Design exploration and optimization under uncertainty

Computational strategies that explicitly quantify uncertainties are becoming increasingly used in aerospace applications to improve the consistency in reliability, robustness, and performance of designs. A major source of uncertainty in simulations is due to the structural assumptions invoked in the formulation of turbulence models. Accounting for the turbulence model-form uncertainty has been described as the greatest challenge in simulation-based engineering design. Despite its importance, design exploration and optimization under turbulence model-form uncertainty is an avenue that has not been investigated in depth in prior literature. In this investigation, we outline methodologies for the design analysis, exploration, and robust optimization under model-form uncertainty due to Reynolds averaged Navier-Stokes models. We exhibit how interval uncertainty estimates enable the use of alternative criteria for decision making under uncertainty in engineering design. It is shown that such criteria can lead to different design choices in design exploration. Finally, we carry out design optimization under mixed uncertainties by using the perturbation framework in conjunction with polynomial chaos expansions. We introduce an approach for engineering design optimization under uncertainty that utilizes physics-based uncertainty estimation along with decision theory criteria under uncertainty to produce designs that are more robust to turbulence model uncertainties. These methodologies are illustrated via their application to complex turbulent flow cases, pertinent to aerospace design applications.