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 the prognostic and health management (PHM), 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 measurement errors (TPWPME) degradation model, and obtains the probability density function (PDF) 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 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.

Remaining Useful Life Prediction for Two-Phase Nonlinear Degrading Systems with Three-Source Variability

“…It is observable from Table 4 that the TMSE of our method is the smallest. Thus, although the MSE value of Chai's method [37] in Figure 10a is smaller than ours in the sixth month, however, in general, the TMSE of our method is still better than Chai's method [37]. In addition, among the four methods, our method has the smallest MAE value and the largest CRA value, because we simultaneously consider the two-phase nonlinearity and the three-source variability of the degradation process.…”

“…The MSE value will be smaller when the PDF of RUL is closely distributed around the actual RUL value [34]. Therefore, the MSE value of Chai's method [37] is slightly smaller than ours in the sixth month. In fact, this is acceptable.…”

“…In addition, due to the influence of the dynamic environment and the non-ideal instruments, the obtained observations inevitably contain noise. Therefore, to characterize the measurement variability between observed values and the true degradation states, the degradation measurement process {Y(t), t ≥ 0} is formulated as follows [25,37],…”

“…The reason for this phenomenon is that the degradation trajectory is equivalent to a single-phase nonlinear degradation process after the changing point appears, thus, Zheng's method [25] that considers three-source variability simultaneously could effectively fit the degradation process. For performance evaluation, two metrics are employed to evaluate the performance of RUL prediction among different methods, including the mean square error (MSE) [22] and the absolute error (AE) [37]. The MSE at each observation point could be defined as follows,…”

A RUL prediction of bearing using fusion network through feature cross weighting

“…Two data driven methods are widely used, mathematical statistics and machine learning [4]. There are many typical statistical models for RUL prediction, including Wiener process model [5][6][7], Markov model [8], inverse Gaussian process model [9], etc. Machine learning based methods, such as, random forest (RF) [10], K nearest neighbor method [11], support vector regression [12,13] deep learning based methods, etc.…”