## 1 Introduction  
As a fast and convenient transportation asset, high-speed trains have drawn world-wide attention in recent years. Under high-speed operating conditions, health monitoring for rotary machinery systems is a crucial technology to guarantee the safety and reliability of high speed trains [1]. With the rapid development of sensor technologies, multiple sources of operational/health data can be collected, supporting online diagnosis and prognosis [2; 3; 4]. For high-speed trains, engineers collect vibration signals of rotary machinery systems such as bearings, gears, axles and wheel treads via on-board monitoring device and then conduct fault recognition, location and isolation based on signal processing technologies. However, diagnosis only provides failure information and provides no guidance for preventive maintenance, which is quite crucial to mitigate malfunction risks. Therefore, it is of urgent necessary to develop advanced prognostic methodologies, which predicts real-time health information to support condition-based maintenance plan. Remaining useful lifetime (RUL) is a main objective of health prognostic, which measures the distance between the latest monitoring time and system malfunction. Currently, RUL prediction methodologies can be substantially partitioned into two types, data-driven approaches and model-based approaches [5; 6; 7]. Data-driven approaches immediately utilize historical sensor data as input and outputs lifetime information. Representative data-driven technology is machine learning, including neural network [8; 9; 10; 11], support vector machine [12; 13] and artificial intelligence approaches [14; 15; 16]. Such technologies can adopt diverse application scenarios, but heavily rely on the quality and size of data. Model-based approaches, on the other hand, utilize statistical or physical modes to characterize the degradation paths. Combined with the measured data, model parameters can be identified and the future degradation behavior can be predicted. So far, lots of RUL prediction models have been developed for rotary machinery systems such as degradation path models [17; 18], Wiener-process-based models [19; 20], Gamma-process-based models [21; 22], as well as some physical models. Particularly, Wiener-process-based models have received more attention as they provide a flexible description of non-monotonous process, which are frequently encountered in practice. [PERSON] et al. conducted a comprehensive review of the development of Wiener-process-based models for degradation analysis and RUL estimation [23]. [PERSON] et al. proposed a novel Wiener-process-based exponential model to describe the degradation signals of bearings [24]. In their research, the particle filtering algorithm is used to estimate the degradation of the bearings and therefore reduce random errors of the stochastic process. [PERSON] et al. proposed a novel two-stage Wiener-process-based linear model to interpret two-phase degradation behaviors of bearings [25]. Different from other studies, they incorporated stage correlation into the prior distributions of model parameters to improve the prediction accuracy. More detailed discussions on Wiener-process-based models can be found in [26; 27; 28]. Except for data-driven approaches and model-based approaches, some other methods based on signal processing can also be used to predict remaining useful life of structures such as vibro-acoustic modulation [29; 30] and so on. Despite the advancement of RUL technology, its application in high-speed wheel train is rather limited without consideration of actual operational environment and failure mechanism. As a susceptible part of a high-speed train, wheel treads are exposed to severe cyclic shocks causing several failure modes including stripping, crack propagation, out-of-round, internal defect, etc. Any failure mode may cause an immediate breakdown of the entire system and leads to catastrophic consequences.