Multi-Fidelity Airfoil Shape Optimization with Adaptive Response Prediction
Slawomir Marcin Koziel, Leifur Leifsson · 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2012
In multi-fidelity shape optimization, a computationally cheap surrogate model is used in lieu of the expensive, but accurate, high-fidelity model in an iterative fashion. A fast and reliable surrogate model can be constructed using a physics-based low-fidelity model and a proper correction technique. In this paper, we introduce a novel correction methodology, referred to as adaptive response prediction (ARP). The ARP technique corrects the lowfidelity model response, represented by the airfoil pressure distribution, through suitable horizontal and vertical adjustments. The adjustments are based on the high-fidelity model data at the reference design and “tracking” of the low-fidelity model response changes due to the adjustments of the airfoil geometry in the course of the optimization. In this work, both the high- and low-fidelity models are based on the compressible Euler equations, however, the latter uses a coarser mesh resolution and relaxed flow solver convergence criteria. The trust-region framework is employed to ensure convergence. The results of several numerical examples of transonic airfoil shape optimization demonstrate that, in some cases, ARP performs better than its predecessor, adaptive response correction (ARC), which only exploits horizontal scaling.