Research Papers

A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis

[+] Author and Article Information
Zhen Hu

e-mail: zh4hd@mst.edu

Xiaoping Du

e-mail: dux@mst.edu
Department of Mechanical and Aerospace Engineering,
Missouri University of Science and Technology,
290D Toomey Hall,
400 West 13th Street,
Rolla, MO 65409-0500

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received December 30, 2012; final manuscript received February 8, 2013; published online May 10, 2013. Assoc. Editor: David Gorsich.

J. Mech. Des 135(7), 071003 (May 10, 2013) (8 pages) Paper No: MD-12-1633; doi: 10.1115/1.4023925 History: Received December 30, 2012; Revised February 08, 2013

Maintaining high accuracy and efficiency is a challenging issue in time-dependent reliability analysis. In this work, an accurate and efficient method is proposed for limit-state functions with the following features: The limit-state function is implicit with respect to time. There is only one stochastic process in the input to the limit-sate function. The stochastic process could be either a general strength or a general stress variable so that the limit-state function is monotonic to the stochastic process. The new method employs a sampling approach to estimate the distributions of the extreme value of the stochastic process. The extreme value is then used to replace the corresponding stochastic process. Consequently the time-dependent reliability analysis is converted into its time-invariant counterpart. The commonly used time-invariant reliability method, the first order reliability method, is then applied to calculate the probability of failure over a given period of time. The results show that the proposed method significantly improves the accuracy and efficiency of time-dependent reliability analysis.

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Fig. 1

Flow chart of the new time-dependent reliability method

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Fig. 2

A Trajectory of a stochastic process

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Fig. 6

Cross section at root of the turbine blade

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Fig. 4

CDFs of maximum load over different time intervals

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Fig. 3

A Beam under random loading

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Fig. 5

Probability of failure of the beam over different time intervals

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Fig. 7

River flow loading on the turbine blade

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Fig. 8

CDFs of maximum river velocity over different time intervals

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Fig. 9

Probability of failure of the hydrokinetic turbine blade



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