The importance of sensitivity analysis in engineering design cannot be over-emphasized. In design under uncertainty, sensitivity analysis is performed with respect to the probabilistic characteristics. Global sensitivity analysis (GSA), in particular, is used to study the impact of variations in input variables on the variation of a model output. One of the most challenging issues for GSA is the intensive computational demand for assessing the impact of probabilistic variations. Existing variance-based GSA methods are developed for general functional relationships but require a large number of samples. In this work, we develop an efficient and accurate approach to GSA that employs analytic formulations derived from metamodels. The approach is especially applicable to simulation-based design because metamodels are often created to replace expensive simulation programs, and therefore readily available to designers. In this work, we identify the needs of GSA in design under uncertainty, and then develop generalized analytical formulations that can provide GSA for a variety of metamodels commonly used in engineering applications. We show that even though the function forms of these metamodels vary significantly, they all follow the form of multivariate tensor-product basis functions for which the analytical results of univariate integrals can be constructed to calculate the multivariate integrals in GSA. The benefits of our proposed techniques are demonstrated and verified through both illustrative mathematical examples and the robust design for improving vehicle handling performance.

1.
Manring
,
N. D.
, 2003, “
Sensitivity Analysis of the Conical-Shaped Equivalent Model of a Bolted Joint
,”
ASME J. Mech. Des.
1050-0472,
125
,
642
646
.
2.
Du
,
X.
, and
Chen
,
W.
, 2004, “
Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design
,”
ASME J. Mech. Des.
1050-0472,
126
(
2
), pp.
225
233
.
3.
Du
,
X.
,
Sudjianto
,
A.
, and
Chen
,
W.
, 2004, “
An Integrated Framework for Optimization under Uncertainty using Inverse Reliability Strategy
,”
ASME J. Mech. Des.
1050-0472,
126
(
4
),
562
570
.
4.
Youn
,
B. D.
, and
Choi
,
K. K.
, 2004, “
An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches
,”
ASME J. Mech. Des.
1050-0472,
126
,
403
411
.
5.
Nikolaidis
,
E.
,
Chen
,
S.
,
Cudney
,
H.
,
Haftka
,
R. T.
, and
Rosca
,
R.
, 2004, “
Comparison of Probability and Possibility for Design Against Catastrophic Failure under Uncertainty
,”
ASME J. Mech. Des.
1050-0472,
126
,
386
394
.
6.
Liu
,
H.
,
Chen
,
W.
, and
Sudjianto
,
A.
, 2004, “
Relative Entropy Based Method for Global and Regional Sensitivity Analysis in Probabilistic Design
,” DETC2004-57500,
2004 ASME Design Automation Conference
, Salt Lake City, UT, September 28–October 2, 2004.
7.
Box
,
G. E. P.
,
Hunter
,
W. G.
, and
Hunter
,
J. S.
, 1978,
Statistics for Experimenters
,
Wiley
, New York.
8.
Saltelli
,
A.
,
Tarantola
,
S.
, and
Chan
,
K.
, 1999, “
A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output
,”
Technometrics
0040-1706,
41
(
1
),
39
56
.
9.
McKay
,
M. D.
,
Morrison
,
J. D.
, and
Upton
,
S. C.
, (1999), “
Evaluating prediction uncertainty in simulation models
,”
Comput. Phys. Commun.
0010-4655,
117
, pp.
44
51
.
10.
Homma
,
T.
, and
Saltelli
,
A.
, 1996, “
Importance Measures in Global Sensitivity Analysis of Nonlinear Models
,”
Reliability Eng. Sys. Safety
0951-8320,
52
, pp.
1
17
.
11.
Sobol
,
I. M.
, 1993, “
Sensitivity Analysis for Nonlinear Mathematical Models
,”
Mat. Model.
,
1
,
407
414
Sobol
,
I. M.
,[translation of Sobol’, 1990, “
Sensitivity Estimates for Nonlinear Mathematical Models
,”
Matematicheskoe Modelirovanie
,
2
,
112
118
(in Russian).
12.
Reedijk
,
C. I.
, 2000,
“Sensitivity Analysis of Model Output: Performance of various local and global sensitivity measures on reliability problems
,” Master’s Thesis, Delft University of Technology, 2000.
13.
Helton
,
J. C.
, 1993, “
Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal
,”
Reliability Eng. Sys. Safety
0951-8320,
42
,
327
367
.
14.
Chan
,
K.
,
Saltelli
,
A.
,
Tarantola
,
S.
