Title: Spherical subset simulation (S³) for solving non-linear dynamical reliability problems

Authors: Lambros Katafygiotis, Sai Hung Cheung, Ka-Veng Yuen

Addresses: Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China. ' Department of Civil Engineering, California Institute of Technology, 1200 East California Boulevard, Pasadena, California, CA 91125, USA. ' Department of Civil and Environmental Engineering, University of Macau, Taipa, Macau, China

Abstract: This paper presents a methodology for general non-linear reliability problems. It is based on dividing the failure domain into a number of appropriately selected subregions and calculating the failure probability as a sum of the probabilities for each subregion. The probability of each subregion is calculated as a product of factors, which can be estimated accurately by a relatively small number of samples generated according to the conditional distribution corresponding to the particular subregion. These samples are generated through Markov Chain Monte Carlo simulations using a slice-sampling based algorithm proposed by the authors. The proposed method is robust and is suitable for high-dimensional problems. This is in contrast to popular importance sampling methods that often break down for high-dimensional problems. The method is found to be significantly more efficient than Monte Carlo simulations. The efficiency of the method is demonstrated with two examples involving 4000 and 1501 random variables.

Keywords: spherical subset simulation; nonlinear reliability; dynamic reliability; failure probability; MCMC; Markov chain Monte Carlo simulation; slice sampling.

DOI: 10.1504/IJRS.2010.032442

International Journal of Reliability and Safety, 2010 Vol.4 No.2/3, pp.122 - 138

Published online: 02 Apr 2010 *

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