## 4 Construction of the Cascaded Model and Training  
### Dnn  
The M-P model, proposed by psychologist [PERSON] and logician [PERSON], is a mathematical model that was developed through an analysis and synthesis of the basic properties of neurons [31]. This model is crucial for the implementation of neural networks and constitutes the foundational unit of a DNN. The structure of this model is depicted in Figure 6. The \(\mathbf{x}=\left(x_{1},x_{2},\cdots,x_{n}\right)^{T}\) represents the \(n\) input features of the neuron, and \(\mathbf{\omega}_{i}=\left(\omega_{i1},\omega_{i2},\cdots,\omega_{in}\right)\) denotes the weight vector responsible for linear weighted connections. The weight vector \(\mathbf{\omega}\) is optimized within neural networks to enhance the accuracy of predictions. The linear weighted output \(\mathbf{Z}\) can be expressed as follows:  
\[Z_{i}=\sum_{j=1}^{n}\omega_{ij}x_{j} \tag{3}\]  
Figure 6 depicts the structure of the M-P neuron model. The difference between \(Z\) and an offset \(\theta\) is used as the input to the function \(f(\cdot)\). The function \(f(\cdot)\) is referred to as the activation function and used to derive the output of the neuron. \(\theta\) can be considered as the weight of input \(x_{0}\) with a fixed value of \(-1\) and is also an optimization target of the neural network. In this paper, the ReLU function is adopted as the activation function because it can more effectively mitigate the occurrence of overfitting. The formula for this is shown in Equation (4).  
\[f_{\text{ReLU}}(x)=\max(0,x) \tag{4}\]  
The output of the activation function is typically used as the input for adjacent layers. DNNs can complete tasks such as regression, classification, and recognition. DNNs are widely used for regression tasks in production and performance evaluation [4; 6; 7; 8; 9; 32]. The  
Figure 6: The structure of the M-P neuron model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Number of Channels**} \\ \hline Datasets & A: 280 & B: 215 (170 from A) \\ \hline Training Set & 184 & 140 \\ \hline Validation Set & 40 & 40 \\ \hline Testing Set & 56 & 40 (5 from the validation set) \\ \hline Total & & 325 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dataset split settings.  
DNN used in this paper, as shown in Figure 7, adopts a standard structure with multiple hidden layers, along with an input layer and a linear regression output layer [33], and employs a fully connected network architecture between its neurons.  
In order to make the model converge better, the training model usually requires a cost function to evaluate the gap between model-predicted values and actual values. In this paper, Smooth L1 [34] is adopted as the cost function:  
\[\text{smooth}_{\text{L1}}=\begin{cases}0.5\times(y_{n}-\hat{y}_{n})^{2}& \text{if}|y_{n}-\hat{y}_{n}|<1\\ |y_{n}-\hat{y}_{n}|-0.5&\text{otherwise}\end{cases}, \tag{5}\]  
where \(y_{n}\) and \(\hat{y}_{n}\) represent the real value and predicted value, respectively.  
The performance of the model is evaluated using the cost function; then, an optimizer is employed to backpropagate and continuously minimize the cost function. The model parameters and weights are continuously updated until the expected performance is achieved. After comparing several different optimizers, the Adam optimizer was ultimately selected for use in this paper [35].