# MTC-GAN Bearing Fault Diagnosis for Small Samples and Variable Operating Conditions
## 1 Introduction  
Bearings are core rotating parts widely used in various types of mechanical equipment. Their state of health is directly related to the reliability and safety of the entire system. For example, in the field of wind power generation, the reliability of bearings directly affects power generation efficiency and maintenance costs; in the automotive industry, the performance of bearings determines the smoothness of vehicle operation and the safety of passengers. Therefore, accurate bearing fault diagnosis techniques are of great significance for ensuring continuous equipment operation and reducing unplanned downtime [1, 2]. Most traditional bearing fault diagnosis methods are based on specific operating conditions and sufficient sample data. These methods typically rely on a large amount of historical data collected under specific operating conditions and identify fault characteristics through statistical analysis, spectral analysis, or physical model-based analysis. However, in practice, bearings are often subjected to variable operating conditions, such as changing loads, speeds, or ambient temperatures. These variations significantly affect the operating conditions and fault characteristics of the bearings, making fault diagnosis more complex. Additionally, due to the random and unpredictable nature of bearing failures, early failures are often difficult to accurately capture with traditional monitoring methods. This is especially true in the early stages when collecting fault data is particularly challenging, leading to insufficient data in practical applications. Variable operating conditions and insufficient data together constitute two major challenges in bearing fault diagnosis research. Many scholars have conducted related research on variable operating conditions. [PERSON] et al. [3] proposed an open set domain adaptive adversarial network frameworkfor bearing fault diagnosis under multiple operating conditions. Their study emphasized the problem of negative migration due to unknown fault samples in the target domain. They effectively addressed this challenge by estimating the similarity of each target domain sample with the known categories in the source domain. [PERSON] et al. [4] proposed an improved adversarial migration network for bearing fault diagnosis under variable operating conditions. This study optimized the feature fusion and domain migration learning performance of the network by combining the short-time Fourier transform and a channel attention module. [PERSON] et al. [4] also proposed an improved adversarial migration network that integrates the short-time Fourier transform and a channel attention module for bearing fault diagnosis under different operating conditions. The method was validated on several datasets. [PERSON] et al. [5] proposed a bearing fault diagnosis method based on complete ensemble empirical modal decomposition and sequential backward selection, combining vibration and electrical signals to improve the accuracy of fault diagnosis under variable operating conditions. [PERSON] et al. [6] proposed a semi-supervised learning-based method to address the problem of bearing fault diagnosis under variable operating conditions and unbalanced unlabeled data. Their method effectively utilizes rich unlabeled samples and improves diagnostic accuracy through the Graph Rebalancing Semi-Supervised Learning (GRSSL) algorithm. [PERSON] et al. [7] introduced a bearing fault diagnosis method based on a Regularized Domain Adaptive Deep Neural Network (RDADNN), which maintains data distribution consistency under variable operating conditions and improves diagnostic accuracy. [PERSON] et al. [5] introduced a method combining complete ensemble empirical modal decomposition (CEEMDAN) and sequential backward selection (SBS) for bearing fault diagnosis under variable operating conditions, incorporating both vibration and electrical signals to verify its effectiveness. For the small sample problem, many scholars have conducted related research. [PERSON] et al.