Research Article: Multi-Objective Aerodynamic Optimization of the Streamlined Shape of High-Speed Trains Based on the Kriging Model

Date Published: January 27, 2017

Publisher: Public Library of Science

Author(s): Gang Xu, Xifeng Liang, Shuanbao Yao, Dawei Chen, Zhiwei Li, Wen-Bo Du.


Minimizing the aerodynamic drag and the lift of the train coach remains a key issue for high-speed trains. With the development of computing technology and computational fluid dynamics (CFD) in the engineering field, CFD has been successfully applied to the design process of high-speed trains. However, developing a new streamlined shape for high-speed trains with excellent aerodynamic performance requires huge computational costs. Furthermore, relationships between multiple design variables and the aerodynamic loads are seldom obtained. In the present study, the Kriging surrogate model is used to perform a multi-objective optimization of the streamlined shape of high-speed trains, where the drag and the lift of the train coach are the optimization objectives. To improve the prediction accuracy of the Kriging model, the cross-validation method is used to construct the optimal Kriging model. The optimization results show that the two objectives are efficiently optimized, indicating that the optimization strategy used in the present study can greatly improve the optimization efficiency and meet the engineering requirements.

Partial Text

The development of high-speed train technology indicates the level of high-tech development of a country. Currently, high-speed trains in China run very close to the ground or along the track at an actual operating speed of approximately 300 km/h, with a draw ratio that is much larger than the ratios of other means of transportation. At high-speed operation, the trains experience more complex aerodynamic characteristics [1–4]. The aerodynamic drag and lift greatly affect the economy and comfort of running trains. The research and development of high-speed trains has shown that streamlined head shapes are critical for the aerodynamic performance of trains. Streamlined design, especially the streamlined head shape design, of high-speed trains remains an important issue in high-speed train research. The optimum shapes can greatly improve the aerodynamic performance of high-speed trains. The aerodynamic drag, the lift, the lateral wind safety performance, the train crossing performance, the aerodynamic performance when passing through tunnels, the aerodynamic noise, and other factors [5–6] of running trains should be considered when designing high-speed train head shapes. Among these factors, the aerodynamic lift of the tail coach is the key aerodynamic load that affects the comfort and safety of running trains. Therefore, reducing the aerodynamic drag and lift of train coaches is the key issue for optimizing the streamlined head shape design of high-speed trains.

The three-coach marshalling model of the head coach, the middle coach, and the train coach is used to evaluate the head shape aerodynamic performance. The computational model is named EMU1. The model and the computational domain of the three-coach marshalling model EMU1 are shown in Fig 4(a).

When optimization is performed based on the Kriging response surface, the parameters for the genetic algorithm are set to an initial population of 200 and a maximum evolution algebra of 1000. The selection operator applies the roulette wheel method, with a crossover probability of 0.9 and a mutation probability of 0.3.

To reduce the computational times of the flow field and to improve the optimization efficiency, the construction method of the Kriging surrogate model is improved in this study. The traditional maximization of the solution is replaced with the cross-validation method to search for more reasonable model parameters. The final optimization results show that this construction method uses fewer sampling points to complete a Kriging model with a prediction accuracy that satisfies the design requirements. Thus, the optimization design efficiency is improved. A Pareto solution set related to the aerodynamic drag and lift of the train are found in the design space based on the new Kriging model and the multi-objective genetic algorithm. A typical design point is chosen for numerical simulation and compared with the aerodynamic performance of the original EMU1 shape. The drag of the typical design point is reduced by approximately 7.2% compared to the original shape. The lift of the train coach is 15.9% smaller than that of the original shape, indicating that the optimization process is efficient enough to be used for the future aerodynamic shape optimization of high-speed trains.




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