Comparing Surrogates for Estimating Aerodynamic Uncertainties of Airfoils

Different surrogate models are compared in terms of their efficiency in estimating statistics of aerodynamic coefficients of the RAE2822 airfoil due to geometric input uncertainties. A comparison with direct integration and polynomial chaos methods is also performed. The aerodynamic coefficients and their partial gradients with respect to the uncertain input parameters are computed with a CFD solver and its adjoint counterpart. Reference statistics are computed in order to quantify the error of the different methods. The efficiency of the different methods is discussed in terms of the error in estimating a statistical quantity as a function of the number of CFD (including adjoint) computations used to construct the surrogate model. The results show that gradient-enhanced surrogate methods achieve better accuracy than direct integration methods for the same computational cost. Sampling techniques are discussed in the context of estimating stochastic quantities used for risk management. While the mean and standard Deviation (used for mean-risk approach) can be efficiently computed by distributing the samples in the input parameter space with its probability density function, the maximum or minimum value (used for worst-case scenario) can be led more accurately by an expected improvement based adaptive sampling technique. This fact indicates that advanced sampling techniques are required for evaluating both the mean risk and worst-case risk at the same time.