Evaluation of Probabilities Using Orientated Simulation
Publication: Journal of Structural Engineering
Volume 118, Issue 6
Abstract
A sampling method to calculate the n‐dimensional integral representing probability of failure, is presented. By means of n‐dimensional polar coordinates, the directions of the sampling point are limited to a hypercone whose axis contains the design point. If β and the direction cosines are known from the first‐order reliability method, only two parameters are necessary to define the integration domain, whatever the problem dimension n may be. The method described in this paper, a straightforward simulation, and the Harbitz method are used in two problems of known solution and in two examples with convex failure domain. It is shown that the orientated simulation allows a drastic reduction in the number of samples needed, especially in certain structural systems and in quality‐control methods with strongly convex failure domain. On the other hand, a procedure using orientated iteration is presented for obtaining β in cases where the usual iterative method is not suitable.
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Published In
Journal of Structural Engineering
Volume 118 • Issue 6 • June 1992
Pages: 1683 - 1704
Copyright
Copyright © 1992 ASCE.
History
Published online: Jun 1, 1992
Published in print: Jun 1992
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