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Asymptotic Expansions for Reliabilities and Moments of Uncertain Dynamic Systems

Papadimitriou, C. and Beck, J. L. and Katafygiotis, L. S. (1997) Asymptotic Expansions for Reliabilities and Moments of Uncertain Dynamic Systems. Journal of Engineering Mechanics, 123 (12). pp. 1219-1229. ISSN 0733-9399. doi:10.1061/(ASCE)0733-9399(1997)123:12(1219).

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An asymptotic approximation is developed for evaluating the probability integrals that arise in the determination of the reliability and response moments of uncertain dynamic systems subject to stochastic excitation. The method is applicable when the probabilities of failure or response moments conditional on the system parameters are available, and the effect of the uncertainty in the system parameters is to be investigated. In particular, a simple analytical formula for the probability of failure of the system is derived and compared to some existing approximations, including an asymptotic approximation based on second-order reliability methods. Simple analytical formulas are also derived for the sensitivity of the failure probability and response moments to variations in parameters of interest. Conditions for which the proposed asymptotic expansion is expected to be accurate are presented. Since numerical integration is only computationally feasible for investigating the accuracy of the proposed method for a small number of uncertain system parameters, simulation techniques are also used. A simple importance sampling method is shown to converge much more rapidly than straightforward Monte Carlo simulation. Simple structures subjected to white noise stochastic excitation are used to illustrate the accuracy of the proposed analytical approximation. Results from the computationally efficient perturbation method are also included for comparison. The results show that the asymptotic method gives acceptable approximations, even for systems with relatively large uncertainty, and in most cases, it outperforms the perturbation method.

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Papadimitriou, C.0000-0002-9792-0481
Additional Information:©ASCE The manuscript for this paper was submitted for review and possible publication on February 20, 1996. This paper is based upon work partly supported by the National Science Foundation under grant BCS-9309149 and by the Hong Kong UPGC Research Infrastructure grant, RIG 94/95.EG02. This support is gratefully acknowledged. This paper was written while J. L. Beck was on sabbatical leave at the Hong Kong University of Science and Technology, and the kind hospitality of J. C. Chen, director of the Research Center, is greatly appreciated. The writers also thank Siu-Kui Au, graduate student at the Hong Kong University of Science and Technology, for his assistance in carrying out part of the numerical computations.
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Hong Kong UPGC Research InfrastructureRIG 94/95.EG02
Issue or Number:12
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33023
Deposited By: Sydney Garstang
Deposited On:08 Aug 2012 22:04
Last Modified:09 Nov 2021 21:31

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