# Classification of Road Surfaces Based on CNN Architecture and Tire Acoustical Signals
## 2 Background Theory
### Convolutional Neural Network (CNN)  
CNN is a type of artificial neural network that optimizes weights based on an input image feature map. The feature map is extracted through a convolution operation between the input data and a predefined convolution kernel. CNN is widely known for its excellent performance in various image-recognition tasks. Recently, CNN techniques have been applied in various fields of mechanical engineering. Defect classification of power driving systems, prediction of tire-transmitted noise, and vehicle structure defect classification are successful applications in mechanical engineering [11; 12; 13]. The modern concept of CNN was first suggested by [PERSON] et al. [14]. In that paper, [PERSON] introduced LeNet-5 to recognize letter patterns. LeNet-5 uses a convolution operation on a 32 \(\times\) 32-pixel input image to achieve this goal. The feature map is then compressed using a pooling operation. After repeating the above process twice, the final feature map was unfolded to flatten and connected to a fully connected layer. The number of nodes in the last fully connected layer was equal to the number of classes. The values at each node were normalized between 0 and 1 using the softmax layer. Using this normalized score, LeNet-5 can determine the class of an input letter. These suggested procedures, from convolution, pooling, and fully connected layers to softmax layers, have become the basic architecture of CNN. Figure 2 illustrates the basic structure of a CNN similar to that of LeNet-5. For visual simplicity, only a few connections between the nodes were expressed in the fully connected layer. The following text provides a more detailed explanation of each layer's operation. The convolution layer is the most important feature of the CNN architecture. Typically, its output is referred to as a feature map. A feature map is a value set resulting from a convolution operation between the input data and filter. The component of \(i\)-th row and \(j\)-th column in the feature map is calculated using Equation (3) [14]. \[y_{i,j,k}=b_{k}+\sum_{u=0}^{f_{h}-1}\sum_{v=0}^{f_{w}-1}\sum_{k^{\prime}=0}^{f_ {c}-1}x_{i^{\prime},j^{\prime},k^{\prime}}\cdot\omega_{u,v,k^{\prime},k} \tag{3}\]  
\(f_{h}\) and \(f_{w}\) are the filter height and width, respectively. \(f_{c}\) denotes the total number of channels in the input data. \(b_{k}\) is the bias for \(k\)-th filter, \(x\) is the pixel value of the input. \(\omega\) is the learnable weight of the filter. As the training proceeds, the weights in the filter are updated to effectively extract the features of the input data. The output of the convolution layer is fed to the activation layer. The activation layer determines the activation level of the fed output using a predefined activation function. To represent the complex boundaries between classes in a high-dimensional feature space, activation functions are usually  
Figure 2: Typical architecture of CNN. defined as nonlinear functions. The most widely used activation function in recent times is the rectified linear unit (ReLu). The definition of ReLu is shown using Equation (4). \[\phi=\max(0,x) \tag{4}\]  
In general, the activation layer is followed by a pooling layer. The pooling layer reduces the size of the feature map generated by the convolution layer. This subsampling process helps reduce the computational cost. It is also known to prevent neural networks from overfitting. The most commonly used pooling operations are max pooling and average pooling. Their mechanism is illustrated in Figure 3.  
After convolution, activation, and pooling operation, the final feature map was delivered to the fully connected layer. As the name implies, every node in the previous layer is connected to every node in the next layer. First, the 3-dimensional feature map is flattened to a 1-dimensional (1D) feature vector. Except for the first conversion process, the other operations were the same as those of the multilayer perceptron.