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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

  • Accepted Manuscript under embargo until: 19th July 2022

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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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 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.
Keywords: Polynomial chaos expansion, Neumann expansion, Model reduction, Uncertainty quantification, Enrichment
College: College of Engineering
Start Page: 103157