A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

Wu, J; Luo, Z; Zhang, N; Zhang, Y

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

Wu, J

Luo, Z

Zhang, N

Zhang, Y

Permalink

Publication Type:: Journal Article
Citation:: Engineering Optimization, 2015, 47 (9), pp. 1264 - 1288
Issue Date:: 2015-09-02

Closed Access

	Filename	Description	Size
	A multi-material level set-based topology and shape optimization method.pdf	Published Version	2.22 MB	Adobe PDF	View/Open

Copyright Clearance Process

Recently Added
In Progress
Closed Access

This item is closed access and not available.

Full metadata record

Field	Value	Language
dc.contributor.author	Wu, J https://orcid.org/0000-0002-4925-4242	en_US
dc.contributor.author	Luo, Z https://orcid.org/0000-0002-6953-3986	en_US
dc.contributor.author	Zhang, N https://orcid.org/0000-0001-6408-0044	en_US
dc.contributor.author	Zhang, Y	en_US
dc.date.issued	2015-09-02	en_US
dc.identifier.citation	Engineering Optimization, 2015, 47 (9), pp. 1264 - 1288	en_US
dc.identifier.issn	0305-215X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/33975
dc.description.abstract	© 2014 © 2014 Taylor & Francis. The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the hypercube polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the simplex polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.	en_US
dc.relation.ispartof	Engineering Optimization	en_US
dc.relation.isbasedon	10.1080/0305215X.2014.963071	en_US
dc.subject.classification	Operations Research	en_US
dc.title	A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials	en_US
dc.type	Journal Article
utslib.citation.volume	9	en_US
utslib.citation.volume	47	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.issue	9	en_US
pubs.publication-status	Published	en_US
pubs.volume	47	en_US

Abstract:

© 2014 © 2014 Taylor & Francis. The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the hypercube polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the simplex polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/33975