# Identification of the Surface Cracks of Concrete Based on ResNet-18 Depth Residual Network
## 3 Deep Learning Model  
### ResNet-18 Network  
The convolutional neural network (CNN) is a deep learning model primarily employed for image recognition and computer vision tasks. The convolution operation, which serves as the fundamental component of a CNN, extracts features by applying a filter (also known as a convolution kernel or feature detector) to the input data, as depicted in Figure 4. The primary steps of a CNN entail the traversal of a convolution layer's filter across the input image, resulting in the generation of a feature map through element-wise multiplication and summation between the input image and the filter. By incorporating multiple filters within the convolutional layer, it becomes feasible to extract more sophisticated features. The function is commonly applied to the resultant feature map following the convolution operation. The incorporation of pooling layers is intended to decrease the spatial dimensions of the feature map and network parameters, while retaining the most significant features. After a series of convolutional and pooling layers, the resulting feature map undergoes transformation into a one-dimensional vector and subsequently traverses the fully connected layer. The output layer determines the appropriate activation function based on the specific task at hand. During the training process, the convolutional neural networks (CNNs) utilize the backpropagation algorithm to iteratively update the network's weights and biases, facilitating gradual acquisition of feature representations from input data. The utilization of convolution operations and hierarchical structures in convolutional neural networks  
Figure 4: Convolutional neural network data handling processes. Figure 3: Labeling with multiple crack images. enables effective feature extraction and learning from images, thereby enhancing robust image processing and analysis capabilities. The deep residual network (DRN) is a deep neural network architecture commonly employed for image classification and deep learning tasks in scientific research. Traditional deep neural networks encounter challenges such as the problem of vanishing and exploding gradients, which impede effective training with increasing network depth. Moreover, the growing number of parameters and computational complexity exacerbates this problem. The incorporation of residual connections in deep residual networks effectively tackles the challenge of training deep networks, thereby enabling the implementation of more intricate network architectures and facilitating optimization. ResNet introduces residual blocks, which consist of identity maps and residual maps. The fundamental form of residual blocks can be expressed as follows:  
\[y=F(x,\{W\_i\})+x \tag{1}\]  
where \(x\) is the input, \(F\) is the residual mapping, \(\{W\_i\}\) represents the learnable parameters in the residual map (such as convolution kernel weights), and \(y\) is the output of the residual block. The primary innovation of ResNet lies in the introduction of residual learning, a concept that has significantly advanced deep neural network architectures. In the conventional deep convolutional neural network, input data are processed through one or more layers to obtain the output. However, in a residual network, an additional skip connection is incorporated alongside the main pathway of network layers. This allows for direct skipping of one or more layers and subsequent addition to the output of the main pathway. The introduction of ResNet effectively addresses the pervasive issues of gradient vanishing and explosion in deep neural networks, thereby enabling the network to safely increase its depth for improved performance. The ResNet-18 functional model was employed in this study based on practical requirements and available computational resources. It encompasses 18 layers (excluding the activation function and pooling layer), rendering it the smallest model within the ResNet series.