Uncertainty in the input parameters to an engineering system may not only degrade the system’s performance but may also cause failure or infeasibility. This paper presents a new sensitivity analysis based approach called design improvement by sensitivity analysis (DISA). DISA analyzes the interval uncertainty of input parameters and using multi-objective optimization, determines an optimal combination of design improvements that will ensure a minimal variation in the objective functions of the system, while also ensuring the feasibility. The approach provides a designer with options for both uncertainty reduction and, more importantly, slight design adjustments. A two-stage sequential framework is used that can employ either the original analysis functions or their metamodels to greatly increase the computational efficiency of the approach. This new approach has been applied to two engineering examples of varying difficulty to demonstrate its applicability and effectiveness. The results produced by these examples show the ability of the approach to ensure the feasibility of a preexisting design under interval uncertainty by effectively adjusting available degrees of freedom in the system without the need to completely redesign the system.

1.
Lee
,
S. H.
, and
Chen
,
W.
, 2009, “
A Comparative Study of Uncertainty Propagation Methods for Black-Box-Type Problems
,”
Struct. Multidiscip. Optim.
1615-147X,
37
(
3
), pp.
239
253
.
2.
Schueller
,
G. I.
, and
Jensen
,
H. A.
, 2008, “
Computational Methods in Optimization Considering Uncertainties—An Overview
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
198
(
1
), pp.
2
13
.
3.
Möller
,
B.
, and
Beer
,
M.
, 2008, “
Engineering Computation Under Uncertainty—Capabilities of Non-Traditional Models
,”
Comput. Struct.
0045-7949,
86
(
10
), pp.
1024
1041
.
4.
Martin
,
J. D.
, and
Simpson
,
T. W.
, 2006, “
A Methodology to Manage System-Level Uncertainty During Conceptual Design
,”
ASME J. Mech. Des.
0161-8458,
128
(
4
), pp.
959
968
.
5.
Guo
,
J.
, and
Du
,
X.
, 2007, “
Sensitivity Analysis With Mixture of Epistemic and Aleatory Uncertainties
,”
AIAA J.
0001-1452,
45
(
9
), pp.
2337
2349
.
6.
Noh
,
Y.
,
Choi
,
K. K.
, and
Lee
,
I.
, 2008, “
MPP-Based Dimension Reduction Method for RBDO Problems With Correlated Input Variables
,”
Proceedings of the 12th AIAA/ISSMO Conference
, Victoria, BC, Canada, Sep. 10–12.
7.
Acar
,
E.
,
Haftka
,
R. T.
, and
Johnson
,
T. F.
, 2007, “
Tradeoff of Uncertainty Reduction Mechanisms for Reducing Weight of Composite Laminates
,”
ASME J. Mech. Des.
0161-8458,
129
(
3
), pp.
266
274
.
8.
Rao
,
S. S.
, and
Cao
,
L. T.
, 2002, “
Optimum Design of Mechanical Systems Involving Interval Parameters
,”
ASME J. Mech. Des.
0161-8458,
124
(
3
), pp.
465
472
.
9.
Qui
,
Z.
,
Hu
,
J.
,
Yang
,
J.
, and
Qishao
,
L.
, 2007, “
Exact Bounds for the Sensitivity Analysis of Structures With Uncertain-But-Bounded Parameters
,”
Appl. Math. Model.
0307-904X,
32
(
6
), pp.
1143
1157
.
10.
Li
,
M.
,
Williams
,
N.
, and
Azarm
,
S.
, 2009, “
Interval Uncertainty Reduction and Sensitivity Analysis With Multi-Objective Design Optimization
,”
ASME J. Mech. Des.
0161-8458,
131
(
3
), p.
031007
.
11.
Li
,
M.
,
Williams
,
N.
,
Azarm
,
S.
,
Al Hashimi
,
S.
,
Almansoori
,
A.
, and
Al Qasas
,
N.
, 2009, “
Integrated Multi-Objective Robust Optimization and Sensitivity Analysis With Irreducible and Reducible Interval Uncertainty
,”
Eng. Optimiz.
0305-215X,
41
(
10
), pp.
889
908
.
12.
Beyer
,
H.
, and
Sendhoff
,
B.
, 2007, “
Robust Optimization—A Comprehensive Survey
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
196
(
33–34
), pp.
3190
3218
.
13.
Joseph
,
V. R.
, 2007, “
Taguchi’s Approach to Robust Parameter Design: A New Perspective
,”
IIE Trans.
0740-817X,
39
(
8
), pp.
805
810
.
14.
Apley
,
D. W.
,
Liu
,
J.
, and
Chen
,
W.
, 2006, “
Understanding the Effects of Model Uncertainty in Robust Design With Computer Experiments
,”
ASME J. Mech. Des.
0161-8458,
128
(
4
), pp.
945
958
.
15.
Giesy
,
D. P.
,
Crespo
,
L. G.
, and
Kenny
,
S. P.
, 2008, “
Approximation of Failure Probability Using Conditional Sampling
,”
Proceedings of the 12th AIAA/ISSMO Conference
, Victoria, BC, Canada, Sep. 10–12.
16.
Du
,
X.
, and
Zhang
,
Y.
, 2008, “
A General Approach to Robustness Assessment for Multidisciplinary Systems
,”
Proceedings of the ASME IDETC/CIE 2008 Conference
, Brooklyn, NY, Aug. 3–6.
17.
Crespo
,
L. G.
,
Giesy
,
D. P.
, and
Kenny
,
S. P.
, 2008, “
Robustness Analysis and Robust Design of Uncertain Systems
,”
AIAA J.
0001-1452,
46
(
2
), pp.
388
396
.
18.
