# Small-Sample Bearings Fault Diagnosis Based on ResNet18 with Pre-Trained and Fine-Tuned Method
## 1 Introduction  
Rolling bearings are crucial components of contemporary mechanical equipment and are extensively employed in a variety of mechanical rotating systems, including automobiles, aircraft, wind turbines and diverse industrial machinery [1]. Their main function is to support the rotating shaft and reduce the friction coefficient in the process of movement, so as to improve the operation efficiency and prolong the service life of the equipment. Thus, implementing effective FD technology not only enhances the operational efficiency and safety of equipment but also offers significant economic savings for businesses [2, 3]. Vibration analysis is an efficient and economic technology in bearing FD. It extracts features by analyzing the collected vibration signals [4]. Recently, numerous techniques have been developed to transform bearing vibration signals into two-dimensional images for analysis. Continuous wavelet transform (CWT) [5], short-time Fourier transform (STFT) [6], Gramian angular field (GAF) [7] and Wigner-Ville distribution (WVD) [8] are typically utilized to transform the time-frequency signal into a characteristic image. However, due to the fixed window, STFT cannot easily and accurately capture the signal's local attributes. CWT's computational requirements are larger than STFT, and the analysis process is cumbersome [9]. As a means of signal visualization, SDP is commonly employed in FD due to its straightforward processing and ability to reduce computational demands during signal conversion [10]. For example, [PERSON] et al. [11] used the SDP method and the squeezez excitation with a convolutional neural network (SE-CNN) model for FD. [PERSON] et al. [12]used the SDP method and the graph cardinality preserving attention network (GCPAT) for FD. [PERSON] et al. [13] introduced a novel FD technique using the enhanced Manhattan distance in the SDP image. Nevertheless, as mechanical vibration responses consist of overlapping multi-frequency feature information, it is crucial to isolate fault characteristics through signal breakdown and filtration for definitive fault determination [14]. Various frequency bands exhibit unique fault-associated traits. The VMD algorithm is capable of partitioning the frequency spectrum of the signal and extracting the relevant decomposition components of the designated signal [15; 16; 17]. Hence, the VMD method should be utilized for fault feature extraction. Based on this characteristic, the vibration signal can be analyzed using the VMD algorithm, and the resulting components can be converted using SDP. Next, features indicative of the petal shape are extracted through image processing techniques, and a suitable pattern recognition approach is employed to conduct FD. In many practical applications, the data available for FD are extremely scarce because the bearing is usually in normal working condition [18]. This lack of data poses a challenge to the training of the FD model based on deep learning, due to the insufficiency of fault data, which may impair the model's ability to learn effectively, resulting in reduced generalization capabilities and FD precision. To address this issue, researchers began to explore the use of the generative confrontation network (GAN) and transfer learning (TL) to enhance the model's performance. The GAN is composed of generators and discriminators [19]. Because generators and discriminators confront each other in the training process, generators will continuously improve the quality of generated data and make it approach the real data. Therefore, GAN can usually generate very realistic data samples to address the issue of a small sample [20; 21; 22]. Although the GAN performs well in generating realistic data, it faces many challenges. Among them, unstable training, mode collapse and evaluation difficulties are the most prominent problems. Furthermore, the training process demands substantial computational resources and meticulous hyperparameter tuning, and it is highly sensitive to hyperparameter settings.