Second‐Order Reliability Approximations
Publication: Journal of Engineering Mechanics
Volume 113, Issue 8
Abstract
A simple method is presented for a second‐order structural reliability approximation. The method is based on an approximating paraboloid which is fitted to the limit‐state surface at discrete points around the point with minimal distance from the origin. An expression for the second‐order error in the approximation is derived, and the error is shown to be small, even for large dimensions and dispersed curvatures. In comparison to the existing approximation method, the proposed method is simpler and requires less computation. It is insensitive to noise in the limit‐state surface, approximately accounts for higher‐order effects, and facilitates the use of an existing formula for the probability content of parabolic sets.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Breitung, K., “Asymptotic Approximations for Multinormal Integrals,” Journal of Engineering Mechanics, ASCE, Vol. 110, No. 3, Mar., 1984, pp. 357–366.
2.
Der Kiureghian, A., “Finite Element Methods in Structural Safety Studies,” in Proceedings, ASCE Symposium on Structural Safety Studies, Denver, Colo., Apr.–May, 1985, pp. 40–52.
3.
Der Kiureghian, A., and Liu, P.‐L., “Structural Reliability Under Incomplete Probability Information,” Journal of Engineering Mechanics, ASCE, Vol. 112, No. 1, Jan., 1986, pp. 85–104.
4.
Ditlevsen, O., “Narrow Reliability Bounds for Structural Systems,” Journal of Structural Mechanics, Vol. 7, No. 4, Dec., 1979, pp. 453–472.
5.
Dolinski, K., “First‐Order Second‐Moment Approximation in Reliability of Structural Systems: Critical Review and Alternative Approach,” Structural Safety, Vol. 1, No. 3, Apr., 1983, pp. 211–231.
6.
Fiessler, B., Neumann, H. J., and Rackwitz, R., “Quadratic Limit States in Structural Reliability,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. 4, Aug., 1979, pp. 661–676.
7.
Grigoriu, M., “Methods for Approximate Reliability Analysis,” Structural Safety, Vol. 1, No. 2, Dec., 1982, pp. 155–165.
8.
Hohenbichler, M., and Rackwitz, R., “Non‐Normal Dependent Vectors in Structural Safety,” Journal of the Engineering Mechanics Division, ASCE, Vol. 107, No. 6, Dec., 1981, pp. 1227–1238.
9.
Madsen, H. O., Krenk, S., and Lind, N. C., Methods of Structural Safety, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1986.
10.
Segal, I. E., “Fiducial Distribution of Several Parameters with Applications to a Normal System,” Proceedings of Cambridge Philosophical Society, Vol. 34, 1938, pp. 41–47.
11.
Shinozuka, M., “Basic Analysis of Structural Safety,” Journal of Structural Engineering, ASCE, Vol. 109, No. 3, Mar., 1983, pp. 721–740.
12.
Todd, J., Survey of Numerical Analysis, McGraw‐Hill, New York, N.Y., 1962.
13.
Tvedt, L., “Two Second‐Order Approximations to the Failure Probability,” Section on Structral Reliability, A/S Vertas Research, Hovik, Norway, 1984.
14.
Tvedt, L., “On the Probability Content of a Parabolic Failure Set in a Space of Independent Standard Normally Disbributed Random Varibles,” Section on Structural Reliability, A/S Vertas Research, Hovik, Norway, 1985.
Information & Authors
Information
Published In
Copyright
Copyright © 1987 ASCE.
History
Published online: Aug 1, 1987
Published in print: Aug 1987
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.