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research-article

Computationally Efficient Imprecise Uncertainty Propagation

[+] Author and Article Information
Dipanjan D. Ghosh

Graduate Research Assistant
Department of Mechanical and Aerospace Engineering,
University at Buffalo-SUNY,
5 Norton Hall, Buffalo, NY 14260

Andrew Olewnik

Mem. ASME
Research Associate
New York State Center for Engineering Design, and Industrial Innovation,
University at Buffalo-SUNY,
5 Norton Hall, Buffalo, NY 14260
e-mail: olewnik@buffalo.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 13, 2012; final manuscript received February 15, 2013; published online April 23, 2013. Assoc. Editor: David Gorsich.

J. Mech. Des 135(5), 051002 (Apr 23, 2013) (12 pages) Paper No: MD-12-1027; doi: 10.1115/1.4023921 History: Received January 13, 2012; Revised February 15, 2013

Modeling uncertainty through probabilistic representation in engineering design is common and important to decision making that considers risk. However, representations of uncertainty often ignore elements of “imprecision” that may limit the robustness of decisions. Furthermore, current approaches that incorporate imprecision suffer from computational expense and relatively high solution error. This work presents a method that allows imprecision to be incorporated into design scenarios while providing computational efficiency and low solution error for uncertainty propagation. The work draws on an existing method for representing imprecision and integrates methods for sparse grid numerical integration, resulting in the computationally efficient imprecise uncertainty propagation (CEIUP) method. This paper presents details of the method and demonstrates the effectiveness on both numerical case studies, and a thermocouple performance problem found in the literature. Results for the numerical case studies, in most cases, demonstrate improvements in both computational efficiency and solution accuracy for varying problem dimension and variable interaction when compared to optimized parameter sampling (OPS). For the thermocouple problem, similar behavior is observed when compared to OPS. The paper concludes with an overview of design problem scenarios in which CEIUP is the preferred method and offers opportunities for extending the method.

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Figures

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Fig. 1

Difference in aleatory and epistemic uncertainty representation [3]

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Fig. 2

Comparison of nonparameterized p-box (left) and parameterized p-box (right) [6]

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Fig. 3

Classification of methods for propagating uncertainty

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Fig. 4

Development of CEIUP

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Fig. 5

P-box representation

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Fig. 6

Effect of dimension on accuracy and efficiency for OPS (gray) and CEIUP (black)

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Fig. 7

Effect of interaction on accuracy and efficiency for OPS (gray) and CEIUP (black)

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Fig. 8

Effect of dimension and interaction on accuracy and efficiency at level 6 for OPS (gray) and CEIUP (black)

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Fig. 9

Accuracy versus function evaluations comparison plot

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