An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty

Yin, S; Yu, D; Luo, Z; Xia, B

An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty

Yin, S Yu, D Luo, Z

Xia, B

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Publication Type:: Journal Article
Citation:: Computer Methods in Applied Mechanics and Engineering, 2018, 332 pp. 280 - 302
Issue Date:: 2018-04-15

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Field	Value	Language
dc.contributor.author	Yin, S	en_US
dc.contributor.author	Yu, D	en_US
dc.contributor.author	Luo, Z https://orcid.org/0000-0002-6953-3986	en_US
dc.contributor.author	Xia, B	en_US
dc.date.issued	2018-04-15	en_US
dc.identifier.citation	Computer Methods in Applied Mechanics and Engineering, 2018, 332 pp. 280 - 302	en_US
dc.identifier.issn	0045-7825	en_US
dc.identifier.uri	http://hdl.handle.net/10453/129722
dc.description.abstract	© 2017 Elsevier B.V. By introducing the arbitrary polynomial chaos theory, the Evidence-Theory-based Arbitrary Polynomial Chaos Expansion Method (ETAPCEM) is proposed to improve the computational accuracy of polynomial chaos expansion methods for the evidence-theory-based analysis of acoustic systems with epistemic uncertainty. In ETAPCEM, the epistemic uncertainty of acoustic systems is treated with evidence theory. The response of acoustic systems in the range of variation of evidence variables is approximated by the arbitrary polynomial chaos expansion, through which the lower and upper bounds of the response over all focal elements can be efficiently calculated by a number of numerical solvers. Inspired by the application of polynomial chaos theory in the interval and random analysis, the weight function of the optimal polynomial basis of ETAPCEM for evidence-theory-based uncertainty analysis is derived from the uniformity approach. Compared with the conventional evidence-theory-based polynomial chaos expansion methods, including the recently proposed evidence-theory-based Jacobi expansion method, the main advantage of ETAPCEM is that the polynomial basis orthogonalized with arbitrary weight functions can be obtained to construct the polynomial chaos expansion. Thereby the optimal polynomial basis of polynomial chaos expansion for arbitrary types of the evidence variable can be established by using ETAPCEM. The effectiveness of the proposed method for acoustic problems has been fully demonstrated by comparing it with the conventional evidence-theory-based polynomial chaos expansionmethods.	en_US
dc.relation.ispartof	Computer Methods in Applied Mechanics and Engineering	en_US
dc.relation.isbasedon	10.1016/j.cma.2017.12.025	en_US
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject.classification	Applied Mathematics	en_US
dc.title	An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty	en_US
dc.type	Journal Article
utslib.citation.volume	332	en_US
utslib.for	091307 Numerical Modelling and Mechanical Characterisation	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	09 Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access	*
pubs.publication-status	Published	en_US
pubs.volume	332	en_US

Abstract:

© 2017 Elsevier B.V. By introducing the arbitrary polynomial chaos theory, the Evidence-Theory-based Arbitrary Polynomial Chaos Expansion Method (ETAPCEM) is proposed to improve the computational accuracy of polynomial chaos expansion methods for the evidence-theory-based analysis of acoustic systems with epistemic uncertainty. In ETAPCEM, the epistemic uncertainty of acoustic systems is treated with evidence theory. The response of acoustic systems in the range of variation of evidence variables is approximated by the arbitrary polynomial chaos expansion, through which the lower and upper bounds of the response over all focal elements can be efficiently calculated by a number of numerical solvers. Inspired by the application of polynomial chaos theory in the interval and random analysis, the weight function of the optimal polynomial basis of ETAPCEM for evidence-theory-based uncertainty analysis is derived from the uniformity approach. Compared with the conventional evidence-theory-based polynomial chaos expansion methods, including the recently proposed evidence-theory-based Jacobi expansion method, the main advantage of ETAPCEM is that the polynomial basis orthogonalized with arbitrary weight functions can be obtained to construct the polynomial chaos expansion. Thereby the optimal polynomial basis of polynomial chaos expansion for arbitrary types of the evidence variable can be established by using ETAPCEM. The effectiveness of the proposed method for acoustic problems has been fully demonstrated by comparing it with the conventional evidence-theory-based polynomial chaos expansionmethods.

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http://hdl.handle.net/10453/129722