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dc.contributor.authorOllar, J
dc.contributor.authorMortished, C
dc.contributor.authorJones, R
dc.contributor.authorSienz, J
dc.contributor.authorToropov, V
dc.description.abstract© 2016 The Author(s)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.
dc.description.sponsorshipThe authors are very grateful to the Altair HyperStudy team for their support throughout this work. Jonathan Ollar, Vassili Toropov and Royston Jones greatly appreciate funding from European Union Seventh Framework Programme FP7-PEOPLE-2012-ITN under grant agreement 316394, Aerospace Multidisciplinarity Enabling DEsign Optimization (AMEDEO)Marie Curie Initial Training Network. Charles Mortished and Johann Sienz greatly appreciate funding from EPSRC EDT (EP/I015507/1) Manufacturing Advances Through Training Engineering Researchers (MATTER). Vassili Toropov is grateful for the support provided by the Russian Science Foundation, project No. 16-11-10150.en_US
dc.format.extent1 - 16
dc.relation.ispartofStructural and Multidisciplinary Optimization
dc.rightsThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
dc.titleGradient based hyper-parameter optimisation for well conditioned kriging metamodels
dc.typeJournal Article
dc.rights.holder© The Author(s) 2016
pubs.organisational-group/Queen Mary University of London
pubs.organisational-group/Queen Mary University of London/Faculty of Science & Engineering
pubs.organisational-group/Queen Mary University of London/Faculty of Science & Engineering/Engineering and Materials Science - Staff

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