This paper proposes a new methodology for uncertainty quantification in systems that require multidisciplinary iterative analysis between two or more coupled component models. This methodology is based on computing the probability of satisfying the interdisciplinary compatibility equations, conditioned on specific values of the coupling (or feedback) variables, and this information is used to estimate the probability distributions of the coupling variables. The estimation of the coupling variables is analogous to likelihood-based parameter estimation in statistics and thus leads to the proposed likelihood approach for multidisciplinary analysis (LAMDA). Using the distributions of the feedback variables, the coupling can be removed in any one direction without loss of generality, while still preserving the mathematical relationship between the coupling variables. The calculation of the probability distributions of the coupling variables is theoretically exact and does not require a fully coupled system analysis. The proposed method is illustrated using a mathematical example and an aerospace system application—a fire detection satellite.

References

1.
Cramer
,
E.
,
Dennis
, Jr,
J.
,
Frank
,
P.
,
Lewis
,
R.
, and
Shubin
,
G.
, 1994, “
Problem Formulation for Multidisciplinary Optimization
,”
SIAM J. Optim.
,
4
, pp.
754
776
.
2.
Alexandrov
,
N.
, and
Lewis
,
R.
, 2000, “
Algorithmic Perspectives on Problem Formulations in MDO
,”
Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on MA & O
, Long Beach, CA, AIAA.
3.
Belytschko
,
T.
, 1980, “
Fluid-Structure Interaction
,”
Comput. Struct.
,
12
(
4
), pp.
459
469
.
4.
Thornton
,
E.
, 1996,
Thermal Structures for Aerospace Applications
,
AIAA
,
Reston, VA
.
5.
Culler
,
A.
,
Crowell
,
A.
, and
McNamara
,
J.
, 2009, “
Studies on Fluid-Structural Coupling for Aerothermoelasticity in Hypersonic Flow
,”
AIAA J.
,
48
, pp.
1721
1738
.
6.
Felippa
,
C.
,
Park
,
K.
, and
Farhat
,
C.
, 2001, “
Partitioned Analysis of Coupled Mechanical Systems
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
24–25
), pp.
3247
3270
.
7.
Michler
,
C.
,
Hulshoff
,
S.
, Van
Brummelen
,
E.
, and
De Borst
,
R.
, 2004, “
A Monolithic Approach to Fluid–Structure Interaction
,”
Comput. Fluids
,
33
(
5
), pp.
839
848
.
8.
Park
,
K.
,
Felippa
,
C.
, and
DeRuntz
,
J.
, 1977, “
Stabilization of Staggered Solution Procedures for Fluid-Structure Interaction Analysis
,”
Computational Methods Fluid-Structure Interaction Problems
, pp.
95
124
.
9.
Braun
,
R.
, 1996, “
Collaborative Optimization: An Architecture for Large-Scale Distributed Design
,” Ph.D. thesis, Stanford University, Stanford, CA.
10.
Braun
,
R.
,
Moore
,
A.
, and
Kroo
,
I.
, 1997, “
Collaborative Approach to Launch Vehicle Design
,”
J. Spacecr. Rockets
,
34
(
4
), pp.
478
486
.
11.
Sobieszczanski-Sobieski
,
J.
, “
Optimization by Decomposition: A Step From Hierarchic to Non-Hierarchic Systems
,” Proceedings, 2nd NASA/USAF Symposium on Recent Advances in Multidisciplinary Analysis and Optimization, Hampton, Virginia, 1988. NASA Report CP-3031.
12.
Wujek
,
B.
,
Renaud
,
J.
, and
Batill
,
S.
, 1997, “
A Concurrent Engineering Approach for Multidisciplinary Design in a Distributed Computing Environment
,”
Proceedings of Multidisciplinary Design Optimization: State-of-the-Art, Proceedings in Applied Mathematics
, Vol.
80
, pp.
189
208
.
13.
Sobieszczanski-Sobieski
,
J.
,
Altus
,
T.
,
Phillips
,
M.
, and
Sandusky
,
R.
, 2003, “
Bilevel Integrated System Synthesis for Concurrent and Distributed Processing
,”
AIAA J.
,
41
(
10
), pp.
1996
2003
.
14.
Kokkolaras
,
M.
,
Mourelatos
,
Z.
, and
Papalambros
,
P.
, 2006, “
Design Optimization of Hierarchically Decomposed Multilevel Systems Under Uncertainty
,”
ASME J. Mech. Des.
,
128
(2)
, p.
503
.
15.
Liu
,
H.
,
Chen
,
W.
,
Kokkolaras
,
M.
,
Papalambros
,
P.
, and
Kim
,
H.
, 2006, “
Probabilistic Analytical Target Cascading: A Moment Matching Formulation for Multilevel Optimization Under Uncertainty
,”
ASME J. Mech. Des.
,
128
(4)
, p.
991
.
16.
Gu
,
X.
,
Renaud
,
J.
,
Batill
,
S.
,
Brach
,
R.
, and
Budhiraja
,
A.
