Time-of-Failure Probability Mass Function Computation Using the First-Passage-Time Method Applied to Particle Filter-based Prognostics

Abstract

One of the main challenges in prognostics corresponds to the estimation of a system’s probability density function (PDF) for the time-of-failure (ToF) prior to reach a fault condition. An appropriate characterization of the ToF-PDF will let the user know about the remaining useful life of the system or component, allowing the users to prevent catastrophic failures through optimal maintenance schedules. However, the ToF-PDF estimation is not an easy task because it involves both the computation of long-term predictions of a fault indicator of the system and the definition of the hazard zone. In most cases, the trajectory of the fault indicator is assumed as a trajectory with monotonic behavior, and the hazard zone may be considered as a deterministic or probabilistic threshold. This monotonic behavior of the fault indicator enables assuming that the system will only fail once when this indicator reaches the hazard zone, and the ToF-PDF will be estimated according to mathematical definitions proposed in the state-of-the-art. Nevertheless, not all the fault indicators may be considered with a monotonic behavior due to its nature as a stochastic process or regeneration phenomenon, which may entail to errors in the ToF-PDF estimation. To overcome this issue, this paper presents an approach for the estimation of the ToF-PDF using the first-passage-time (FPT) method. This method is focused on the computation of the FPT-PDF when the stochastic process under analysis reaches a specified threshold for the first time only. Accordingly, this work aims to analyze the impact in the estimation of the ToF-PMF (probability mass function) when particle-filter-based prognostics algorithms are used to perform long-term predictions of the fault indicator and compute the probability of failure considering specific hazard zones (which may be characterized by a deterministic value or by a failure likelihood function). A hypothetical self regenerative degradation process is used as a case study to evaluate the performance of the proposed methods.