, 1997, “
Sensitivity Analysis of Model Output: Variance-Based Methods Make the Difference
,”
Proceedings of the 1997 Winter Simulation Conference
.
15.
Chen
,
W.
,
Allen
,
J. K.
,
Schrage
,
D. P.
, and
Mistree
,
F.
, 1997, “
Statistical Experimentation Methods for Achieving Affordable Concurrent Design
,”
AIAA J.
0001-1452,
35
(
5
),
893
900
.
16.
Hardy
,
R. L.
, 1971, “
Multiquadratic equations of topography and other irregular surfaces
,”
J. Geophys. Res.
0148-0227,
76
, pp.
1905
1915
.
17.
Dyn
,
N.
,
Levin
,
D.
, and
Rippa
,
S.
, 1986, “
Numerical procedures for surface fitting of scattered data by radial basis functions
,”
SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204,
7
(
2
), pp.
639
659
.
18.
Sacks
,
J.
,
Welch
,
W. J.
,
Mitchell
,
T. J.
, and
Wynn
,
H. P.
, 1989, “
Design and Analysis of Computer Experiments
,”
Stat. Sci.
0883-4237,
4
, No.
4
, pp.
409
435
.
19.
Currin
,
C.
,
Mitchell
,
T.
,
Morris
,
M. D.
, and
Ylvisaker
,
D.
, 1991, “
Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments
,”
J. Am. Stat. Assoc.
0162-1459,
86
(
416
),
953
963
.
20.
Owen
,
A. B.
, 1999, “
Monte Carlo quasi-Monte Carlo and Randomized quasi-Monte Carlo
,” in
H.
Niederreiter
and
J.
Spanier
, eds.,
Monte Carlo and quasi-Monte Carlo Methods
, pp.
86
97
.
21.
Friedman
,
J. H.
, 1991, “
Multivariate Adaptive Regression Splines
,”
Ann. Stat.
0090-5364,
19
(
1
), pp.
1
141
.
22.
Jin
,
R.
, 2004, “
Enhancements of Metamodeling Techniques in Engineering Design
,” PhD dissertation, University of Illinois at Chicago, Chicago, IL.
23.
Phadke
,
M. S.
, 1989,
Quality Engineering Using Robust Design
,
Prentice Hall
, Englewood Cliffs, NJ.
24.
Hastie
,
T.
,
Tibshirani
,
R.
,
Friedman
,
J.
, 2001,
The Elements of Statistical Learning: data mining, inference, and prediction
,
Springer-Verlag
, New York.
25.
Mohamedshah
,
Y.
,
Council
,
F.
, 1997, “
Synthesis of Rollover Research
,” March 10, 1997.
26.
Chen
,
W.
,
Garimella
,
R.
, and
Michelena
,
N.
, 2001, “
Robust Design for Improved Vehicle Handling Under a Range of Maneuver Conditions
,”
Eng. Optimiz.
0305-215X,
33
, No
3
,
303
326
.
27.
Sayers
,
M. W.
, and
Riley
,
S. M.
, 1996, “
Modeling Assumptions for Realistic Multibody Simulations of the Yaw and Roll Behavior of Heavy Trucks
,”
SAE Paper No. 960173
.
Society of Automotive Engineers
, Warrendale, PA.
28.
Michelena
,
N.
, and
Kim
,
H.-M.
, 1998, “
Worst-Case Design for Vehicle Handling
,”
Fourth Annual Conference on Modeling and Simulation of Ground Vehicles
, The Automotive Research Center,
The University of Michigan
, Ann Arbor, May 19–20, 1998.
29.
Jin
,
R.
,
Chen
,
W.
, and
Sudjianto
,
A.
, “
An Efficient Algorithm for Constructing Optimal Design of Computer Experiments
,” DETC-DAC48760,
2003 ASME Design Automation Conference
, Chicago, IL, September 2–6, 2003, to appear in Journal of Statistical Planning and Inference.
30.
Jin
,
R.
,
Chen
,
W.
, and
Simpson
,
T.
, 2001, “
Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria
,”
Journal of Structural & Multidisciplinary Optimization
,
23
(
1
), pp.
1
13
.
31.
Chen
,
W.
,
Jin
,
R.
, and
Sudjianto
,
A.
, 2004, “
Analytical Uncertainty Propagation in Simulation-Based Design under Uncertainty
,” AIAA-2004-4356,
10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
, Albany, NY, August 30–September 1, 2004.
You do not currently have access to this content.