## 3 Methodology
### Signal Recognition and Classification Based on DenseNet  
In this section, we demonstrate the recognition and classification ability of the above comprehensive methods for Lamb wave signals of different defects in composite materials. Now we consider using neural networks for signal classification. When the network selected for signal classification is very deep, the effect of the model becomes worse (the higher the error rate), indicating that the deeper the network is, the better. When the network level increases to a certain number, the training accuracy and test accuracy are rapidly reduced, which shows that when the network becomes very deep, the deep network becomes more difficult to train. In the process of back propagation, the neural network needs to continuously propagate the gradient. When the number of network layers deepens, the gradient will gradually disappear in the process of propagation, which makes it impossible to effectively adjust the weight of the previous network layer. Therefore, deep residual network (ResNet) [27] is considered. The residual network is easier to be optimized by adding shortcut connections to \"skip connections\". Several layers of networks containing a shortcut connection are called a residual block, as shown in the following Figure 9:  
As shown in the figure above, x represents the input, \(F\left(x\right)\) represents the output of the residual block before the activation function of the second layer, and \(\sigma\) Represents the ReLU activation function. The output of the final residual block is \(\left(F\left(x\right)+x\right)\). Directly transfer the input x to the output as the initial result, and the output result is \(H\left(x\right)=F\left(x\right)+x\). When \(F(x)=0\), then \(H(x)=x\), that is, the identity mapping mentioned above. Thus, ResNet is equivalent to changing the learning goal. It is no longer a complete output of learning, but the difference between the target value \(H\left(x\right)\) and \(x\), that is, the so-called residual \(F(x)=H\left(x\right)-x\). Stochastic depth shortens [28] ResNet by randomly dropping layers during training to allow better information and gradient flow. The basic idea of the densely connected constructive network (DenseNet) model is the same as ResNet, but it establishes a dense connection between all the preceding layers and the following layers, and its name comes from this. One advantage of ResNet is that gradients can flow directly from the following layer to the front layer through the identity function. However, the output of the identity function and H is cumulative, which may hinder the information flow in the network. To improve the problem of information flow between different layers, DenseNet directly connects all inputs to the output layer. Specifically, each layer will accept all the layers in front of it as its additional input. The connection method is through element-level addition. To preserve the feed-forward nature, each layer obtains additional inputs from all preceding layers and passes  
Figure 9: Schematic diagram of depth residual network. on its own feature-maps to all subsequent layers. In DenseNet, each layer is connected to the channel dimensions of all previous layers and is used as the input of the next layer. Another major feature of DenseNet is feature reuse through feature connections on the channel. These features enable DenseNet to achieve better performance than ResNet with fewer parameters and computing costs [29]. Besides better parameter efficiency, one big advantage of DenseNets is their improved flow of information and gradients throughout the network, which makes them easy to train. Each layer has direct access to the gradients from the loss function and the original input signal, leading to an implicit deep supervision. The performance differences between the main transmission forms of these two types of networks are shown below.