Aerospace designers routinely manipulate shapes in engineering systems toward design goals—e.g., shape optimization of an airfoil. The computational tools for such manipulation include parameterized geometries, where the parameters provide a set of independent variables that control the geometry. Recent work has developed and exploited active sub-spaces in the map from geometry parameters to design quantities of interest (e.g., lift or drag of an airfoil); the active subspace is a set of directions in the geometry parameter space that changes the associated quantity of interest more, on average over the design space, than directions orthogonal to the active subspace. The active directions produce insight-rich geometry perturbations; however, these perturbations depend on the chosen geometry parameterization. In this work, we use tools and concepts from differential geometry to develop parameterization independent active subspaces with respect to a given scalar field (e.g., the pressure field surrounding a turbine blade). The differential geometry setup leads to consistent numerical discretization based on the supporting analysis. We show how the framework can yield insight into the design of an airfoil independent of the choice of engineering parameterization.
展开▼
