Many modern engineering systems use multiple sensors for monitoring, diagnosis and control. Some of these sensors contain not only time domain and frequency domain information, but also valuable spatial domain information to which little attention has been paid. This paper presents a new method for capturing the spatial characteristics of the sensor signals. The basic idea is to model the spatial information of the signals using a Be´zier surface. For example, given m one-dimensional force signals: $X1t,X2t,…,Xmt,$ at each time instance t, a Be´zier surface can be constructed, which describes the distribution of the force. Furthermore, lining up the surfaces at different time $t1,t2,…,tn,$ will show how the force changes as a function of time. Since the graph looks like a snake skeleton, the new method is called the snake skeleton graph. The paper first describes how the snake skeleton graph is constructed using a demonstration example: a foot walking on a plate. Then it presents an application for fault diagnosis in sheet metal stamping operation. Future research topics are also discussed.

1.
Du, R., 2000, “Fault Diagnosis,” Encyclopedia of Electrical and Electronics Engineering, edited by John G. Webster, Article No. 2608, John Wiley, New York.
2.
Qu
,
L.
et al.
,
1989
, “
The Holospectrum: A New Method for Rotor Surveillance and Diagnosis
,”
Mech. Syst. Signal Process.
,
3
, pp.
255
267
.
3.
Du
,
R.
,
Chen
,
Y. D.
, and
Chen
,
Y. B.
,
1996
, “
Four Dimensional Holospectrum—A New Method for Analyzing Force Distributions
,”
ASME J. Manuf. Sci. Eng.,
,
119
, pp.
95
104
.
4.
Choi
,
H.
, and
Williams
,
W. J.
,
1989
, “
Improved Time-Frequency Representation of Multicomponent Signals Using Exponential Kernels
,”
IEEE Trans. Acoust., Speech, Signal Process.
,
37
, pp.
862
871
.
5.
Mallat
,
S. G.
,
1989
, “
Multifrequency Channel Decomposition of Images and Wavelet Models
,”
IEEE Trans. Acoust., Speech, Signal Process.
,
37
, pp.
2091
2110
.
6.
Wu, Y., Escand, P., and Du, R., 2001, “
A New Method for Real Time Tool Condition Monitoring of Transfer Machining Stations,” Trans. ASME, J. Manuf. Sci. Eng., 123(2), pp. 339-347.
7.
Mendel
,
J. M.
,
1991
, “
Tutorial on Higher-Order Statistics (Spectra) in Signal Processing and System Theory: Theoretical Results and Some Applications
,”
Proc. IEEE
,
79
, pp.
278
305
.
8.
Zhang, G. C. et al., 2000, “Bispectrum Analysis for On-Line Monitoring of Stamping Operations,” submitted to Int. J. of Real-Time Automation.
9.
Aronson
,
R.
,
1998
, “
Intelligent Presses
,”
Manuf. Eng.
,
121
, pp.
70
75
.
10.
Brueninghaus
,
G.
, 1988, “Process Monitoring in the Sheet Metal Processing Industry,” V. D. I. Zeit, 130, pp. 99–101.
11.
Brueninghaus
,
G.
, 1994, “Process Supervision of Automatic Stamping Presses,” Wire, 44, pp. 130–135.
12.
Du, R., and Xu, Y. S., 2002, “A Review on Sensing and Monitoring of Sheet Metal Stamping Operations,” Proceedings of the 4th S. M. Wu Conference on Manufacturing Science and Technology, Dalian, China.
13.
Mettert, B. K., 1990, “Load Sensors Placement and Tonnage Data for Underdrive Presses,” SME Technical Paper No. MS90-384.
14.
Du
,
H.
, and
Klamechi
,
B. E.
,
1999
, “
Force Sensors Embedded in Surfaces for Manufacturing and Other Tribologic Process Monitoring
,”
ASME J. Manuf. Sci. Eng.,
,
121
, pp.
739
748
.
15.
Hao
,
S.
,
Klamechi
,
B. E.
, and
Ramalingam
,
S.
,
1999
, “
Friction Measurement Apparatus for Sheet Metal Forming
,”
Wear
,
224
, pp.
1
7
.
16.
Kernosky
,
S. K.
et al.
,
1998
, “
Development of a Die Shoulder Force Transducer for Sheet Metal Forming
,”
ASME J. Manuf. Sci. Eng.,
,
120
, pp.
42
48
.
17.
Koh
,
C. K. H.
,
Shi
,
J.
,
Williams
,
W. J.
, and
Ni
,
J.
,
1999
, “
Multiple Faults Detection and Isolation Using the Haar Transform, Part 1: Theory
,”
ASME J. Manuf. Sci. Eng.,
,
121
, pp.
290
294
.
18.
Koh
,
C. K. H.
,
Shi
,
J.
,
Williams
,
W. J.
, and
Ni
,
J.
,
1999
, “
Multiple Faults Detection and Isolation Using the Haar Transform, Part 2: Application to the Stamping Process
,”
ASME J. Manuf. Sci. Eng.,
,
121
, pp.
295
299
.
19.
Jin
,
J.
, and
Shi
,
J.
,
2000
, “
Diagnostic Feature Extraction From Stamping Tonnage Signals Based on Design of Experiments
,”
ASME J. Manuf. Sci. Eng.,
,
122
, pp.
360
369
.
20.
Mangrulkar, S. M., Spoto, T. A., and Rankin, J. S. II, 1994, “Method and System for Real-Time Statistical Process Monitoring,” United States Patent No. 5,311,759.
21.
Mangrulkar, S. M., 1996, “Method and System for Real-Time Statistical Process Monitoring,” United States Patent No. 5,586,041.
22.
Siegert, K., and Haller, D., 2001, “Controllable Nitrogen Cylinders for Deep Drawing Dies,” SAE Technical Paper No. 2001-01-1137.