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.

1.
Kim
,
W. -S.
, and
Raman
,
S.
, 2000, “
On the Selection of Flatness Measurement Points in Coordinate Measuring Machine Inspection
,”
Int. J. Mach. Tools Manuf.
0890-6955,
40
(
3
), pp.
427
443
.
2.
Badar
,
M. A.
,
Raman
,
S.
, and
Pulat
,
P. S.
, 2003, “
Intelligent Search-Based Selection of Sample Points for Straightness and Flatness Estimation
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
125
(
2
), pp.
263
271
.
3.
Badar
,
M. A.
,
Raman
,
S.
, and
Pulat
,
P. S.
, 2005, “
Experimental Verification of Manufacturing Error Pattern and Its Utilization in Form Tolerance Sampling
,”
Int. J. Mach. Tools Manuf.
0890-6955,
45
(
1
), pp.
63
73
.
4.
Badar
,
M. A.
,
Raman
,
S.
,
Pulat
,
P. S.
, and
Shehab
,
R. L.
, 2005, “
Experimental Analysis of Search-Based Selection of Sample Points for Straightness and Flatness Estimation
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
127
(
1
), pp.
96
103
.
5.
Aguirre-Cruz
,
J. A.
, and
Raman
,
S.
, 2005, “
Torus Form Inspection Using Coordinate Sampling
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
127
(
1
), pp.
84
95
.
6.
Prakasvudhisarn
,
C.
, and
Raman
,
S.
, 2004, “
Framework for Cone Feature Measurement Using Coordinate Measuring Machines
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
126
(
1
), pp.
169
177
.
7.
Vapnik
,
V. N.
, 1982,
Estimation of Dependences Based on Empirical Data
,
Springer
,
New York
.
8.
Vapnik
,
V. N.
, 1995,
The Nature of Statistical Learning Theory
,
Springer
,
New York
.
9.
Shawe-Taylor
,
J.
, and
Cristianini
,
N.
, 2004,
Kernel Methods for Pattern Analysis
,
Cambridge University Press
,
Cambridge, UK
.
10.
Schölkopf
,
B.
, and
Smola
,
A. J.
, 2002,
Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
,
MIT
,
Cambridge, MA
.
11.
Platt
,
J. C.
, 1999, “
Using Analytic QP and Sparseness to Speed Training of Support Vector Machines
,”
Advances in Neural Information Processing Systems
,
M. S.
Kearns
,
S. A.
Solla
, and
D. A.
Cohn
, eds.,
MIT
,
Cambridge, MA
, Vol.
11
, pp.
557
563
.
12.
Mangasarian
,
O. L.
, and
Musicant
,
D. R.
, 2002, “
Large Scale Kernel Regression Via Linear Programming
,”
Mach. Learn.
0885-6125,
46
(
1–3
), pp.
255
269
.
13.
Trafalis
,
T. B.
, and
Gilbert
,
R. C.
, 2006, “
Robust Classification and Regression Using Support Vector Machines
,”
Eur. J. Oper. Res.
0377-2217,
173
(
3
), pp.
893
909
.
14.
Bazaraa
,
M. S.
,
Sherali
,
H. D.
, and
Shetty
,
C. M.
, 2006,
Nonlinear Programming: Theory and Algorithms
,
3rd ed.
,
Wiley-Interscience
,
Hoboken, NJ
.
15.
Saad
,
Y.
, 1996,
Iterative Methods for Sparse Linear Systems
,
PWS
,
Boston, MA
.
16.
Murthy
,
T. S. R.
, and
Abdin
,
S. Z.
, 1980, “
Minimum Zone Evaluation of Surfaces
,”
Int. J. Mach. Tool Des. Res.
0020-7357,
20
(
2
), pp.
123
136
.
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