## 4 One-Dimensional Residual Attention Convolutional Neural Network Model  
### One-Dimensional Convolutional Neural Network  
Convolutional Neural Networks (CNNs) are deep feedforward networks primarily utilized in the field of computer vision for tasks such as image classification and target detection. The concept of convolution and downsampling layers can be traced back to 1980, when [PERSON] [22] proposed it. In 1990, [PERSON] and colleagues [23,24] published a paper introducing the principles of the modern CNN framework. However, it was not until 2012, when AlexNet [25] achieved significant success on the ImageNet dataset, that CNNs began to receive widespread attention.  
The one-dimensional Convolutional Neural Network (1D CNN) is a variant of the CNN primarily used to process one-dimensional sequence data. Its network structure is similar to that of two-dimensional CNNs, encompassing a convolution layer, pooling layer, and fully connected layer. Subsequently, the attention mechanism [26] and the residual network [27] are applied to the convolutional neural network.  
In the convolution layer, the input feature map undergoes convolution with the convolution kernel to yield an output feature map, which is then subjected to nonlinear transformation via the activation function. The computational method for this process can be expressed by the following formula:  
\[X_{j}^{l}=f\left(\sum_{i\in M_{j}}X_{j}^{l-1}*w_{ij}^{l}+b_{j}^{l}\right) \tag{15}\]  
In the formula, \(X_{j}^{l}\) is the output of layer \(l\), \(f\) is the nonlinear activation function, \(M_{j}\) is the set of all input feature graphs associated with the output feature graph of layer \(l-1\), \(X_{j}^{l-1}\) indicates the input feature map in layer, \({}^{*}\) rep \(l-1\) resents the convolution operation between the convolution kernel and the input, \(w\) is the weight matrix corresponding to the convolution kernel, and \(b\) is the bias matrix.  
The pooling layer serves to decrease the size and quantity of parameters within the feature map. This reduces the risk of overfitting while retaining the essential features. The computational process of the pooling layer unfolds as follows:  
\[X_{j}^{l}=f\left(\beta_{j}^{l}\cdot down\left(X_{j}^{l-1}\right)+b_{j}^{l}\right) \tag{16}\]  
In the above formula, \(\beta\) represents the weight matrix, while b denotes the bias matrix,and 'down' signifies the down-sampling function. The one-dimensional pooling layer is primarily categorized into two types, namely, maximum pooling and average pooling. Maximum pooling selects the maximum value within each window for output, whereas average pooling computes the average value within each window for output. Generally, maximum pooling reflects the most prominent features while average pooling smooths the region and selects the smoothing feature.  
The fully connected layer is employed to classify or regress the outputs of the convolution layer and the pooling layer. The outputs of the fully connected layer are as follows:  
\[\delta i=f(w_{i}p_{i}+b_{i}) \tag{17}\]  
In the formula, \(i=1,2,\ldots,k\); there are \(k\) outputs, with \(\delta i\) being the \(i\) output; \(w_{i}\) and \(b_{i}\) are the weights and thresholds of \(i\) neuron, respectively; and \(f\) is the activation function.