# Prediction Method of Underwater Acoustic Transmission Loss Based on Deep Belief Net Neural Network
## 3 Dataset Construction and Model Training
### Model Initialization and Training  
First, we initialized the model to determine the momentum factor, learning rate, maximum number of iterations, and the number of hidden layer nodes related to the RBM training process. In addition, because DBN does not clearly define the most suitable layer number, the determination of the layer number needs to determine the depth of the DBN model through experimental evaluation results. Then, we set the relevant parameters of RBM, set the initial value of learning rate to 0.1 according to experience, and set the initial momentum to 0.5, where the number of input nodes is the number of characteristic parameters in Table 1, and the number of output nodes is four nodes equal to the number of acoustic models. The number of pre-training iterations (epochs) was selected as 200, and the number of global reverse fine-tuning was 100. In order to prevent over-fitting, we randomly selected 3/4 of each type of data as training samples, and the rest as test samples. The number of the random sample training batch size was 20. Table 3 shows the performance of the DBN neural network at different depths. It can be seen that as the depth of the DBN model increases, the time cost also doubles. When the depth is greater than 5, the classification accuracy does not increase significantly. The training time has been increasing by a large margin, so for comprehensive training time and classification accuracy, five layers is a more reasonable depth choice. The training of DBN mainly consists of two parts. The first part is unsupervised bottom-up layer-by-layer pre-training, which transfers the feature vector from the input to the output. The second part is the supervised top-down reverse fine-tuning. The output value is compared with the given data label to get the error, and the error is back propagated from the output end to the input end to achieve the purpose of adjusting the DBN parameters. The overall training process is shown in Figure 4: \begin{table}
\begin{tabular}{c c c} \hline \hline
**DBN Layers** & **Accuracy (\%)** & **Training Time (s)** \\ \hline
3 & 75.135 & 210.752 \\
4 & 93.456 & 420.456 \\
5 & 95.876 & 590.456 \\
6 & 94.123 & 760.356 \\
7 & 95.756 & 900.456 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Deep Belief Net (DBN) layers and performance. The specific training steps are as follows:  
* Preprocess the dataset constructed in Section 3.1 and input data into the model in batches for training. * Set the bias of the visible layer and the hidden layer and the initial value of the weight between each neuron \(\theta=\{b,c,w\}\). \(b\) represents the bias of the input data layer or visual layer, \(c\) represents the bias of each hidden layer or data output layer, and \(w\) represents the connection weight of each layer. According to the research of [PERSON] et al., the connection weight \(w\) of each layer is initialized to obey the normal distribution \(N\) (0,1), and the initial value of the bias \(b\) of the visible layer and the bias \(c\) of the hidden layer is set to 0. * Next, we perform iterative training on DBN. In the DBN model, each layer of RBM learns the characteristics of the input data forward and unsupervised, and uses the greedy unsupervised learning algorithm to update the bias value of each unit of each layer and the weight between the hidden layer. * After completing the network pre-training, we add the Softmax output layer, and use fine-tuning to transform the entire network from a generative model to a discriminative model. This network loss function can be defined as: \[L(\lambda)=-\frac{1}{N}\sum_{n=1}^{N}1\{label(n)=1\}\log\Bigl{(}\exp\Bigl{(}W_ {0}{}^{(n)}x+b^{(n)}\Bigr{)}\Bigr{)}/\sum_{n=1}^{N}\exp(W_{0}x+b)\] (10)  
In the formula, \(1\)[label(\(n\)) = 1] means that the condition in brackets is set to 1 when the condition is satisfied, and 0 is not satisfied. \(W_{0}{}^{(n)}\) and \(b^{(n)}\) are the connection weight vector of the nth node in the output layer and its offset; x is the response of the upper node.