## 2 Conventional Convolutional Neural Networks  
CNNs have been commonly used to detect damage to SHM in recent years. According to the form of model input, there are usually two categories of CNN-based SHM methods, which are 1D-CNN and 2D-CNN-based methods. The former method takes a one-dimensional sequence directly as input [21; 33], and the last method usually takes a numerical matrix or picture as input [29; 32]. In this paper, 2D-CNNs are used to extract damage features. 2D-CNNs have a great advantage of using the matrix as input compared to other damage-detection methods. First, compared to PB methods, 2D-CNN does not require any prior physical knowledge. Moreover, 2D-CNN has a more efficient feature-extraction capability than 1D-CNN through the convolution of the height and width of the sample. A basic 2D-CNN for damage region recognition mainly contains a convolutional layer, a general pooling layer, a global average pooling layer, and a fully connected layer. A conventional process for a recognition task using 2D-CNN is shown in Figure 1.  
The convolutional layer is the heart component of CNN, which operates as shown in Figure 2a. A convolution kernel of set size slides over the input data in preset steps and computes the dot product with the covered data to achieve feature extraction. Specifically, the parameters of the convolution kernel are shared when performing the sliding convolution calculation. In conventional convolution, each input data needs to be convolved with several different convolution kernels. Therefore, the number of channels of the output features of the convolutional layer coincides with the number of convolutional kernels. The performance of the model can be improved by optimizing the size and number of convolutional kernels. In addition, the model depth can be expanded by connecting multiple convolutional layers in series to improve performance. However, it will increase the complexity of the model and the risk of overfitting. The convolution layer is usually followed by batch normalization (BN) and an activation function. The BN layer prevents gradients from disappearing or exploding and speeds up training by normalizing the current batch of data. The activation function can extract non-linear features and accelerate convergence.  
The general pooling layer is shown in Figure 2b. It can reduce the feature map size and filter important information through downsampling. The pooling process may cause some  
Figure 1: Simple process chart of 2D-CNN for damage region identification.  
information loss. In addition, global averaging pooling (GAP) is often used in 2D-CNNs as shown in Figure 2c. GAP turns the feature map into a mean by averaging the 2D images of each channel. Feeding the mean sequence into the fully connected layer for classification will greatly reduce the parameters and the risk of overfitting.  
After feature extraction in the convolutional layer and compression in the pooling layer, as shown in Figure 2d, the fully connected layer would perform combination and classification operations. The output of the fully connected layer is a set of numbers indicating the probability of different categories. Finally, SoftMax functions are used to filter the output of fully connected layers, and then we can obtain the most probable classification or prediction for SHM.