A density-matching approach for optimization under uncertainty

TL;DR

This paper introduces a density-matching metric for optimization under uncertainty, enabling designers to match system response distributions to target densities, demonstrated through CFD airfoil optimization.

Contribution

It proposes a novel density-matching approach for OUU using a distance metric, Gaussian kernel density estimates, and heuristics, applied to CFD airfoil design.

Findings

Effective in matching response densities to targets

Provides a new perspective compared to multi-objective robust optimization

Applicable to complex CFD-based design problems

Abstract

Modern computers enable methods for design optimization that account for uncertainty in the system---so-called optimization under uncertainty. We propose a metric for OUU that measures the distance between a designer-specified probability density function of the system response the target and system response's density function at a given design. We study an OUU formulation that minimizes this distance metric over all designs. We discretize the objective function with numerical quadrature and approximate the response density function with a Gaussian kernel density estimate. We offer heuristics for addressing issues that arise in this formulation, and we apply the approach to a CFD-based airfoil shape optimization problem. We qualitatively compare the density-matching approach to a multi-objective robust design optimization to gain insight into the method.