Title: Reliability analysis using a 'Taylor expansion-expected value' saddlepoint approximation

Authors: Jia Wang, Siu-Kui Au, Ka-Veng Yuen

Addresses: College of Civil Engineering, Hunan University, Changsha City, Hunan Province, China. ' Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China. ' Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Taipa, Macau, China

Abstract: The problem of reliability analysis of dynamical systems is considered. Failure event in the problem is formulated as the exceedance of a performance variable over a prescribed threshold level. Saddlepoint approximation technique provides a choice to estimate the Cumulative Distribution Function (CDF) of the performance variable. The failure probability is obtained as the value of the complement of the CDF at a specified threshold. The method requires finding the saddlepoint from a simple algebraic equation that depends on the Cumulant Generating Function (CGF) of the performance variable. Two different methods, which respectively use Taylor series expansion and statistical averaging, are investigated for estimating the CGF of the performance variable based on its random samples. A ten-storey shear building model subjected to white noise excitation is used to show the preference of a combination of these two methods in terms of accuracy and efficiency.

Keywords: CGF; cumulant generating function; failure probability; reliability analysis; saddlepoint approximation; cumulative distribution function; ten-storey shear building; modelling; white noise excitation.

DOI: 10.1504/IJRS.2011.037346

International Journal of Reliability and Safety, 2011 Vol.5 No.1, pp.44 - 65

Published online: 31 Mar 2015 *

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