Neumann enriched polynomial chaos approach for stochastic finite element problems

Pryse, Eilir; Adhikari, Sondipon

doi:10.1016/j.probengmech.2021.103157

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Neumann enriched polynomial chaos approach for stochastic finite element problems

Eilir Pryse, Sondipon Adhikari

Probabilistic Engineering Mechanics, Volume: 66, Start page: 103157

Swansea University Authors: Eilir Pryse, Sondipon Adhikari

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DOI (Published version): 10.1016/j.probengmech.2021.103157

Abstract

An enrichment scheme based upon the Neumann expansion method is proposed to augment the deterministic coefficient vectors associated with the polynomial chaos expansion method. The proposed approach relies upon a split of the random variables into two statistically independent sets. The principal va...

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Published in:	Probabilistic Engineering Mechanics
ISSN:	0266-8920
Published:	Elsevier BV 2021
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa57433
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first_indexed	2021-07-22T07:47:01Z
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spelling	2021-08-19T16:35:33.2538164 v2 57433 2021-07-22 Neumann enriched polynomial chaos approach for stochastic finite element problems ae581a15681d3dc1b3a96a7b904e9ef9 Eilir Pryse Eilir Pryse true false 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2021-07-22 FGSEN An enrichment scheme based upon the Neumann expansion method is proposed to augment the deterministic coefficient vectors associated with the polynomial chaos expansion method. The proposed approach relies upon a split of the random variables into two statistically independent sets. The principal variability of the system is captured by propagating a limited number of random variables through a low-ordered polynomial chaos expansion method. The remaining random variables are propagated by a Neumann expansion method. In turn, the random variables associated with the Neumann expansion method are utilised to enrich the polynomial chaos approach. The effect of this enrichment is explicitly captured in a new augmented definition of the coefficients of the polynomial chaos expansion. This approach allows one to consider a larger number of random variables within the scope of spectral stochastic finite element analysis in a computationally efficient manner. Closed-form expressions for the first two response moments are provided. The proposed enrichment method is used to analyse two numerical examples: the bending of a cantilever beam and the flow through porous media. Both systems contain distributed stochastic properties. The results are compared with those obtained using direct Monte Carlo simulations and using the classical polynomial chaos expansion approach. Journal Article Probabilistic Engineering Mechanics 66 103157 Elsevier BV 0266-8920 Polynomial chaos expansion, Neumann expansion, Model reduction, Uncertainty quantification, Enrichment 1 10 2021 2021-10-01 10.1016/j.probengmech.2021.103157 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-08-19T16:35:33.2538164 2021-07-22T08:44:13.3051549 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Eilir Pryse 1 Sondipon Adhikari 2 57433__20440__dbca9c5626bd42d59a7e9c1c8d9d589b.pdf 57433.pdf 2021-07-22T08:46:01.9969931 Output 1075062 application/pdf Accepted Manuscript true 2022-07-19T00:00:00.0000000 ©2021 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title	Neumann enriched polynomial chaos approach for stochastic finite element problems
spellingShingle	Neumann enriched polynomial chaos approach for stochastic finite element problems Eilir Pryse Sondipon Adhikari
title_short	Neumann enriched polynomial chaos approach for stochastic finite element problems
title_full	Neumann enriched polynomial chaos approach for stochastic finite element problems
title_fullStr	Neumann enriched polynomial chaos approach for stochastic finite element problems
title_full_unstemmed	Neumann enriched polynomial chaos approach for stochastic finite element problems
title_sort	Neumann enriched polynomial chaos approach for stochastic finite element problems
author_id_str_mv	ae581a15681d3dc1b3a96a7b904e9ef9 4ea84d67c4e414f5ccbd7593a40f04d3
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author	Eilir Pryse Sondipon Adhikari
author2	Eilir Pryse Sondipon Adhikari
format	Journal article
container_title	Probabilistic Engineering Mechanics
container_volume	66
container_start_page	103157
publishDate	2021
institution	Swansea University
issn	0266-8920
doi_str_mv	10.1016/j.probengmech.2021.103157
publisher	Elsevier BV
college_str	Faculty of Science and Engineering
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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	1
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description	An enrichment scheme based upon the Neumann expansion method is proposed to augment the deterministic coefficient vectors associated with the polynomial chaos expansion method. The proposed approach relies upon a split of the random variables into two statistically independent sets. The principal variability of the system is captured by propagating a limited number of random variables through a low-ordered polynomial chaos expansion method. The remaining random variables are propagated by a Neumann expansion method. In turn, the random variables associated with the Neumann expansion method are utilised to enrich the polynomial chaos approach. The effect of this enrichment is explicitly captured in a new augmented definition of the coefficients of the polynomial chaos expansion. This approach allows one to consider a larger number of random variables within the scope of spectral stochastic finite element analysis in a computationally efficient manner. Closed-form expressions for the first two response moments are provided. The proposed enrichment method is used to analyse two numerical examples: the bending of a cantilever beam and the flow through porous media. Both systems contain distributed stochastic properties. The results are compared with those obtained using direct Monte Carlo simulations and using the classical polynomial chaos expansion approach.
published_date	2021-10-01T04:13:10Z
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Neumann enriched polynomial chaos approach for stochastic finite element problems

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