## 4 Airfoil Noise Prediction Model Construction  
A Convolutional Neural Network (CNN) [21] is a specialized neural network designed to process grid-structured data. CNNs excel at extracting features from grid-based datasets and are widely used in fields such as object recognition, speech recognition, and image recognition. For this study, CNNs are employed to identify airfoil data. However, traditional CNN models face limitations as their depth increases, particularly due to gradient vanishing or gradient explosion issues during training in deep neural networks. Residual Neural Networks (ResNet) [22; 23] effectively overcome these limitations. As shown in  
Figure 12: Partial noise sample. (**a**) NACA64618 noise samples (**b**) CQU-DTU B18 noise samples. (**c**) New airfoil noise sample 1 (**d**) New airfoil noise sample 2. Figure 13, ResNet introduces residual connections to the standard CNN structure. The model's objective during training is to learn the residual function \(F(x)=H(x)-x\). When \(F(x)=0\), it implies \(H(x)=x\), which corresponds to an identity mapping. Residual connections allow the output of one layer to bypass several intermediate layers and connect directly to a subsequent layer's input, effectively mitigating the gradient vanishing or exploding problems. The output and input relationship can be expressed as:  
\[H(x)=F(x)+x \tag{25}\]  
where: \(H(x)\) represents the final output, and \(F(x)\) is the result of operations such as convolution and pooling. In this study, a wind turbine airfoil noise prediction model is constructed using the ResNet-18 architecture. The model structure is illustrated in Figure 14. The input layer consists of two-dimensional airfoil data. After initial convolution and pooling operations, the data are passed through the residual blocks of ResNet-18. Subsequently, a Global Average Pooling (GAP) layer processes the data into a one-dimensional form. The output layer is then connected, where the number of neurons is set to 31, corresponding to the number of frequency points in the noise label set. The parameters of the ResNet-18 structure are detailed in Table 2. The framework to build the deep learning models is provided by MATLAB's deep learning toolbox. As shown in Figure 15, each airfoil image is digitized into a two-dimensional matrix, where each pixel corresponds to a parameter in the matrix. Noise data for each airfoil, obtained via BPM theory, are transformed into a 1 \(\times\) 31 vector. Thus, each airfoil and its corresponding noise data are converted into a format suitable for training the neural network model. Figure 14: Airfoil noise calculation model ResNet-18 structure. Figure 13: Residual connection. The dataset comprises 18,300 samples, where:14,640 airfoils and noise data are used as the training set 1830 airfoils and noise data are used for validation during training, and 1830 airfoils and noise data are used as the test set. The ratio of the number of samples in the training set, validation set, and test set is 8:1:1. The data were split using a random division method. Both the two-dimensional airfoil matrix data and the noise data were preprocessed using linear normalization to enhance computational efficiency. During ResNet-18 model training, the Stochastic Gradient Descent with Momentum (SGDM) algorithm is used for optimization. The training settings include: Batch size: 80, Max Epochs: 1200, Learning rate: 0.006, Learning rate decay factor: 0.5 (learning rate decreases every 240 epochs), Validation frequency: 5000 iterations, Validation patience: 20 epochs. This framework effectively processes airfoil data and corresponding noise vectors, leveraging the ResNet-18 architecture to improve the accuracy and robustness of noise prediction. The above data processing work is completed in MATLAB.