Prognosis for Stochastic Degradation Devices: A Perspective of Lebesgue Sampling

Abstract

Lebesgue sampling (LS) has emerged as an efficient paradigm for remaining useful life (RUL) prediction in stochastic degrading devices, because model updates are triggered only when critical degradation states are reached. However, its practical application is hindered by interval censoring under discrete monitoring, where the exact threshold-crossing time cannot be directly observed. Existing methods usually replace this hidden trigger time with deterministic point approximations, which introduces systematic bias into sequential estimation. To address this issue, this article proposes a probabilistic prognostic framework for Wiener-process-driven degradation systems. Specifically, a Brownian-bridge-based observation likelihood is constructed to quantify the probabilistic consistency between a candidate trigger time and its interval-censored observation pair within adjacent monitoring instants. This likelihood is then integrated into a Lebesgue-time-space model (LTSM) and a particle-filtering (PF) framework for sequential state estimation and RUL prediction. Experiments on the CALCE lithium-ion battery dataset and the PRONOSTIA bearing dataset show that the proposed method improves prediction accuracy while maintaining the computational efficiency of event-triggered updating. The framework therefore provides an effective solution for online RUL prediction of reliability-critical degrading devices under resource-constrained monitoring conditions.