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Efficient Detection of Permissible Design Spaces in an Early Design Stage

The design process in engineering takes place for a high-dimensional input space with few result parameters. The calculation of these result parameters is due to the corresponding nonlinear deterministic simulation time-consuming. Limited resources force the development of efficient surrogate models. The design process could be done by different procedures e.g., investigation of different variants, optimization methods or the solution of the inverse problem. The design is characterized by constraints for the parameters which have to be fulfilled. The resulting design should be safe, robust, efficient, sustainable and versatile and should always satisfy the constraints. This contribution presents an efficient method for numerical assessment of high-dimensional datasets which is assigned to the solution of inverse problems. The method enables the possibility to analyse datasets and helps to understand the associated model behaviour. The method is divided into three parts. First of all it is necessary to analyse the input space of the existing dataset with the help of cluster methods. The application of these methods provides the detection of independent possible design spaces. Due to unknown assumptions for the cluster analysis, it is necessary to investigate more than one cluster configuration. The second step is to evaluate each single cluster configuration. Therefore different measures are presented. The “best” cluster configurations are the initial points for the third step, the description of the single clusters. This description could be done by hypercubes, or with regard to interaction. For hybercubes the aim is to find ranges for each input dimension which contains only permissible solutions. This calculation is an optimization task; the objective could be the maximization of the volume or the smallest range. The applicability of the proceeding is demonstrated by an example from the field of automotive design. An outlook shows possibilities to take uncertainties of the input variables into account.