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Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias
Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system. Product Development Department, School of Engineering, Jönköping University, Jönköping, Sweden. (Materialmekanik, Mechanics of Materials)ORCID-id: 0000-0001-7534-0382
Department of Mechanical Engineering, School of Science and Technology, University of Örebro, Sweden.
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, 2017. Vol. 55, nr 4, s. 1453-1469
Emneord [en]
Metamodeling, Radial basis function, Design optimization, Design of experiment
HSV kategori
Forskningsprogram
INF201 Virtual Production Development; INF203 Virtual Machining; Materialmekanik
Identifikatorer
URN: urn:nbn:se:his:diva-13556DOI: 10.1007/s00158-016-1569-0ISI: 000398951100020Scopus ID: 2-s2.0-84989170510OAI: oai:DiVA.org:his-13556DiVA, id: diva2:1094979
Tilgjengelig fra: 2017-05-11 Laget: 2017-05-11 Sist oppdatert: 2019-01-22bibliografisk kontrollert
Inngår i avhandling
1. Metamodel Based Multi-Objective Optimization with Finite-Element Applications
Åpne denne publikasjonen i ny fane eller vindu >>Metamodel Based Multi-Objective Optimization with Finite-Element Applications
2018 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

As a result of the increase in accessibility of computational resources and the increase of computer power during the last two decades, designers are able to create computer models to simulate the behavior of complex products. To address global competitiveness, companies are forced to optimize the design of their products and production processes. Optimizing the design and production very often need several runs of computationally expensive simulation models. Therefore, integrating metamodels, as an efficient and sufficiently accurate approximate of the simulation model, with optimization algorithms is necessary. Furthermore, in most of engineering problems, more than one objective function has to be optimized, leading to multi-objective optimization(MOO). However, the urge to employ metamodels in MOO, i.e., metamodel based MOO (MB-MOO), is more substantial.Radial basis functions (RBF) is one of the most popular metamodeling methods. In this thesis, a new approach to constructing RBF with the bias to beset a priori by using the normal equation is proposed. The performance of the suggested approach is compared to the classic RBF and four other well-known metamodeling methods, in terms of accuracy, efficiency and, most importantly, suitability for integration with MOO evolutionary algorithms. It has been found that the proposed approach is accurate in most of the test functions, and it was the fastest compared to other methods. Additionally, the new approach is the most suitable method for MB-MOO, when integrated with evolutionary algorithms. The proposed approach is integrated with the strength Pareto evolutionary algorithm (SPEA2) and applied to two real-world engineering problems: MB-MOO of the disk brake system of a heavy truck, and the metal cutting process in a turning operation. Thereafter, the Pareto-optimal fronts are obtained and the results are presented. The MB-MOO in both case studies has been found to be an efficient and effective method. To validate the results of the latter MB-MOO case study, a framework for automated finite element (FE) simulation based MOO (SB-MOO) of machining processes is developed and presented by applying it to the same metal cutting process in a turning operation. It has been proved that the framework is effective in achieving the MOO of machining processes based on actual FE simulations.

sted, utgiver, år, opplag, sider
Högskolan i Skövde, 2018. s. 179
Serie
Dissertation Series ; 22 (2018)
HSV kategori
Forskningsprogram
Produktion och automatiseringsteknik
Identifikatorer
urn:nbn:se:his:diva-15145 (URN)978-91-984187-4-3 (ISBN)
Disputas
2018-05-25, Portalen, Insikten, 10:00 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2018-05-14 Laget: 2018-05-14 Sist oppdatert: 2019-07-04bibliografisk kontrollert

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