Estimating Remaining Useful Life With Three-Source Variability in Degradation Modeling

The use of the observed degradation data of a system can help to estimate its remaining useful life (RUL). However, the degradation progression of the system is typically stochastic, and thus the RUL is also a random variable, resulting in the difficulty to estimate the RUL with certainty. In general, there are three sources of variability contributing to the uncertainty of the estimated RUL: 1) temporal variability, 2) unit-to-unit variability, and 3) measurement variability. In this paper, we present a relatively general degradation model based on a Wiener process. In the presented model, the above three-source variability is simultaneously characterized to incorporate the effect of three-source variability into RUL estimation. By constructing a state-space model, the posterior distributions of the underlying degradation state and random effect parameter, which are correlated, are estimated by employing the Kalman filtering technique. Further, the analytical forms of not only the probability distribution but also the mean and variance of the estimated RUL are derived, and can be real-time updated in line with the arrivals of new degradation observations. We also investigate the issues regarding the identifiability problem in parameter estimation of the presented model, and establish the according results. For verifying the presented approach, a case study for gyros in an inertial platform is provided, and the results indicate that considering three-source variability can improve the modeling fitting and the accuracy of the estimated RUL.