On the Optimal Decomposition of High-Dimensional Solution Spaces of Complex Systems

Author:

Erschen Stefan1,Duddeck Fabian2,Gerdts Matthias3,Zimmermann Markus1

Affiliation:

1. Vehicle Dynamics, Preliminary Design, BMW Group Research and Innovation Center, Knorrstrasse 147, Munich 80788, Germany e-mail:

2. Computational Mechanics, Technical University of Munich, Arcisstr. 21, Munich 80333, Germany e-mail:

3. Institut für Mathematik and Rechneranwendung, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, Neubiberg, Munich 85577, Germany e-mail:

Abstract

In the early development phase of complex technical systems, uncertainties caused by unknown design restrictions must be considered. In order to avoid premature design decisions, sets of good designs, i.e., designs which satisfy all design goals, are sought rather than one optimal design that may later turn out to be infeasible. A set of good designs is called a solution space and serves as target region for design variables, including those that quantify properties of components or subsystems. Often, the solution space is approximated, e.g., to enable independent development work. Algorithms that approximate the solution space as high-dimensional boxes are available, in which edges represent permissible intervals for single design variables. The box size is maximized to provide large target regions and facilitate design work. As a result of geometrical mismatch, however, boxes typically capture only a small portion of the complete solution space. To reduce this loss of solution space while still enabling independent development work, this paper presents a new approach that optimizes a set of permissible two-dimensional (2D) regions for pairs of design variables, so-called 2D-spaces. Each 2D-space is confined by polygons. The Cartesian product of all 2D-spaces forms a solution space for all design variables. An optimization problem is formulated that maximizes the size of the solution space, and is solved using an interior-point algorithm. The approach is applicable to arbitrary systems with performance measures that can be expressed or approximated as linear functions of their design variables. Its effectiveness is demonstrated in a chassis design problem.

Publisher

ASME International

Subject

Mechanical Engineering,Safety Research,Safety, Risk, Reliability and Quality

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