Estimating the Battery State of Health with Quantified Aleatoric and Epistemic Uncertainty

Abstract

Batteries are crucial in the transition towards a sustainable society. There is therefore an increased interest in battery health management. In battery health management, one of the key quantities is the State of Health (SoH), i.e., the maximum capacity of a battery, which decreases over time as the battery degrades. Accurate SoH estimations are needed to plan operations and battery replacements.

A crucial challenge in SoH estimation is to quantify the uncertainty of the estimates. Two types of uncertainty must be considered. First, aleatoric uncertainty is irreducible and caused by inherent noise in the data. Quantifying this uncertainty gives a lower bound on the SoH. Second, epistemic uncertainty is reducible and is caused by, among other factors, a lack of training data. Epistemic uncertainty can be used to identify if a test sample differs from the training samples, i.e., if it is Out-Of-Distribution (OOD).

In this paper, we estimate the SoH during discharge based on the current and voltage measurements obtained during charge. For this, we employ a Bidirectional Gated Recurrent Unit (Bi-GRU) neural network with attention. We estimate the aleatoric uncertainty using Simultaneous Quantile Regression (SQR), while we estimate the epistemic uncertainty by applying Orthonormal Certificates (OC). We test our approach on the fast charging dataset of Toyota. We achieve good results with high accuracy, with an RMSE of only 0.00343 Ampere hours, and good calibration. The model estimations become less accurate near the End of Life (EoL) of the batteries, but the corresponding data samples are correctly identified as OOD due to the high epistemic uncertainty.