Surrogate-based robust airfoil design under aleatory operating-conditions and geometric uncertainties

In this paper, efficient robust design optimization methods are studied, under the uncertainties of aleatory flight conditions and geometry shapes. Three different uncertainty propagation methods, namely inexpensive Monte Carlo (IMC) simulation, kernel density estimation (KDE) and reduced integral (RI) method, are developed and implemented. For IMC and KDE methods, design of experiments (DoE) is used to sample the uncertain variables and the sample points are evaluated by computational fluid dynamics (CFD) simulations. Then surrogate models are built, and the uncertainties can be propagated through these surrogate models, instead of CFD code itself. In turn, the efficiency of calculating mean and variance of the objective functions or constraints is dramatically improved. The RI method gives mean and variance via a weighted sum of fewer samples, instead of conventional integral from probability distribution function (PDF) which needs large number of samples. Three robust aerodynamic design cases, under uncertain Mach number, uncertain Mach number and angle of attack, uncertain geometry shapes, are considered respectively. The objective is to reduce the weighted sum of mean drag coefficient and its variance, subject to the constraints of mean lift, mean pitching moment and airfoil area. A surrogate-based optimizer, “SurroOpt”, is used to solve this constrained optimization problem. Remarkable difference in aerodynamic characteristics can be observed between the results of robust design and deterministic design. The optimal robust designs exhibit low sensitivity to uncertainties. while keeping a low-level of drag coefficient. The RI method demonstrates the highest efficiency with sufficient accuracy while IMC and KDE have comparable performance.