Journal article
Uncertainty quantification of high‐dimensional complex systems by multiplicative polynomial dimensional decompositions
International journal for numerical methods in engineering, Vol.94(3), pp.221-247
04/20/2013
DOI: 10.1002/nme.4437
Abstract
SUMMARYThe central theme of this paper is multiplicative polynomial dimensional decomposition (PDD) methods for solving high‐dimensional stochastic problems. When a stochastic response is dominantly of multiplicative nature, the standard PDD approximation, predicated on additive function decomposition, may not provide sufficiently accurate probabilistic solutions of a complex system. To circumvent this problem, two multiplicative versions of PDD, referred to as factorized PDD and logarithmic PDD, were developed. Both versions involve a hierarchical, multiplicative decomposition of a multivariate function, a broad range of orthonormal polynomial bases for Fourier‐polynomial expansions of component functions, and a dimension‐reduction or sampling technique for estimating the expansion coefficients. Three numerical problems involving mathematical functions or uncertain dynamic systems were solved to corroborate how and when a multiplicative PDD is more efficient or accurate than the additive PDD. The results show that indeed, both the factorized and logarithmic PDD approximations can effectively exploit the hidden multiplicative structure of a stochastic response when it exists. Since a multiplicative PDD recycles the same component functions of the additive PDD, no additional cost is incurred. Finally, the random eigensolutions of a sport utility vehicle comprising 40 random variables were evaluated, demonstrating the ability of the new methods to solve industrial‐scale problems. Copyright © 2013 John Wiley & Sons, Ltd.
Details
- Title: Subtitle
- Uncertainty quantification of high‐dimensional complex systems by multiplicative polynomial dimensional decompositions
- Creators
- Vaibhav Yadav - The University of IowaSharif Rahman - The University of Iowa
- Resource Type
- Journal article
- Publication Details
- International journal for numerical methods in engineering, Vol.94(3), pp.221-247
- DOI
- 10.1002/nme.4437
- ISSN
- 0029-5981
- eISSN
- 1097-0207
- Number of pages
- 17
- Language
- English
- Date published
- 04/20/2013
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984064574702771
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