## 2 Research Status
### Research Status of Small Sample Issues in Fault Diagnosis  
Deep learning-based fault diagnosis methods rely heavily on vast amounts of data accumulation. However, in practical application scenarios, equipment often operates normally under most conditions, resulting in a scarcity of fault samples. This imbalance between fault samples and healthy samples leads to a decline in the performance of deep learning-based fault diagnosis methods. In response to this issue, numerous scholars have proposed various solutions. Research on methods based on data preprocessing and model structure  
Some scholars adopted sampling technology to solve the problems of sparse input data and class imbalance in diagnostic models, which effectively improves the diagnostic performance of the model [9; 10]. However, sampling technology has the potential to alter the distribution of the original data-set, resulting in distortion of the model, which will reduce the accuracy of fault diagnosis. [PERSON] [11] designed a new learning mechanism to train the deep neural network by improving the loss function so that the deep neural network can maintain the accurate feature representation driven by the consistency of trend features and ensure the accurate fault classification driven by the consistency of the fault direction. The accuracy of this method can reach about 90% with only 100 samples polluted by strong noise. [PERSON] [12] proposed a compact convolutional neural network fault diagnosis model based on multi-scale feature extraction. This model utilized the multi-scale feature extraction unit to extract fault features of different time scales and comprehensively analyze them through the compact neural network, allowing for the extraction of more sensitive features with relatively shallow structures. This improvement led to enhanced diagnostic accuracy under conditions of small samples. [PERSON] [13] added a classification branch to the Siamese network, replaced the Euclidean distance measurement with a network measurement, and constructed an improved fault diagnosis model based on the Siamese neural network, consisting of a feature extraction network, a relationship measurement network, and a fault classification network. The similarity of the extracted features is measured by the relationship measurement network, which effectively guarantees the accuracy of fault diagnosis in the case of small samples. [PERSON] [14] introduced a vision transformer model that incorporates multi-information fusion and leverages a time frequency representation graph. This model first decomposes the original vibration signal into various sub-signals of different scales through a discrete wavelet transform. Subsequently, it converts these sub-signals into time-frequency representation graphs using a continuous wavelet transform. Finally, the model serially inputs these graphs into its framework for accurate fault diagnosis. The experimental results show that this method can diagnose the fault of small sample bearing and has strong universality and robustness. [PERSON] [15] combined wavelet and depthwise separable convolutional neural networks to design a few-parameter branch for time-frequency feature extraction. This branch captured fault features from a limited number of samples to realize fault diagnosis under small samples together with regular convolution. (2) Research on methods based on transfer learning  
The process of dealing with small samples and class imbalanced problems by data preprocessing and improved neural networks is often complex and less versatile. The rise of transfer learning [16] provides a new direction for solving this problem. [PERSON] [17] introduced a generalized transfer framework equipped with evolutionary capabilities, aimed at tackling the challenge of limited fault samples in industrial process fault diagnosis.