Active Subspaces for Shape Optimization

Abstract

Aerodynamic shape optimization plays a fundamental role in aircraft design. However, useful parameterizations of shapes for engineering models often result in high-dimensional design spaces which can create challenges for both local and global optimizers. In this paper, we employ an active subspace method (ASM) to discover and exploit low-dimensional, monotonic trends in the quantity of interest as a function of the design variables. The trend enables us to efficiently and effectively find an optimal design in appropriate areas of the design space. We apply this approach to the ONERA-M6 transonic wing, parameterized with 50 Free-Form Deformation (FFD) design variables. Given an initial set of 300 designs, the ASM discovered a low-dimensional linear subspace of the input space that explained the majority of the variability in the drag and lift coefficients. This revealed a global trend that we exploited to find an optimal design with reduced computational cost.

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Advances in Bayesian Optimization with Applications in Aerospace Engineering

“…39,40 In particular gradient-enhanced Kriging (GEK) 41,14,42,43 has been developed in the context of optimization. 44,45 Previous works focused on the expected improvement utility function. 10,46,47,48 In the following, we present an extension of the Knowledge Gradient (KG) utility function 49 that incorporates sensitivity information.…”

Aerodynamic Shape Design by Evolutionary Optimization and Support Vector Machines

“…In addition, Koziel and Leifsson [4] applied a shape optimization strategy using variable-fidelity CFD models to the optimization of a transonic airfoil parameterized by the NACA four-digit definition with three design variables. The work in [5] employs an active subspace method for effectively searching the design space in the optimization of the ONERA M6 transonic wing, parameterized with 50 Free-Form Deformation (FFD) design variables. In [6,7] a surrogate based on Proper Orthogonal Decomposition (POD) is applied to the aerodynamic shape optimization of an airfoil geometry parameterized by 16 design variables defined with Class Shape Transformation (CST) method.…”