# Surrogate Based Optimization of Aerodynamic Noise for Streamlined Shape of High Speed Trains
## 6 Results and Discussion  
As parameters for GA operation, the size of initial population is set to 100. The probability of crossover is 0.9 while the probability of mutation is set to 0.3. The size of evolution generations is set to 100. The value of \(\theta\) varies from 0 to 10. After adding points for three times, the Kriging model meets the accuracy requirement. Figure 11 shows the convergence history of the fitness and the exact value for each variable. The total aerodynamic drag coefficient and the equivalent continuous SPL are treated as the optimization objectives, and the multi-objective optimization of the streamlined shape has been performed on the final built Kriging model. The adaptive genetic approach with a population number of 200 is adopted. Three thousand generations have been performed in the optimization process. The roulette method is used as the selection operator, while the probabilities of crossover and mutation are set as 0.9 and 0.3, respectively. Figure 12 shows the Pareto set of the two objectives. It can be concluded that the optimal solutions of the objectives are both limited in a small zone, indicating that specific individual in the Pareto set shows no large differences, while all the individuals are better than the initial one. In order to demonstrate the mechanism for aerodynamic performance improvement, a specific individual is chosen randomly in Figure 12 as an example, just as the red spot shows. Figure 10: Schematic drawing of the observation probes in the far field. Figure 9: The grids on the longitudinal section of wake region. The drag coefficient of the whole train and the equivalent continuous SPL for the prototype of EMU1 are 0.314 and 81.93 BBA, respectively, while the objectives in the Pareto set are all more optimal than those of the prototype. Table 4 shows the comparison between the CFD calculations and prediction from the Kriging model. It can be seen that excellent agreement exists between the two approaches. The errors for both objectives are 0.493% and 0.027%, respectively, which can meet the engineering requirement. It can be concluded that the Kriging model built in the present paper could reveal the relationships between the design variables and the objectives. Figure 11: The convergence history of the fitness and the exact value for each variable. Figure 12: The Pareto front based on the drag of the whole train and the equivalent continuous SPL. As shown above, the green one represents the prototype and the orange one represents the optimal shape. Good smoothness can be observed on the shape after optimization. The width of the bottom of the streamline and the shape of the cowcatcher keep unchanged, while the width of the upper part of the streamline decreases and the heights of the nose and the cab window are both lowered. Table 5 shows the variations of the design variables compared to the prototype model. \(W_{1}\) controls the width of the streamline, \(W_{2}\) controls the height of the cab window, \(W_{3}\) controls the height of the nose and \(W_{4}\) controls the width of the drainage. It can be seen that all the design variables get smaller. Table 6 shows the comparison of the objectives before and after optimization. Results reveal that the aerodynamic performance gets improved for the optimal shape. The drag coefficient and the equivalent continuous SPL are reduced by 7.1% and 1.26 dB, respectively. For the optimization of aerodynamic drag, reducing the inviscid drag plays an important role. As seen in Table 3, the inviscid drag is reduced by 17.33%. In order to better understand the aerodynamic performance before and after optimization and investigate on the influence on the specific car by the deformation of streamlined head, the drag coefficients of each carriage before and after optimization are given in Figure 14: