Probe-type Coordinate Measuring Machines (CMMs) rely on the measurement of several discrete points to capture the geometry of part features. The sampled points are then fit to verify a specified geometry. The most widely used fitting method, the least squares fit (LSQ), occasionally overestimates the tolerance zone. This could lead to the economical disadvantage of rejecting some good parts and the statistical disadvantage of normal (Gaussian) distribution assumption. Support vector machines (SVMs) represent a relatively new revolutionary approach for determining the approximating function in regression problems. Its upside is that the normal distribution assumption is not required. In this research, support vector regression (SVR), a new data fitting procedure, is introduced as an accurate method for finding the minimum zone straightness and flatness tolerances. Numerical tests are conducted with previously published data and the results are found to be comparable to the published results, illustrating its potential for application in precision data analysis such as used in minimum zone estimation.

Issue Section:
Technical Papers
Keywords:
coordinate measuring machines, tolerance analysis, statistical analysis, learning automata, manufacturing processes
Topics:
Algorithms, Coordinate measuring machines, Support vector machines, Gaussian distribution, Manufacturing, Errors, Fittings, Geometry
1.
ASME Y14.5M-1994, 1995, Dimensioning and Tolerancing, The American Society of Mechanical Engineers, New York, NY.
2.
Vapnik, V., 1995, The Nature of Statistical Learning Theory, Springer Verlag, New York.
3.
Smola, A. J., and Scholkopf, B., 1998, A Tutorial on Support Vector Regression, NeuroCOLT Technical Report NC-TR-98-030, Royal Holloway College, University of London, UK.
4.
Vapnik, V., Golowich, S. E., and Smola, A., 1997, “Support Vector Method for Function Approximation, Regression Estimation, and Signal Processing,” M. Mozer, M. Jordan, and T. Petsche, eds., Adv. in Neural Inf. Proc. Sys., Vol. 9, pp. 281–287, MIT Press, Cambridge, MA.
5.
Drucker, H., Burges, C. J. C., Kaufman, L., Smola, A., and Vapnik, V., 1997, “Support Vector Regression Machines,” M. Mozer, M. Jordan, and T. Petsche, eds., Advances in Neural Information Processing Systems, Vol 9, pp. 155–161, MIT Press, Cambridge, MA.
6.
Scho¨lkopf, B., Bartlett, P. L., Smola, A., and Williamson, R., 1999, “Shrinking the Tube: A New Support Vector Regression Algorithm,” M. S. Kearns, S. A. Solla, and D. A. Cohn, eds., Advances in Neural Inf. Processing Systems, Vol. 11, pp. 330–336, MIT Press, Cambridge, MA.
7.
Traband
,
M. T.
,
Joshi
,
S.
,
Wysk
,
R. A.
, and
Cavalier
,
T. M.
,
1989
, “
Evaluation of Straightness and Flatness Tolerances Using the Minimum Zone
,”
Manufacturing Review
,
2
(
3
), pp.
189
–
195
.
8.
Samuel
,
G. L.
, and
Shunmugam
,
M. S.
,
1999
, “
Evaluation of Straightness and Flatness Error Using Computational Geometric Techniques
,”
Comput.-Aided Des.
,
31
(
13
), pp.
829
–
843
.
9.
Shunmugam
,
M. S.
,
1987
, “
Comparison of Linear and Normal Deviations of Forms of Engineering Surfaces
,”
Precis. Eng.
,
9
(
2
), pp.
96
–
102
.
10.
Shunmugam
,
M. S.
,
1987
, “
New Approach for Evaluating Form Errors of Engineering Surfaces
,”
Comput.-Aided Des.
,
19
(
7
), pp.
368
–
374
.
11.
Shunmugam
,
M. S.
,
1991
, “
Establishing Reference Figures for Form Evaluation of Engineering Surfaces
,”
J. Manuf. Syst.
,
10
(
4
), pp.
314
–
321
.
12.
Wang
,
Y.
,
1992
, “
Minimum Zone Evaluation of Form Tolerances
,”
Manufacturing Review
,
5
(
3
), pp.
213
–
220
.
13.
Kanada
,
T.
, and
Suzuki
,
S.
,
1993
, “
Evaluation of Minimum Zone Flatness by Means of Nonlinear Optimization Techniques and Its Verification
,”
Precis. Eng.
,
15
(
2
), pp.
93
–
99
.
14.
Kanada
,
T.
, and
Suzuki
,
S.
,
1993
, “
Application of Several Computing Techniques for Minimum Zone Straightness
,”
Precis. Eng.
,
15
(
4
), pp.
274
–
280
.
15.
Carr
,
K.
, and
Ferreira
,
P.
,
1995
, “
Verification of Form Tolerances, Part 1: Basic Issues, Flatness, and Straightness
,”
Precis. Eng.
,
17
(
2
), pp.
131
–
143
.
16.
Malyscheff
,
A. M.
,
Trafalis
,
T. B.
, and
Raman
,
S.
,
2002
, “
From Support Vector Machine Learning to the Determination of the Minimum Enclosing Zone
,”
Computers and Industrial Engrg
,
42
, pp.
59
–
74
.
17.
Scho¨lkopf, B., Bartlett, P. L., Smola, A., and Williamson, R., 1998, “Support Vector Regression With Automatic Accuracy Control,” L. Niklasson, M. Boden, and T. Ziemke, eds., Proceedings of ICANN’98, Perspectives in Neural Computing, pp. 111–116, Springer Verlag, Berlin.
18.
Huang
,
S. T.
,
Fan
,
K. C.
, and
Wu
,
J. H.
,
1993
, “
A New Minimum Zone Method for Evaluating Straightness Errors
,”
Precis. Eng.
,
15
(
3
), pp.
158
–
165
.
19.
Huang
,
S. T.
,
Fan
,
K. C.
, and
Wu
,
J. H.
,
1993
, “
A New Minimum Zone Method for Evaluating Flatness Errors
,”
Precis. Eng.
,
15
(
1
), pp.
25
–
32
.
Copyright © 2003
 by ASME
You do not currently have access to this content.