Keywords: shape optimization, high-speed train, genetic algorithm, metamodel, Bézier curves.

Over the last ten years travel has increased and according to experts, this vital trend is not going to be reversed in the coming years. More mobility is a problem to which the train can be a proper answer. In particular, high-speed trains are becoming more and more important because of their increasing travel speed and lightness, which make them more efficient. However, new aerodynamic problems are introduced, and a multi-objective optimization problem should be considered. The aim of this research is an aerodynamic optimization of ICE 2 high-speed train in order to reduce its drag coefficient when acting front wind.

For years, aerodynamic optimization has relied on a manual trial-and-error approach when designing or trying to improve design performance, heavily depending on previous analyses. As modern engineering relies ever more on high-fidelity computer simulations, automatic optimization of aerodynamic shapes is proposed here. This method involves the use of genetic algorithms (GAs) as the optimization tool [1]. GAs are a technique that mimic the mechanics of natural evolution. However, the main drawback when using a GA is their need for a large number of evaluations of the objective function. Furthermore, this problem is considerably more important when evaluations are computational cost effective. To remedy this inconvenience, the use of metamodels is proposed here. Metamodels exploit surrogates or approximations of the expensive analysis results obtained from accurate simulation models in order to speed up the optimization process. In this paper all the optimization scheme is introduced, presenting the most relevant elements acting on the process, and introducing feasibility of using GAs to carry out shape optimization for a real high-speed train.

A GA requires codified structures to represent each optimal candidate. Thus, a parameterized design is defined for the nose of a high-speed train. A review of different strategies have been completed, and Bézier curves to build up the section boxes in which the whole body has been divided were considered as the best solution in this case. The ICE 2 train nose was parametrised using thirty one design variables to express the three-dimensional curved shapes of the four section boxes (roof, windshield, hood and underbody). The range of variation for each design variable was defined wide enough to include different geometries in the design space while avoiding unrealistic geometries. Once geometries were defined by its Bézier curves, the body volume was obtained using the CAD software CATIA in the pre-processing step before meshing. Metamodel theory has also been presented.

1

D.E. Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning", Addison Wesley, 1989.

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