Cokriging for robust design optimization

Abstract

This paper addresses the problem of robust design optimization. Such formulations are inevitably multi-objective because the designer wants good performance and also small variations in that performance. The desire for processes that produce robust designs stems from the observation that if only nominal performance is considered during design optimization, sensitive designs often result, and these commonly fail to meet objectives when the inevitable uncertainties of manufacture, operating conditions, and degradation in operation are considered. It is assumed that design is carried out using analysis codes that are expensive to run. Because of this and the need for the multiple calls associated with Monte Carlo methods, use is made of surrogate-based optimization tools to speed up the search. Here, the methodology of cokriging is examined to allow results from using differing numbers of Monte Carlo samples to be simply combined. The primary aim was avoid always having to use large numbers of samples in the Monte Carlo assessment of design robustness. The application of these methods is illustrated by considering a gas-turbine compressor blade optimization, in which a range of shape errors are considered that simulate foreign object damage, erosion damage, and manufacturing errors. Consideration is also given to variation in operating conditions. Copyright © 2012 by Andy J. Keane.