Secant Hyperplane Method for Structural Reliability Analysis
Publication: Journal of Engineering Mechanics
Volume 142, Issue 3
Abstract
The first-order reliability method (FORM) is a powerful tool for structural reliability analysis, providing a good trade-off between computational accuracy and efficiency. Nevertheless, it has two main drawbacks: (1) its approximation is not necessarily adequate for limit state surfaces which depart significantly from linearity, and (2) it does not give information about the degree of accuracy achieved. In this paper, the secant hyperplane method (SHM) is proposed, which is a new linear approximation of the limit state surface based on the support vector method (SVM). The key idea is to treat structural reliability as a classification problem and to seek a suitable secant hyperplane to the limit state that gives improved approximation over the use of a tangent hyperplane. The two drawbacks of FORM are thereby resolved, while keeping the geometrical simplicity and ease of implementation of FORM. The implication of very high-dimensional geometry is examined, demonstrating that FORM can give good approximations if reinterpreted as a linear classifier, and SHM has the potential of scalability to spaces of high dimensionality. Two numerical examples, including stochastic dynamic analysis, show the accuracy and effectiveness of SHM.
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Acknowledgments
The authors acknowledge the research grants (R-302-501-009-305) funded by the Agency for Science, Technology, and Research of Singapore. The first author wishes to thank the mentorship and fruitful discussions of Prof. Armen Der Kiureghian of the University of California at Berkeley during his stay in University of California, Berkeley from September 2008 to May 2009. The authors wish to thank two anonymous reviewers that with their comments have contributed to the improvement of the paper.
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Published In
Journal of Engineering Mechanics
Volume 142 • Issue 3 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Oct 13, 2014
Accepted: Sep 14, 2015
Published online: Nov 2, 2015
Published in print: Mar 1, 2016
Discussion open until: Apr 2, 2016
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