A condition-based prognostic approach for age- and state-dependent partially observable nonlinear degrading system

To deal with age- and state-dependent degradation, unit-to-unit variability and partially observable or hidden degradation in remaining useful life prediction jointly, this paper proposes a condition-based prognostic approach for age- and state-dependent partially observable nonlinear degrading system. The dynamics and nonlinearity of the system degradation process are described by the age- and state-dependent nonlinear diffusion process. The nonlinear relationship between observations and the hidden degradation state is characterized by a state space model. To derive the distribution of the remaining useful life, we apply the extended Kalman filtering and expectation-maximization algorithm to adaptively estimate the degradation states and the unknown model parameters. Based on the estimated degradation states and model parameters, we derive the approximately analytical distribution of remaining useful life in the concept of the first hitting time. Furthermore, the distribution of remaining useful life can be updated according to the newly available data, thereby realizing real-time remaining useful life estimation. An illustrative example is given to explain the application of the proposed approach in the specific age- and state-dependent nonlinear degradation model. Finally, a numerical example and a case study for bearing degradation data are presented to verify the accuracy and effectiveness of the proposed model.