## 1 Introduction  
Railway transportation plays a crucial role in contemporary social development [1]. In recent years, rail transit, represented by high-speed rail, has developed rapidly. As a high-quality \"name card\" of China, it has promoted the development and realization of the \"belt and road\" strategy and the \"going global\" strategy of China's high-speed railway [2]. In the context of railway systems, a train is typically classified as \"high-speed\" if it can travel at speeds of 250 km/h (155 mph) or more on newly built tracks, or 200 km/h (124 mph) on existing tracks. This classification is essentially based on international standards set by organizations such as the International Union of Railways (UIC) and is crucial for differentiating between conventional and high-speed rail systems. The axes of high-speed trains are specifically designed to withstand these higher operational speeds, which requires enhanced durability and safety standards. How to incorporate the rapid development of big data technology to enhance the safety of train operations has become the top priority of current high-speed train development. As a crucial part of the train, the train bearing and axle box must withstand all the train's weight. Since the train should commonly run at high speed during operation, the vibration shock due to the rough track and irregular road crossings could exhibit a remarkable impact on the bearing, so the most vulnerable parts of the train include the bearings and the axle box [3]. In general, high-speed train bearings are also the main pieces of equipment to ensure the safe operation of trains [4]. When the bearing fails and deteriorates quickly, it even endangers the safety of the train operation [5]. Therefore, effective monitoring and fault diagnosis of high-speed train bearings is an essential way to ensure the safety of train operations [6]. High-speed train axes are subject to significant mechanical and thermal stress during operation, making temperature monitoring crucial for ensuring safety and performance. While much attention has been paid to bearing temperatures, other key components, such as brake systems, also experience substantial thermal loads. In particular, brake friction pairs can be exposed to extreme temperatures, especially under conditions of brake blockage or malfunction. In such scenarios, excessive heat can be generated, which could potentially impact axle safety and performance. Therefore, comprehensive temperature monitoring, which includes the thermal behavior of both bearings and brake systems, is essential to effectively detect and mitigate risks. At present, the bearing fault diagnosis method mainly includes the diagnosis approach based on temperature data [7], the diagnostic method based on fault signal (such as acoustic signal [8; 9] and vibration signal [10; 11; 12]), the detection and diagnosis method based on ferro-spectral analysis, the oil-based diagnosis method [13], and the diagnosis method based on oil film resistance monitoring. However, in practical application, the bearing monitoring method, which is extensively accepted in China, collects the axial temperature data through the bearing monitoring system's sensor [14]. Since train operation monitoring and fault diagnosis technology plays a significant role in railway transportation, companies and investigators at home and abroad significantly contribute to the research of train operation monitoring and fault diagnosis technology. In the 1980s, the United States developed a bypass acoustic detection system. Through the analysis of the sound signal of the train bearings, it was combined with the infrared thermal shaft detection system to achieve the effect of detecting bearing faults in advance. SKF in Sweden proposed to use the vibration signal and shaft temperature data of bearings to monitor the working state of the axle system.