Shape Classification of Battery Cycling Profiles via K-Means Clustering based on a Sobolev distance

Battery cycling, both in application and Research and Development (R&D) environments, generates a wealth of information that often remains underexploited. Thus, potentially valuable information contained in electrical transients is frequently overlooked. In this framework, battery response modelling and model-based data analysis provide powerful tools to extract valuable information on battery status, its evolution and its correlation with functional performance. In this scenario, recently, we have developed a PDE model of battery potential response controlled by electrode shape changes in the BCs for high energy-density metal electrodes. In this work, on the basis of this model, we carry out a classification of the potential transient types, to enable a systematic comparison between model solution and experimental time-series. For transient shape classification purposes, we found that cluster analysis can play a key role in discovering hidden structures within the data. Specifically, in this paper, we apply the K-Means clustering algorithm to classify voltage profiles obtained as numerical solutions of the PDE model for the case of symmetric Li/Li cells. We introduce a weighted discrete Sobolev distance that allows us to spot changes in the shape of the voltage profiles, such as formation of peaks, valleys and concavities, that standard metrics such as the L2 norm fail to capture. As an application, we consider a selection of experimental galvanostatic discharge-charge potential time-series to classify their shape in terms of cluster centroids. Moreover, we show that the new clustering algorithm can provide a segmentation of the parameter space of the PDE model. This partitioning is useful to link the experimental profiles to specific parameter ranges. In particular, we report an example to validate the fitting results of a recent publication of ours obtained via a Deep Learning approach for the same measured profiles.