An Adaptive Prognostic Approach Incorporating Inspection Influence for Deteriorating Systems

Degradation data obtained through inspections have been widely used to estimate the remaining useful life (RUL) of deteriorating systems. At the same time, such inspections may introduce external stress or release interior stress on the degradation processes of systems. However, current studies have paid little attention to the influence of such inspections during degradation modeling and RUL estimation. In this paper, we incorporate the inspection influence into Wiener-process-based degradation modeling and develop an approach to estimate the RUL of deteriorating systems. In the proposed method, the lifetime and RUL distribution with the consideration of the inspection influence on degrading systems are derived under the concept of first hitting time. To achieve an adaptive estimation of the RUL when new observations arrive, we constructed a state-space model by augmenting the drift coefficient and the inspection influence as state variables and treating the degradation increments as the observation variables. To do so, a Kalman filter is employed to update the state estimation, and then, an analytical result of the estimated RUL distribution for periodic-inspected systems is achieved. To implement the proposed prognostic method, we apply the expectation maximization algorithm to estimate unknown parameters in the constructed state-space model based on the historical observations of inspections. Finally, the proposed approach is illustrated by a numerical example and demonstrated by a case study using the mechanical gyroscopes.