Robust Airfoil Optimization under Inherent and Model-Form Uncertainties using Stochastic Expansions


The objective of this paper was to introduce a computationally efficient approach for robust aerodynamic optimization under aleatory (inherent) and epistemic (model-form) uncertainties using stochastic expansions that are based on Non-Intrusive Polynomial Chaos method. The stochastic surfaces were used as surrogates in the optimization process. To create the surrogates, a combined non-intrusive polynomial chaos expansion approach was utilized, which is a function of both the design and the uncertain variables. In this paper, two stochastic optimization formulations were given: (1) optimization under pure aleatory uncertainty and (2) optimization under mixed (aleatory and epistemic) uncertainty. The formulations were demonstrated for the drag minimization of NACA 4-digit airfoils de-scribed with three geometric design variables over the range of uncertainties at transonic flow conditions. The deterministic CFD simulations were performed to solve steady, 2-D, compressible, turbulent RANS equations. The pure aleatory uncertainty case included the Mach number as the uncertain variable. For the mixed uncertainty case, a k factor which is multiplied with the turbulent eddy-viscosity coefficient is introduced to the problem as the epistemic uncertain variable. The results of both optimization cases confirmed the effectiveness of the robust optimization approach with stochastic expansions by giving the optimum airfoil shape that has the minimum drag over the range of aleatory and epistemic uncertainties. The optimization under pure aleatory uncertainty case required 90deterministic CFD evaluations, whereas the optimization under mixed uncertainty case required 126 CFD evaluations to create the stochastic response surfaces, which show the computational efficiency of the proposed stochastic optimization approach. The stochastic optimization methodology described in this paper is general in the sense that it can be applied to aerodynamic optimization problems that utilize different shape parameterization techniques.

Meeting Name

50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (2012: Jan. 9-12, Nashville, TN)


Mechanical and Aerospace Engineering

Document Type

Article - Conference proceedings

Document Version


File Type





© 2012 American Institute of Aeronautics and Astronautics (AIAA), All rights reserved.

Publication Date

12 Jan 2012

This document is currently not available here.