This paper develops and illustrates a probabilistic approach for uncertainty representation and propagation in system analysis, when the information on the uncertain input variables and/or their distribution parameters may be available as either probability distributions or simply intervals (single or multiple). A unique aggregation technique is used to combine multiple interval data and to compute rigorous bounds on the system response cumulative distribution function. The uncertainty described by interval data is represented through a flexible family of probability distributions. Conversion of interval data to a probabilistic format enables the use of computationally efficient methods for probabilistic uncertainty propagation. Two methods are explored for the implementation of the proposed approach, based on (1) sampling and (2) optimization. The sampling-based strategy is more expensive and tends to underestimate the output bounds. The optimization-based methodology improves both aspects. The proposed methods are used to develop new solutions to challenge problems posed by the Sandia epistemic uncertainty workshop (Oberkampf et al., 2004, “Challenge Problems: Uncertainty in System Response Given Uncertain Parameters,” Reliab. Eng. Syst. Saf., 85, pp. 11–19). Results for the challenge problems are compared with earlier solutions.
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e-mail: kaiszaman@yahoo.com
e-mail: mark.p.mcdonald@vanderbilt.edu
e-mail: sankaran.mahadevan@vanderbilt.edu
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February 2011
Research Papers
Probabilistic Framework for Uncertainty Propagation With Both Probabilistic and Interval Variables
Kais Zaman,
Kais Zaman
Department of Civil and Environmental Engineering,
e-mail: kaiszaman@yahoo.com
Vanderbilt University
, Nashville, TN 37235
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Mark McDonald,
Mark McDonald
Department of Civil and Environmental Engineering,
e-mail: mark.p.mcdonald@vanderbilt.edu
Vanderbilt University
, Nashville, TN 37235
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Sankaran Mahadevan
Sankaran Mahadevan
Professor of Civil and Environmental Engineering
Department of Civil and Environmental Engineering,
e-mail: sankaran.mahadevan@vanderbilt.edu
Vanderbilt University
, Nashville, TN 37235
Search for other works by this author on:
Kais Zaman
Department of Civil and Environmental Engineering,
Vanderbilt University
, Nashville, TN 37235e-mail: kaiszaman@yahoo.com
Mark McDonald
Department of Civil and Environmental Engineering,
Vanderbilt University
, Nashville, TN 37235e-mail: mark.p.mcdonald@vanderbilt.edu
Sankaran Mahadevan
Professor of Civil and Environmental Engineering
Department of Civil and Environmental Engineering,
Vanderbilt University
, Nashville, TN 37235e-mail: sankaran.mahadevan@vanderbilt.edu
J. Mech. Des. Feb 2011, 133(2): 021010 (14 pages)
Published Online: February 8, 2011
Article history
Received:
September 4, 2009
Revised:
May 12, 2010
Online:
February 8, 2011
Published:
February 8, 2011
Citation
Zaman, K., McDonald, M., and Mahadevan, S. (February 8, 2011). "Probabilistic Framework for Uncertainty Propagation With Both Probabilistic and Interval Variables." ASME. J. Mech. Des. February 2011; 133(2): 021010. https://doi.org/10.1115/1.4002720
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