# Prediction Method of Underwater Acoustic Transmission Loss Based on Deep Belief Net Neural Network
## 4 Experimental Results and Discussion
### Forecast Result Analysis  
To make a more scientific assessment of the overall performance of the underwater acoustic transmission loss prediction by the new method, we applied the root mean square error (RMSE) to evaluate the transmission loss and the transmission loss of the underwater acoustic model mismatch prediction by this method. The actual transmission loss of sea trials was compared with errors to evaluate the forecast accuracy of this method. The specific definition is as Equation (12):  
\[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{N}\left(\hat{y_{i}}-y_{i}\right)^{2}}{N}} \tag{12}\]  
where \(\hat{y_{i}}\) represents the predicted transmission loss; \(y_{i}\) represents the actual transmission loss; and \(N\) represents the predicted transmission loss point. The smaller the value of RMSE, the smaller the difference between the predicted transmission loss data and the sea trial transmission loss data, that is, the more accurate the forecasting ability. According to the above-mentioned marine environmental characteristic parameters, we selected the characteristic parameters mentioned in Table 1, and input them into the DBN neural network constructed in this article for underwater acoustic model adaptation and underwater acoustic transmission loss prediction. As shown in Figure 10, Comparing the prediction results of the model selected by the new method with the prediction results of other underwater acoustic models, it can be seen that the prediction results of the model selected by the new method were the most consistent. In the figure, the \(x\)-axis is the transmission distance in m, and the \(y\)-axis is the energy intensity in dB. Figure 11a shows that the ocean transmission loss predicted by the new method using this system is basically in line with the actual transmission loss. Although there are error fluctuations between the predicted curve and the actual curve, it can be seen in Figure 11 that the system has the smallest prediction error. The calculated RMSE error is shown in  
Figure 10: Sound speed profile. Table 5. The average RMSE error of the transmission loss data under each array element was 6.31 dB, which was the smallest error compared to other models. Figure (b)b shows that the transmission loss curve predicted by Bellhop had a certain error deviation from the actual transmission loss curve. The calculated RMSE error is shown in Table 5. The average RMSE error of the transmission loss data under each array element was 11.56 dB. Comparing Figure (a)a with Figure (b)b, it can be seen that the predicted transmission loss curve was actually very close, and in Figure 12, it can be seen that the error curve was also very close. In this case, in actual application, if there is no rich expert experience, it is difficult to choose the best matching underwater acoustic propagation model. The RMSE of the transmission loss result predicted by this method was compared with the  
Figure 11. Comparison of system prediction TL and sea trial TL. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Array Element** & **Systematic Prediction** & **Bellhop Prediction** & **RAMGeo Prediction** & **Scooter Prediction** \\
**Depth (m)** & **Error (dB)** & **Error (dB)** & **Error (dB)** & **Error (dB)** \\ \hline
181 & 6.86 & 13.56 & 18.05 & 58.52 \\
261 & 5.85 & 13.45 & 17.45 & 57.65 \\
311 & 6.75 & 12.74 & 16.85 & 56.60 \\
411 & 5.95 & 12.45 & 19.76 & 55.35 \\
511 & 6.34 & 12.06 & 17.76 & 55.98 \\ Average RMSE & 6.35 & 12.852 & 17.974 & 56.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 5. Root Mean Square Error (RMSE) error comparison (245 Hz). transmission loss RMSE predicted by Bellhop, and the error was reduced by 5.25 dB. The results show that this method can easily match a suitable underwater acoustic propagation model and calculate accurate underwater acoustic transmission loss prediction in a complex ocean environment. As shown in Figure 11c, it can be seen that there were obvious errors between the actual sea test data and the data predicted by the RAMGeo model, and there was a model mismatch.