Nonlinear forms such as the cone, sphere, cylinder, and torus present significant problems in representation and verification. In this paper we examine linear and nonlinear forms using a heavily modified support vector machine (SVM) technique. The SVM approach applied to regression problems is used to derive quadratic programming problems that allow for generalized symbolic solutions to nonlinear regression. We have tested our approach to several geometries and achieved excellent results even with small data sets, making this method robust and efficient. More importantly, we identify process or inspection tendencies that could help in better designing the processes. Adaptive feature verification can be achieved through effective identification of the manufacturing pattern.
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August 2009
Research Papers
Mathematical Foundations for Form Inspection and Adaptive Sampling
Robin C. Gilbert,
Robin C. Gilbert
School of Industrial Engineering,
webmaster@robingilbert.com
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631
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Shivakumar Raman,
Shivakumar Raman
School of Industrial Engineering,
raman@ou.edu
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631
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Theodore B. Trafalis,
Theodore B. Trafalis
School of Industrial Engineering,
ttrafalis@ou.edu
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631
Search for other works by this author on:
Suleiman M. Obeidat,
Suleiman M. Obeidat
School of Industrial Engineering,
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631
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Juan A. Aguirre-Cruz
Juan A. Aguirre-Cruz
School of Industrial Engineering,
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631
Search for other works by this author on:
Robin C. Gilbert
School of Industrial Engineering,
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631webmaster@robingilbert.com
Shivakumar Raman
School of Industrial Engineering,
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631raman@ou.edu
Theodore B. Trafalis
School of Industrial Engineering,
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631ttrafalis@ou.edu
Suleiman M. Obeidat
School of Industrial Engineering,
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631
Juan A. Aguirre-Cruz
School of Industrial Engineering,
University of Oklahoma
, Room 124, 202 West Boyd Street, Norman, OK 73019-0631J. Manuf. Sci. Eng. Aug 2009, 131(4): 041001 (8 pages)
Published Online: July 7, 2009
Article history
Received:
September 7, 2007
Revised:
November 25, 2008
Published:
July 7, 2009
Citation
Gilbert, R. C., Raman, S., Trafalis, T. B., Obeidat, S. M., and Aguirre-Cruz, J. A. (July 7, 2009). "Mathematical Foundations for Form Inspection and Adaptive Sampling." ASME. J. Manuf. Sci. Eng. August 2009; 131(4): 041001. https://doi.org/10.1115/1.3160582
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