## 4 Metro Track Geometry Defect Identification Model and Its Optimization Method
### MTGDI-CNN Based on DARTS
#### 4.2.3 Computing Operation Architecture  
The 2D computing operations were employed as the cell edge to process the sample data \(\mathbf{X}_{s}\) for solving the CVD-based metro-TGD identification problem. The cell edge included a 2D depth separable convolution block (2D DSCB), 2D dilated separable convolution block (2D DiSCB), 2D max pooling (2D MaxPool), 2D average pooling (2D AvgPool), and void operation (only connecting without computing). Specific architectures of the 2D DSCB and 2D DiSCB are described in the following paragraphs.  
The convolution-extracted feature is determined using the channel number of the convolution kernel. Therefore, the channel number of the kernel increases layerwise in a CNN model to fully extract the features. The kernel operates with all channels of the input feature map in an ordinary convolution. If ordinary convolution is used to process the CVD, the number of neural network computations will increase rapidly owing to the  
Figure 7: Cell architecture (the number 0-3 means the order of the intermediate nodes).  
increase in the number of channels and cells, which leads to complexity in model training and a sub-par identification performance.  
To mitigate this problem, several efficient neural networks have recently introduced operations such as deep separable convolution (DSC) [48] and dilation convolution (DiC) [49]. The DSC consists of two core elements: depthwise convolution and pointwise convolution. Depthwise convolution maintains a certain kernel width, but each kernel only processes one channel of the input feature map. The width of the pointwise convolution kernel is 1, and all channels of the input feature map are processed simultaneously. Using such a two-step convolution, a reduction in the computation number can be achieved while maintaining the feature extraction capability. The kernel of the DiC does not operate with the continuous adjacent elements of the input feature map but operates at a certain interval. For example, when the kernel width is three and the dilation parameter is one, the elements of the input data \(\mathbf{X}\) for the \(i\)th operation with the DiC kernel change from \([\mathbf{x}_{i-1},\mathbf{x}_{i},\mathbf{x}_{i+1}]\) to \([\mathbf{x}_{i-2},\mathbf{x}_{i},\mathbf{x}_{i+2}]\). The number of computations does not change, and the receptive field of the kernel expands. Such a DiC allows the kernel to cover a larger range of data by using the same number of computations, thereby improving the efficiency of feature extraction.  
Therefore, to ensure accuracy and considerably reduce the computation number, 2D DSCB and 2D DiSCB were used to replace ordinary convolution when constructing the cells of MTGDI-CNN in this study. In addition to depthwise, pointwise, and dilation convolution, 2D DSCB and 2D DiSCB also include 2D batch normalization (2D BN) [50] and nonlinear rectified unit (ReLU) [51] to maintain the capability of independent feature extraction and replacement of arbitrary edges in a cell. The operations in a 2D DSCB or 2D DiSCB are arranged in the order of ReLU-Conv-BN [47,52], as illustrated in Figure 8. The kernel sizes in the 2D DSCB and 2D DiSCB can be set to different values to extract different sizes of TGD vibration features.