For the design and optimization of multistage assembly processes, a computationally cheap mathematical model that links design parameters with the final product dimensional quality is highly desirable. We propose a systematic approach to building a surrogate model of simulations of multistage assembly processes. At the heart of this approach is a multiple-input-multiple-output surrogate modeling framework that uses a recently developed integrated emulation technique. The unique feature of this technique is that the surrogate models for multiple outputs are fitted simultaneously. The corresponding experimental design issues are also addressed. The proposed method provides good prediction accuracy and requires minimal physical knowledge of the underlying system. The effectiveness of the method is demonstrated through a case study.

References

References
1.
Shiu
,
B. W.
,
Ceglarek
,
D.
, and
Shi
,
J.
, 1996, “
Multi-Stations Sheet Metal Assembly Modeling and Diagnostics
,”
Trans NAMRI/SME
,
24
, pp.
199
204
.
2.
Jin
,
J.
, and
Shi
J.
, 1999, “
State Space Modeling of Sheet Metal Assembly for Dimensional Control
,”
Trans. ASME J. Manuf. Sci. Eng.
,
121
(
4
), pp.
756
762
.
3.
Ding
,
Y.
,
Ceglarek
,
D.
, and
Shi
,
J.
, 2000, “
Modeling and Diagnosis of Multistage Manufacturing Processes: Part I State Space Model
,”
Proceedings of the 2000 Japan/USA Symposium on Flexible Automation
,
Ann Arbor
,
MI
, 2000JUSFA-13146.
4.
Ceglarek
,
D.
,
Huang
,
W.
,
Zhou
,
S.
,
Ding
,
Y.
,
Kumar
,
R.
, and
Zhou
,
Y.
, 2004, “
Time-Based Competition in Manufacturing: Stream-of-Variation Analysis (SOVA) Methodology-Review
,”
Int. J. Flexible Manuf. Syst.
,
16
(
1
), pp.
11
44
.
5.
Huang
,
W.
,
Lin
,
J.
,
Bezdecny
M.
,
Kong
,
Z.
, and
Ceglarek
,
D.
, 2007, “
Stream-of-Variation Modeling I: A Generic 3D Variation Model for Rigid Body Assembly in Single Station Assembly Processes
,”
ASME 2006 International Manufacturing Science and Engineering Conference (MSEC2006)
,
Ypsilanti
,
Michigan
, pp.
661
672
.
6.
Huang
,
W.
,
Lin
,
J.
,
Kong
,
Z.
, and
Ceglarek
,
D.
, 2007, “
Stream-of-Variation Modeling II: A Generic 3D Variation Model for Rigid Body Assembly in Multi Station Assembly Processes
,”
ASME Trans. J. Manuf. Sci. Eng.
,
129
(
4
), pp.
832
842
.
7.
Huang
,
W.
,
Phoomboplab
,
T.
, and
Ceglarek
,
D.
, 2009, “
Process Capability Surrogate Model-Based Tolerance Synthesis for Multi-Station Manufacturing Systems (MMS)
,”
IIE Trans.
,
41
(
4
), pp.
309
322
.
8.
Chen
,
S.
,
Wang
,
H.
, and
Huang
,
Q.
, 2009, “
Multistage Machining Process Design and Optimization Using Error Equivalence Method
,”
ASME-MSEC
, MSEC Paper No. 2009-84359.
9.
Kong
,
Z.
,
Ceglarek
,
D.
, and
Huang
,
W.
, 2008, “
Multiple Fault Diagnosis Method in Multistation Assembly Processes Using Orthogonal Diagonalization Analysis
,”
J. Manuf. Sci. Eng.
,
130
(
1
), pp.
11
14
.
10.
Phoomboplab
,
T.
, and
Ceglarek
,
D.
, 2008, “
Process Yield Improvement Through Optimum Design of Fixture Layouts in 3D Multistation Assembly Systems
,”
J. Manuf. Sci. Eng.
,
130
, p.
061005
.
11.
Izquierdo
,
L.
,
Hu
,
J.
,
Du
,
H.
,
Jin
,
R.
,
Jee
,
H.
, and
Shi
,
J.
, 2009, “
Robust Fixture Layout Design for a Product Family Assembled in a Multistage Reconfigurable Line
,”
J. Manuf. Sci. Eng.
,
131
, pp.
1
9
.
12.
Zhong
,
J.
,
Liu
,
J.
, and
Shi
,
J.
, 2010, “
Predictive Control Considering Model Uncertainty for Variation Reduction in Multistage Assembly Processes
,”
IEEE Trans. Autom. Sci. Eng.
,
7
(
4
), pp.
724
735
.
13.
Kim
,
P.
, and
Ding
,
Y.
