Adaptive Shape Control for Aerodynamic Design

Abstract

We present an approach to aerodynamic optimization in which the shape control is adaptively parameterized. Starting from a coarse set of design variables, a sequence of higher-dimensional nested search spaces is automatically generated. Refinement can be either uniform or adaptive, in which case only the most important shape control is added. The relative importance of candidate design variables is determined by comparing objective and constraint gradients, computed at low cost via adjoint solutions. A search procedure for finding an effective ensemble of shape parameters is also given. We first demonstrate this system on a multipoint drag miminization problem in 2D with many constraints, showing that an adaptive parameterization approach consistently achieves smoother, more robust, and faster design improvement than fixed parameterizations. We also establish a 3D shapematching benchmark, where we demonstrate that our approach automatically discovers the necessary parameters to match a target shape. By largely automating shape parameterization, this work also aims to remove a time-consuming aspect of shape optimization.

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

“…If refinement is triggered too early the underexploitation of design space can result in slower convergence and possibly a poorer final result, and if it is triggered too late, over-exploitation of the design space can waste resources. A method for approximating the optimum refinement time was proposed by Anderson 27 where refinement was triggered when the convergence of the objective function with respect to the iterations dropped below some proportion t < 1 of the maximum attained. A slightly modified version of this is implemented in this work.…”

“…This approach was first used in an aerodynamic optimisation setting by Beux and Dervieux 18 and has since been applied to a range of aerofoil optimisation problems using a variety of different parameterisation frameworks such as Bèzier curves [19][20][21][22] , Bèzier surface FFD [23][24][25][26] , RBFs 27 and B-splines with a knot insertion algorithm 28,29 . In general, it was shown that implementation of multi-level nested parameterisations can improve the convergence rate, robustness and final solution of an optimisation procedure.…”

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

“…If refinement is triggered too early the underexploitation of design space can result in slower convergence and possibly a poorer final result, and if it is triggered too late, over-exploitation of the design space can waste resources. A methods for approximating the optimum refinement time was proposed by Anderson [27] where refinement was triggered when the convergence of the objective function with respect to the iterations dropped below some proportion t < 1 of the maximum attained. A slightly modified version of this is implemented in this work.…”

“…This approach is akin to a multi-grid method for parameterisation and was first used in an aerodynamic optimisation setting by Beux and Dervieux [18]. It has since been applied to a range of aerofoil optimisation problems using a variety of different parameterisation frameworks such as Bèzier curves [19,20,21,22], Bèzier surface FFD [23,24,25,26], RBFs [27] and B-Splines with a knot insertion algorithm [28,29]. In general, they have shown that implementation of progressive nested parameterisations can improve the convergence rate, robustness and final solution of an optimisation procedure.…”

Three-Dimensional Subdivision Parameterisation for Aerodynamic Shape Optimisation

“…This approach is akin to a multi-grid method for parameterisation and was first used in an aerodynamic optimisation setting by Beux and Dervieux 6 . It has since been applied to a range of aerofoil optimisation problems using a variety of different parameterisation frameworks such as Bèzier curves [7][8][9][10] , Bèzier surface FFD [11][12][13][14] , RBFs 15 and B-Splines with a knot insertion algorithm 16,17 .…”