# Structural Design and Parameter Optimization of Bionic Exhaust Tailpipe of Tractors
## 3 Results and Discussion
### Structural Parameter Optimization  
From the transmission loss curve of Figure 10, there is a downward trend in transmission loss as the frequency increases, which is the minimum near 490 Hz in the range of the target frequency between 10 Hz and 490 Hz. Therefore, the frequency of 490 Hz is selected as the target optimization frequency. It is obvious from Figure 10 that when the number of circumferential columns is 24, the transmission loss is at maximum, so the top angle and height need to be optimized for parameters. The transmission loss values corresponding to different heights and top angles at 490 Hz are summarized in Table 3. The optimization analysis of the neural network algorithm based on genetic algorithm optimization is used to obtain the optimal size parameter and the maximum transmission loss at 490 Hz so that the transmission loss in the range of 10-490 Hz is improved as a whole. When the BP neural network optimized by a genetic algorithm is used for size optimization, the population size is 50, crossover probability selection is 0.3, mutation probability selection is 0.1, and evolution algebra is 20. In the process of transmission loss of tractor bionic exhaust tailpipes optimization, since the fitting function has two input parameters and one output parameter, the transmission loss (TL), top angle \(\theta\), and texture height h were selected for BP neural network optimization analysis based on genetic algorithm optimization. The variables listed are shown in Table 3. During the optimization process, the input parameters are the bionic texture including top angle \(\theta\), texture height h, and the maximum transmission loss is the output parameter. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **TL (dB)** & \(\theta\) (\({}^{\circ}\)) & **h (mm)** & **Case** & **TL (dB)** & \(\theta\) (\({}^{\circ}\)) & **h (mm)** \\ \hline
1 & \(-\)0.728 & 30 & 0.5 & 14 & 0.346 & 60 & 1.25 \\
2 & \(-\)0.636 & 30 & 0.75 & 15 & \(-\)0.824 & 60 & 1.5 \\
3 & \(-\)0.051 & 30 & 1 & 16 & \(-\)0.749 & 75 & 0.5 \\
4 & \(-\)0.728 & 30 & 1.25 & 17 & \(-\)0.56 & 75 & 0.75 \\
5 & \(-\)0.638 & 30 & 1.5 & 18 & \(-\)0.773 & 75 & 1 \\
6 & \(-\)0.766 & 45 & 0.5 & 19 & \(-\)0.681 & 75 & 1.25 \\
7 & \(-\)0.17 & 45 & 0.75 & 20 & \(-\)0.597 & 75 & 1.5 \\
8 & 0.039 & 45 & 1 & 21 & \(-\)0.548 & 90 & 0.5 \\
9 & \(-\)0.287 & 45 & 1.25 & 22 & \(-\)0.636 & 90 & 0.75 \\
10 & \(-\)0.736 & 45 & 1.5 & 23 & \(-\)0.036 & 90 & 1 \\
11 & 0.216 & 60 & 0.5 & 24 & 0.128 & 90 & 1.25 \\
12 & \(-\)0.754 & 60 & 0.75 & 25 & 0.132 & 90 & 1.5 \\
13 & 0.425 & 60 & 1 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Transmission loss at 490 Hz corresponding to different heights and top angles (\(\theta\) is top angle, h is texture height, TL is transmission loss). As shown in Figure 11, under different top angles and heights before and after optimization, the trend of the corresponding transmission loss remains the same. The theoretical value of the optimal parameter of the bionic triangle texture was obtained after optimization. When the top angle is 61\({}^{\circ}\) and the texture height is 0.95 mm, the transmission loss corresponding to 490 Hz is the maximum. The air cavity of bionic exhaust tailpipes with the structural parameters was modeled in three dimensions, and an acoustic simulation was conducted using LMS Virtual Lab acoustic simulation software. Figure 12 shows the comparison of the transmission loss curves of the prototype and the optimized bionic exhaust tailpipe. The increased value represents the difference between the transmission loss of the optimized bionic tailpipe and the prototype tailpipe. In the target frequency range, the bionic exhaust tailpipe transmission loss improved by 1.009 dB to 9.62 dB compared with the prototype after optimization. The transmission loss increased by 9.62 dB at 30 Hz and increased by 1.009 dB at 490 Hz. From the beginning of 10 Hz, the increment value increases, and the increment value was at maximum at 30 Hz and then gradually decreases above 30 Hz.