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First Excursion Probabilities for Linear Systems by Very Efficient Importance Sampling

Au, S. K. and Beck, J. L. (2001) First Excursion Probabilities for Linear Systems by Very Efficient Importance Sampling. Probabilistic Engineering Mechanics, 16 (3). pp. 193-207. ISSN 0266-8920. doi:10.1016/S0266-8920(01)00002-9.

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An analytical study of the failure region of the first excursion reliability problem for linear dynamical systems subjected to Gaussian white noise excitation is carried out with a view to constructing a suitable importance sampling density for computing the first excursion failure probability. Central to the study are 'elementary failure regions', which are defined as the failure region in the load space corresponding to the failure of a particular output response at a particular instant. Each elementary failure region is completely characterized by its design point, which can be computed readily using impulse response functions of the system. It is noted that the complexity of the first excursion problem stems from the structure of the union of the elementary failure regions. One important consequence of this union structure is that, in addition to the global design point, a large number of neighboring design points are important in accounting for the failure probability. Using information from the analytical study, an importance sampling density is proposed. Numerical examples are presented, which demonstrate that the efficiency of using the proposed importance sampling density to calculate system reliability is remarkable.

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Additional Information:© 2001 Elsevier Science Ltd. This paper is based upon work partly supported by the Pacific Earthquake Research Center under National Science Foundation Cooperative Agreement No. CMS-9701568. This support is gratefully acknowledged.
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Subject Keywords:First excursion problem; First passage problem; Linear systems; Importance sampling; Monte Carlo simulation; Reliability
Issue or Number:3
Record Number:CaltechAUTHORS:20120809-162001049
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33069
Deposited By: Sydney Garstang
Deposited On:13 Aug 2012 22:41
Last Modified:09 Nov 2021 21:32

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