Comparison of chaos optimization functions for performance improvement of fitting of non-linear geometries |
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| Affiliation: | 1. School of Mechanical Engineering, Tongji University, 48000 Cao An Road, 201804 Shanghai, PR China;2. Mechanical Engineering Department, Politecnico di Milano, Via La Masa 1, 20156 Milan, Italy;3. Manufacturing Metrology Team, Faculty of Engineering, The University of Nottingham, NG7 2RD Nottingham, UK;1. Hubei Collaborative Innovation Center for High-efficiency Utilization of Solar Energy, Hubei University of Technology, Wuhan 430068, PR China;2. Faculty of Health, Engineering and Sciences, University of Southern Queensland, Toowoomba, QLD 4350, Australia;3. Guangdong Biolight Meditech Co., Ltd., Zhuhai 510006, PR China;1. Department of Wood Science and Paper Technology, Karaj Branch, Islamic Azad University, Karaj, Iran;2. Department of Wood Science and Paper Technology, Chalous Branch, Islamic Azad University, Chalous, Iran;3. Department of Wood Mechanics and Technology, Forestry Faculty, Karadeniz Technical University, 61080 Trabzon, Turkey;4. Department of Wood Mechanics and Technology, Forestry Faculty, Istanbul University, Bahcekoy, Sariyer, 34473 Istanbul, Turkey;1. Departamento de Engenharia Elétrica, Universidade Estadual de Londrina, Caixa Postal 10039, Londrina, PR 86057-970, Brazil;2. Departamento de Física, Universidade Estadual de Londrina, Caixa Postal 10011, Londrina, PR 86057-970, Brazil;3. Departamento de Ciência e Tecnologia dos Alimentos, Universidade Estadual de Londrina, Caixa Postal 10.011, Londrina, PR 86057-970, Brazil |
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| Abstract: | Fitting algorithms play an important role in the whole measuring cycle in order to derive a measurement result. They involve associating substitute geometry to a point cloud obtained by an instrument. This situation is more difficult in the case of non-linear geometry fitting since iterative method should be used. This article addresses this problem. Three geometries are selected as relevant case studies: circle, sphere and cylinder. This selection is based on their frequent use in real applications; for example, cylinder is a relevant geometry of an assembly feature such as pin-hole relationship, and spherical geometry is often found as reference geometry in high precision artifacts and mechanisms.In this article, the use of Chaos optimization (CO) to improve the initial solution to feed the iterative Levenberg–Marquardt (LM) algorithm to fit non-linear geometries is considered. A previous paper has shown the performance of this combination in improving the fitting of both complete and incomplete geometries. This article focuses on the comparison of the efficiency of different one-dimensional maps of CO. This study shows that, in general, logistic-map function provides the best solution compared to other types of one-dimensional functions. Finally, case studies on hemispheres and industrial cylinders fitting are presented. |
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| Keywords: | Least-square fitting Non-linear optimization Chaos optimization One dimensional map |
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