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Research Papers: Design Automation

A Spatial-Random-Process Based Multidisciplinary System Uncertainty Propagation Approach With Model Uncertainty

[+] Author and Article Information
Zhen Jiang

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: zhenjiang2015@u.northwestern.edu

Wei Li

School of Aeronautics,
Northwestern Polytechnical University,
Xi'an, Shaanxi 710072, China
e-mail: liwiair@gmail.com

Daniel W. Apley

Department of Industrial Engineering
and Management Sciences,
Northwestern University,
Evanston, IL 60208
e-mail: dapley@northwestern.edu

Wei Chen

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: weichen@northwestern.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 9, 2014; final manuscript received July 1, 2015; published online August 10, 2015. Assoc. Editor: Gary Wang.

J. Mech. Des 137(10), 101402 (Aug 10, 2015) (13 pages) Paper No: MD-14-1779; doi: 10.1115/1.4031096 History: Received December 09, 2014

The performance of a multidisciplinary system is inevitably affected by various sources of uncertainties, usually categorized as aleatory (e.g., input variability) or epistemic (e.g., model uncertainty) uncertainty. In the framework of design under uncertainty, all sources of uncertainties should be aggregated to assess the uncertainty of system quantities of interest (QOIs). In a multidisciplinary design system, uncertainty propagation (UP) refers to the analysis that quantifies the overall uncertainty of system QOIs resulting from all sources of aleatory and epistemic uncertainty originating in the individual disciplines. However, due to the complexity of multidisciplinary simulation, especially the coupling relationships between individual disciplines, many UP approaches in the existing literature only consider aleatory uncertainty and ignore the impact of epistemic uncertainty. In this paper, we address the issue of efficient uncertainty quantification of system QOIs considering both aleatory and epistemic uncertainties. We propose a spatial-random-process (SRP) based multidisciplinary uncertainty analysis (MUA) method that, subsequent to SRP-based disciplinary model uncertainty quantification, fully utilizes the structure of SRP emulators and leads to compact analytical formulas for assessing statistical moments of uncertain QOIs. The proposed method is applied to a benchmark electronic packaging design problem. The estimated low-order statistical moments of the QOIs are compared to the results from Monte Carlo simulations (MCSs) to demonstrate the effectiveness of the method. The UP result is then used to facilitate the robust design optimization of the electronic packaging system.

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Figures

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Fig. 1

Illustration of SRP modeling

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Fig. 2

A notional multidisciplinary system and its possible sources of uncertainties: block A—input variability (aleatory) and block B—model uncertainty (epistemic)

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Fig. 3

The procedure of the proposed SRP-based MUA method

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Fig. 4

Electronic packaging problem

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Fig. 5

(a) Model prediction (after model bias correction) and (b) estimation of bias function for linking variable y11

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Fig. 6

Histograms of system QOIs: (a) y1 and (b) y4

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Fig. 7

Scatter plots of y6 and y11: (a) considering only aleatory uncertainty (for which they are positively correlated) and (b) considering both uncertainties (for which they are negatively correlated)

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Fig. 8

Variances of (a) y1, (b) y11, and (c) y12 contributed by aleatory and epistemic uncertainties in three different scenarios

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Fig. 9

Relationship between a multiplicative increase in model uncertainty and the resulting increase in the system QOIs' SD

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Fig. 10

Relationship between a multiplicative increase in model uncertainty and the resulting increase in the proportion of total variance of system QOIs due to model uncertainty

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Fig. 11

Contour plots of the variances of (a) y11 and (b) y12 induced by model uncertainty over the design region of x1 and x2

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