Remaining Useful Life Prediction for Hybrid Systems Under Intermittent Fault Using Doubly Stochastic Process Model

This paper proposes a stochastic process based remaining useful life (RUL) prediction method for hybrid systems in the presence of intermittent fault. The failure of an intermittently faulty component is determined as a fault appearance with its severity exceeding failure threshold. This failure process is referred to as an event-triggered cooperative failure process (ETCFP). To depict the ETCFP in the hybrid system, a doubly stochastic process model is developed. In this model, the fault occurrence process is characterized by a compound non-homogeneous Poisson process with mode- and degradation-dependent fault occurrence rate and random external impacts, while the degradation process is composed of the external impacts and a Wiener process with the mode-dependent drift coefficient. Then, a multi-stage expectation maximization algorithm is proposed to estimate the unknown parameters in the doubly stochastic process model. In this approach, the stochastic integrals are approximated by the numerical integration with progressively refined step sizes at each stage. After that, the formulation of RUL distribution is derived based on the failure mechanism of ETCFP. To solve the RUL distribution that consists of stochastic integrals, a particle filter based numerical method is employed. Finally, the experimental study is carried out on a hybrid circuit system to show the effectiveness of the proposed method. Note to Practitioners—This paper is motivated by the remaining useful life (RUL) prediction problem of hybrid systems under intermittent fault. The existing degradation models for intermittent fault are deterministic models and the RUL is predicted by extrapolating the degradation trajectory to the failure threshold. However, the random occurrence characteristic of intermittent fault challenges the applicability of these approaches, as the fault may disappear when the extrapolated degradation trajectory reaches the failure threshold, meaning that the intermittently faulty component will not fail immediately. In practice, failure under intermittent fault occurs only when two conditions are met simultaneously: (1) the degradation process exceeds the preset threshold, and (2) a fault appears. This failure process, termed the event-triggered cooperative failure process (ETCFP), results from the interaction between a fault occurrence process and a degradation process. Given the limitations in capturing the stochastic nature of fault occurrence, the deterministic model based methods may not be the suitable solutions. To solve this problem, a doubly stochastic process model is developed, which could characterize the fault occurrence process and the degradation process simultaneously. After that, a multi-stage expectation maximization algorithm is proposed to estimate the unknown parameters in the doubly stochastic process model, using numerical integration to approximate stochastic integrals with progressively refined step sizes at each stage. Finally, the reliability analysis is conducted based on the failure mechanism of the ETCFP, and the RUL distribution is derived from the reliability function. A particle filter-based numerical method is employed to solve this distribution in the presence of stochastic integrals. In this way, both the probability of the degradation trajectory exceeding the failure threshold and the fault occurrence rate can be considered in the derivation of RUL distribution, by which an improved RUL prediction performance can be expected.