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 "how important is the choice of how to represent input uncertainties mathematically in robust airfoil optimization?", specifically comparing 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.

Optimization Using Multiple Dominance Criteria for Aerospace Design Under Uncertainty

“…Robust airfoil shape optimization is a practical aerospace design problem that has been considered multiple times in the literature. Existing studies show that a lift-to-drag ratio optimization subject to uncertain Mach number gives a Pareto front with a large trade off between statistical moments [35,4,7,18,8]. From the results of such studies, we expect that many of the designs on the Pareto front for such a problem will be stochastically dominated, and so expect to see improved results using both Pareto dominance and FSD in out proposed formulation.…”

Toward the feasible solution of a long-lasting dynamic similitude problem

“…Airfoil geometry parametrization can be performed in various ways, Ref. 42 used Hicks–Henne bump functions at different chord locations. Non-uniform rational B-Splines have been used for airfoil shape parametrization.…”

Selecting Technologies in Aircraft Conceptual Design Using Probabilistic Inversion

“…Many design queries can be answered with optimization approaches. When including uncertainty, one can use either robust design optimization or reliability-based design optimization [1][2][3]. These approaches usually convert a probability distribution into scalar measures like mean and variance.…”

“…1 shows it is adopted here as well. However, an alleviating remark is made by Cook and Jarrett [2], who address the question of "How important is the choice of how to represent input uncertainties mathematically in robust airfoil optimization?" as an example of what effect the specific choice of uncertainty distribution has on the outcome.…”