Adaptive Shape Control for Aerodynamic Design

We present an approach to aerodynamic optimization in which the shape parameterization is progessively and automatically refined. The process consists of an alternating sequence of optimizing within the current search space, and then refining the parameterization to enable the discovery of superior designs. We show that this approach reduces computational cost by optimizing in search spaces of appropriate dimensionality. By automating time-consuming aspects of shape control refinement, it also reduces human cost and dependence on designer expertise. In addition to uniform shape control refinement, we also discuss adaptive refinement, where the goal is to selectively add only the shape control with the most potential to improve the aerodynamic performance. Potential design improvement is estimated by comparing local objective and constraint gradients, which are computed at low cost by reusing existing adjoint solutions. A priority queue of the most effective candidate shape parameters is then maintained using an efficient constructive search procedure. We first demonstrate adaptive shape control on an multipoint airfoil drag miminization problem with many constraints, where our system achieves equivalent design improvement to a fine, fixed parameterization, but in one-third of the wall-clock time. We also establish a 3D shape-matching benchmark, in which our system automatically discovers the shape parameters necessary to match a target shape. This approach is an important step towards greater automation in solving the unfamiliar aerodynamic shape design problems of the future.