Variable Fidelity Optimization Using a Kriging Based Scaling Function
Shawn Gano, Brian Sanders, John E. Renaud · 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2004
Solving design problems that rely on very complex and computationally expensive cal-culations using standard optimization methods may not be feasible given design cycle time constraints. Variable fidelity methods address this issue by using lower fidelity models and a scaling function to approximate the higher fidelity models in a provably convergent framework. In the past, scaling functions have mainly been either first order multiplica-tive 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 fidelity 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 different methods are theoretically described and then compared using two demonstration problems. The first 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 fidelity function calls required for convergence. The results also indicate the hybrid method is effective.