, 2005, “
Optimal Engineering Design Guided by Data-Mining Methods
,”
Technometrics
,
47
(
3
), pp.
336
348
.
14.
Loose
,
J. P.
,
Chen
,
N.
, and
Zhou
,
S.
, 2009, “
Surrogate Modeling of Dimensional Variation Propagation in Multistage Assembly Processes
,”
IIE Trans.
,
41
(
10
), pp.
893
904
.
15.
Sacks
,
J.
,
Schiller
,
S. B.
, and
Welch
W. J.
, 1989, “
Designs for Computer Experiments
,”
Technometrics
,
31
, pp.
41
47
.
16.
Sacks
,
J.
,
William
,
J. W.
,
Mitchell
,
T. J.
, and
Wynn
H. P.
, 1989, “
Design and Analysis of Computer Experiments
,”
Statist. Sci.
,
4
, pp.
409
423
.
17.
Currin
,
C.
,
Mitchell
,
T.
,
Morris
,
M.
, and
Ylvisaker
,
D.
, 1991, “
Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments
,”
J. Am. Statist. Assoc.
,
86
, pp.
953
963
.
18.
Santner
,
T. J.
,
Williams
,
B. J.
, and
Notz
,
W. I.
, 2003,
The Design and Analysis of Computer Experiments
,
Springer
,
New York
.
19.
Zhou
,
Q.
,
Qian
,
P. Z. G.
, and
Zhou
,
S.
, (2011), “
A Simple Approach to Emulation for Computer Models With Qualitative and Quantitative Factors
,”
Technometrics
,
53
(
3
), pp.
266
273
.
20.
Ding
,
Y.
,
Kim
,
P.
,
Ceglarek
,
D.
, and
Jin
,
J.
, 2003, “
Optimal Sensor Distribution for Variation Diagnosis in Multistation Assembly Processes
,”
IEEE Trans. Rob. Autom.
,
19
(
4
), pp.
543
556
.
21.
Cai
,
W.
,
Hu
,
S. J.
, and
Yuan
,
J. X.
, 1997, “
A Variational Method of Robust Fixture Configuration Design for 3-D Workpieces
,”
Trans. ASME J. Manuf. Sci. Eng.
,
119
(
4/A
), pp.
593
602
.
22.
Ceglarek
,
D.
, and
Shi
,
J.
, 1995, “
Dimensional Variation Reduction for Automotive Body Assembly
,”
Manuf. Rev.
,
8
(
2
), pp.
139
154
.
23.
McKay
,
M. D.
,
Beckman
,
R. J.
, and
Conover
,
W. J.
, 1979, “
A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
,”
Technometrics
,
21
, pp.
239
245
.
24.
Lophaven
,
S. N.
,
Nielsen
,
H. B.
, and
Sondergaard
,
J.
, 2002,
Matlab Kriging toolbox DACE
, Version 2.5. http://www2.imm.dtu.dk/∼hbn/dace/http://www2.imm.dtu.dk/∼hbn/dace/.
25.
Qian
,
P. Z. G.
,
Wu
,
H.
, and
Wu
,
C. F. J.
, 2008, “
Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors
,”
Technometrics
,
50
(
3
), pp.
283
396
.
26.
Kim
,
P.
, and
Ding
Y.
, 2004, “
Optimal Design of Fixture Layout in Multi-Station Assembly Processes
,”
IEEE Trans. Autom. Sci. Eng.
,
1
(
2
), pp.
133
145
.
27.
Gramacy
,
R. B.
, and
Lee
,
H.
, 2008, “
Bayesian Treed Gaussian Process Models With an Application to Computer Modeling
,”
J. Am. Statist. Assoc.
,
103
(
483
), pp.
1119
1130
.
28.
Stinstra
,
E.
,
den Hertog
,
D.
,
Stehouwer
,
P.
, and
Vestjens
,
A.
, 2003, “
Constrained Maximin Designs for Computer Experiments
,”
Technometrics
,
45
(
4
), pp.
340
346
.
29.
Trosset
,
M. W.
, 1999, “
Approximate Maximin Distance Designs
,”
ASA Proceedings of the Section on Physical and Engineering Sciences
, pp.
223
227
.
30.
Chuang
,
S. C.
, and
Hung
,
Y. C.
, 2010, “
Uniform Designs Over General Input Domains With Applications to Target Region Estimation in Computer Experiments
,”
Comput. Stat. Data Anal.
,
54
(
1
), pp.
219
232
.
31.
Jin
,
R.
,
Chen
,
W.
, and
Simpson
,
T. W.
, 2001, “
Comparative Studies of Metamodeling Techniques Under Multiple Modeling Criteria
,”
Struct. Multidiscip. Optim.
,
23
(
1
), pp.
1
13
.
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