Robust engineering design optimization with non-uniform rational B-splines-based metamodels

Abstract

Non-uniform rational B-splines (NURBs) demonstrate properties that make them attractive as metamodels, or surrogate models, for engineering design purposes. Previous research has resulted in the development of algorithms capable of fitting NURBs-based metamodels to engineering design spaces, and optimizing these models. This article presents an approach to robust optimization that employs NURBs-based metamodels. This robust optimization technique exploits the unique structure of NURBs-based metamodels to derive a simple but effective robustness metric. An algorithm is demonstrated that uses this metric to weigh robustness against optimality, and visualizes the trade-offs between these metamodel properties. This approach is demonstrated with test problems of increasing dimensionality, including several practical design challenges.

Keywords:

• robust design
• NURBs
• metamodels
• splines

Acknowledgements

This research would not have been possible without the support of the National Science Foundation under grant no. CMMI-0900182 and the Colorado School of Mines, College of Engineering and Computer Science. Any opinions, findings and conclusions are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Colorado School of Mines.