# Prediction Method of Underwater Acoustic Transmission Loss Based on Deep Belief Net Neural Network
## 2 Deep Belief Net (DBN)
### DBN Model Structure  
The structure of the DBN model constructed in this paper is shown in Figure 2. The first visible layer and the second hidden layer constitute the first RBM, and the second hidden layer and the third hidden layer form the second RBM, by analogy, a total of five RBM are formed. Input the data of the fifth RBM into a supervised classifier, and use BP to fine-tune the relevant parameters of the DBN to form a complete DBN to classify the input data. \(X=\{x_{1},x_{2},\,\ldots,x_{n}\}\) is the input of the first visual layer, representing the current marine environment and signal characteristic parameters (as shown in Table 1). \(h_{x,y}\) are the states of \(y\) unit in the \(x\) hidden layer; \(\{x_{1},x_{2},x_{3},x_{4},x_{5}\}\) are the connection weight vectors between adjacent layers. The top-level classifier network structure uses the BP backpropagation neural network and \(w_{bp}\) is the weight vector of the BP neural network. If the output result cannot get the expected tag data, the BP backpropagation adjustment is used to continuously approach the expected output of the representative label.  
As shown in Figure 3, the training DBN was divided into three stages. The first stage is the model initialization stage. Regarding any two adjacent layers in the DBN as an RBM, input the output vector of the previous RBM to the next RBM, and initialize the parameters in the DBN layer by layer. The second stage is the unsupervised forward learning stage. The preprocessed marine environment features and signal features are input to the first visual layer. The greedy unsupervised learning method is used to train layer by layer, and the activation function of each unit is sigmoid. In the second stage, the shallow original features are expressed at a high level. Since the unsupervised algorithm cannot optimize the entire network parameters, it is necessary to enter the third stage, the reverse supervised learning stage, which uses the BP supervised algorithm to reversely fine-tune the DBN to optimize the underwater acoustic transmission loss prediction under the large-scale marine environment and the changeable signal frequency band. This training mode directly maps data from input to output through unsupervised training, shortening the time of supervised training, and is also the key to a powerful feature rule extraction capability.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Characteristic Parameters** & **Symbol** & **Range** & **Definition** \\ \hline Frequency/(Hz) & Fs & 10–30,000 & The frequency of the signal emitted by the sound source. \\ Sound source depth/(m) & SD & 100–4000 & Depth of emitted sound source. \\ Sound source opening angle/(\({}^{\circ}\)) & SA & \(-\)90–90 & The opening angle of the emitted sound source. \\ Horizontal distance/(km) & R & 0.5–500 & Distance between sound source and receiving array. \\ Sea-depth/(m) & H & 10–4000 & The depth of the sea. \\ Distance-independent/related & RI/RD & 0/1 & Is the ocean characteristic only related to depth, or is it \\ Deposition sound velocity/(m\(\cdot\)s\({}^{-1}\)) & Cs & 1520–1836 &
\begin{tabular}{c} Sound propagation velocity of seabed sediments \\ Density of seabed sediments \\ \end{tabular} \\ Deposit density/(g\(\cdot\)cm\({}^{-3}\)) & \(p\) & 1.421–2.034 & Density of seabed sediments \\ Deposition layer thickness/(m) & Mt & 5–50 & The thickness of the deposited layer \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristic parameters.  
Figure 2: Deep Belief Net (DBN) mode structure.