Remaining Useful Life Estimation for Systems with Time-varying Mean and Variance of Degradation Processes

This paper focuses on the problem of how to estimate remaining useful life (RUL) for a class of systems with high fluctuating dagradation caused by time‐varying mean and variance. In engineering practice, the fluctuation of the degradation data can reflect the system stability, and hence it can serve as an additional indicator for the system's health state in addition to the degradation observations. To estimate the RUL for this class of systems, three issues should be considered jointly: (i) how to model the degradation data with high fluctuation, (ii) how to define an indicator denoting the fluctuation's level, and (iii) how to combine the degradation path and the fluctuation for the RUL estimating task. In responses to the above issues, this paper characterizes the degree of the fluctuation by the standard deviation of the stochastic degradation process and defines the standard deviation as an additional performance variable. Moreover, a stochastic degradation model is proposed to reflect the high fluctuating degradation data, in which the standard deviation is time dependent. To obtain the marginal distribution of the RUL derived by the standard deviation, the failure threshold of the standard deviation is given according to its influence on the degradation process. Another marginal distribution derived by the degradation data is also obtained by the time distribution of the degradation process crossing the degradation threshold. Then, through deriving the correlation between the two marginal distributions based on the probability theory, the joint distribution of the RUL is obtained. Finally, a practical case study for gyro is conducted. The results demonstrate the feasibility and applicability of the proposed model.