Numerical Approximations of Design Points in Reliability Analysis under Parametric Changes
Publication: Journal of Engineering Mechanics
Volume 133, Issue 11
Abstract
Traditional approaches for repeatedly updating reliability estimates, as needed in reliability-based optimal designs or real-time system control, require the iterative application of a reliability method. This paper explores a new strategy for repeatedly estimating reliability under frequent parameter variations. The central idea is to update the design point in the parameter domain, rather than in the traditional random variable domain, by evaluating several parametric sensitivity measures which are systems of nonlinear first-order ordinary differential equations relating the design point to parameter changes. Four numerical algorithms for evaluating the sensitivity measures are developed using the Euler and the improved Euler algorithms. Two solution procedures are applied. One procedure solves for the updated design point directly, while the other solves for both the unit normal vector at the design point and the reliability index separately, and evaluates the product of these to determine the updated design point. The numerical techniques are thoroughly compared with the classical Hasofer and Lind-Rackwitz and Fiessler (HL-RF) algorithm in five numerical examples regarding efficiency and accuracy. It is found that they are efficient and robust under given conditions.
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Acknowledgments
The writers really appreciate the careful review and constructive suggestions of the reviewers. The writers are grateful to Professor Ricardo Foschi, University of British Columbia for insightful comments regarding an earlier version of this work. They also thank their colleagues in the Environmental Systems Research Group at UBC, particularly Mr. Ali Naghibi, Ph.D. student, for fruitful discussions regarding this project. Financial support for this research was provided to the first writer in the form of a Postgraduate D Scholarship from the Natural Science and Engineering Research Council of CanadaNRC (NSERC) and an NSERCNRC Supplement Scholarship from the Prairie Adaptation Research Collaborative, Canada. The second writer was supported by NSERC Discovery Research Grant Award No. NRC201025-03.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 11 • November 2007
Pages: 1213 - 1221
Copyright
© 2007 ASCE.
History
Received: Apr 5, 2006
Accepted: May 8, 2007
Published online: Nov 1, 2007
Published in print: Nov 2007
Notes
Note. Associate Editor: Arvid Naess
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