Global optimization of benchmark aerodynamic cases using physics-based surrogate models

Abstract

The paper proposes the combination of physics-based surrogate models, adaptive sampling of the design space and evolutionary optimization towards the solution of aerodynamic design problems. The Proper Orthogonal Decomposition is used to extract the main features of the flow field and Radial Basis Function networks allow the surrogate model to predict the target response over the entire design space. In order to train accurate and usable surrogates, ad hoc in-fill criteria are provided which smartly rank and select new samples to enrich the model database. The solution of two aerodynamic benchmark problems is proposed within the framework of the AIAA Aerodynamic Design Optimization Discussion Group. The two benchmark problems consist respectively in the drag minimization of the RAE 2822 airfoil in transonic viscous flow and of the NACA 0012 airfoil in transonic inviscid flow. The shape parameterization approach is based on the Class-Shape Transformation (CST) method with a sufficient degree of Bernstein polynomials to cover a wide range of shapes. Mesh convergence is demonstrated on single-block C-grid structured meshes. The in-house ZEN flow solver is used for Euler/RANS aerodynamic solution. Results show that, thanks to the combined usage of surrogate models and adaptive training in an evolutionary optimization framework, optimal candidates may be located even with limited computational resources with respect to plain evolutionary approaches and similar standard methodologies.