Automating The Selection Of Battery Models With Bayesian Quadrature And Bayesian Optimization

Abstract

The development of modern physics-based battery models increasingly specializes in individual processes in a cell. Selecting from the competing explanations for itemized phenomena grows more complicated. The scope of this challenge is visible in the wide variety of submodels offered in the modular battery model software PyBaMM [1]. The ability to parameterize any combination of submodels for a given measurement is crucial, as differing specialized routines are unfeasible for the large variety of submodels. This challenge gets addressed by Aitio et al. [2] and Kuhn et al. [3], which utilize Markov-Chain Monte Carlo methods to directly fit a model to the measured voltage. However, different submodels may fit with similar accuracy to the same data. Often this results from overparameterization, other times this happens because the difference gets lost in measurement noise. In either case, just the quality of the fit does not reliably tell whether the data supports the model, as shown by Adachi, Kuhn et al. [4]. To remedy that, they propose the Bayesian Quadrature algorithm BASQ [5] to calculate how well the data support a model, and verify its reliability on impedance data. BASQ considers not only a fit of the model to data but also the model-data distance for a wide range of model parameter values [5]. With this information, BASQ can discern two models for their ability to explain a particular dataset. Still, BASQ needs to find a good fit of the model to data as a basis for reliable model selection. However, the ability of BASQ to find said good fit directly depends on the initialization samples taken from the Prior. A Prior is, simply put, the weighted search area in the model parameter space, given in the form of a probability distribution. In this work, we find that the dependency of BASQ on the Prior can be alleviated by preconditioning the Prior with a parameterization algorithm. We choose EP-BOLFI from Kuhn et al. [3] as the parameterization algorithm, as it scales better with the model complexity than Metropolis-Hastings from Aitio et al. [2] does. EP-BOLFI has the additional benefit of itemizing its result into the given features one defines on the data. With featurization, we find that EP-BOLFI more quickly discerns the correlations, i.e., interdependencies, between the model parameters, long before it narrows down to a specific model fit. BASQ [5] profits off these correlations more than from a narrower search area, allowing us to preserve its model selection capability across a wide range of model parameters. We showcase the synergy between EP-BOLFI and BASQ on the example used in Adachi, Kuhn et al. [4], the determination of the length of the RC-chain in a R-RC-RC-etc. equivalent circuit model. The authors acknowledge support by the Helmholtz Association through grant no KW-BASF-6 (Initiative and Networking Fund as part of the funding measure "ZeDaBase-Batteriezelldatenbank").