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Application of saddlepoint approximation in reliability analysis of dynamic systems

Ka-Veng Yuen (Èî¼ÒÈÙ)¹, Jia Wang (Íõ ¼Ò)¹ and Siu-Kui Au (ÇøÕ×¾Ô)²

1. Faculty of Science and Technology, University of Macau, Macao, China
2. Department of Building and Construction, City University of Hong Kong, Hong Kong, China

Abstract:The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The 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 CDF at a specified threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function (CGF) of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and efficiency of the proposed methodology.

Keywords: cumulant generating function; failure probability; reliability analysis; saddlepoint approximation
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