A bounded Transformed Wiener process with change-points with an application to lithium-ion batteries degradation data

Many technological units are subjected during their operating life to a degradation process that, in the long run, leads to their failure. Usually, a failure is assumed to occur when their degradation level exceeds an assigned failure threshold. The capability to accurately describe and predict the temporal evolution of the degradation of these units is critical for remaining useful life prediction and maintenance planning. The existing literature gives evidence that, frequently, the degradation process of these units exhibits change-points where the degradation rate or the mechanism of degradation changes abruptly, e.g. due to altered material properties or to the action of unobservable external factors. The diagnostic and prognostic accuracy of the model adopted to describe these degradation phenomena highly depends on their capability to account for the presence of these change-points. In this paper, we propose some degradation models with change-points that describe the whole degradation phenomenon via bounded Transformed Wiener processes where the functional form of the drift function and other features of the model can be phase-specific. The main properties of the model are illustrated. The distribution of the degradation level at a given time and the conditional distribution of the future degradation increment are formulated. The estimation of its parameters, including the change-points location, is performed by maximum likelihood. An application to a real set of degradation data of lithium-ion batteries is presented, which proves the utility of the proposed model and the feasibility of the adopted estimation procedure.

Keywords: Wiener process, change-points, bounded degradation phenomena, maximum likelihood estimation.