Structural uncertainty analysis with the multiplicative dimensional reduction–based polynomial chaos expansion approach

This paper presents an efficient polynomial chaos expansion approach for structural uncertainty analysis in conjunction with the multiplicative dimensional reduction method. The development of a standard polynomial chaos expansion model needs to evaluate a large number of multivariate integrals for...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2021-10, Vol.64 (4), p.2409-2427
Main Authors: Zhang, Xufang, Pandey, Mahesh D., Luo, Haoyang
Format: Article
Language:English
Subjects:
Algorithms
Bivariate analysis
Computational Mathematics and Numerical Analysis
Design optimization
Engineering
Engineering Design
Monte Carlo simulation
Multivariate analysis
Polynomials
Quadratures
Reduction
Reliability engineering
Research Paper
Structural reliability
Theoretical and Applied Mechanics
Thermal expansion
Uncertainty analysis
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Summary:This paper presents an efficient polynomial chaos expansion approach for structural uncertainty analysis in conjunction with the multiplicative dimensional reduction method. The development of a standard polynomial chaos expansion model needs to evaluate a large number of multivariate integrals for the expansion coefficient. The utility of the multiplicative dimensional reduction approach is able to approximate the multivariate integral as the product of univariate and bivariate expectations. Together with the standard Gauss-quadrature scheme for accurate low-variate integration results, an effective polynomial chaos expansion model is proposed to mimic the true performance function for structural uncertainty analysis. Since only dimensionally reduced univariate and bivariate component functions are involved, the proposed algorithm is able to overcome the curse of dimensionality problem in the ordinary polynomial chaos expansion procedure. Engineering applications of the proposed approach are demonstrated by several structural reliability and reliability-based design optimization problems in the literature. Compared to benchmark results provided by the brutal force Monte Carlo simulation, the high accuracy and efficiency of the multiplicative dimensional reduction–based polynomial chaos expansion algorithm have justified its potential applications for various structural uncertainty problems.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-021-02996-y