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Research Papers

Uncertainty Quantification of Time-Dependent Reliability Analysis in the Presence of Parametric Uncertainty

[+] Author and Article Information
Zhen Hu

Department of Civil and Environmental
Engineering,
Vanderbilt University,
272 Jacobs Hall, VU Mailbox: PMB 351831, Nashville, TN 37235
e-mail: zhen.hu@vanderbilt.edu

Sankaran Mahadevan

Department of Civil and Environmental
Engineering,
Vanderbilt University,
272 Jacobs Hall, VU Mailbox: PMB 351831, Nashville, TN 37235
e-mail: sankaran.mahadevan@vanderbilt.edu

Xiaoping Du

Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
272 Toomey Hall, 400 West 13th Street, Rolla, MO 65409-0050
e-mail: dux@mst.edu

1Corresponding author.

Manuscript received March 26, 2015; final manuscript received December 4, 2015; published online July 1, 2016. Assoc. Editor: Ioannis Kougioumtzoglou.

ASME J. Risk Uncertainty Part B 2(3), 031005 (Jul 01, 2016) (11 pages) Paper No: RISK-15-1050; doi: 10.1115/1.4032307 History: Received March 26, 2015; Accepted December 04, 2015

Limited data of stochastic load processes and system random variables result in uncertainty in the results of time-dependent reliability analysis. An uncertainty quantification (UQ) framework is developed in this paper for time-dependent reliability analysis in the presence of data uncertainty. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of UQ in time-dependent reliability analysis results in a double-loop implementation procedure, which is computationally expensive. This paper proposes an efficient method for the UQ of time-dependent reliability analysis by integrating the fast integration method and surrogate model method with time-dependent reliability analysis. A surrogate model is built first for the time-instantaneous conditional reliability index as a function of variables with imprecise parameters. For different realizations of the epistemic uncertainty, the associated time-instantaneous most probable points (MPPs) are then identified using the fast integration method based on the conditional reliability index surrogate without evaluating the original limit-state function. With the obtained time-instantaneous MPPs, uncertainty in the time-dependent reliability analysis is quantified. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.

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Figures

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Fig. 1

UQ of time-dependent reliability analysis

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Fig. 2

General procedure of the direct surrogate-model method

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Fig. 3

Overall framework of UQ in time-dependent reliability analysis

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Fig. 4

Experimental data of Y1(t) and X2

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Fig. 5

MSE of the conditional reliability index

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Fig. 6

Results based on 100 cycles of Y1(t) and 100 samples of X2. (a) Trajectories of pf(t0,te) up to 30 cycles (inner figure is the distribution at t=30). (b) pf(0,30) obtained from three methods.

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Fig. 7

Comparison of posterior distributions of pf(0,30)

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Fig. 8

Beam subjected to a concentrated stochastic load

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Fig. 9

Historical and experimental data of F(t) and σu

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Fig. 10

MSE of the conditional reliability index

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Fig. 11

Results of pf(t0,te) obtained based on 200 cycles of F(t) and 200 samples of σu. (a) Updated posterior distributions of pf(t0,te) up to 50 cycles. (b) Comparison of pf(0,50) obtained from three methods.

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Fig. 12

Comparison of updated posterior distributions of pf(0,50)

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Fig. 13

Updated posterior distributions with more observations of σu

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