Robust Airfoil Optimization Using Maximum Expected Value and Expected Maximum Value Approaches

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Deterministic engineering design often leads to unexpected or physically unrealizable results. This is due to the fact that deterministic design is not able to capture the effects of even slight natural fluctuations of parameters. Deterministic transonic shape optimization is no exception: deterministic designs can result in dramatically inferior performance when the actual operating conditions are different from the design conditions used during a deterministic optimization procedure. The goal of this paper is to overcome the off-design performance degradation of deterministic transonic shape optimization by using two different optimization approaches to produce robust designs. Two criteria, the well-known maximum/minimum expected value criterion (MEV) and the alternative expected maximum/minimum value criterion (EMV), are studied and applied to improve an initial RAE 2822 design. It turns out that EMV is much easier to implement than MEV, given a deterministic optimization code, and may provide a promising method for optimizing design shapes under uncertainty.