Keywords: high-speed train, shape optimization, multi-objective optimization, evolutionary algorithm, computational fluid dynamics, aerodynamic property.

Design of high-speed trains are determined with consideration of various aerodynamic properties such as aerodynamic drag, response to crosswind, tunnel micro-pressure waves, flow-induced car vibrations in tunnels, aerodynamic forces affecting other trains and trackside structures. A shape optimization method for improving each single aerodynamic property has been studied by several researchers. For example, Iida et al. [1] presented the optimum cross-sectional area variation (but not the three-dimensional shape) of the train nose for reducing the tunnel micro-pressure wave. Shinkansen trains have been designed based on their study, because the micro-pressure waves cause an environmental problem which is one of critical issues in Japan. However, few studies of multi-objective optimization have been conducted to satisfy the many requirements simultaneously. Here, a new design technique is proposed for the high-speed trains using a multi-objective evolutionary algorithm to balance the many aerodynamic properties.

An outline of the method is as follows. First, initial values, of the design variables that define the initial train shape, are given randomly. Then the flow field around the train is calculated and the aerodynamic properties are estimated. Next, new possible design variables are set by the evolutionary algorithm, before returning to the flow simulation stage. The process is repeated until the objective functions converge.

The emphasis is on a shape parameterization technique which is a very important aspect of the optimization in the practical application. Higher degrees of flexibility to represent the shapes using fewer parameters are required. In this paper, the cross-sectional shapes are parameterized using third-order B-spline curves, which is one of the most popular approaches for airfoil design. The cross-sectional area is set to be in accordance with the optimum cross-sectional area variation for reducing the tunnel micro-pressure wave. The three-dimensional surface of the train is formed by connecting the cross-sections by a Coons patch. This treatment enables the representation of realistic train shapes with the optimum cross-sectional area variation to reduce the tunnel micro-pressure wave automatically.

As the flow calculation places a heavy burden on computational resources and time, the reduction of these costs is the key to make the optimization feasible. Using a message passing interface, each processor is allocated to each individual in the process of the evolutionary algorithm and the aerodynamic estimations of all individuals are conducted simultaneously.

To show the feasibility of this method, the train shape was optimized with two objective functions: the aerodynamic drag and the aerodynamic forces affecting the other trains. After the evolutionary calculation of the tenth generation with 512 individuals, physically reasonable Pareto solutions were successfully obtained.

1

M. Iida, T. Matsumura, K. Nakatani, T. Fukuda, T. Maeda, "Effective nose shape for reducing tunnel sonic boom", QR of RTRI, 38(4), 206-211, 1997.

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