Aggressive design: A density-matching approach for optimization under uncertainty

Optimization under uncertainty methodologies -- such as robust design optimization and reliability-based design optimization -- have been applied in a variety of engineering disciplines. These methods typically use multi-objective optimization algorithms, which are computationally expensive and for certain applications may even be prohibitive. Another limitation of these strategies is that they typically utilize the first two statistical moments -- the mean and variance -- and ignore higher-order moments as objective functions that may be critical in influencing design decisions. To address these two issues -- the large computational overhead of multi-objective optimization and the use of higher-order moments -- we propose a new approach for optimization under uncertainty: aggressive design. Aggressive design is a novel approach, which enables the designer to find the optimal design given a specification of the system's behavior under uncertain inputs by solving a single-objective optimization problem. In this paper we present a computational method that finds the design probability density function (pdf) of the response that best matches the desired pdf of the response. Our approach makes use of kernel density estimates to yield a differentiable objective function. We test this method on a linear model problem and the computational design of an airfoil.