Lee
,
T. W.
, 2006, “
A Study for Robustness of Objective Function and Constraints in Robust Design Optimization
,”
J. Mech. Sci. Technol.
1738-494X,
20
(
10
), pp.
1662
1669
.
19.
Li
,
M.
, and
Azarm
,
S.
, 2008, “
Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation
,”
ASME J. Mech. Des.
0161-8458,
130
(
8
), p.
081402
.
20.
Wang
,
P.
,
Youn
,
B. D.
,
Xi
,
Z.
, and
Kloess
,
A.
, 2009, “
Bayesian Reliability With Evolving, Insufficient, and Subjective Data Sets
,”
ASME J. Mech. Des.
0161-8458,
131
(
11
), p.
111008
.
21.
Qu
,
X.
,
Haftka
,
R. T.
,
Venkataraman
,
S.
, and
Johnson
,
T. F.
, 2003, “
Deterministic and Reliability-Based Optimization of Composite Laminates for Cryogenic Environments
,”
AIAA J.
0001-1452,
41
(
10
), pp.
2029
2036
.
22.
Kale
,
A. A.
, and
Haftka
,
R. T.
, 2008, “
Tradeoff of Weight and Inspection Cost in Reliability-Based Structural Optimization
,”
J. Aircr.
0021-8669,
45
(
1
), pp.
77
85
.
23.
Haukaas
,
T.
, 2008, “
Unified Reliability and Design Optimization for Earthquake Engineering
,”
Probab. Eng. Mech.
0266-8920,
23
(
4
), pp.
471
481
.
24.
Iman
,
R. L.
, and
Helton
,
J. C.
, 1998, “
An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models
,”
Risk Anal.
0272-4332,
8
(
1
), pp.
71
90
.
25.
Huang
,
B. Q.
, and
Du
,
X. P.
, 2006, “
Uncertainty Analysis by Dimension Reduction Integration and Saddle Point Approximations
,”
ASME J. Mech. Des.
0161-8458,
128
(
1
), pp.
26
33
.
26.
Castillo
,
E.
,
Minguez
,
R.
, and
Castillo
,
C.
, 2008, “
Sensitivity Analysis in Optimization and Reliability Problems
,”
Reliab. Eng. Syst. Saf.
0951-8320,
93
(
12
), pp.
1788
1800
.
27.
Qiu
,
Z. P.
,
Ma
,
Y.
, and
Wang
,
X. J.
, 2004, “
Comparison Between Non-Probabilistic Interval Analysis Method and Probabilistic Approach in Static Response Problem of Structures With Uncertain-But-Bounded Parameters
,”
Commun. Numer. Methods Eng.
1069-8299,
20
(
4
), pp.
279
290
.
28.
Du
,
X.
, 2008, “
Unified Uncertainty Analysis by the First Order Reliability Method
,”
ASME J. Mech. Des.
0161-8458,
130
(
9
), p.
091401
.
29.
Shan
,
S.
, and
Wang
,
G. G.
, 2008, “
Survey of Modeling and Optimization Strategies for High-Dimensional Design Problems
,”
Proceedings of the 12th AIAA/ISSMO Conference
, Victoria, BC, Canada, Sep. 10–12.
30.
Wang
,
G. G.
, and
Shan
,
S.
, 2007, “
Review of Metamodeling Techniques in Support of Engineering Design Optimization
,”
ASME J. Mech. Des.
0161-8458,
129
(
4
), pp.
370
380
.
31.
Allaire
,
D.
, and
Willcox
,
K.
, 2008, “
Surrogate Modeling for Uncertainty Assessment With Application to Aviation Environmental System Models
,”
Proceedings of the 12th AIAA/ISSMO Conference
, Victoria, BC, Canada, Sep. 10–12.
32.
Martin
,
J. D.
, and
Simpson
,
T. W.
, 2005, “
Use of Kriging Models to Approximate Deterministic Computer Models
,”
AIAA J.
0001-1452,
43
(
4
), pp.
853
863
.
33.
Ju
,
B. H.
, and
Lee
,
B. C.
, 2008, “
Reliability-Based Design Optimization Using a Moment Method and a Kriging Metamodel
,”
Eng. Optimiz.
0305-215X,
40
(
5
), pp.
421
438
.
34.
Srivastava
,
A.
,
Hacker
,
K.
, and
Lewis
,
K.
, 2004, “
A Method for Using Legacy Data for Metamodel-Based Design of Large-Scale Systems
,”
Struct. Multidiscip. Optim.
1615-147X,
28
(
2–3
), pp.
146
155
.
35.
Moore
,
R. E.
, 1966,
Interval Analysis
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
36.
Deb
,
K.
,
Pratap
,
A.
,
Agarwal
,
S.
, and
Meyarivan
,
T.
, 2002, “
A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II
,”
IEEE Trans. Evol. Comput.
1089-778X,
6
(
2
), pp.
182
197
.
37.
Arora
,
J. S.
, 2004,
Introduction to Optimum Design
, 2nd ed.,
Elsevier Academic
,
San Diego, CA
.
38.
Williams
,
N.
,
Azarm
,
S.
, and
Kannan
,
P. K.
, 2008, “
Engineering Product Design Optimization for Retail Channel Acceptance
,”
ASME J. Mech. Des.
0161-8458,
130
(
6
), p.
061402
.
39.
Hamel
,
J.
,
Li
,
M.
, and
Azarm
,
S.
, 2009, “
Design Improvement By Sensitivity Analysis (DISA) Under Interval Uncertainty Using Multi-Objective Optimization
,”
Proceedings of the ASME IDETC/CIE 2008 Conference
, San Diego, CA, Aug. 30–Sep. 2.
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