Remaining useful life prediction based on degradation signals using monotonic B-splines with infinite support

Degradation modeling traditionally relies on monitoring degradation signals to model the underlying degradation process. In this context, failure is typically defined as the point where the degradation signal reaches a pre-specified threshold level. Many models assume that degradation signals are completely observed beyond the failure threshold, whereas the issue of truncated degradation signals still remains a challenge. Moreover, based on the physics of a degradation process, the degradation signal should be inherently monotonic. However, it is almost inevitable that most of the sensor-based degradation signals are subject to noise, which can lead to misleading prediction results. In this article, a non-parametric approach to modeling and prognosis of degradation signals using B-splines in a mixed effects setting is proposed. In order to deal with the issue of truncated historical degradation signals, our approach is based on augmenting B-spline basis functions with functions of infinite support. Moreover, to model the degradation signal more accurately and robustly in a noisy setting, necessary and sufficient conditions to ensure monotonic evolution of the modeled signals are derived. Appropriate procedures for online updating of random coefficients of mixed effects model considering derived monotonicity constraints based on degradation data collected from an in-service unit are also presented. The performance of the proposed framework is investigated and benchmarked through analysis based on numerical studies and a case study using real-world data from automotive lead-acid batteries.