## 3 Transfer Learning Applied to Fault Diagnosis Methods
### Fault Diagnosis Model  
#### 3.3.1 ResNet  
ResNet (Residual Network) is a type of deep convolutional neural network. The core idea of ResNet is the residual module, which allows input information to bypass certain layers and skip directly to the output, forming a residual mapping. This skip connection addresses issues such as vanishing gradients and gradient explosion during deep network training, ultimately improving network performance [22].  
The traditional neural network module is shown in Figure 10a, and the residual module is illustrated in Figure 10b. They process the input x, which is passed through two convolution operations and a ReLU activation function, resulting in the output H(x).  
ResNet18 is a residual network with an 18-layer structure consisting of four residual modules. Compared to models like ResNet34 and ResNet50, the ResNet18 model has a moderate number of layers, faster training convergence, and benefits from lower network complexity, reduced computational resource consumption, and faster computing speed.  
In ResNet-18, the number of residual blocks is fixed, with a total of 8 residual blocks. The network consists of 4 stages, each containing 2 BasicBlocks, with the specific distribution of [2; 2; 2; 2]. The ResNet model used in this paper includes convolutional layers, batch normalization layers, ReLU activation functions, maximum pooling layers, residual modules, and fully connected layers. In ResNet-18, each convolutional layer is immediately followed by a batch normalization layer and a ReLU activation function. The convolutional layer is used to extract features from the data, while the batch normalization layer standardizes these features to ensure that the feature data in the same batch have a similar distribution. The ReLU activation function improves computational efficiency in neural networks and helps avoid vanishing gradients. The structure of the ResNet18 model is shown in Figure 11.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Basic Unit Name** & **Input Channel** & **Output Channel** & **Convolutional Kernel Size** & **Stride** \\ \hline Convolutional layer & 1 & 64 & 7 & 2 \\ Residual layer 1 & 64 & 64 & 3 & 2 \\ Residual layer 2 & 128 & 128 & 3 & 2 \\ Residual layer 3 & 256 & 256 & 3 & 2 \\ Residual layer 4 & 512 & 512 & 3 & 2 \\ fully connected layer & 512 & 10 & / & / \\ \hline \hline \end{tabular}
\end{table}
Table 1: ResNet network structure.  
Figure 11: ResNet-18 model structure.  
The convolutional layer uses a convolution kernel that slides over the input one-dimensional vibrational signal to extract local features. The batch normalization layer (BN) is a common regularization method used in deep neural networks. The ReLU activation function keeps positive values unchanged while setting negative values to 0.  
\[\mathrm{f(x)}=\mathrm{max}(0,x) \tag{12}\]  
Here, x represents the input value, and the ReLU activation function is used to enhance the computational efficiency of the neural network. The implementation process of the residual module is shown in Figure 10b, and the output formula is  
\[\mathrm{Y}=\mathrm{F(x)}+\mathrm{x} \tag{13}\]  
In this formula, the input is x, the desired output is Y, and the skip connection directly adds the input x to the transformed output F(x).