Comparison of Uncertainty Quantification Approaches in a Supersonic Biplane Airfoil Problem

Abstract

In this paper, uncertainty quantification approaches are compared quantitatively in an aerodynamic uncertainty quantification problem for a 2D supersonic biplane airfoil. Three advanced uncertainty quantification approaches are compared: an inexpensive Monte-Carlo simulation approach using a Kriging response surface model, an intrusive polynomial chaos approach, and a point collocation non-intrusive polynomial chaos approach. Two-dimensional inviscid compressible flow around the supersonic biplane airfoil is considered with an uncertainty of the freestream Mach number as a normal distribution. A choking phenomenon occurs in this problem setting, which gives discontinuous changes in aerodynamic performance with fluctuation of the freestream Mach number. The accuracies and characteristics of the three uncertainty quantification approaches are investigated. The inexpensive Monte-Carlo simulation approach shows the best performance with larger numbers of sample points in this study. The results of the non-intrusive polynomial chaos approach are sensitive to sampling strategies. Although the intrusive polynomial chaos approach is applied only with lower orders of polynomial chaos, it shows comparable accuracy with the other two approaches from the viewpoint of model accuracy when weighted at the center region of the uncertain input space.