, 2000, “
Worst Case Propagated Uncertainty of Multidisciplinary Systems in Robust Design Optimization
,”
Struct. Multidiscip. Optim.
,
20
(
3
), pp.
190
213
.
17.
Du
,
X.
, and
Chen
,
W.
, 2005, “
Collaborative Reliability Analysis Under the Framework of Multidisciplinary Systems Design
,”
Optim. Eng.
,
6
(
1
), pp.
63
84
.
18.
Mahadevan
,
S.
, and
Smith
,
N.
, 2006, “
Efficient First-Order Reliability Analysis of Multidisciplinary Systems
,”
Int. J. Reliab. Saf.
,
1
(
1
), pp.
137
154
.
19.
Zhang
,
X.
, and
Huang
,
H.
, 2010, “
Sequential Optimization and Reliability Assessment for Multidisciplinary Design Optimization Under Aleatory and Epistemic Uncertainties
,”
Struct. Multidiscip. Optim.
,
40
(
1
), pp.
165
175
.
20.
Agarwal
,
H.
,
Renaud
,
J.
,
Preston
,
E.
, and
Padmanabhan
,
D.
, 2004, “
Uncertainty Quantification Using Evidence Theory in Multidisciplinary Design Optimization
,”
Reliab. Eng. Syst. Saf.
,
85
(
1
), pp.
281
294
.
21.
Li
,
M.
, and
Azarm
,
S.
, 2008, “
Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation
,”
ASME J. Mech. Des.
,
130
,
081402
.
22.
Du
,
X.
,
Guo
,
J.
, and
Beeram
,
H.
, 2008, “
Sequential Optimization and Reliability Assessment for Multidisciplinary Systems Design
,”
Struct. Multidiscip. Optim.
,
35
(
2
), pp.
117
130
.
23.
Chiralaksanakul
,
A.
, and
Mahadevan
,
S.
, 2007, “
Decoupled Approach to Multidisciplinary Design Optimization Under Uncertainty
,”
Optim. Eng.
,
8
(
1
), pp.
21
42
.
24.
Smith
,
N.
, 2007, “
Probabilistic Design of Multidisciplinary Systems
,” Ph.D. thesis, Vanderbilt University, Nashville, TN.
25.
Haldar
,
A.
, and
Mahadevan
,
S.
, 2000,
Probability, Reliability, and Statistical Methods in Engineering Design
,
John Wiley & Sons
,
New York
.
26.
Zaman
,
K.
, 2010, “
Modeling and Management of Epistemic Uncertainty for Multidisciplinary System Analysis and Design
,” Ph.D. thesis, Vanderbilt University, Nashville, TN.
27.
Fisher
,
R. A.
, 1912, “
On an Absolute Criterion for Fitting Frequency Curves
,”
Messenger Math.
,
41
(
1
), pp.
155
160
.
28.
Aldrich
,
J.
, 1997, “
R.A. Fisher and the Making of Maximum Likelihood 1912-1922
,”
Stat. Sci.
,
12
(
3
), pp.
162
176
.
29.
Edwards
,
A. W. F.
, 1972,
Likelihood
,
Cambridge University Press
,
Cambridge (expanded edition, 1992, Johns Hopkins University Press, Baltimore)
.
30.
Pawitan
,
Y.
, 2001,
In all Likelihood: Statistical Modelling and Inference Using Likelihood
,
Oxford University Press
,
Oxford, England
.
31.
Singpurwalla
,
N.
, 2006,
Reliability and Risk: A Bayesian Perspective
, Vol.
637
,
Wiley
,
Hoboken, NJ
.
32.
Singpurwalla
,
N.
, 2007, “
Betting on Residual Life: The Caveats of Conditioning
,”
Stat. Probab. Lett.
,
77
(
12
), pp.
1354
1361
.
33.
Rackwitz
,
R.
, and
Flessler
,
B.
, 1978, “
Structural Reliability Under Combined Random Load Sequences
,”
Comput. Struct.
,
9
(
5
), pp.
489
494
.
34.
Hajela
,
P.
,
Bloebaum
,
C.
, and
Sobieszczanski-Sobieski
,
J.
, 1990, “
Application of Global Sensitivity Equations in Multidisciplinary Aircraft Synthesis
,”
J. Aircr.
,
27
, pp.
1002
1010
.
35.
McKeeman
,
W.
, 1962, “
Algorithm 145: Adaptive Numerical Integration by Simpson’s Rule
,”
Commun. ACM
,
5
(
12
), p.
604
.
36.
Wertz
,
J.
, and
Larson
,
W.
, 1999,
Space Mission Analysis and Design
,
Microcosm, Inc.
,
Torrance, CA
.
37.
Ferson
,
S.
,
Tucker
,
W.
,
Paredis
,
C.
,
Bulgak
,
Y.
, and
Kreinovich
,
V.
, 2009, “
Accounting for Epistemic and Aleatory Uncertainty in Early System Design
,” NASA SBIR, Technical Report.
You do not currently have access to this content.