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Gradient based hyper-parameter optimisation for well conditioned kriging metamodels

Jonathan Ollar, Charles Mortished, Royston Jones, Johann Sienz Orcid Logo, Vassili Toropov

Structural and Multidisciplinary Optimization, Volume: 55, Issue: 6, Pages: 2029 - 2044

Swansea University Author: Johann Sienz Orcid Logo

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DOI (Published version): 10.1007/s00158-016-1626-8

Abstract

In this work a two step approach to efficiently carrying out hyper parameter optimisation, required for building kriging and gradient enhanced kriging metamodels, is presented. The suggested approach makes use of an initial line search along the hyper-diagonal of the design space in order to find a...

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Published in: Structural and Multidisciplinary Optimization
ISSN: 1615-147X 1615-1488
Published: Springer Science and Business Media LLC 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa31213
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first_indexed 2016-11-24T14:27:29Z
last_indexed 2020-07-31T18:47:55Z
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spelling 2020-07-31T17:31:35.2917802 v2 31213 2016-11-24 Gradient based hyper-parameter optimisation for well conditioned kriging metamodels 17bf1dd287bff2cb01b53d98ceb28a31 0000-0003-3136-5718 Johann Sienz Johann Sienz true false 2016-11-24 FGSEN In this work a two step approach to efficiently carrying out hyper parameter optimisation, required for building kriging and gradient enhanced kriging metamodels, is presented. The suggested approach makes use of an initial line search along the hyper-diagonal of the design space in order to find a suitable starting point for a subsequent gradient based optimisation algorithm. During the optimisation an upper bound constraint is imposed on the condition number of the correlation matrix in order to keep it from being ill conditioned. Partial derivatives of both the condensed log likelihood function and the condition number are obtained using the adjoint method, the latter has been derived in this work. The approach is tested on a number of analytical examples and comparisons are made to other optimisation approaches. Finally the approach is used to construct metamodels for a finite element model of an aircraft wing box comprising of 126 thickness design variables and is then compared with a sub-set of the other optimisation approaches. Journal Article Structural and Multidisciplinary Optimization 55 6 2029 2044 Springer Science and Business Media LLC 1615-147X 1615-1488 Hyper-parameter optimisation; SQP; Adjoint method; Condition number; Kriging; Gradient-enhanced kriging; Gaussian processes 1 6 2017 2017-06-01 10.1007/s00158-016-1626-8 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2020-07-31T17:31:35.2917802 2016-11-24T12:34:49.4746355 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Jonathan Ollar 1 Charles Mortished 2 Royston Jones 3 Johann Sienz 0000-0003-3136-5718 4 Vassili Toropov 5 0031213-06012017130042.pdf ollar2016v2.pdf 2017-01-06T13:00:42.9800000 Output 599689 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution License (CC-BY). true eng http://creativecommons.org/licenses/by/4.0/
title Gradient based hyper-parameter optimisation for well conditioned kriging metamodels
spellingShingle Gradient based hyper-parameter optimisation for well conditioned kriging metamodels
Johann Sienz
title_short Gradient based hyper-parameter optimisation for well conditioned kriging metamodels
title_full Gradient based hyper-parameter optimisation for well conditioned kriging metamodels
title_fullStr Gradient based hyper-parameter optimisation for well conditioned kriging metamodels
title_full_unstemmed Gradient based hyper-parameter optimisation for well conditioned kriging metamodels
title_sort Gradient based hyper-parameter optimisation for well conditioned kriging metamodels
author_id_str_mv 17bf1dd287bff2cb01b53d98ceb28a31
author_id_fullname_str_mv 17bf1dd287bff2cb01b53d98ceb28a31_***_Johann Sienz
author Johann Sienz
author2 Jonathan Ollar
Charles Mortished
Royston Jones
Johann Sienz
Vassili Toropov
format Journal article
container_title Structural and Multidisciplinary Optimization
container_volume 55
container_issue 6
container_start_page 2029
publishDate 2017
institution Swansea University
issn 1615-147X
1615-1488
doi_str_mv 10.1007/s00158-016-1626-8
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description In this work a two step approach to efficiently carrying out hyper parameter optimisation, required for building kriging and gradient enhanced kriging metamodels, is presented. The suggested approach makes use of an initial line search along the hyper-diagonal of the design space in order to find a suitable starting point for a subsequent gradient based optimisation algorithm. During the optimisation an upper bound constraint is imposed on the condition number of the correlation matrix in order to keep it from being ill conditioned. Partial derivatives of both the condensed log likelihood function and the condition number are obtained using the adjoint method, the latter has been derived in this work. The approach is tested on a number of analytical examples and comparisons are made to other optimisation approaches. Finally the approach is used to construct metamodels for a finite element model of an aircraft wing box comprising of 126 thickness design variables and is then compared with a sub-set of the other optimisation approaches.
published_date 2017-06-01T03:38:07Z
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score 11.016235

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