New Analytical Solution of the First-Passage Reliability Problem for Linear Oscillators
Publication: Journal of Engineering Mechanics
Volume 138, Issue 6
Abstract
The classical first-passage reliability problem for linear elastic single-degree-of-freedom (SDOF) oscillators subjected to stationary and nonstationary Gaussian excitations is explored. Several analytical approximations are available in the literature for this problem: the Poisson, classical Vanmarcke, and modified Vanmarcke approximations. These analytical approximations are widely used because of their simplicity and their lower computational cost compared with simulation techniques. However, little is known about their accuracy in estimating the time-variant first-passage failure probability (FPFP) for varying oscillator properties, failure thresholds, and types of loading. In this paper, a new analytical approximation of the FPFP for linear SDOF systems is proposed by modifying the classical Vanmarcke hazard function. This new approximation is verified by comparing its failure probability estimates with the results obtained using existing analytical approximations and the importance sampling using elementary events method for a wide range of oscillator properties, threshold levels, and types of input excitations. It is shown that the newly proposed analytical approximation of the hazard function yields a significantly more accurate estimate of the FPFP compared with the Poisson, classical Vanmarcke, and modified Vanmarcke approximations.
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Acknowledgments
The writers gratefully acknowledge support of this research by the Louisiana Board of Regents (LA BoR) through the Pilot Funding for New Research (Pfund) Program of the National Science Foundation (NSF) Experimental Program to Stimulate Competitive Research (EPSCoR) under Award No. LEQSF(2011)-PFUND-225; the LA BoR through the Louisiana Board of Regents Research and Development Program, Research Competitiveness (RCS) subprogram, under Award No. LESQSF(2010-13)-RD-A-01; the Longwell’s Family Foundation through the Fund for Innovation in Engineering Research (FIER) Program; and the LSU Council on Research through the 2009–2010 Faculty Research Grant Program. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the writers and do not necessarily reflect the views of the sponsors.
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Published In
Journal of Engineering Mechanics
Volume 138 • Issue 6 • June 2012
Pages: 695 - 706
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Jun 28, 2011
Accepted: Dec 6, 2011
Published online: Dec 8, 2011
Published in print: Jun 1, 2012
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