## 2 Methods
### Residual Neural Network  
ResNets was proposed by [PERSON] et al. [16]. In the traditional deep layer, with increasing network layers, the gradient disappears, which leads to a poor training effect. To solve the negative optimization problem, residual blocks were introduced into the network. A residual block (RB) contains a shortcut connection and a main connection composed of several convolutions. The structure is shown in Figure 2a.  
[PERSON] et al. further optimized the RB structure, as shown in Figure 2b. First, the identity mapping range of the shortcut join is enlarged. Secondly, the order of BN, RELU, and convolution layers is adjusted. The training effect is improved after these changes.  
Bearing fault signals are typically nonstationary and nonlinear, with fault characteristics in different signal frequency ranges [17]. Therefore, feature extraction methods are used for extracting feature information from data at different scales. Features at various scales can capture data structures and patterns at different levels. Wavelet transform is a multi-scale analysis method that can decompose a signal into low-frequency and high-frequency subbands, the former corresponding to the overall trend of the signal and the latter to its details and edge features [18].  
Based on [19], wavelet transform and residual neural networks are combined in this paper, and their respective advantages can be fully utilized. Wavelet transform can transform signals into subbands with different frequency ranges and provide abundant information in the frequency domain. These subbands can then be passed as inputs to a residual neural network for further feature extraction and learning. The network can learn the correlation between and the importance of different frequency subbands to obtain a more discriminative feature representation [20]. At the same time, a residual connection can reduce the information loss when the signal propagates in the deep network and accelerates the network's convergence and training process.  
The diagnosis process of wavelet transform and residual network proposed in this paper is as follows: firstly, wavelet transform is performed on the original one-dimensional vibration signal to obtain time-frequency matrix, and then the obtained two-dimensional signal is input into ResNets, and the network learns the energy characteristics of different frequencies and in time-frequency matrix. Finally, softmax is input into the full connection  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Before Improvement** & **Improved** \\ \hline Normalization factor & 1 & \(\beta/\sqrt{2\pi}\) \\ Center frequency \(\omega_{0}\) & \(\pi\) & \(2\pi\) \\ Parameter \(\beta\) range & [0.1, 4] & [0.5, 1.82] \\ \(\beta\) Number of test values & 40 & 7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Morlet wavelet parameters.  
Figure 2: Residual block structure. (**a**) before optimization (**b**) optimized structure.  
layer for fault-type classification diagnosis. It should be noted that the wavelet bases used in this paper can be altered flexibly according to the characteristics of the data. The specific flow chart of the method is shown in Figure 3, and the specific parameters of the model are shown in Table 2.  
The model consists of 4 convolution layers, 2 residual blocks, and 1 fully connected layer. The convolution kernel size of the first layer is 3 \(\times\) 3, and the number of channels is 8. Then, it passes through the pooling layer with a size of 2 \(\times\) 2. The convolution kernel size of the second layer is 3 \(\times\) 3, the number of channels is 16, and the pooling layer size is also 2 \(\times\) 2. The residual fast is located in the third and fourth layers, its convolution kernel is 3 \(\times\) 3, and the number of channels is 16. Then, it is input to the fully connected layer, and the output size is 32. Finally, the output layer size is 10; that is, the classification results in 10 delineations.