Battery state-of-health modelling by multiple linear regression

Abstract

The introduction of raw measurement data from field operated batteries when modelling battery state-of-health (SOH) has both advantages and disadvantages. An advantage being the reduction in the amount of expensive laboratory testing in the analysed application. A clear disadvantage is the increase in amount of data which needs to be processed and transmitted from the battery to a server. The work presented in this paper aims to reduce the amount of data which needs to be transmitted by the extraction of descriptive features of the voltage, and then reducing the number of features. The extracted features are reduced in two stages. The first stage uses principle components analysis (PCA) and a variation proportion, p, to limit the number of features used to those accounting p% of the variation. The state-of-health is not used in this process, i.e. it is a reduction based solely on the feature set. The second stage selects features from the PCA reduced feature set. In this stage two types of selection are employed and compared: (1) step-wise selection, and (2) L1-regularisation (also called the lasso method). These methods were used to model the relationship between the features and two SOH measures: capacity and internal resistance. The two selection methods were also compared to using all features in the PCA reduced feature set – creating a total of six models (three for both of SOH measures) for each of the PCA reduced features sets. The mean absolute percentage error (MAPE), calculated on the validation set, never exceeded 5% for any of the three models, and at any of the PCA reduced feature sets; even when accounting for only 50% of the variation. Furthermore, if the PCA reduced feature set accounted for more than 50% of the variation, then the MAPE for the lasso method never exceeded 3%, and achieved MAPE’s as low as 1.13% and 1.24%, when modelling the capacity and internal resistance, respectively.