An Additive Wiener Process-Based Prognostic Model for Hybrid Deteriorating Systems

Hybrid deteriorating systems, which are made up of both linear and nonlinear degradation parts, are often encountered in engineering practice, such as gyroscopes which are frequently utilized in ships, aircraft, and weapon systems. However, little reported literature can be found addressing the degradation modeling for a system of this type. This paper proposes a general degradation modeling framework for hybrid deteriorating systems by employing an additive Wiener process model that consists of a linear degradation part and a nonlinear part. Furthermore, we derive the analytical solution of the remaining useful life distribution approximately for the presented model. For a specific system in service, the posterior estimates of the stochastic parameters in the model are updated recursively by using the condition monitoring observations based on a Bayesian framework with the consideration that the stochastic parameters in the linear and nonlinear deteriorating parts are correlated. Thereafter, the posterior distribution of stochastic parameters is used to update in real-time the distribution of the remaining useful life where the uncertainties in the estimated stochastic parameters are incorporated. Finally, a numerical example and a practical case study are provided to verify the effectiveness of the proposed method. Compared with two existing methods in literature, our proposed degradation modeling method increases the one-step prediction accuracy slightly in terms of mean squared error, but gains significant improvements in the estimated remaining useful life.