Remaining Useful Life Prediction Based on a General Expression of Stochastic Process Models

In remaining useful life (RUL) prediction, stochastic process models are widely used to describe the degradation processes of systems. For age-dependent stochastic process models, the RUL probability density function (PDF) can be calculated using a closed-form solution. For state-dependent models, however, it is difficult to calculate such a closed-form solution. Therefore, the RUL is always approximately estimated using a sequential Monte Carlo-based method, but this method has some limitations. First, it only provides a numerical approximation result whose accuracy highly relies on the quality and quantity of the simulated degradation trajectories. Second, the time interval is unable to be adjusted during the state transition process, resulting in too few discrete probability densities in the result near the end-of-life. This paper describes the degradation processes using a general expression of age- and state-dependent models. The analytical solution of the RUL PDF is derived from the general expression. After that, a new RUL prediction method is proposed. In this method, a series of degradation trajectories are generated through degradation process simulation. The RUL PDF is estimated by inputting the state values of the degradation trajectories into the analytical solution. The validity of the proposed method is verified using fatigue-crack-growth data.