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A New Adaptive Importance Sampling Scheme for Reliability Calculations

Au, S. K. and Beck, J. L. (1999) A New Adaptive Importance Sampling Scheme for Reliability Calculations. Structural Safety, 21 (2). pp. 135-158. ISSN 0167-4730.

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An adaptive importance sampling methodology is proposed to compute the multidimensional integrals encountered in reliability analysis. It is based on a Markov simulation algorithm due to Metropolis et al. (Metropolis, Rosenbluth, Rosenbluth and Teller, Equations of state calculatons by fast computing machines. Journal of Chemical Physics, 1953;21(6): 1087-1092). In the proposed methodology, samples are simulated as the states of a Markov chain and are distributed asymptotically according to the optimal importance sampling density. A kernel sampling density is then constructed from these samples which is used as the sampling density in an importance sampling simulation. The Markov chain samples populate the region of higher probability density in the failure region and so the kernel sampling density approximates the optimal importance sampling density for a large variety of shapes of the failure region. This adaptive feature is insensitive to the probability level to be estimated. A variety of numerical examples demonstrates the accuracy, efficiency and robustness of the methodology.

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Additional Information:© 1999 Elsevier Science Ltd. This paper is based upon work partly supported by the Paci®c Earthquake Engineering Research Center under National Science Foundation Cooperative Agreement No. CMS-9701568. This support is gratefully acknowledged.
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Subject Keywords:Importance sampling; Markov chain; Metropolis method; Reliability
Record Number:CaltechAUTHORS:20120829-134911107
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33672
Deposited By: Carmen Nemer-Sirois
Deposited On:29 Aug 2012 21:39
Last Modified:29 Aug 2012 21:39

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