Uncertainty-based design optimization approach based on cumulative distribution matching

• Published in: Structural and multidisciplinary optimization Vol. 60; no. 4; pp. 1571 - 1582
• Main Authors: Hu, Xingzhi, Chen, Xiaoqian, Parks, Geoffrey T., Tong, Fulin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019; Springer Nature B.V
• Subjects: Aerospace engineering; Computational Mathematics and Numerical Analysis; Computer simulation; Design optimization; Distribution functions; Engineering; Engineering Design; Matching; Numerical analysis; Probability density functions; Research Paper; Response functions; Robustness (mathematics); Subspaces; System reliability; Systems design; Theoretical and Applied Mechanics; Uncertainty analysis; Uncertainty-based design optimization; Density/distribution matching; Uncertainty analysis; Reduced subspace; Cumulative distribution function
• DOI: 10.1007/s00158-019-02286-8
• ISSN: 1615-147X

Uncertainty-based design optimization (UBDO) is becoming increasingly important with great attention to critical system reliability and robustness. However, most traditional UBDO methods only consider low-order response moments and a limited number of aleatory uncertainties, which desiderates to be resolved. In this study, an efficient UBDO approach based on cumulative distribution matching is presented to address all response moments under mixed aleatory and epistemic uncertainties. The mathematical formulation of cumulative distribution function (CDF) matching is systematically derived including the distance metric definition and numerical computation process. Uncertainty analysis within the CDF matching optimization loop is also investigated, including the identification of active subspaces and the propagation of constructed surrogate model in reduced dimensions. Extended active subspaces are furthered discussed for mixed uncertainty analysis to obtain the bounds of CDF efficiently, instead of the time-consuming full-dimensional simulation. The proposed approach is illustrated by three typical optimization examples, i.e., response function matching, standard NASA test problem, and satellite system design in aerospace engineering. The UBDO results based on the CDF matching are discussed and compared with the probability density function matching, which exhibits higher efficiency and better convergence in tackling constrained optimization design problems subject to mixed uncertainties.