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Radial Basis Functions as Surrogate Models with A Priori Bias in Comparison with a Posteriori Bias
Product Development Department, School of Engineering, Jönköping University, Jönköping, Sweden; School of Engineering Science, University of Skövde, Skövde, Sweden.
Örebro universitet, Institutionen för naturvetenskap och teknik. Department of Mechanical Engineering.ORCID-id: 0000-0001-6821-5727
2017 (engelsk)Inngår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 55, nr 4, s. 1453-1469Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In order to obtain a robust performance, the established approach when using radial basis function networks (RBF) as metamodels is to add a posteriori bias which is defined by extra orthogonality constraints. We mean that this is not needed, instead the bias can simply be set a priori by using the normal equation, i.e. the bias becomes the corresponding regression model. In this paper we demonstrate that the performance of our suggested approach with a priori bias is in general as good as, or even for many test examples better than, the performance of RBF with a posteriori bias. Using our approach, it is clear that the global response is modelled with the bias and that the details are captured with radial basis functions. The accuracy of the two approaches are investigated by using multiple test functions with different degrees of dimensionality. Furthermore, several modeling criteria, such as the type of radial basis functions used in the RBFs, dimension of the test functions, sampling techniques and size of samples, are considered to study their affect on the performance of the approaches. The power of RBF with a priori bias for surrogate based design optimization is also demonstrated by solving an established engineering benchmark of a welded beam and another benchmark for different sampling sets generated by successive screening, random, Latin hypercube and Hammersley sampling, respectively. The results obtained by evaluation of the performance metrics, the modeling criteria and the presented optimal solutions, demonstrate promising potentials of our RBF with a priori bias, in addition to the simplicity and straight-forward use of the approach.

sted, utgiver, år, opplag, sider
Springer Publishing Company, 2017. Vol. 55, nr 4, s. 1453-1469
Emneord [en]
metamodeling, radial basis function, design optimization, design of experiment
HSV kategori
Forskningsprogram
Maskinteknik
Identifikatorer
URN: urn:nbn:se:oru:diva-56960DOI: 10.1007/s00158-016-1569-0ISI: 000398951100020Scopus ID: 2-s2.0-84989170510OAI: oai:DiVA.org:oru-56960DiVA, id: diva2:1087041
Tilgjengelig fra: 2017-04-05 Laget: 2017-04-05 Sist oppdatert: 2018-01-13bibliografisk kontrollert

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