Variable Fidelity Optimization Using a Kriging Based Scaling Function

Abstract

Solving design problems that rely on very complex and computationally expensive calculations using standard optimization methods may not be feasible given design cycle time constraints. Variable fldelity methods address this issue by using lower fldelity models and a scaling function to approximate the higher fldelity models in a provably convergent framework. In the past, scaling functions have mainly been either flrst order multiplicative or additive corrections; recently these have been extended to second order. In this work a kriging based scaling function is introduced to better approximate the high fldelity response on a more global level. An adaptive hybrid method is also studied. It combines the additive and multiplicative approaches so that the designer doesn’t have to determine which is better before optimization. The difierent methods are theoretically described and then compared using two demonstration problems. The flrst problem is analytic, while the other is a design of a supercritical high-lift airfoil. The results show that the warm-started kriging based scaling methods have the potential to improve computational expense by lowering the number of high fldelity function calls required for convergence. The results also indicate the hybrid method is efiective.