## 1 Introduction  
In energy transportation, the pipeline system is the core carrier for transporting fluid resources such as oil and tap water, and its safety and operational efficiency directly affect the national energy strategy [1]. Modern pipeline transportation networks rely on key rotating equipment such as pump units and compressors to continuously provide power. As the core component of such rotating equipment, the bearing's health condition has a direct impact on the pipeline system's dependability [2, 3, 4, 5]. However, due to long-term operation and complex working conditions, the aging or failure of equipment is inevitable. In severe cases, it may even cause casualties. Therefore, to guarantee the regular operation of mechanical equipment, a dependable and effective intelligent bearing fault diagnosis (FD) solution is required [6]. In recent years, in order to deeply reveal the failure mechanism of locally defective bearings, many scholars have not only relied on theoretical modeling, but also utilized the collaborative means of high-precision numerical simulation and experimental methods [7, 8]. [PERSON] et al. [9] studied the vibration characteristics induced by spalling defects of the bearings under various speeds and axial force parameters, using simulations and experimental verifications. [PERSON] and [PERSON] [10] developed a five-degree-of-freedom dynamics model, taking into account static and dynamic unbalance, as well as waviness perturbations of the bearing components, and demonstrated that waviness perturbations of the bearings have a significant effect on micro-vibrations. [PERSON] and [PERSON] [11] studied the influence of the waviness defect parameter on the frequency amplitude. They found that the vibration was intense when the waviness order was equal to the number of balls. [PERSON] et al. [12] established a numerical model of rolling bearings using measured defect profiles, which can accurately predict the vibration characteristics of defective bearings. [PERSON] et al. [13] introduced the theories of additional deflection and multiple impacts to establish a bearing dynamics model. The dynamic behavior of defective bearings under different conditions was accurately simulated. [PERSON] and [PERSON] [14] established a dynamic model of a bearing with waviness in the raceway and added dynamic loads. The vibration response of the bearing was obtained. [PERSON] and [PERSON] [15] conducted a detailed analysis of rolling bearings with defects in different components under harmonic load conditions. They found that the bearings with inner ring defects had no additional harmonic components. In order to analyze the influence of local outer ring faults on bearings' dynamic characteristics in depth, [PERSON] et al. [16] proposed and verified a nonlinear model of contact force and stiffness considering angular changes. [PERSON] et al. [17] established a raceway irregular defect model integrating edge propagation and morphological features. This model revealed the influence of the rolling element-defect contact mechanism varying with size on the vibration response. The above-mentioned research reveals that the location and size of local defects have a significant impact on the vibration response. These studies provided theoretical support and an engineering basis for fault identification and health management. Meanwhile, various methods for FD have made great progress. Traditional signal processing methods have been widely applied. However, traditional signal processing methods mainly rely on expert experience, lack self-learning ability, and have relatively poor generalization in the face of complex working conditions [18]. With the development of deep learning (DL) and machine learning (ML), intelligent fault diagnosis (IFD) has also made significant progress [19]. ML-based fault detection techniques use shallow learning models, including support vector machines [20], random forests [21], and decision trees [22], to learn the characteristics of the original signals and accomplish fault categorization.