# Surrogate Based Optimization of Aerodynamic Noise for Streamlined Shape of High Speed Trains
## 6 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Objectives** & **Leg (dBA)** & **Cd** & **Cd\_inviscid** \\ \hline
**Original** & 81.9316 & 0.314114 & 0.165 \\
**Test Case** & 80.676 & 0.2919 & 0.1364 \\
**Reduction** & 1.5\% & 7.1\% & 17.33\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The comparison of the objectives before and after optimization. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Objectives** & **Real Leg (dBA)** & **Kriging (dBA)** & **Error** & **Real Cd** & **Kriging** \\ \hline
**Test Case** & 80.676 & 80.698 & 0.027\% & 0.2919 & 0.29046 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The comparison between the CFD calculations and prediction from the Kriging model. Figure 13: Comparison of the streamlined shape between the prototype and the optimal shape. (**a**) View from the direction of positive \(y\); and (**b**) view from the direction of negative \(y\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variations** & \(W_{1}\)**/mm** & \(W_{2}\)**/mm** & \(W_{3}\)**/mm** & \(W_{4}\)**/mm** \\ \hline
**Test Case** & \(-40.85\) & \(-38.50\) & \(-50.81\) & \(-61.55\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The variations of the design variables compared to the prototype model (1:1). As shown above, the inviscid drag mainly exists on the leading car and trailing car. The inviscid drag is reduced by 5.2% and 27.6% for the leading car and trailing car, respectively. Meanwhile, the inviscid drag on the middle car is also reduced. The inviscid drag is the main source for drag optimization. The pressure contour on the leading car before and after optimization is shown in Figure 15.  
The height of the nose is reduced for the optimal model. Consequently, the high-pressure zone in front of the nose varies. The high-pressure zone mainly covers the region between the nose and the cowcatcher. Lower nose leads to a relatively smaller high-pressure zone, which results in a relatively smaller inviscid drag. The pressure contour on the trailing car before and after optimization is shown in Figure 16.  
An obvious higher-pressure zone behind the trailing nose could be observed for the optimal model, which could provide a thrust on the trailing car. As a result, the inviscid drag on the trailing train could be effectively reduced. Figure 16: Pressure contour on the trailing car before and after optimization. Figure 14: Comparison of drag coefficients of each carriage before and after optimization. Figure 15: Pressure contour on the leading car before and after optimization (Pressure: Pa). The pressure coefficient along the longitudinal profile of the leading car and trailing car before and after optimization is also investigated, as shown in Figure 17.  
It can be seen that the biggest variation exists at the bottom part of the trailing nose. Higher pressure could be observed along the lower longitudinal profile for the optimal model, which is the root for the relatively lower inviscid drag of the trailing car. Then, the acoustic characteristics in the far field are analyzed. As mentioned above, the equivalent continuous SPL is reduced by 1.26 dB. Figure 18 shows the A-weighted overall sound pressure level (OASPLA) of all the probes before and after optimization. It can be seen that the OASPLAs of most probes for the optimal shape are reduced in a certain extent, compared to the prototype. Results reveal that the noise circumstance in the far field is improved after optimization. In order to investigate on the influence of each design variable on the optimization objectives, it is necessary to perform the sensitivity analysis for the design variables. Sensitivity analysis is performed  
Figure 17: Pressure coefficient along the longitudinal profile of the leading car and trailing car before and after optimization. Figure 18: The Overall A-weighted Sound Pressure Levels (OASPLAs) of all the probes before and after optimization. by studying the correlations between the design variables and the objectives.