Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-30T23:26:41.270Z Has data issue: false hasContentIssue false
  • English
  • Français

Performance study of dimensionality reduction methods formetrology of nonrigid mechanical parts

Published online by Cambridge University Press:  06 March 2014

H. Radvar-Esfahlan  and
S.-A. Tahan
Get access

Abstract

The geometric measurement of parts using a coordinate measuring machine (CMM) has beengenerally adapted to the advanced automotive and aerospace industries. However, for thegeometric inspection of deformable free-form parts, special inspection fixtures, incombination with CMM’s and/or optical data acquisition devices (scanners), are used. As aresult, the geometric inspection of flexible parts is a consuming process in terms of timeand money. The general procedure to eliminate the use of inspection fixtures based ondistance preserving nonlinear dimensionality reduction (NLDR) technique was developed inour previous works. We sought out geometric properties that are invariant to inelasticdeformations. In this paper we will only present a systematic comparison of somewell-known dimensionality reduction techniques in order to evaluate their accuracy andpotential for non-rigid metrology. We will demonstrate that even though these techniquesmay provide acceptable results through artificial data on certain fields like patternrecognition and machine learning, this performance cannot be extended to all realengineering metrology problems where high accuracy is needed.

Keywords

Computer aided inspectiongeometric inspectionflexible partsdimensionality reduction
Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 4 , Issue 3 , 2013 , pp. 193 - 200
Copyright
© EDP Sciences 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abenhaim, G.N., Desrochers, A., Tahan, A., Nonrigid parts’ specification and inspection methods: notions, challenges, and recent advancements, Int. J. Adv. Manuf. Technol. 63, 741–752 (2012) CrossRefGoogle Scholar
H. Radvar-Esfahlan, S.A. Tahan, Nonrigid geometric inspection using intrinsic geometry, Proceedings of The Canadian Society for Mechanical Engineering Forum 2010, Victoria, British Columbia (2010)
Radvar-Esfahlan, H., Tahan, S.A., Nonrigid Geometric Metrology using Generalized Numerical Inspection Fixtures, Precis. Eng. 36, 1–9 (2011) CrossRefGoogle Scholar
H. Radvar-Esfahlan, S.A. Tahan, Distance preserving dimensionality reduction methods and their applications in geometric inspection of nonrigid parts, 5th SASTECH Conference, Iran, 2011
Radvar-Esfahlan, H., Tahan, S.-A., Robust generalized numerical inspection fixture for the metrology of compliant mechanical parts, Int. J. Adv. Manuf. Technol. 70, 1101–1112 (2013) CrossRefGoogle Scholar
I. Jolliffe, Principal Component Analysis (Wiley Online Library, 2005)
J.A. Lee, M. Verleysen, Nonlinear Dimensionality Reduction (Springer, 2007)
Gower, J.C., Some distance properties of latent root and vector methods used in multivariate analysis, Biometrika 53, 325–338 (1966) CrossRefGoogle Scholar
Torgerson, W.S., Multidimensional scaling: I. Theory and method, Psychometrika 17, 401–419 (1952) CrossRefGoogle Scholar
Young, G., Householder, A.S., Discussion of a set of points in terms of their mutual distances, Psychometrika 3, 19–22 (1938) CrossRefGoogle Scholar
D. Burago, Y. Burago, S. Ivanov, A course in metric geometry (American Mathematical Society, 2001)
J. De Leeuw, Applications of convex analysis to multidimensional scaling (Department of Statistics Papers, Department of Statistics, UCLA, 2005)
I. Borg, P.J.F. Groenen, Modern multidimensional scaling: Theory and applications (Springer Verlag, 2005)
Tenenbaum, J.B., De Silva, V., Langford, J.C., A global geometric framework for nonlinear dimensionality reduction, Science 290, 2319–2323 (2000) CrossRefGoogle Scholar
Dijkstra, E., A note on two problems in connexion with graphs, Numer. Math. 1, 269–271 (1959) CrossRefGoogle Scholar
K.Q. Weinberger, L.K. Saul, Unsupervised learning of image manifolds by semidefinite programming, in Computer Vision and Pattern Recognition, 2004. CVPR 2004. Proceedings of the 2004 IEEE Computer Society Conference on, 2004, Vol. 2, pp. II-988–II-995
Vandenberghe, L., Boyd, S., Semidefinite programming, SIAM Rev. 38, 49–95 (1996) CrossRefGoogle Scholar
Van der Maaten, L., Postma, E., Van den Herik, H., Dimensionality reduction: A comparative review, J. Mach. Learn. Res. 10, 1–41 (2009) Google Scholar
Sammon, J.W. Jr., A nonlinear mapping for data structure analysis, Comput. IEEE Trans. 100, 401–409 (1969) CrossRefGoogle Scholar
Demartines, P., Hérault, J., Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets, Neural Netw. IEEE Trans. 8, 148–154 (1997) CrossRefGoogle ScholarPubMed
A. Gersho, R.M. Gray, Vector Quantization and Signal Compression (Kluwer Academic Pub., 1992), Vol. 159
J.A. Lee, A. Lendasse, M. Verleysen, Curvilinear distance analysis versus isomap, in Proceedings of ESANN, 2002, pp. 185–192
Roweis, S.T., Saul, L.K., Nonlinear dimensionality reduction by locally linear embedding, Science 290, 2323–2326 (2000) CrossRefGoogle Scholar
C.J. de Medeiros, J.A.F. Costa, L.A. Silva, A comparison of dimensionality reduction methods using topology preservation indexes, in Intelligent Data Engineering and Automated Learning-IDEAL 2011 (Springer, 2011), pp. 437–445
Yin, H., Nonlinear dimensionality reduction and data visualization: a review, Int. J. Automat. Comput. 4, 294–303 (2007) CrossRefGoogle Scholar
Chen, J., Liu, Y., Locally linear embedding: a survey, Artif. Intell. Rev. 36, 29–48 (2011) CrossRefGoogle Scholar