A wide variety of battery models are available, and it is not always obvious which model `best' describes a dataset. This paper presents a Bayesian model selection approach using Bayesian quadrature. The model evidence is adopted as the selection metric, choosing the simplest model that describes the data, in the spirit of Occam's razor. However, estimating this requires integral computations over parameter space, which is usually prohibitively expensive. Bayesian quadrature offers sample-efficient integration via model-based inference that minimises the number of battery model evaluations. The posterior distribution of model parameters can also be inferred as a byproduct without further computation. Here, the simplest lithium-ion battery models, equivalent circuit models, were used to analyse the sensitivity of the selection criterion to given different datasets and model configurations. We show that popular model selection criteria, such as root-mean-square error and Bayesian information criterion, can fail to select a parsimonious model in the case of a multimodal posterior. The model evidence can spot the optimal model in such cases, simultaneously providing the variance of the evidence inference itself as an indication of confidence. We also show that Bayesian quadrature can compute the evidence faster than popular Monte Carlo based solvers.

翻译：摘要：现有多种电池模型，但如何选择最能描述数据集的“最佳”模型尚不明确。本文提出一种基于贝叶斯求积的贝叶斯模型选择方法。采用模型证据作为选择指标，遵循奥卡姆剃刀原则，选择能够解释数据的最简模型。然而，计算模型证据需要对参数空间进行积分，通常代价高昂。贝叶斯求积通过基于模型的推断实现样本高效的积分，最大程度减少电池模型评估次数。模型参数的后验分布也可作为副产品一并推断，无需额外计算。本文以最简单的锂离子电池模型——等效电路模型为例，分析选择准则对不同数据集和模型配置的敏感性。研究表明，当后验分布呈多峰形态时，均方根误差和贝叶斯信息准则等常用模型选择准则可能无法选出简约模型。在此类情况下，模型证据能够识别最优模型，同时提供证据推断本身的方差作为置信度指标。此外，贝叶斯求积计算模型证据的速度优于常用的基于蒙特卡洛的求解器。