A new sequential sampling method for constructing the high-order polynomial surrogate models

Wu, J; Luo, Z; Zhang, N; Gao, W

A new sequential sampling method for constructing the high-order polynomial surrogate models

Wu, J

Luo, Z

Zhang, N

Gao, W

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Publisher:: Emerald
Publication Type:: Journal Article
Citation:: Engineering Computations, 2017, 34 (7), pp. 1 - 21
Issue Date:: 2017-07-30

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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	Gao, W	en_US
dc.date.available	2017-03-29	en_US
dc.date.issued	2017-07-30	en_US
dc.identifier.citation	Engineering Computations, 2017, 34 (7), pp. 1 - 21	en_US
dc.identifier.issn	1758-7077	en_US
dc.identifier.uri	http://hdl.handle.net/10453/105457
dc.description.abstract	Purpose - The sampling methods (or design of experiments) which have large influence on the performance of the surrogate model will be mainly studied. To improve the adaptability of modelling, a new sequential sampling method termed as sequential Chebyshev sampling method (SCSM) is proposed in this study. Design/methodology/approach - The high-order polynomials are used to construct the global surrogated model, which retains the advantages of the traditional low-order polynomial models while overcoming their disadvantage in accuracy. Firstly, the zeros of Chebyshev polynomials with the highest allowable order will be used as sampling candidates to improve the stability and accuracy of the high-order polynomial model. In the second step, some initial sampling points will be selected from the candidates by using a coordinate alternation algorithm, which keeps the initial sampling set be uniformly distributed. Thirdly, a fast sequential sampling scheme based on the space-filling principle is developed to collect more samples from the candidates, and the order of polynomial model is also updated in this procedure. The final surrogate model will be determined as the polynomial that has the largest adjusted R-square after the sequential sampling is terminated. Findings - The SCSM has better performance in efficiency, accuracy, and stability compared with several popular sequential sampling methods, e.g. LOLA-Voronoi algorithm and global Monte Carlo method from the SED toolbox, and the Halton sequence. Originality/value – The SCSM has good performance in building the high-order surrogate model, including the high stability and accuracy, which may save a large amount of cost in solving complicated engineering design or optimization problems.	en_US
dc.publisher	Emerald	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP150102751
dc.relation.ispartof	Engineering Computations	en_US
dc.subject.classification	Applied Mathematics	en_US
dc.title	A new sequential sampling method for constructing the high-order polynomial surrogate models	en_US
dc.type	Journal Article
utslib.citation.volume	7	en_US
utslib.citation.volume	34	en_US
utslib.for	0905 Civil Engineering	en_US
utslib.for	0913 Mechanical Engineering	en_US
utslib.for	0915 Interdisciplinary 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.consider-herdc	true	en_US
pubs.issue	7	en_US
pubs.publication-status	Accepted	en_US
pubs.volume	34	en_US

Abstract:

Purpose - The sampling methods (or design of experiments) which have large influence on the performance of the surrogate model will be mainly studied. To improve the adaptability of modelling, a new sequential sampling method termed as sequential Chebyshev sampling method (SCSM) is proposed in this study. Design/methodology/approach - The high-order polynomials are used to construct the global surrogated model, which retains the advantages of the traditional low-order polynomial models while overcoming their disadvantage in accuracy. Firstly, the zeros of Chebyshev polynomials with the highest allowable order will be used as sampling candidates to improve the stability and accuracy of the high-order polynomial model. In the second step, some initial sampling points will be selected from the candidates by using a coordinate alternation algorithm, which keeps the initial sampling set be uniformly distributed. Thirdly, a fast sequential sampling scheme based on the space-filling principle is developed to collect more samples from the candidates, and the order of polynomial model is also updated in this procedure. The final surrogate model will be determined as the polynomial that has the largest adjusted R-square after the sequential sampling is terminated. Findings - The SCSM has better performance in efficiency, accuracy, and stability compared with several popular sequential sampling methods, e.g. LOLA-Voronoi algorithm and global Monte Carlo method from the SED toolbox, and the Halton sequence. Originality/value – The SCSM has good performance in building the high-order surrogate model, including the high stability and accuracy, which may save a large amount of cost in solving complicated engineering design or optimization problems.

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http://hdl.handle.net/10453/105457