Robust Airfoil Optimization and the Importance of Appropriately Representing Uncertainty

Abstract

The importance of designing airfoils to be robust with respect to uncertainties in operating conditions is well recognized. However, often, the probability distribution of such uncertainties does not exist or is unknown, and a designer looking to perform a robust optimization is tasked with deciding how to represent these uncertainties within the optimization framework. This paper asks the following: “How important is the choice of how to represent input uncertainties mathematically in robust airfoil optimization?” It specifically compares probabilistically based aleatory uncertainties and interval-based epistemic uncertainties. This is first investigated by considering optimizations on several algebraic test problems, which illustrate the mechanisms by which the representation of uncertainty becomes significant in a robust optimization. This insight is then used to predict and subsequently demonstrate that, for two airfoil design problems, the advantage of doing a robust optimization over a deterministic optimization is similar, regardless of how the input uncertainties are represented mathematically. The benefit of this is potentially eliminating the time required to establish an accurate representation of the uncertainties from the preliminary stage of design, where time is a valuable resource.

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