Remaining lifetime of degrading systems continuously monitored by degrading sensors

We consider degrading engineering systems monitored by degrading sensors. Since accurate information is crucial for predicting system health condition and the subsequent decision-making, considering the effect of sensor degradation is highly important to determine the justified reliability characteristics of systems such as the remaining useful life (RUL). Although the concept of sensor degradation has been introduced previously in the literature, the remaining useful life estimation in this case or parameter estimation in the presence of sensor degradation has not been studied in detail. To fill the gap, this study aims to estimate the RUL of a system that is continuously monitored by a degrading sensor. In this work, to distinguish sensor degradation from that of the main system, an additional calibration sensor is used to accurately inspect the system health condition at certain points of time. Subsequently, maximum-a-posteriori estimation technique is employed to estimate the parameters for the system degradation process and maximum likelihood estimation is used to estimate the parameters of sensor degradation. A Kalman filter is then used to estimate the system and sensor states, followed by system RUL evaluation. A numerical example with simulated data is employed to illustrate the effectiveness of the proposed method. It is shown through the numerical study that neglecting sensor degradation can result in significant errors in RUL estimation, which can further impact the subsequent maintenance decisions.