Remaining Useful Life Prediction With Fusing Failure Time Data and Field Degradation Data With Random Effects

Abstract

Accurate remaining useful life (RUL) prediction has a great significance to improve the reliability and safety for key equipment. However, it often occur imperfect or even no prior degradation information in practical application for the existing RUL prediction methods, which could produce prediction error. To solve this issue, this paper proposes a two-step RUL prediction method based on Wiener processes with reasonably fusing the failure time data and field degradation data. First, we obtain some interesting natures of parameters estimation based on the basic linear Wiener process. These natures explain the relationship between the parameters estimation results and the feature of degradation data, i.e. item sample numbers, detection time and detect frequency, and give the basis regarding how to reasonably fuse the failure time data and field degradation data. Second, under the Bayesian framework, we further propose a two-step method by fusing the failure time data and field degradation data with considering the random effects based on the proposed natures of parameters estimation. In this method, we propose an EM algorithm to estimate the mean and variance drift parameter of Wiener processes by the failure time data. Next, we generalize this two-step RUL prediction method to the nonlinear Wiener process. Last, we use two case studies to demonstrate the usefulness and superiority of the proposed method. INDEX TERMS Remaining useful life prediction, wiener processes, fusing, failure time data, field degradation data, random effects, Bayesian framework.

Remaining Useful Life Prediction Under Imperfect Prior Degradation Information

“…By substituting the (33)- (35) into k L , we can obtain the profile likelihood function about  , as shown in (36).…”

“…As the field degradation data increases, the credibility of the field degradation information becomes higher. Therefore, the number of iterations of parameters updating can be selected based on the credibility of the prior information and the number of field degradation data, which reflects the credibility of the field degradation data [35]. In the later simulation experiments, it is found that the converged results of the EM algorithm are a certain distance away from the MLE, which may be caused by the "Fminsearch" search function in Matlab.…”

“…For example, the gamma distribution and its deformation can describe the life distribution and the distribution of the RUL of the gamma degradation process in different situations [24]. The life distribution and the RUL distribution of the inverse Gaussian degradation process under different conditions can be described by the inverse Gaussian distribution and its deformation [19][20][21] Third, it is convenient to fuse the prior information based on historical degradation data, failure time data and the field degradation data under Bayesian framework [25][26][27][28][29][30][31][32][33][34][35]. In the degradation model based on stochastic process, the connection between the prior information and field data was first established by Gebraeel et al [25][26][27] under the Bayesian framework, which can reasonably fuse the prior information into the RUL prediction based on on-site degradation data.…”

“…However, none of the above studies considered the random effects representing the differences among congeneric items. Tang et al [35] fused the failure time data into prior degradation information with considering the random effects and achieved good results. However, this method can only use historical failure time data of congeneric items, which cannot use the degradation data of congeneric items.…”

“…into (33)-(35) can obtain the estimated results of other parameters in the (i+1)th step.It is noted that since ( 1) value can be searched by the "Fminsearch" function in Matlab. The above E-step and M-step need to be repeated for iterative calculation until ( ) ( )…”