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A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM

Chenfeng Li Orcid Logo, Yuntian Feng Orcid Logo, Roger Owen Orcid Logo, D. F. Li, Ian Davies

International Journal for Numerical Methods in Engineering, Volume: 73, Issue: 13, Pages: 1942 - 1965

Swansea University Authors: Chenfeng Li Orcid Logo, Yuntian Feng Orcid Logo, Roger Owen Orcid Logo, Ian Davies

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DOI (Published version): 10.1002/nme.2160

Abstract

In the numerical modelling of a physical system involving random media, the firstkey step is usually to represent, with a finite set of deterministic primary functions andrandom variables, the associated stochastic field (e.g. random Young’s modulus andrandom Poisson’s ratio) which is often defined...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2008
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URI: https://cronfa.swan.ac.uk/Record/cronfa12322
first_indexed 2013-07-23T12:07:50Z
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spelling 2022-12-07T16:32:29.8732775 v2 12322 2012-08-09 A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false d66794f9c1357969a5badf654f960275 0000-0002-6396-8698 Yuntian Feng Yuntian Feng true false 0303b9485caf6fbc8787397a5d926d1c 0000-0003-2471-0544 Roger Owen Roger Owen true false 3eddb437f814b8134d644309f8b5693c Ian Davies Ian Davies true false 2012-08-09 ACEM In the numerical modelling of a physical system involving random media, the firstkey step is usually to represent, with a finite set of deterministic primary functions andrandom variables, the associated stochastic field (e.g. random Young’s modulus andrandom Poisson’s ratio) which is often defined by its statistical moments. In this paper,an efficient and accurate method is presented to represent a stochastic field given by itsexpectation and covariance functions. Based on the Karhunen-Loève expansion, thismethod represents stochastic fields in terms of multiple Fourier series and a vector ofmutually uncorrelated random variables. The result can be treated as a semi-analyticsolution of the Karhunen-Loève expansion, which is achieved by minimizing themean-squared error of the characteristic equation and solving a standard algebraiceigenvalue problem. To verify the proposed method, exponential covariance functionswith exact Karhunen-Loève expansion solutions are employed and good agreementsare observed on both eigenvalues and eigenfunctions. Representations of stochasticfields with Gaussian covariance functions are also performed to demonstrate theeffectiveness and robustness. As no meshing is required in this method, its efficiencyand accuracy are not sensitive to the dimensions or the correlation distance of thestochastic field under consideration. Journal Article International Journal for Numerical Methods in Engineering 73 13 1942 1965 Wiley 0029-5981 1097-0207 26 3 2008 2008-03-26 10.1002/nme.2160 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2022-12-07T16:32:29.8732775 2012-08-09T11:56:20.6369259 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Chenfeng Li 0000-0003-0441-211X 1 Yuntian Feng 0000-0002-6396-8698 2 Roger Owen 0000-0003-2471-0544 3 D. F. Li 4 Ian Davies 5
title A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM
spellingShingle A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM
Chenfeng Li
Yuntian Feng
Roger Owen
Ian Davies
title_short A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM
title_full A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM
title_fullStr A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM
title_full_unstemmed A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM
title_sort A Fourier-Karhunen-Loève discretization scheme for stationary random material properties in SFEM
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
d66794f9c1357969a5badf654f960275
0303b9485caf6fbc8787397a5d926d1c
3eddb437f814b8134d644309f8b5693c
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
d66794f9c1357969a5badf654f960275_***_Yuntian Feng
0303b9485caf6fbc8787397a5d926d1c_***_Roger Owen
3eddb437f814b8134d644309f8b5693c_***_Ian Davies
author Chenfeng Li
Yuntian Feng
Roger Owen
Ian Davies
author2 Chenfeng Li
Yuntian Feng
Roger Owen
D. F. Li
Ian Davies
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 73
container_issue 13
container_start_page 1942
publishDate 2008
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.2160
publisher Wiley
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 0
active_str 0
description In the numerical modelling of a physical system involving random media, the firstkey step is usually to represent, with a finite set of deterministic primary functions andrandom variables, the associated stochastic field (e.g. random Young’s modulus andrandom Poisson’s ratio) which is often defined by its statistical moments. In this paper,an efficient and accurate method is presented to represent a stochastic field given by itsexpectation and covariance functions. Based on the Karhunen-Loève expansion, thismethod represents stochastic fields in terms of multiple Fourier series and a vector ofmutually uncorrelated random variables. The result can be treated as a semi-analyticsolution of the Karhunen-Loève expansion, which is achieved by minimizing themean-squared error of the characteristic equation and solving a standard algebraiceigenvalue problem. To verify the proposed method, exponential covariance functionswith exact Karhunen-Loève expansion solutions are employed and good agreementsare observed on both eigenvalues and eigenfunctions. Representations of stochasticfields with Gaussian covariance functions are also performed to demonstrate theeffectiveness and robustness. As no meshing is required in this method, its efficiencyand accuracy are not sensitive to the dimensions or the correlation distance of thestochastic field under consideration.
published_date 2008-03-26T12:23:53Z
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score 11.102871

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