A Modification to HL-RF Method for Computation of Structural Reliability Index in Problems with Skew-distributed Variables

다국어 초록 (Multilingual Abstract)

The Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method in reliability analysis is a popular iterative method for obtaining thereliability index. However, in the cases of limit state functions with skew-distributed variables, HL-RF method may giveinappropriate answers. This paper represents a modification to HL-RF method in order to improve its performance in such problems.
Based on this modification, non-normal distributions are replaced with equivalent skew-normal distributions instead of equivalentnormal distributions. By this modification, asymmetric non-normal distributions are not replaced with symmetric distributionsanymore. It is demonstrated that this consideration of skewness of non-normal distributions improves the behavior of HL-RF methodand makes the proposed method more reliable. This improvement is shown through illustrative examples.

참고문헌 (Reference)

1 Ranganathan, R., "Structural reliability: analysis and design" Jico Publishing House 2000

2 Rackwitz, R., "Structural reliability under combined random load sequences" 9 (9): 489-494, 1978

3 Luo, Y., "Structural reliability assessment based on probability and convex set mixed model" 87 (87): 1408-1415, 2009

4 Ditlevsen, O., "Structural Reliability Methods" Wiley 1996

5 Rubinstein, R. Y., "Simulation and the Monte Carlo Method" Wiley 1981

6 Kiureghian, D. A., "Second order reliability approximations" ASCE 113 (113): 1208-1225, 1987

7 Wang, L. P., "Safety index calculation using intervening variables for structural reliability analysis" 59 (59): 1139-1148, 1996

8 Rackwitz, R., "Reliability analysis-a review and some perspectives" 23 (23): 365-395, 2001

9 Liu, P. L., "Optimization algorithms for structural reliability analysis" Department of Civil Engineering, Division of Structural Engineering and Structural Mechanics, University of Calif 1986

10 Liu, P. L., "Optimization algorithms for structural reliability" 9 (9): 161-177, 1991

11 Bjerager, P., "On computation methods for structural reliability analysis" 9 (9): 79-96, 1990

12 Hohenbichler, M., "New light on first- and second-order reliability methods" 4 (4): 267-284, 1987

13 Mahadevan, S., "Multiple linearization method for nonlinear reliability analysis" 127 (127): 1165-1173, 2001

14 Shayanfar, M. A., "Locating design point in structural reliability analysis by introduction of a control parameter and moving limited regions" 126 : 196-202, 2017

15 Azzalini, A., "Further results on a class of distributions which includes the normal ones" 46 (46): 199-208, 1986

16 Hasofer, A. M., "Exact and invariant secondmoment code format" ASCE 100(EMl) (100(EMl)): 111-121, 1974

17 Zhao-Hui Lu, "Estimation of load and resistance factors based on the fourth moment method" 국제구조공학회 36 (36): 19-36, 2010

18 Harbitz, A., "Efficient and accurate probability of failure calculation by use of the importance sampling technique" 825-836, 1983

19 G.I. Schueller, "Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis - recent advances" 국제구조공학회 32 (32): 1-20, 2009

20 Yang, D., "Chaos control for numerical instability of first order reliability method" 15 (15): 3131-3141, 2010

21 Maes, M. A., "Asymptotic importance sampling" 12 (12): 167-183, 1993

22 Breitung, K., "Asymptotic approximations for multinormal integrals" ASCE 110 (110): 357-366, 1984

23 Shayanfar, M. A., "An efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method" 47 : 223-237, 2017

24 Chen, Z., "An adaptive decoupling approach for reliability-based design optimization" 117 : 58-66, 2013

25 Bucher, C. G., "Adaptive sampling-an iterative fast Monte Carlo procedure" 5 (5): 119-126, 1988

26 Gong, J. X., "A robust iterative algorithm for structural reliability analysis" 43 (43): 519-527, 2011

27 Roudak, M. A., "A robust approximation method for nonlinear cases of structural reliability analysis" 133C : 11-20, 2017

28 Cornell, C. A., "A probability based structural code" 66 (66): 974-985, 1969

29 Henze, N., "A probabilistic representation of the 'skew-normal' distribution" 13 (13): 271-275, 1986

30 Roudak, M. A., "A new three-phase algorithm for computation of reliability index and its application in structural mechanics" 2017

31 Lee, J. O., "A comparative study on reliability-index and target-performance-based probabilistic structural design optimization" 80 (80): 257-269, 2002

32 Azzalini, A., "A class of distributions which includes the normal ones" 12 (12): 171-178, 1985

33 Ehsan Jahani, "A New Adaptive Importance Sampling Monte Carlo Method for Structural Reliability" 대한토목학회 17 (17): 210-215, 2013