Chance-Constrained Optimization Approach Based on Density Matching and Active Subspaces

Chance-constrained optimization has recently been receiving much attention from the engineering community. Uncertainties are being incorporated in increasingly large numbers to ensure reliability and robustness. However, the efficiency and accuracy of chance-constrained optimization under multiple uncertainties remains challenging. In this study, a constrained density-matching optimization methodology is established to address these pressing issues in chance-constrained optimization. The methodology employs an alternative objective metric between a designer-given target and system response, enables more uncertainties in design variables and random parameters to be handled, and accommodates multiple chance constraints with an adaptive penalty function. An active subspace identification strategy and a dynamic response surface are given to overcome the curse of uncertainty dimensionality and to guarantee sufficient samples for kernel density estimation in an uncertainty analysis. The efficacy is demonstrated on three optimization examples: a response function problem, a standard NASA test, and a practical application in the conceptual design of a satellite system. Different quadrature points, penalty functions, and target forms are discussed, respectively. The methodology exhibits high accuracy and strong adaptability at considerably reduced computational cost, thus providing a potential template for tackling a wide variety of chance-constrained optimization problems.