Keywords: response surface methodology, multibody systems, design optimization, train crashworthiness.

The increasing demands in passive safety of trains are putting new challenges for the design methodologies. The designers nowadays require not only simulation tools based on complex models, but also simplified simulation tools with optimization procedures that can be used efficiently in the earlier design stages. In this paper, 1D and 2D design tools based on multibody dynamic formulations are used to analyse train structure for well identified collisions scenarios while the optimization process is performed by response surface methods. This optimization approach attempts to find the optimum by use of explicit approximation for the objective and constraint functions until an acceptable accuracy is achieved.

The use of approximation techniques promises to be an effective approach for multibody systems if suitable approximations are used, in addition approximations concepts can combine different simulation tools with different optimization algorithms that work well for predefined explicit functions. There are several response surface models used to approximate system responses, the most commonly used are the polynomial forms. Response surfaces have a tendency to capture globally optimal regions because of their smoothness and global approximation properties which avoids local minima. This methodology is shown to be efficient for optimization problems if the simulation models require high computational costs, because a reduced number of simulations are performed for most of the applications.

The computation and use of these approximations were demonstrated using two examples of train crashworthiness design that represent some of the challenging features of train crashes. The procedure applied is developed in order to optimize several design parameters related to the crash such as the energy distribution along trains, accelerations and deformations of an end-underframe structure.

Response surface methodology, see Myers [1], presents an enormous potential in the field of optimization, as demonstrated by the recent work of Etman [2] in multibody dynamics applications and Marklund [3] in impact dynamics applications. The use of approximation techniques to solve an optimization problem consists in replace the original optimization problem by a sequence of simpler approximate optimization problems that are valid in a sub-region of the design space. In each iteration cycle the original problem is substituted by an approximate problem that uses response surface functions. The solution of an individual sub-region becomes the starting point for the next step and the search sub-region is positioned in the center-point of the previous optimum design. The move limits are changed and the optimization is repeated iteratively until the optimum is reached. For each sub-problem the objective and constraint function values must be evaluated for a limited number of simulations carefully chosen by design of experiments techniques.

1

Myers, R.H., Montgomery, D.C., "Response Surface Methodology : Process and Products Optimization Using Designed Experiments", 2002.

2

Etman, L.P., "Optimization of Multibody Systems using Approximation Concepts", Ph.D. Thesis, Technische Universiteit Eindhoven, 1997.

3

Marklund, P.-O., "Optimization of car Body Component Subjected to Impact", Ph.D. Thesis, Linkoping University, Sweden, 1999.

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