Robust design optimization under dependent random variables by a generalized polynomial chaos expansion

New computational methods are proposed for robust design optimization (RDO) of complex engineering systems subject to input random variables with arbitrary, dependent probability distributions. The methods are built on a generalized polynomial chaos expansion (GPCE) for determining the second-moment...

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Bibliographic Details
Published inStructural and multidisciplinary optimization Vol. 63; no. 5; pp. 2425 - 2457
Main Authors Lee, Dongjin, Rahman, Sharif
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2021
Springer Nature B.V
Subjects
Algorithms
Computational Mathematics and Numerical Analysis
Dependent variables
Design analysis
Design optimization
Design standards
Engineering
Engineering Design
Polynomials
Random variables
Research Paper
Robust design
Sensitivity analysis
Shape optimization
Statistical analysis
Steering
Theoretical and Applied Mechanics
Design sensitivity analysis
Second-moment analysis
GPCE
RDO
Stochastic optimization
Score functions
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Summary:New computational methods are proposed for robust design optimization (RDO) of complex engineering systems subject to input random variables with arbitrary, dependent probability distributions. The methods are built on a generalized polynomial chaos expansion (GPCE) for determining the second-moment statistics of a general output function of dependent input random variables, an innovative coupling between GPCE and score functions for calculating the second-moment sensitivities with respect to the design variables, and a standard gradient-based optimization algorithm, establishing direct GPCE, single-step GPCE, and multi-point single-step GPCE design processes. New analytical formulae are unveiled for design sensitivity analysis that is synchronously performed with statistical moment analysis. Numerical results confirm that the proposed methods yield not only accurate but also computationally efficient optimal solutions of several mathematical and simple RDO problems. Finally, the success of conducting stochastic shape optimization of a steering knuckle demonstrates the power of the multi-point single-step GPCE method in solving industrial-scale engineering problems.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-020-02820-z