Sensitivity analysis for uncertainty propagation and robust design

Abstract

Three methodologies for uncertainty propagation and robust aerodynamic shape optimization are presented in this paper. These are the perturbation technique based on first and second-order Taylor expansion, the asymptotic expansion based on Laplace integrals and the sparse-grid approach, based on Hermite quadrature integration rules. The up-to fourth-order sensitivity analysis, required for these approaches, with respect to both the uncertain and the shape controlling parameters is presented and the most efficient approach is applied to the robust shape optimization of the transonic flow around a 2D airfoil for minimum drag-to-lift ratio, incorporating uncertainties of the flow conditions. © 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.