Abstract
Modern computers enable methods for design optimization that account for uncertainty in the system—so-called optimization under uncertainty (OUU). We propose a metric for OUU that measures the distance between a designer-specified probability density function of the system response (the target) and the 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 we 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.
Highlights
Modern computing power enables industrial-scale design optimization with high-fidelity numerical simulations of physical systems
We present a metric for optimization under uncertainty formulations
We assume that a designer has provided a target pdf of the system response, and we minimize the distance between the design-dependent response pdf and the given target over possible designs
Summary
Modern computing power enables industrial-scale design optimization with high-fidelity numerical simulations of physical systems. The optimization is often formulated with multiple objective functions (e.g., maximize mean and minimize variance), which leads to a Pareto front of solutions representing a trade-off between robustness and performance. The statistical measures in the RDO and RBDO objective functions and constraints are typically low-order moments – e.g., mean and variance – or probabilities associated with the system response. Compared to other OUU formulations, density-matching is appropriate when the designer is able to specify her desiderata for the uncertain response as a pdf. The density-matching approach finds the design that best matches the designer’s specified pdf, and there is no need to estimate the Pareto front of a multi-objective optimization (as in RDO) or minimize a failure probability (as in RBDO). We qualitatively compare the optimal designs to those generated by a multi-objective RDO strategy
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