Probabilistic analysis and design of large-scale structures requires repeated finite-element analyses of large models, and each analysis is expensive. This paper presents a methodology for probabilistic analysis and reliability-based design optimization of large-scale structures that consists of two re-analysis methods, one for estimating the deterministic vibratory response and another for estimating the probability of the response exceeding a certain level. The deterministic re-analysis method can analyze efficiently large-scale finite-element models consisting of tens or hundreds of thousand degrees of freedom and design variables that vary in a wide range. The probabilistic re-analysis method calculates very efficiently the system reliability for different probability distributions of the random variables by performing a single Monte Carlo simulation of one design. The methodology is demonstrated on probabilistic vibration analysis and reliability-based design optimization of a realistic vehicle model. It is shown that the computational cost of the proposed re-analysis method for a single reliability analysis is about 1/20 of the cost of the same analysis using MSC/NASTRAN. Moreover, the probabilistic re-analysis approach enables a designer to perform reliability-based design optimization of the vehicle at a cost almost equal to that of a single reliability analysis. Without using the probabilistic re-analysis approach, it would be impractical to perform reliability-based design optimization of the vehicle.

1.
Madsen
,
H. O.
,
Krenk
,
S.
, and
Lind
,
N. C.
, 1986,
Methods of Structural Safety
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
2.
Melchers
,
R. E.
, 2001,
Structural Reliability Analysis and Prediction
,
Wiley
,
New York
.
3.
Moses
,
F.
, 1995, “
Probabilistic Analysis of Structural Systems
,”
Probabilistic Structural Mechanics Handbook: Theory and Industrial Applications
,
C.
Raj Sundararajan
, ed.,
Chapman and Hall
,
London
, pp.
166
187
.
4.
Frangopol
,
D. M.
, 1995, “
Reliability-Based Optimum Structural Design
,”
Probabilistic Structural Mechanics Handbook: Theory and Industrial Applications
,
C.
Raj Sundararajan
, ed.,
Chapman and Hall
,
London
, pp.
352
387
.
5.
Liang
,
J.
,
Mourelatos
,
Z. P.
, and
Nikolaidis
,
E.
, 2007, “
A Single-Loop Approach for System Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
0161-8458,
129
, pp.
1215
1224
.
6.
Ayyub
,
B.
, and
Mccuen
,
R.
, 1995, “
Simulation-Based Reliability Methods
,”
Probabilistic Structural Mechanics Handbook: Theory and Industrial Applications
,
C.
Raj Sundararajan
, ed.,
Chapman and Hall
,
London
, pp.
53
69
.
7.
Du
,
X.
, and
Chen
,
W.
, 2004, “
Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design
,”
ASME J. Mech. Des.
0161-8458,
126
(
2
), pp.
225
233
.
8.
Haldar
,
A.
, and
Mahadevan
,
S.
, 1995, “
First and Second Order Reliability Methods
,”
Probabilistic Structural Mechanics Handbook: Theory and Industrial Applications
,
C.
Raj Sundararajan
, ed.,
Chapman and Hall
,
London
, pp.
27
52
.
9.
Der Kiureghian
,
A.
, 2000, “
The Geometry of Random Vibrations and Solutions by FORM and SORM
,”
Probab. Eng. Mech.
0266-8920,
15
, pp.
81
91
.
10.
Wu
,
Y. T.
,
Millwater
,
H. R.
, and
Cruse
,
T. A.
, 1990, “
Advanced Probabilistic Structural Analysis Method for Implicit Performance Functions
,”
AIAA J.
0001-1452,
28
(
9
), pp.
1663
1669
.
11.
Rodriguez
,
J. F.
,
Renaud
,
J. E.
, and
Watson
,
L. T.
, 1998, “
Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization
,”
ASME J. Mech. Des.
0161-8458,
120
, pp.
58
66
.
12.
Gayton
,
N.
,
Bourinet
,
J. M.
, and
Lamaire
,
M.
, 2003, “
CQ2RS: A New Statistical Approach to the Response Surface Method for Reliability Analysis
,”
Struct. Safety
,
25
, pp.
99
121
. 0167-4730
13.
Papadrakakis
,
M.
, and
Lagaros
,
N. D.
, 2002, “
Reliability-Based Structural Optimization Using Neural Networks and MC Simulation
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
191
, pp.
3491
3507
.
14.
Shan
,
S.
, and
Wang
,
G. G.
, 2006, “
Failure Surface Frontier for Reliability Assessment on Expensive Performance Function
,”
ASME J. Mech. Des.
0161-8458,
128
, pp.
1227
1235
.
15.
Chandu
,
S. V. L.
, and
Grandhi
,
R. V.
, 1995, “
General Purpose Procedure for Reliability Based Structural Optimization Under Parametric Uncertainties
,”
Adv. Eng. Software
0965-9978,
23
, pp.
7
14
.
16.
Grandhi
,
R. V.
, and
Wang
,
L.
, 1998, “
Reliability-Based Structural Optimization Using Improved Two Point Adaptive Nonlinear Approximations
,”
Finite Elem. Anal. Design
0168-874X,
29
, pp.
35
48
.
17.
Qu
,
X.
, and
Haftka
,
R. T.
, 2003, “
A Reliability-Based Design Optimization Using Probabilistic Safety Factor
,” AIAA Paper No. 2003–1657.
18.
Ridgeway
,
G.
, and
Madigan
,
D.
, 2003, “
A Sequential MC Method for Bayesian Analysis of Massive Datasets
,”
Data Min. Knowl. Discov.
,
7
, pp.
301
319
. 1384-5810
19.
Balakrishnan
,
S.
, and
Madigan
,
D.
, 2006, “
A One-Pass Sequential MC Method for Bayesian Analysis of Massive Datasets
,”
J. Bayesian Anal.
,
1
(
2
), pp.
