# 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  
This article mainly studied the prediction method of underwater acoustic transmission loss, so it focused on the influence of different underwater acoustic characteristic parameters on the prediction results of the acoustic propagation model. The problem of sound transmission under water is mainly studied by two methods: one method is the wave theory, which studies the changes in the amplitude and phase of the acoustic signal in the sound field; and the other method is the ray theory, which can be used in a high-frequency range, sound wave is regarded as a beam of rays, and the change of the sound intensity in the sound field with the beam of rays is usually studied. From these two theories, several classic underwater acoustic transmission models have been developed to characterize the underwater acoustic propagation process including NM, RM, PE model, etc. [3]. In underwater acoustics, the standard measure of sound field signal strength versus distance is the transmission loss (\(TL\)), which is the ratio of the sound intensity \(I(r,z)\) at a certain point in the sound field to the sound intensity \(I_{0}\) at a distance of 1 m from the sound source. It can be expressed as Equation (9):  
\[TL=-10\,\log\frac{I(r,z)}{I_{0}}=-20\,\log\frac{|p(r,z)|}{|P_{0}|} \tag{9}\]  
where \(p(r,z)\) is the sound pressure at a certain point in the sound field; \(r\) is the distance from the sound source position to a certain point in the sound field; \(z\) is the receiving depth of a certain point in the sound field; \(P_{0}\) is the sound pressure value at a distance of 1 m from the sound source; and TL is the value of the transmission loss of the sound field in decibels (dB). This paper selected the Bellhop model in ray mode for research. This model was written by [PERSON] and [PERSON] [21] in 1987 using the Gaussian beam tracking method to calculate the sound field in a horizontally non-uniform environment (conditions related to distance). The experimental data of this model in the frequency range of 600 Hz-30 KHz were consistent with the theoretical model [22]. It is suitable for near-field conditions. The important characteristic length of the water depth or sound velocity profile should be greater than 20 wavelengths [23]. For the normal model, this paper selected the Kraken model for research. This model was jointly developed by the U.S. Naval Ocean System Center (NOSC) and the U.S. Naval Research Laboratory (NRL) using the finite difference method to solve the normal wave equation. It is suitable for low-frequency (lower than 500 Hz) shallow sea and far-field calculation under uniform horizontal (distance-independent) marine environmental conditions, and the seabed structure must be given in the calculation, that is, the parameters of Cs, Kd, \(p\), and Mt in Table 1.  
For the fast field program model (FFP model), we choose the Scooter model for research. This model applies fast Fourier transform (FFT) technology to solve the wave equation. It is limited to the condition of a horizontally layered homogeneous medium  
Figure 3: Deep Belief Net (DBN) model training. that is not related to distance, near-field environment, and is suitable for calculations in the low-frequency range (below 500 Hz). For the parabolic equation (PE) model, the RAMGeo model was selected. This model is an approximate solution of the wave equation with a narrow angle (\(<\)\(\pm\)20\({}^{\circ}\)) considering the coupling effect of acoustic diffraction and normal waves of various numbers. It is suitable for calculating narrow angles. The calculation speed for low frequency (lower than 500 Hz) and shallow sea is very fast. When the frequency increases and the depth increases, the calculation time increases rapidly, therefore, this model is not applicable. The above far-field and near-field rules are constrained by the characteristic parameter horizontal distance (R).