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Research Papers

Likelihood-Based Approach to Multidisciplinary Analysis Under Uncertainty

[+] Author and Article Information
Shankar Sankararaman

ProfessorJohn R. Murray Sr. Chair in Engineering, Department of Civil and Environmental Engineering,  Vanderbilt University, VU Station B # 351831, 2301 Vanderbilt Place, Nashville, TN 37235shankar.sankararaman@vanderbilt.edu

Sankaran Mahadevan1

ProfessorJohn R. Murray Sr. Chair in Engineering, Department of Civil and Environmental Engineering,  Vanderbilt University, VU Station B # 351831, 2301 Vanderbilt Place, Nashville, TN 37235sankaran.mahadevan@vanderbilt.edu

1

Corresponding author.

J. Mech. Des 134(3), 031008 (Mar 06, 2012) (12 pages) doi:10.1115/1.4005619 History: Received March 28, 2011; Revised December 13, 2011; Published March 02, 2012; Online March 06, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A multidisciplinary system

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Figure 3

Multidisciplinary system: Partially decoupled

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Figure 4

Use of FORM to estimate the CDF value

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Figure 5

Functional relationships

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Figure 7

Cumulative distribution function of u12

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Figure 9

A three-subsystem fire detection satellite

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Figure 10

Schematic diagram for the spacecraft solar array

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Figure 11

PDF of coupling variable PACS

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Figure 12

PDF of total output power Ptot

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Figure 13

PDF of area of solar array

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Figure 14

PDF of total torque τtot

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