345
362
.
20.
Fonseca
,
J. R.
, 2007, “
Efficient Robust Design Via MC Simulation Sample Reweighting
,”
Int. J. Numer. Methods Eng.
,
69
, pp.
2279
2301
. 0029-5981
21.
Abu Kassim
,
A. M.
, and
Topping
,
B. H. V.
, 1987, “
Static Re-Analysis: A Review
,”
J. Struct. Eng.
0733-9445,
113
, pp.
1029
1045
.
22.
Arora
,
J. S.
, 1976, “
Survey of Structural Re-Analysis Techniques
,”
J. Struct. Eng.
,
102
, pp.
783
802
. 0733-9445
23.
Barthelemy
,
J. -F. M.
, and
Haftka
,
R. T.
, 1993, “
Approximation Concepts for Optimum Structural Design—A Review
,”
Struct. Optim.
0934-4373,
5
, pp.
129
144
.
24.
Keane
,
A. J.
, and
Nair
,
P. B.
, 2005, “
Sensitivity Analysis and Approximation Concepts
,”
Computational Approaches for Aerospace Design, The Pursuit of Excellence
,
Wiley
,
Chichester, England
.
25.
Balmes
,
E.
, 1996, “
Optimal Ritz Vectors for Component Mode Synthesis Using the Singular Value Decomposition
,”
AIAA J.
,
34
(
6
), pp.
1256
1260
. 0001-1452
26.
Balmes
,
E.
,
Ravary
,
F.
, and
Langlais
,
D.
, 2004, “
Uncertainty Propagation in Modal Analysis
,”
Proceedings of IMAC-XXII: A Conference and Exposition on Structural Dynamics
, Dearborn, MI, Jan.
27.
Yasui
,
Y.
, 1998, “
Direct Coupled Load Verification of Modified Structural Component
,”
AIAA J.
,
36
(
1
), pp.
94
101
. 0001-1452
28.
Liu
,
J. K.
, 1999, “
A Universal Matrix Perturbation Technique for Structural Dynamic Modification Using Singular Value Decomposition
,”
J. Sound Vib.
,
228
(
2
), pp.
265
274
. 0022-460X
29.
Zhang
,
G.
,
Castanier
,
M. P.
, and
Pierre
,
C.
, 2005, “
Integration of Component-Based and Parametric Reduced-Order Modeling Methods for Probabilistic Vibration Analysis and Design
,”
Proceedings of the Sixth European Conference on Structural Dynamics
, Paris, France, Sept.
30.
Zhang
,
G.
, 2005, “
Component-Based and Parametric Reduced-Order Modeling Methods for Vibration Analysis of Complex Structures
,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
31.
Kirsch
,
U.
, 2002,
Design-Oriented Analysis of Structures
,
Kluwer
,
Dordrecht
.
32.
Kirsch
,
U.
, 2003, “
Design-Oriented Analysis of Structures—A Unified Approach
,”
J. Eng. Mech.
0733-9399,
129
, pp.
264
272
.
33.
Kirsch
,
U.
, 2003, “
A Unified Re-Analysis Approach for Structural Analysis, Design and Optimization
,”
Struct. Multidiscip. Optim.
1615-147X,
25
, pp.
67
85
.
34.
Chen
,
S. H.
, and
Yang
,
X. W.
, 2000, “
Extended Kirsch Combined Method for Eigenvalue Re-Analysis
,”
AIAA J.
,
38
, pp.
927
930
. 0001-1452
35.
Kirsch
,
U.
, 2003, “
Approximate Vibration Re-Analysis of Structures
,”
AIAA J.
,
41
, pp.
504
511
. 0001-1452
36.
Kirsch
,
U.
, and
Bogomolni
,
M.
, 2004, “
Procedures for Approximate Eigenproblem Re-Analysis of Structures
,”
Int. J. Numer. Methods Eng.
0029-5981,
60
, pp.
1969
1986
.
37.
Kirsch
,
U.
, and
Bogomolni
,
M.
, 2004, “
Error Evaluation in Approximate Re-Analysis of Structures
,”
Struct. Optim.
,
28
, pp.
77
86
. 0934-4373
38.
Rong
,
F.
,
Chen
,
S. M.
, and
Chen
,
Y. D.
, 2003, “
Structural Modal Re-Analysis for Topological Modifications With Extended Kirsch Method
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
192
, pp.
697
707
.
39.
Chen
,
S. H.
,
Yang
,
X. W.
, and
Lian
,
H. D.
, 2000, “
Comparison of Several Eigenvalue Re-Analysis Methods for Modified Structures
,”
Struct. Multidiscip. Optim.
1615-147X,
20
, pp.
253
259
.
40.
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
.
41.
Clough
,
R. W.
, and
Penzien
,
J.
, 1993,
Dynamics of Structures
,
2nd ed.
,
McGraw-Hill
,
New York
.
42.
Lophaven
,
S. N.
,
Nielsen
,
H. B.
, and
Sondergaard
,
J.
, 2002, “
DACE-A MATLAB Kriging Tool Box
,” Technical Report No. IMM-TR-2002–12.
43.
Sacks
,
J.
,
Welch
,
W.
,
Mitchell
,
T. J.
, and
Wynn
,
H. P.
, 1989, “
Design and Analysis of Computer Experiments
,”
Stat. Sci.
0883-4237,
4
(
4
), pp.
409
435
.
44.
Ye
,
K. Q.
,
Li
,
W.
, and
Sudjianto
,
A.
, 2000, “
Algorithmic Construction of Optimal Symmetric Latin Hypercube Designs
,”
J. Stat. Plan. Infer.
0378-3758,
90
, pp.
145
159
.
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