• robust design;
  • optimization;
  • structures;
  • uncertainty;
  • solution space;
  • high-dimensional systems


In some engineering problems, tolerance to variation of design parameters is essential. In an early development phase of a distributed development process for example, the system performance should reach the design goal even under large variations of uncertain component properties. The tolerance to parameter variations may be measured by the size of a solution space on which the system is guaranteed to deliver the required performance. In order to decouple dimensions, the solution space is described as multi-dimensional box with permissible intervals for each design parameter. An algorithm is presented that computes solution spaces for arbitrary non-linear high-dimensional systems. Starting from a design point with required performance, a candidate box is iteratively evaluated and modified. The evaluation is performed by Monte Carlo sampling and Bayesian statistics. The modification algorithm drives the evolution toward increasing box size. Robustness and reliability with respect to the required performance can be assessed without knowledge of the particular kind of uncertainty. Sensitivity to design parameters can be quantified by the widths of solution intervals. Designs failing to meet the performance requirement can be improved by adjusting parameter values to lie within the solution space. The approach is motivated and illustrated by automotive crash design problems. Copyright © 2012 John Wiley & Sons, Ltd.