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Modern computers enable methods for design optimization that account foruncertainty in the system---so-called optimization under uncertainty. Wepropose a metric for OUU that measures the distance between adesigner-specified probability density function of the system response thetarget and system response's density function at a given design. We study anOUU formulation that minimizes this distance metric over all designs. Wediscretize the objective function with numerical quadrature and approximate theresponse density function with a Gaussian kernel density estimate. We offerheuristics for addressing issues that arise in this formulation, and we applythe approach to a CFD-based airfoil shape optimization problem. Wequalitatively compare the density-matching approach to a multi-objective robustdesign optimization to gain insight into the method.

A density-matching approach for optimization under uncertainty