## 3 Neural Network Selection and Computation
### ResNet18  
Residual neural network is a new deep convolutional neural network architecture proposed by [PERSON] et al. in 2015, and its main core idea is to solve the gradient vanishing and expression bottleneck problem in deep neural networks by introducing \"residual blocks\". Traditional deep networks have the problem of gradient vanishing, as the number of network layers increases, the backpropagated gradient signal becomes weaker and weaker, resulting in training difficulties. Residual blocks, on the other hand, allow direct connections across layers, making it easier to transfer information. The residual block structure is shown in Figure 10. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Network Structure** & **Accuracy (Denoised Samples)** & **Training Time(s)** \\ \hline Single CNN & 73.67\% & 311 \\ AlexNet & 87.83\% & 346 \\ GoogleNet & 89.83\% & 637 \\ LeNet-5 & 67.33\% & 401 \\ ResNet18 & 89.50\% & 251 \\ ResNet50 & 90.17\% & 1065 \\ VGG16 & 87.33\% & 1009 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of training results of different network models. Figure 9: Comparing the loss of denoised sample sets for neural network training. In Figure 10, \(x\) is the input, \(F(x)\) is the mapping function, and \(G(x)=F(x)+x\) is the constant mapping function. By constant mapping, it means that \(G(x)=x\) when \(F(x)\) tends to 0. The corresponding mathematical expression for the residual block is:  
\[y_{l}=h(x_{l})+F(x_{l},W_{l})x_{l+1}=f(y_{l}) \tag{13}\]  
where \(x_{l}\) and \(x_{(l+1)}\) represent the input and output of the lth residual unit, respectively, \(F()\) represents the residual function, \(h(x_{l})=x_{l}\) denotes the constant mapping, and f is the ReLU activation function. Based on Equation (12), the learning feature from shallow \(l\) to deep \(L\) can be obtained as:  
\[x_{L}=x_{l}+\sum_{i=l}^{L-1}F(x_{l},W_{l}) \tag{14}\]  
The introduction of residual blocks into the residual connection structure can play key roles, such as connecting and transferring gradients, learning residuals, extracting high-level features, and increasing network depth. These roles make the residual connection structure have better convergence, stronger expressiveness, and higher performance in training deep neural networks. By combining different numbers of residual blocks, residual neural network architectures with different numbers of layers can be derived. Some of the more common ones are ResNet-18, ResNet-34, ResNet-50, ResNet-101, and ResNet-152. The numerical designation of these ResNet models indicates the number of layers. For example, ResNet-18 consists of 18 convolutional layers, while ResNet-50 consists of 50 convolutional layers. As the number of layers increases, the network becomes deeper and is able to learn more complex feature representations. As can be seen from Section 3.1, ResNet-18 is chosen for fault classification recognition in this paper, which consists of four residual modules, each containing two convolutional layers and a jump connection. These convolutional layers typically have a 3 \(\times\) 3 convolutional kernel size and use the ReLU activation function. Between each residual module, downsampling operations are used to reduce the size of the feature maps. The ResNet-18 structure is shown in Figures 11 and 12. Figure 10: Residual block structure diagram. The network input is an RGB image with a size of 224 \(\times\) 224 pixels and three channels. The output corresponds to ten different failure modes. To extract features and generate 64 output channels, the input image undergoes a convolution operation using 64 convolution kernels, each with a size of 3 \(\times\) 3, a stride of 2, and a padding of 1. The convolutional layer's output size is 112 \(\times\) 112 \(\times\) 64 in the ResNet-18 network. The network has four residual connected structures. The convolution operation's step size is 2 in residual blocks a-1 and b-1, reducing the output feature maps' spatial size by half while keeping the number of channels the same.