Non-Gradient–Based Algorithm for Structural Reliability Analysis
Publication: Journal of Engineering Mechanics
Volume 140, Issue 6
Abstract
In reliability analysis, the first-order reliability method (FORM) and various optimization algorithms are widely used to locate the most probable point (MPP) and calculate the reliability index. These algorithms generally require first-order response sensitivities or gradients of the limit-state function. However, in engineering, the reliability analysis is often merged with finite-element (FE) analysis or other structural/mechanical analyses, and the limit-state function is implicit. The sensitivity analysis may be computationally intensive or cumbersome, and several techniques were developed to deal with this problem. In the present paper, a general iterative algorithm that does not need gradients is proposed. This algorithm produces series of sequence points iteratively in the standard normal space. It is proven that the series of points will converge to the same point, which is just the MPP, and its distance to the origin is the reliability index. The proposed algorithm also introduces new step lengths to control the convergence of the sequence. These step lengths are new because they may be constant during the iteration or varied using the interim evaluations of the reliability index, which means a self-adjust process in essence. Eighteen examples are given to verify the effectiveness of the proposed algorithm. It is indicated that the proposed algorithm is effective and robust.
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Acknowledgments
The authors thank the anonymous reviewers for useful and helpful comments and assistance and for referring them to the latest publications in this area. The work was supported by the Natural Science Foundation of China (Nos. 11102033 and 51138001) and the Fundamental Research Funds for the Central Universities, which are gratefully acknowledged by the authors.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 6 • June 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jan 29, 2013
Accepted: Sep 30, 2013
Published online: Jan 28, 2014
Published in print: Jun 1, 2014
Discussion open until: Jun 28, 2014
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