## 1 Introduction  
As the backbone of the modern transportation system, rail vehicles serve an irreplaceable function in enhancing travel efficiency and cargo transportation capacity. However, with the rapid expansion of rail transit networks and the continuous increase in train operating speeds, the operational safety of rail vehicles (including high-speed electric multiple units (EMUs), intercity express trains, and subway systems) has been recognized as a critical research focus in this field [1, 2]. Notably, the malfunction of key components, such as bogies, braking systems, and traction power supply equipment, can not only result in train delays and operational disruptions but also potentially cause severe safety accidents, thereby posing a direct threat to the lives and property of passengers [3]. Therefore, it is imperative to conduct research on fault detection for key components of rail transit systems. Faults of rail vehicles can primarily be categorized into mechanical faults, electrical faults, and rail system faults. Among these categories, mechanical failures occur most frequently, comprising approximately 50% to 70% of all reported faults [4]. In particular, the bearings, as the core components of the mechanical system in rail vehicles, are exposed to complex dynamic loads under extreme operating conditions. On the one hand, bearingsreplace sliding friction with rolling contact, thereby significantly reducing operational energy consumption. On the other hand, in the traction system, the normal functioning of bearings is directly linked to the efficiency of power transmission. However, statistical data indicate that among the mechanical faults of rail trains, those associated with bearings account for as much as 28% to 35%, making them one of the primary mechanical causes of unplanned train suspensions [5; 6]. Therefore, the development of advanced early fault detection and intelligent diagnosis methods for bearings is considered crucial for enhancing operational reliability, ensuring rail vehicles running safety, and preventing catastrophic accidents [7; 8]. At present, the primary detection methods can be categorized into temperature monitoring, acoustic emission analysis, vibration-based diagnostics, and machine learning-driven fault detection. Among these, temperature monitoring utilizes infrared thermal imagers or embedded temperature sensors to track bearing temperature increases and triggers alerts upon detecting anomalies. Nevertheless, external heat sources, such as braking systems, may lead to false alarms. Acoustic emission technology identifies faults by detecting high-frequency stress waves generated during crack propagation or spalling within bearing materials, leveraging parameters like event counts and energy levels. However, advanced acoustic emission systems are costly and often necessitate offline inspections. Machine learning-based fault detection models extract time-frequency characteristics from vibration and temperature signals, enabling efficient fault classification. Nonetheless, this approach depends on acquiring expensive fault samples and faces challenges in deploying edge devices [9; 10; 11]. Notably, traditional vibration analysis employs accelerometers to collect bearing vibration signals and analyzes their time-domain and frequency-domain features to achieve cost-effective fault detection. Nonetheless, this method relies solely on single-frequency-domain analysis via Fast Fourier Transform (FFT), which struggles to adaptively decompose non-stationary signals, leading to a lower fault recognition rate. To make up for the defect of modal aliasing, this paper proposes a bearing fault diagnosis method based on the energy distribution characteristics of the EEMD eigenfunction. Different from the literature [12], in this paper, the energy values of each EEMD eigenfunction are calculated successively and normalized. These values are used as feature vectors to diagnose whether there are faults in the bearings.