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Research Papers: Design Automation

Treating Epistemic Uncertainty Using Bootstrapping Selection of Input Distribution Model for Confidence-Based Reliability Assessment

[+] Author and Article Information
Min-Yeong Moon

Mem. ASME
Department of Mechanical Engineering,
College of Engineering,
The University of Iowa,
Iowa City, IA 52242
e-mail: minyeong-moon@uiowa.edu

K. K. Choi

Mem. ASME
Department of Mechanical Engineering,
College of Engineering,
The University of Iowa,
Iowa City, IA 52242
e-mail: kyung-choi@uiowa.edu

Nicholas Gaul

Mem. ASME
RAMDO Solutions, LLC,
Iowa City, IA 52240
e-mail: nicholas-gaul@ramdosolutions.com

David Lamb

US Army RDECOM/TARDEC,
Warren, MI 48397-5000
e-mail: david.lamb@us.army.mil

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 31, 2018; final manuscript received November 26, 2018; published online January 10, 2019. Assoc. Editor: Xiaoping Du. This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Mech. Des 141(3), 031402 (Jan 10, 2019) (14 pages) Paper No: MD-18-1607; doi: 10.1115/1.4042149 History: Received July 31, 2018; Revised November 26, 2018

Accurately predicting the reliability of a physical system under aleatory uncertainty requires a very large number of physical output testing. Alternatively, a simulation-based method can be used, but it would involve epistemic uncertainties due to imperfections in input distribution models, simulation models, and surrogate models, as well as a limited number of output testing due to cost. Thus, the estimated output distributions and their corresponding reliabilities would become uncertain. One way to treat epistemic uncertainty is to use a hierarchical Bayesian approach; however, this could result in an overly conservative reliability by integrating possible candidates of input distribution. In this paper, a new confidence-based reliability assessment method that reduces unnecessary conservativeness is developed. The epistemic uncertainty induced by a limited number of input data is treated by approximating an input distribution model using a bootstrap method. Two engineering examples and one mathematical example are used to demonstrate that the proposed method (1) provides less conservative reliability than the hierarchical Bayesian analysis, yet (2) predicts the reliability of a physical system that satisfies the user-specified target confidence level, and (3) shows convergence behavior of reliability estimation as numbers of input and output test data increase.

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Figures

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Fig. 1

Approximation of an uncertain input distribution model using the bootstrap method

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Fig. 2

Complementary CDF of reliability that represents uncertain reliability

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Fig. 3

True output distribution (solid line) and five output test data (circle) for G1 (top-left), G2 (top-right), and G3 (bottom)

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Fig. 4

Comparison of uncertainty distribution of reliability between two methods—(1) proposed method and (2) reference method—for G1 (top-left), G2 (top-right), and G3 (bottom)

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Fig. 5

Comparison of histogram of 100 confidence-based reliabilities: (a) constraint 1, (b) constraint 2, and (c) constraint 3

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Fig. 6

True output distribution (solid line) and five output test data (circle) for G1 (top-left), G2 (top-right), and G3 (bottom)

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Fig. 7

Comparison of the uncertainty distribution of reliability between two methods—(1) proposed method and (2) reference method—for G1 (top-left), G2 (top-right), and G3 (bottom)

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Fig. 8

Comparison of histograms of 100 confidence-based reliabilities: (a) constraint 1, (b) constraint 2, and (c) constraint 3

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Fig. 9

Comparison of the uncertainty distribution (CCDF) of reliability under different numbers of input and output test data

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