## 4 Proposed Model
### Feature Extraction Architecture  
The feature extraction architecture of the residual VGG is an enhanced version of the original VGG model [40], as illustrated in Figure 4. The residual VGG consisted of multiple convolutional layers and the max pooling layer. The fully connected layer was replaced by a global average pooling layer, and a residual learning architecture was incorporated. The smart fault diagnosis method for induction motors had a good diagnostic effect on the Siamese network feature extraction layer. The characteristics of this kind of model include the greatly reduced number of model parameters, avoiding gradient vanishing during model training, extracting data features, and enhancing the model's nonlinearity. The meanings of the architectures are described below. 1. Multiple convolutional layers and convolution kernel selection  
The setting of multiple convolutional layers could increase the receptive field of the model, so that the model could obtain more feature information, and the classification capacity could be enhanced effectively. Additionally, this enhances the model's nonlinearity,  
Figure 4: Residual VGG-based Siamese network model architecture. enabling it to learn more complex features [41]. The receptive field size of each layer can be computed by Equation (9) [42]:  
\[R_{l}=R_{l-1}+(K_{l}-1)\prod_{i=1}^{l}S_{i} \tag{9}\]  
where \(R_{l}\) is the receptive field size of the \(l\)-th layer, \(R_{l-1}\) is the receptive field size of the neural network in the layer above the \(l\)-th layer, \(K_{l}\) is the size of the convolutional kernel, and \(S_{i}\) is the stride of the convolutional kernel. A small convolution kernel was set for each convolution layer, and it could greatly reduce the number of model parameters to reduce the amount of computation of hardware facilities [43]. For example, one \(5\times 5\) convolution layer was substituted by two \(3\times 3\) convolutional layers. When the numbers of input and output channels \(C\) were identical, the numbers of parameters were \(2(3\times 3)C^{2}\) and \(5\times 5\times C^{2}\). According to the example, if the convolution kernel parameter was small, the number of model parameters was small. To reduce the dimensionality of feature vectors and model parameters while preserving feature information, the max pooling layer was employed for local maximum feature extraction and operation [44; 45]. The global average pooling layer calculates the average value of all elements in the feature map, and the parameter count is \(C_{in}\times C_{out}\). In contrast, the parameter count of the first fully connected layer is \(C_{in}\times C_{out}\times size_{fm}^{2}\). Here, \(C_{in}\) and \(C_{out}\), respectively, represent the number of input and output channels, and \(size_{fm}^{2}\) is the size of the input feature map. Thus, replacing the fully connected layer with a global average pooling layer significantly reduces the number of model parameters, as demonstrated in Table 2. As a result, overfitting is less likely to occur during model training, and the model can be normalized, effectively enhancing the model's generalization ability. 3. Residual learning  
The residual VGG added batch normalization in each max pooling layer to solve the vanishing gradient problem in the initial training period of the depth model so that the model could converge easily in the initial training period [46]. However, because of the degradation problem, the deep neural networks were still difficult to optimize during the training period. Deep neural networks have a degradation problem during training. This problem indicates that the model has achieved accuracy saturation during training, but the gradient vanishing is generated so that the internal parameters of the model cannot be updated. The gradual increase in training loss and the decrease in training accuracy led to failure in the convergence of the model.