# Acoustic Shooting and Bounce Ray Method for Calculating Echoes of Complex Underwater Targets
## 7 Simulation Evaluation
### Algorithm Validation  
The verification of the simulation algorithm is carried out from the perspective of correctness, effectiveness and information completeness by using the main sphere, cylinder and other standard models. At the same time, the classical mathematical model is used to verify its engineering applicability. 1. Verify the correctness  
The sphere and cylinder model with a radius of 1 m shown in Table 1 were taken as objects to verify the correctness of the algorithm. The aperture of the acoustic beam pipeline was set as 0.005 m, plane angle scanning was carried out on the sphere model, and plane frequency scanning was carried out on the cylinder model on the orthogonal surface of the cylinder. The comparison between the model target intensity results obtained by the simulation and the theoretical analytical values was shown in Figures 7 and 8. As can be seen from the figure, under the conditions of a sweep angle and sweep frequency, the deviation between the simulation results of the target strength of the standard model and the theoretical analytical values is less than 3 dB (as demonstrated by the mid-point line \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model Type** & **Sphere** & **Cylindrical** & **Cross Column** & **Benchmark** \\ \hline \multirow{2}{*}{The model size} & \multirow{2}{*}{Radius 1 m/5 m} & Radius 1.5 m & Radius 1.5 m & Length 65.0 m \\  & & Length 10 m & Length 10 m & Width 7.5 m \\  & & & (Center cross) & High: 11.0 m \\ \hline Surface mesh & 0.5 \(\lambda\) (0.05 m)/2 & & & \\ aperture & \(\lambda\) (0.2 m) & & & \\ \hline Bin number & 11,636/18,252 & 68,670 & 157,342 & 132,040 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of calculation model. 2. Verification of validity  
The 1 m radius sphere model shown in Table 1 was used as the object to verify the effectiveness of the algorithm. According to Table 1, at this time, the meshing precision of the sphere model surface element was 0.05 m, and the aperture of the acoustic beam pipeline was set as 0.01 m and 0.005 m, respectively. Plane frequency scanning was carried out on the sphere model, and the calculated results of the target intensity were shown in Figure 9. According to the analysis of Figure 9, as the incidence wave frequency increases, its wavelength becomes shorter, the meshing accuracy of the surface element of the incident wavelength becomes lower, and the fluctuation of the calculated results increase. However, the results of the fluctuation can be significantly suppressed by reducing the pipeline aperture of the low beam to reduce the proportion of the pipeline split during GA calculation. Thus, it is proved that the TD-ASBR algorithm can be effectively applied to the bandwidth signals in a certain frequency band through the corresponding adjustment of the surface element grid and the pipeline aperture of the acoustic beam. 3. Verify information completeness  
TD-ASBR method is used to generate the time domain echo simulation signals of the model targets listed in Table 1, such as sphere, cross column and Benchmark submarine, as shown in Figure 10. Acoustic ISAR imaging results of the above time domain echoes are shown in Figure 11.  
Figure 9: Sphere frequency–intensity curve. In addition to echo delay, the Doppler frequency modulation, phase lag and other time-domain echo simulation signals usually contain one-dimensional information, the acoustic ISAR imaging results can accurately reflect the shape, size and spatial distribution characteristics of the target model, and intuitively prove that the simulation signals generated by the TD-ASBR method have higher completeness (d) Analysis of classical submarine target echo The pipeline division accuracy is 0.005 m. Under the LFM pulse incidence condition, the conventional integral dimension reduction method is adopted to calculate the target echo in the time domain of the Benchmark submarine at different incidence angles and can carry out the time-domain correlation analysis.