Remaining useful life prediction for nonlinear two-phase degradation process with measurement errors and imperfect prior information

Abstract Remaining useful life (RUL) prediction is one of the most important issues of prognostic and health management, which can improve the reliability and security of the system. Due to the changeable internal mechanism and external environmental factors, the two-phase degradation process is frequently seen in practice. In addition, measurement errors in degradation signals and the case with imperfect prior degradation information are common, which could decrease the accuracy of RUL prediction. However, the current studies on two-phase degradation usually assume that each phase is linear. Furthermore, the effect of measurement errors and the possibility of incomplete prior degradation data are generally not taken into account simultaneously. Therefore, this paper proposes a novel linear–nonlinear two-phase Wiener process with a measurement errors degradation model, and obtains the probability density function expression of the RUL by fully considering the unknown degradation state at the change point. Meanwhile, in the absence of multiple sets of historical data, a parameter estimation method which only requires a set of prior information is proposed based on an expectation maximization (EM) algorithm and Kalman smoothing. Finally, a numerical example and two practical examples are used to illustrate the effectiveness and superiority of the proposed method.