## 1 Preface  
Along with the continuous progress of modern manufacturing technology, the structure of mechanical and electrical systems is more and more complex, which brings new challenges to fault prediction and health management of the system. Parts are important components of mechanical and electrical product systems, once the parts fail, it may affect the healthy operation of the whole system, or even cause serious loss of life and property. Therefore, the remaining useful life (RUL) prediction of parts has become a key research issue of fault prediction and health management [1; 2; 3]. [PERSON] et al. [4] provided a review on machinery prognostics following is whole program, i.e., from data acquisition to RUL prediction. [PERSON] et al. [5] provided a review on the system design of prognostics and health management, and gave a tutorial for the selection of RUL prediction approaches by comparing their advantages and disadvantages. At present, a number of research on the RUL prediction of parts have reported [6; 7; 8], and approaches of RUL prediction can be roughly grouped into three categories. The first category is the prediction method based on physical models, which estimates the RUL of parts according to the degradation mechanism. [PERSON] et al. [9] validated the crack growth modeling method using damage diagnosis data based on structural health monitoring, and a probabilistic prediction of RUL is formed for a metallic, single-edge notch tension specimen with a fatigue crack growing under mixed-mode conditions. [PERSON] et al. [10] evaluated the stress of A310 aircraft wings during each loading cycle through a finite element analysis, and they predicted the RUL of A310 wings using the Paris Law technique based on linear elastic fracture mechanics. [PERSON] et al. [11] developed a novel computational modelling technique for the prediction of crack growth in load bearing orthopaedic alloys subjected to fatigue loading, which can predict the RUL of parts through the crack path. The second category is the prediction method based on probability statistics, which fit the failure data of parts to obtain the characteristic distribution of life through a statistical distribution model. [PERSON] et al. [12] proposed a novel method based on the three-parameterWeibull distribution proportional hazards model to predict the RUL of rolling bearings, the model is able to produce accurate RUL predictions for the tested bearings and outperforms the popular two-parameter model. [PERSON] et al. [13] proposed a remanufacturability evaluation scheme based on the average RUL of the structural arm, and made a comprehensive evaluation by establishing the reliability parameter model of the structural arm. [PERSON] et al. [14] discussed the influence of different distribution function values on the prediction results by analyzing different parameter estimation methods, and established the RUL prediction model based on the failure data of parts. [PERSON] et al. [15] determined the average useful life of the pump truck boom based on the Weibull distribution function by using the failure data, and predicted the RUL of the boom by using the used time. The third category is the data-driven prediction method. [PERSON] et al. [16] analyzed the time-domain and frequency-domain characteristics of rolling bearing vibration signals, and established the RUL prediction model of rolling bearing based on deep neural networks. [PERSON] et al. [17] proposed an RUL prediction framework based on multiple health state assessments that divide the entire bearing life into several health states, where a local regression model can be built individually. [PERSON] et al. [18] proposed a methodology for the estimation of the RUL of parts based on particle filtering. [PERSON] et al. [19] used support vector machines to build degradation models for bearing RUL prediction. [PERSON] et al. [20] proposed a combination of a relevance vector machine and model fitting as a prognostic procedure for estimating the RUL of degraded thrust ball bearings. [PERSON] et al.