousands of battery model executions. To solve this, we adopt a novel integration technique called Bayesian quadrature, and the benefits are three-fold: over 100 times computational speed acceleration, simultaneous parameter estimation, and providing uncertainty estimates for the evidence metric itself. We demonstrate that the model evidence can identify the correct battery model to fit to data where existing criteria cannot. The variance of the model evidence also indicates the reliability of the estimation, suggesting whether the dataset or model needs to be rethought. The resulting parameter posteriors indicate the battery parameters (e.g. probabilistic distributions of the values of R’s and C’s in a circuit model) from observed data, including an estimation uncertainty. This information can benefit battery engineers by helping them to robustly identifying a plausible model for analysis, system identification, BMS use, and creating digital twins. This talk is associated with the paper: https://arxiv.org/abs/2210.172…