The interval uncertain optimization strategy based on Chebyshev meta-model

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

The interval uncertain optimization strategy based on Chebyshev meta-model

Wu, J

Luo, Z

Zhang, N

Zhang, Y

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Publication Type:: Conference Proceeding
Citation:: Springer Proceedings in Mathematics and Statistics, 2015, 95 pp. 203 - 216
Issue Date:: 2015-01-01

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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	Zhang, Y	en_US
dc.date.issued	2015-01-01	en_US
dc.identifier.citation	Springer Proceedings in Mathematics and Statistics, 2015, 95 pp. 203 - 216	en_US
dc.identifier.isbn	9783319083766	en_US
dc.identifier.issn	2194-1009	en_US
dc.identifier.uri	http://hdl.handle.net/10453/44969
dc.description.abstract	© Springer International Publishing Switzerland 2015. This paper proposes a new design optimization method for structures subject to uncertainty. Interval model is used to account for uncertainties of uncertain-but-bounded parameters. It only requires the determination of lower and upper bounds of an uncertain parameter, without necessarily knowing its precise probability distribution. The interval uncertain optimization problem containing interval design variables and/or interval parameters will be formulated as a nested double-loop procedure, in which the outer loop optimization updates the midpoint of interval variables while the inner loop optimization calculates the bounds of objective and constraints. However, the nested double-loop optimization strategy will be computationally prohibitive, and it may be trapped into some local optimal solutions. To reduce the computational cost, the interval arithmetic is applied to the inner loop to directly evaluate the bounds of interval functions, so as to eliminate the optimization of the inner loop. The Taylor interval inclusion function is introduced to control the overestimation induced by the intrinsic wrapping effect of interval arithmetic. Since it is hard to evaluate the high-order coefficients in the Taylor inclusion function, a Chebyshev meta-model is proposed to approximate the Taylor inclusion function. Two numerical examples are used to demonstrate the effectiveness of the proposed method in the uncertain design optimization.	en_US
dc.relation.ispartof	Springer Proceedings in Mathematics and Statistics	en_US
dc.relation.isbasedon	10.1007/978-3-319-08377-3_21	en_US
dc.title	The interval uncertain optimization strategy based on Chebyshev meta-model	en_US
dc.type	Conference Proceeding
utslib.citation.volume	95	en_US
utslib.for	0913 Mechanical 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	95	en_US

Abstract:

© Springer International Publishing Switzerland 2015. This paper proposes a new design optimization method for structures subject to uncertainty. Interval model is used to account for uncertainties of uncertain-but-bounded parameters. It only requires the determination of lower and upper bounds of an uncertain parameter, without necessarily knowing its precise probability distribution. The interval uncertain optimization problem containing interval design variables and/or interval parameters will be formulated as a nested double-loop procedure, in which the outer loop optimization updates the midpoint of interval variables while the inner loop optimization calculates the bounds of objective and constraints. However, the nested double-loop optimization strategy will be computationally prohibitive, and it may be trapped into some local optimal solutions. To reduce the computational cost, the interval arithmetic is applied to the inner loop to directly evaluate the bounds of interval functions, so as to eliminate the optimization of the inner loop. The Taylor interval inclusion function is introduced to control the overestimation induced by the intrinsic wrapping effect of interval arithmetic. Since it is hard to evaluate the high-order coefficients in the Taylor inclusion function, a Chebyshev meta-model is proposed to approximate the Taylor inclusion function. Two numerical examples are used to demonstrate the effectiveness of the proposed method in the uncertain design optimization.

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http://hdl.handle.net/10453/44969