Design sensitivity analysis with polynomial chaos for robust optimization

Chengkun Ren, Fenfen Xiong*, Bo Mo, Anik Chawdhury, Fenggang Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Polynomial chaos (PC) methods with Gauss-type quadrature formulae have been widely applied for robust design optimization. During the robust optimization, gradient-based optimization algorithms are commonly employed, where the sensitivities of the mean and variance of the output response with respect to design variables are calculated. For robust optimization with computationally expensive response functions, although the PC method can significantly reduce the computational cost, the direct application of the classical finite difference method for the analysis of the design sensitivity is impractical with a limited computational budget. Therefore, in this paper, a semi-analytical design sensitivity analysis method based on the PC method is proposed, in which the sensitivity is directly derived based on the Gauss-type quadrature formula without additional function evaluations. Comparative studies conducted on several mathematical examples and an aerodynamic robust optimization problem revealed that the proposed method can reduce the computational cost of robust optimization to a certain extent with comparable accuracy compared with the finite difference-based PC method.

Original languageEnglish
Pages (from-to)357-373
Number of pages17
JournalStructural and Multidisciplinary Optimization
Volume63
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • Design sensitivity
  • Gauss-type quadrature
  • Polynomial chaos
  • Robust design optimization

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