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Radial basis functions with a priori bias as surrogate models: A comparative study
University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Engineering Science. (Maskinteknik)ORCID iD: 0000-0001-7534-0382
University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre. (Production and automation engineering)ORCID iD: 0000-0001-5436-2128
University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre. (Production and automation engineering)ORCID iD: 0000-0003-0111-1776
2018 (English)In: Engineering applications of artificial intelligence, ISSN 0952-1976, E-ISSN 1873-6769, Vol. 71, p. 28-44Article in journal (Refereed) Published
Abstract [en]

Radial basis functions are augmented with a posteriori bias in order to perform robustly when used as metamodels. Recently, it has been proposed that the bias can simply be set a priori by using the normal equation, i.e., the bias becomes the corresponding regression model. In this study, we demonstrate the performance of the suggested approach (RBFpri) with four other well-known metamodeling methods; Kriging, support vector regression, neural network and multivariate adaptive regression. The performance of the five methods is investigated by a comparative study, using 19 mathematical test functions, with five different degrees of dimensionality and sampling size for each function. The performance is evaluated by root mean squared error representing the accuracy, rank error representing the suitability of metamodels when coupled with evolutionary optimization algorithms, training time representing the efficiency and variation of root mean squared error representing the robustness. Furthermore, a rigorous statistical analysis of performance metrics is performed. The results show that the proposed radial basis function with a priori bias achieved the best performance in most of the experiments in terms of all three metrics. When considering the statistical analysis results, the proposed approach again behaved the best, while Kriging was relatively as accurate and support vector regression was almost as fast as RBFpri. The proposed RBF is proven to be the most suitable method in predicting the ranking among pairs of solutions utilized in evolutionary algorithms. Finally, the comparison study is carried out on a real-world engineering optimization problem. © 2018 Elsevier Ltd

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 71, p. 28-44
Keywords [en]
Kriging, Metamodeling, Multivariate adaptive regression splines, Neural networks, Radial basis function, Support vector regression, Surrogate models, Errors, Evolutionary algorithms, Functions, Heat conduction, Image segmentation, Interpolation, Mean square error, Optimization, Regression analysis, Statistical methods, Radial basis functions, Support vector regression (SVR), Surrogate model, Radial basis function networks
National Category
Mechanical Engineering
Research subject
Mechanics of Materials; Production and Automation Engineering
Identifiers
URN: urn:nbn:se:his:diva-14999DOI: 10.1016/j.engappai.2018.02.006ISI: 000436213000003Scopus ID: 2-s2.0-85042877194OAI: oai:DiVA.org:his-14999DiVA, id: diva2:1194437
Available from: 2018-04-01 Created: 2018-04-03 Last updated: 2018-07-13
In thesis
1. Metamodel Based Multi-Objective Optimization with Finite-Element Applications
Open this publication in new window or tab >>Metamodel Based Multi-Objective Optimization with Finite-Element Applications
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Högskolan i Skövde, 2018. p. 179
Series
Dissertation Series ; 22 (2018)
Identifiers
urn:nbn:se:his:diva-15145 (URN)978-91-984187-4-3 (ISBN)
Public defence
2018-05-25, Portalen, Insikten, 10:00 (English)
Opponent
Available from: 2018-05-14 Created: 2018-05-14 Last updated: 2018-05-14Bibliographically approved

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Amouzgar, KavehBandaru, SunithNg, Amos H. C.

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