Active Subspaces for Shape Optimization

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.