Radial Basis Function Surrogates for Uncertainty Quantification and Aerodynamic Shape Optimization under Uncertainties

Abstract

This paper investigates the adequacy of radial basis function (RBF)-based models as surrogates in uncertainty quantification (UQ) and CFD shape optimization; for the latter, problems with and without uncertainties are considered. In UQ, these are used to support the Monte Carlo, as well as, the non-intrusive, Gauss Quadrature and regression-based polynomial chaos expansion methods. They are applied to the flow around an isolated airfoil and a wing to quantify uncertainties associated with the constants of the γ−R˜eθt transition model and the surface roughness (in the 3D case); it is demonstrated that the use of the RBF-based surrogates leads to an up to 50% reduction in computational cost, compared with the same UQ method that uses CFD computations. In shape optimization under uncertainties, solved by stochastic search methods, RBF-based surrogates are used to compute statistical moments of the objective function. In applications with geometric uncertainties which are modeled through the Karhunen–Loève technique, the use on an RBF-based surrogate reduces the turnaround time of an evolutionary algorithm by orders of magnitude. In this type of applications, RBF networks are also used to perform mesh displacement for the perturbed geometries.

Keywords

• radial basis functions
• uncertainty quantification
• surrogates
• shape optimization
• design under uncertainties
• evolutionary algorithms