A General Stochastic Degradation Modeling Approach for Prognostics of Degrading Systems With Surviving and Uncertain Measurements

This paper is concerned with estimating remaining useful life (RUL) for a class of stochastic degrading systems with surviving degradation paths and uncertain measurements. The motivation comes from two engineering facts: the system's degradation state is discretely monitored and the measured degradation signals are taken from a survival degradation path, i.e., its lifetime is greater than the latest observation time, and the underlying degradation state cannot be perfectly observed due to the noise, disturbance, nonideal instruments, etc. Thus, the measured degradation signals are uncertain, but related to the underlying degradation state. Toward this end, we first present a general stochastic degradation modeling approach to account for the facts. Then, a non-Gaussian degradation state transition equation is derived considering the constraint of the survival path and thus the particle filtering algorithm is used to estimate the underlying degradation state in real time from uncertain measurements. Furthermore, we derive the RUL distribution based on the first-passage time concept which incorporates the uncertainty of the estimation for the degradation state and can be real-time updated based on the available surviving yet uncertain measurements. The novelty of this paper is to allow us to exclude the probability of failure between discrete monitoring times and to account for the impacts of surviving and uncertain measurements on estimating both the degradation state and the RUL. To apply the presented methodology, a maximum likelihood estimation framework is provided to determine the model parameters based on the expectation maximization algorithm together with particle filtering and smoothing methods. As a special case fallen into the presented framework, a linear degradation modeling and prognostic realization is discussed. Finally, we demonstrate the proposed approach by a case study.