# Prediction Method of Underwater Acoustic Transmission Loss Based on Deep Belief Net Neural Network
## 3 Dataset Construction and Model Training
### Feature Parameter Rules and Sample Set Construction
Suppose that the total spacing of the uniform linear array element D = m \(\times\) d; m is the number of array element spacing; the highest frequency wavelength of the sound source (the minimum wavelength of the sound source) is \(\lambda_{min}\), if the sound source is at the level of the array Distance R \(>\) 2D\({}^{2}\), it is the far-field model, otherwise it is the near-field model. Under the near-field model, sound waves are regarded as spherical waves, and under the far-field model, sound waves are regarded as plane waves. The calculation of underwater acoustic transmission loss mainly includes characteristic parameters such as signal frequency, sea depth, and seabed environment. The specific parameters and parameter ranges are shown in Table 1.  
The optimal characteristic parameter ranges of the above four types of underwater acoustic transmission loss models are shown in Table 2.  
Sample data generation is very important for neural network training, and the distribution and statistical characteristics of the sample will also directly affect the training efficiency and prediction effect of the neural network. Based on the above constraints, we built a dataset with a normal distribution to train the neural network model. The training set generation method is as follows:  
1. Select an underwater acoustic propagation model, and generate the data on the principle of a normal distribution within the constraint range according to the above-mentioned constraint conditions of the parameters of the selected model. 2. Set labels for the samples in the established training set. The labels of each sample are different. Usually, a combination of 0-K (K is the number of models) is used to set the corresponding label. The labels are formed into a new set corresponding to the input data. 3. Combine different marine environment characteristics and signal characteristics according to the above steps to form a large training set. Then, after making a one-to-one correspondence between the input data and the label, randomly shuffle the order of the input data, and recombine the training set. The purpose of shuffling the data is to prevent too much noise data of the same type from clustering together, causing over-fitting. Different feature parameters have different weights in the adaptation model. In the DBN neural network, the weight of each feature parameter is automatically optimized according to the training data, and finally, the optimal weight is achieved through iterative training. If we want the neural network to learn these rules in-depth, we will build more data for the network's learning of the feature parameters with larger weight, and the rest of the feature parameters can be iterated by the neural network to obtain the optimal weight. As shown in Table 2, we extracted a total of nine feature parameters. Compared with other \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Mode** & **Fs (Hz)** & **SD (m)** & **SA (\({}^{\circ}\))** & **R (Km)** & **H (m)** & **RI/RD (0/1)** & **Cs** & \(p\)** & **Mt** \\ \hline Ray Mode & 600–30,000 & 210–4000 & \(-\)90–90 & 0.5–500 & 200–4000 & 1 & 1520–1836 & 1.421–2.034 & 5–50 \\ Normal Mode & 0–500 & 10–800 & \(-\)90–90 & 100–500 & 10–800 & 0 & 1520–1836 & 1.421–2.034 & 5–50 \\ FFP Model & 0–500 & 210–4000 & \(-\)90–90 & 0.5–100 & 200–4000 & 0 & 1520–1836 & 1.421–2.034 & 5–50 \\ PE Model & 0–500 & 10–500 & \(-\)20–20 & 0.5–500 & 10–500 & 0/1 & 1520–1836 & 1.421–2.034 & 5–50 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Underwater acoustic transmission loss mode characteristic parameter range. models, Fs is a significant feature parameter in the ray mode and has a larger weight, so we increased the number of Fs parameters in the ray mode training. For the ray model, we increased the number of samples for the feature parameter Fs with a larger weight, and constructed 50 different values within the constraint range.