Research Papers: Design Automation

Stochastic Multidisciplinary Analysis Under Epistemic Uncertainty

[+] Author and Article Information
Chen Liang

Department of Civil and Environmental
Vanderbilt University,
Nashville, TN 37235

Sankaran Mahadevan

Department of Civil and Environmental
Vanderbilt University,
Nashville, TN 37235
e-mail: sankaran.mahadevan@vanderbilt.edu

Shankar Sankararaman

SGT, Inc.,
Moffett Field, CA 94035

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 8, 2014; final manuscript received November 12, 2014; published online December 11, 2014. Assoc. Editor: Christopher Mattson.

J. Mech. Des 137(2), 021404 (Feb 01, 2015) (12 pages) Paper No: MD-14-1155; doi: 10.1115/1.4029221 History: Received March 08, 2014; Revised November 12, 2014; Online December 11, 2014

This paper presents a probabilistic framework to include the effects of both aleatory and epistemic uncertainty sources in coupled multidisciplinary analysis (MDA). A likelihood-based decoupling approach has been previously developed for probabilistic analysis of multidisciplinary systems, but only with aleatory uncertainty in the inputs. This paper extends this approach to incorporate the effects of epistemic uncertainty arising from data uncertainty and model errors. Data uncertainty regarding input variables (due to sparse and interval data) is included through parametric or nonparametric distributions using the principle of likelihood. Model error is included in MDA through an auxiliary variable approach based on the probability integral transform. In the presence of natural variability, data uncertainty, and model uncertainty, the proposed methodology is employed to estimate the probability density functions (PDFs) of coupling variables as well as the subsystem and system level outputs that satisfy interdisciplinary compatibility. Global sensitivity analysis (GSA), which has previously considered only aleatory inputs and feedforward or monolithic problems, is extended in this paper to quantify the contribution of model uncertainty in feedback-coupled MDA by exploiting the auxiliary variable approach. The proposed methodology is demonstrated using a mathematical MDA problem and an electronic packaging application example featuring coupled thermal and electrical subsystem analyses. The results indicate that the proposed methodology can effectively quantify the uncertainty in MDA while maintaining computational efficiency.

Copyright © 2015 by ASME
Topics: Errors , Uncertainty
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Fig. 1

Multidisciplinary system

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Fig. 2

One iteration of coupled analysis

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Fig. 3

Multidisciplinary system: partially decoupled

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Fig. 4

Family of distributions

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Fig. 5

Optimization framework for maximum likelihood method

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Fig. 6

FORM with auxiliary variable

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Fig. 7

Output uncertainty due to model errors

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Fig. 8

Functional relations of the mathematical MDA model

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Fig. 9

Nonparametric PDF of x5

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Fig. 10

PDFs of coupling variables U12 (left) and U21 (right)

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Fig. 11

Electronic packaging problem: feedback-coupled MDA. (a) Geometry of a regular heatsink. (b) Disciplinary analyses and coupling variables.

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Fig. 12

Mean and 95% bound of GP prediction, accounting for discretization error (thermal analysis)

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Fig. 13

PDF of coupling variables: component heat y4. (left) and temperature y5 (right)

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Fig. 14

PDF of system output: power density

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Fig. 15

Comparison of results from LAMDA and SOFPI for (a) temperature, (b) component heat, and (c) power density



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