The New Approximate Calculation Method for the First Order Reliability


The new method is presented for computing engineering structure reliability by direct searching the next checking point and accelerating convergence based on the analysis of errors in the center point method and borrowing ideas form the merits of the other First-Order Second Moment (FOSM) methods. The idea of the direct searching method is constructing a new explicit searching formula to make the new checking point being more closed to the failure surface based on the results of the center point method. The new checking point has steepest descent character because the searching path is the gradient of the approximate surface. An example shows that the method presented in this article has well precision. Although the direct searching formula may not reach the globally optimal point, the error can be controlled owing to the locally optimal plan at each searching step.

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G. Hao, X. Liang and S. Zhang, "The New Approximate Calculation Method for the First Order Reliability," Applied Mathematics, Vol. 4 No. 3, 2013, pp. 505-509. doi: 10.4236/am.2013.43075.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] G. F. Zhao, “Theory and Application of Reliability in Engineering Structure,” Dalian University of Technology Press, Dalian, 1996, pp. 1-2. (In Chinese)
[2] S. W. Wu, “Structural Reliability Analysis,” China Communications Press, Beijing, 1996, pp. 22-31. (In Chinese)
[3] G. F. Zhao, J. Y. Cao and K. Q. Zhang, “Engineering Structural Reliability,” Wate Conservancy and Hydropower Press, Beijing, 1984, pp. 51-65. (In Chinese)
[4] Y. G. Li and G. F. Zhao, “The First Order Reliability Method of General Stochastic Space,” Journal of Dalian University of Technology, Vol. S1, 1993, pp. 1-5. (In Chinese)
[5] G. Q. Li and W. J. Yang, “A Simplified Calculating Method on Reliability,” Journal of Changsha Communications Universrty, Vol. 15, No. 3, 1999, pp. 62-67.
[6] Q. X. Wu, T. R. Lv and S. W. Wu. “Computing of Structural Reliability Index for Correlated Variables,” Applied Mathematics: A Journal of Chinese Universities, Vol. 3, 1987, pp. 323-329.
[7] A. M. Hasofer and N. C. Lind, “Exact and Invariant Second-Moment Code Format,” Journal of the Engineering Mechanics Division, Vol. 100, No. 1, 1974, pp. 111-121.
[8] R. Rackwitz and B. Fiessler, “Structural Reliability under Combined Random Load Sequences Computers and Structures,” Computers and Structures, Vol. 9, No. 5, 1978, pp. 489-494. doi:10.1016/0045-7949(78)90046-9
[9] M. Shinozuka, “Basic Analysis of Structural Safety,” Journal of Structural Engineering, Vol. 109, No. 3, 1983, pp. 721-740. doi:10.1061/(ASCE)0733-9445(1983)109:3(721)
[10] A. Der Kiureghian and T. Dakessian, “Multiple Design Points in First and Second-Order Reliability,” Structural Safety, Vol. 20, No. 1, 1998, pp. 37-49. doi:10.1016/S0167-4730(97)00026-X
[11] P. Bjerager and S. Krenk, “Sensitivity Measures in Structural Reliability Analysis,” Reliability and Optimization of Structural Systems, Proceedings of the First IFIP WG 7.5 Working Conference, Springer-Verlag, Aalborg, 1987, pp. 459-470.
[12] A. Harbitz, “An Efficient Method for Probability of Failure Calculation,” Structural Safety, Vol. 3, No. 2, 1986, pp. 109-115. doi:10.1016/0167-4730(86)90012-3
[13] X. L. Guan and R. E. Melchers, “Multi-Tangent-Plane Surface Method for Reliability Calculation,” Journal of Engineering Mechanics, Vol. 123, No. 10, 1997, pp. 996-1002. doi:10.1061/(ASCE)0733-9399(1997)123:10(996)
[14] S. Mahadevan and P. Shi, “Multiple Linearization Method for Nonlinear Reliability Analysis,” Journal of Engineering Mechanics, Vol. 127, No. 11, 2001, pp. 1165-1173. doi:10.1061/(ASCE)0733-9399(2001)127:11(1165)
[15] Q. X. Wu, “Structural Reliability Analysis and Random Finite Element Method,” China Machine Press, Beijing, 2005, pp. 63-73. (In Chinese)
[16] W. T. Liu, “Design Handbook for Structural Reliability,” National Defense Industry Press, Beijing, 2008, pp. 493-501. (In Chinese)

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