Abstract

Response surface methods or metamodels are commonly used to approximate large computationally expensive engineering systems. Five response surface methods are studied: Stepwise Regression, Moving Least Square, Kriging, Multiquadric, and Adaptive and Interactive Modeling System. A real-world frontal impact design problem is used as an example, which is a complex, highly nonlinear, transient, dynamic, large deformation finite element model. To study the accuracy of the metamodel, the optimal Latin Hypercube Sampling method is used to distribute the sampling points uniformly over the entire design space. The Root Mean Square Error (RMSE) is used as the error indicator. Convergence rate, widely used in the arena of the finite element method for evaluating new element’s performance, was exploited in this vehicle impact example.

Issue Section:
Technical Papers
Keywords:
vehicles, impact (mechanical), response surface methodology, regression analysis, deformation, finite element analysis, sampling methods, mean square error methods
Topics:
Design, Metamodeling, Modeling, Simulation, Vehicles, Deformation, Response surface methodology, Errors, Sampling methods
1.
Craig
,
K. J.
,
Stander
,
N.
,
Dooge
,
D. A.
, and
Varadappa
,
S.
, 2005, “
Automotive Crashworthiness Design Using Response Surface-Based Variable Screening and Optimization
,”
Eng. Comput.
0177-0667,
22
(
1
), pp.
38
–
61
.
Crossref
Search ADS
 
2.
Wang
,
X.
,
Liu
,
Y.
, and
Antonsson
,
E.
, 1999, “
Fitting Functions to Data in High Dimensional Design Space
,” in
Proceedings of DETC 99, 1999 ASME Design Engineering Technical Conferences
, DETC99∕DAC-8622.
Crossref
Search ADS
 
3.
Sobieski
,
J.
,
Kodiyalam
,
S.
, and
Yang
,
R. J.
, 2001, “
Optimization of Car Body under Constraints of Noise, Vibration, and Harshness (NVH), and Crash
,”
Struct. Multidiscip. Optim.
1615-147X,
22
, pp.
295
–
306
.
Crossref
Search ADS
 
4.
Jin
,
R.
,
Chen
,
W.
, and
Simpson
,
T. W.
, 2000, “
Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria
,” AIAA-2000-4801.
5.
Yang
,
R. J.
,
Gu
,
L.
,
Liaw
,
L.
,
Gearhart
,
C.
,
Tho
,
C. H.
,
Liu
,
X.
, and
Wang
,
B. P.
, 2000, “
Approximations for Safety Optimization of Large Systems
,”
ASME Design Automation Conference
, Paper No. DETC2000∕DAC-14245.
6.
Lu
,
Stephen C-Y.
, and
Cheng
,
D. K.
, 1991, “
Building Layered Models to Support Engineering Decision Making: A Machine Learning Approach
,”
J. Eng. Ind.
0022-0817, ASME Transactions,
13
(
1
), pp.
1
–
9
.
Crossref
Search ADS
 
7.
Ge
,
P.
, and
Wang
,
N.
, 2000, “
DoE Study in Building Surrogate Models for Complex Systems
,” in
Proceedings of DETC’2000
, Baltimore.
Crossref
Search ADS
 
8.
Simpson
,
T. W.
,
Booker
,
A. J.
,
Ghosh
,
D.
,
Giunta
,
A. A.
,
Koch
,
P. N.
, and
Yang
,
R. J.
, 2004, “
Approximation Methods in Multidisciplinary Analysis and Optimization: A Panel Discussion
,”
Struct. Multidiscip. Optim.
1615-147X,
27
, pp.
302
–
313
.
9.
Simpson
,
T. W.
,
Clarke
,
S. M.
, and
Griebsch
,
J. H.
, 2005, “
Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses
,”
ASME J. Mech. Des.
1050-0472,
127
(
6
) pp.
1077
-
1087
.
Crossref
Search ADS
 
10.
Efroymson
,
M.
, 1960, “
Multiple Regression Analysis
,”
Mathematical Methods for Digital Computers
, edited by
A.
Ralston
 and
H.
Wilf
,
Wiley
, New York, pp.
191
–
203
.
11.
Lancaster
,
P.
, and
Salkauskas
,
K.
, 1981, “
Surfaces Generated by Moving Least Squares Methods
,”
Math. Comput.
0025-5718,
37
, pp.
141
–
158
.
Crossref
Search ADS
 
12.
Hawkins
,
D. M.
, and
Cressie
,
N.
, 1984, “
Robust Kriging—a Proposal
,”
Journal of the International Association for Mathematical Geology
,
16
, pp.
3
–
18
.
Crossref
Search ADS
 
13.
Oliver
,
M. A.
, and
Webster
,
R.
, 1990, “
Kriging: A Method of Interpolation for Geographical Information Systems
,”
Int. J. Geograph. Inf. Sci.
1365-8816,
4
, pp.
313
–
332
.
Crossref
Search ADS
 
14.
Cressie
,
N. C. A.
, 1993,
Statistics for Spatial Data
,
Wiley
, New York.
15.
Ripley
,
B. D.
, 1987,
Stochastic Simulation
,
Wiley
, New York.
Crossref
Search ADS
 
16.
Kodiyalam
,
S.
,
Yang
,
R. J.
,
Gu
,
L.
, and
Tho
,
C-H.
, 2004, “
Multidisciplinary Design Optimization of a Vehicle System in a Scalable, High Performance Computing Environment
,”
Struct. Multidiscip. Optim.
1615-147X,
26
, pp.
235
–
248
.
17.
Hardy
,
R. L.
, 1971, “
Multiquadric Equations Of Topography and Other Irregular Surfaces
,”
J. Geophys. Res.
0148-0227,
76
, pp.
1905
–
1915
.
Crossref
Search ADS
 
18.
Hardy
,
R. L.
, 1990, “
Theory and Application of the Multiquadric-Biharmonic Method
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
19
, pp.
163
–
208
.
19.
Wang
,
B. P.
, 2004, “
Parameter Optimization in Multiquadric Response Surface Approximation
,”
Struct. Multidiscip. Optim.
1615-147X,
26
, pp.
219
–
223
.
Crossref
Search ADS
 
20.
RADIOSS User’s Manual, Version 4.1, MECALOG, France, 1998.
21.
MADYMO User’s Manual, Version 5.3, TNO, Netherlands, 1998.
Copyright © 2005
 by American Society of Mechanical Engineers
You do not currently have access to this content.