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Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation

Au, Siu-Kui and Beck, James L. (2001) Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation. Probabilistic Engineering Mechanics, 16 (4). pp. 263-277. ISSN 0266-8920. doi:10.1016/S0266-8920(01)00019-4.

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A new simulation approach, called 'subset simulation', is proposed to compute small failure probabilities encountered in reliability analysis of engineering systems. The basic idea is to express the failure probability as a product of larger conditional failure probabilities by introducing intermediate failure events. With a proper choice of the conditional events, the conditional failure probabilities can be made sufficiently large so that they can be estimated by means of simulation with a small number of samples. The original problem of calculating a small failure probability, which is computationally demanding, is reduced to calculating a sequence of conditional probabilities, which can be readily and efficiently estimated by means of simulation. The conditional probabilities cannot be estimated efficiently by a standard Monte Carlo procedure, however, and so a Markov chain Monte Carlo simulation (MCS) technique based on the Metropolis algorithm is presented for their estimation. The proposed method is robust to the number of uncertain parameters and efficient in computing small probabilities. The efficiency of the method is demonstrated by calculating the first-excursion probabilities for a linear oscillator subjected to white noise excitation and for a five-story nonlinear hysteretic shear building under uncertain seismic excitation.

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Additional Information:© Elsevier Science Ltd. This paper is based upon work partly supported by the Pacific Earthquake Engineering Research Center under National Science Foundation Cooperative Agreement No. CMS-9701568. This support is gratefully acknowledged.
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Subject Keywords:Markov chain Monte Carlo method; Monte Carlo simulation; Reliability; First excursion probability; First passage problem; Metropolis algorithm
Issue or Number:4
Record Number:CaltechAUTHORS:20120809-162908584
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33070
Deposited By: Sydney Garstang
Deposited On:13 Aug 2012 22:27
Last Modified:09 Nov 2021 21:32

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