Abstract
The Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method in reliability analysis is a popular iterative method for obtaining the reliability index. However, in the cases of limit state functions with skew-distributed variables, HL-RF method may give inappropriate 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 equivalent normal distributions. By this modification, asymmetric non-normal distributions are not replaced with symmetric distributions anymore. It is demonstrated that this consideration of skewness of non-normal distributions improves the behavior of HL-RF method and makes the proposed method more reliable. This improvement is shown through illustrative examples.
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Azzalini, A. (1985). “A class of distributions which includes the normal ones.” Scand. J. Statist., Vol. 12, No. 2, pp. 171–178.
Azzalini, A. (1986). “Further results on a class of distributions which includes the normal ones.” Statistica., Vol. 46, No. 2, pp. 199–208, DOI: 10.6092/issn.1973-2201/711.
Bjerager, P. (1990). “On computation methods for structural reliability analysis.” Struct. Saf., Vol. 9, Issue 2, pp. 79–96, DOI: 10.1016/ 0167-4730(90)90001-6.
Breitung, K. (1984). “Asymptotic approximations for multinormal integrals.” J. Eng. Mech. ASCE, Vol. 110, No. 3, pp. 357–366, DOI: 10.1061/(ASCE)0733-9399(1984)110:3(357).
Bucher, C. G. (1988). “Adaptive sampling—an iterative fast Monte Carlo procedure.” Struct. Saf., Vol. 5, No. 2, pp. 119–126, DOI: 10.1016/0167-4730(88)90020-3.
Chen, Z., Qiu, H., Gao, L., Su, L., and Li, P. (2013). “An adaptive decoupling approach for reliability-based design optimization.” Comput. Struct., Vol. 117, pp. 58–66, DOI: 10.1016/j.compstruc.2012.12.001.
Cornell, C. A. (1969). “A probability based structural code.” J. Am. Concr. Insf., Vol. 66, Issue 12, pp. 974–985.
Ditlevsen, O. and Madsen, H. O. (1996). “Structural Reliability Methods.” Wiley, Chichester.
Gong, J. X. and Yi, P. (2011). “A robust iterative algorithm for structural reliability analysis.” Struct. Multidisc. Optim., Vol. 43, Issue 4, pp. 519–527, DOI: 10.1007/s00158-010-0582-y.
Harbitz, A. (1983). “Efficient and accurate probability of failure calculation by use of the importance sampling technique.” Proc. of the 4th int. conf. on app. of statist. and prob. in soils and struct. eng., ICASP-4. Pitagora Editrice, Bologna, pp. 825–836.
Hasofer, A. M. and Lind, N. C. (1974). “Exact and invariant secondmoment code format.” J. Engng. Mech. Div. ASCE Vol. 100(EMl), Issue 1, pp. 111–121.
Henze, N. (1986). “A probabilistic representation of the ‘skew-normal’ distribution.” Scand. J. Statist., Vol. 13, No. 4, pp. 271–275.
Hohenbichler, M., Gollwitzer, S., Kruse, W., and Rackwitz, R. (1987). “New light on first-and second-order reliability methods.” Struct. Saf., Vol. 4, Issue 4, pp. 267–284, DOI: 10.1016/0167-4730(87)90002-6.
Jahani, E., Shayanfar, M. A., and Barkhordari, M. A. (2013). “A new adaptive importance sampling Monte Carlo method for structural reliability.” KSCE J. Civ. Eng., Vol. 17, No. 1, pp. 210–215, DOI: 10.1007/s12205-013-1779-6.
Kiureghian, D. A., Lin, H. Z., and Hwang, S. J. (1987). “Second order reliability approximations.” J. Eng. Mech. ASCE, Vol. 113, Issue 8, pp. 1208–1225, DOI: 10.1061/(ASCE)0733-9399(1987)113:8(1208).
Lee, J. O., Yang, Y. S., and Ruy, W. S. (2002). “A comparative study on reliability-index and target-performance-based probabilistic structural design optimization.” Comput. Struct., Vol. 80, Nos. 3–4, pp. 257–269, DOI: 10.1016/S0045-7949(02)00006-8.
Liu, P. L. and Kiureghian, A. D. (1986). “Optimization algorithms for structural reliability analysis.” Report no. UCB/SESM-86/09, Department of Civil Engineering, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley, CA.
Liu, P. L. and Kiureghian, A. D. (1991). “Optimization algorithms for structural reliability.” Struct. Saf., Vol. 9, No. 3, pp. 161–177, DOI: 10.1016/0167-4730(91)90041-7.
Lu, Z. H., Zhao, Y. G., and Ang, A. H. S. (2010). “Estimation of load and resistance factors based on the fourth Moment method.” Struct. Eng. Mech., Vol. 36, No. 1, pp. 19–36, DOI: 10.12989/sem.2010.36. 1.019.
Luo, Y., Zhan, K., and Li, A. (2009). “Structural reliability assessment based on probability and convex set mixed model.” Comput. Struct., Vol. 87, No. 21, pp. 1408–1415, DOI: 10.1016/j.compstruc.2009.06.001.
Maes, M. A., Breitung, K., and Dupuis, D. J. (1993). “Asymptotic importance sampling.” Struct. Saf., Vol. 12, Issue 3, pp. 167–183, DOI: 10.1016/0167-4730(93)90001-H.
Mahadevan, S. and Shi, P. (2001). “Multiple linearization method for nonlinear reliability analysis.” ASCE J. Eng. Mech., Vol. 127, No. 11, pp. 1165–1173 (2001), DOI: 10.1061/(ASCE)0733-9399(2001) 127:11(1165).
Rackwitz, R. (2001). “Reliability analysis-a review and some perspectives.” Struct. Saf., Vol. 23, No. 4, pp. 365–395, DOI: 10.1016/S0167-4730(02)00009-7.
Rackwitz, R. and Fiessler, B. (1978). “Structural reliability under combined random load sequences.” Camput. Struct., Vol. 9, Issue 5, pp. 489–494, DOI: 10.1016/0045-7949(78)90046-9.
Ranganathan, R. (2000). Structural reliability: analysis and design, Jico Publishing House.
Roudak, M. A., Shayanfar, M. A., Barkhordari, M. A., and Karamloo, M. (2017a). “A new three-phase algorithm for computation of reliability index and its application in structural mechanics.” Mech. Res. Commun. (In Press), DOI: 10.1016/j.mechrescom.2017.08.008.
Roudak, M. A., Shayanfar, M. A., Barkhordari, M. A., and Karamloo, M. (2017b). “A robust approximation method for nonlinear cases of structural reliability analysis.” Int. J. Mech. Sci., Vol. 133C, pp. 11–20, DOI: 10.1016/j.ijmecsci.2017.08.038.
Rubinstein, R. Y. (1981). Simulation and the Monte Carlo Method, Wiley, New York, NY.
Schueller, G. I. (2009), “Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis-recent advances.” Struct. Eng. Mech., Vol. 32, No. 1, pp. 1–20, DOI: 10.12989/sem. 2009.32.1.001.
Shayanfar, M. A., Barkhordari, M. A., and Roudak, M. A. (2017). “An efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method.” Commun. Nonlinear Sci. Numer. Simulat., Vol. 47, pp. 223–237, DOI: 10.1016/j.cnsns.2016.11.021.
Shayanfar, M. A., Barkhordari, M. A., and Roudak, M. A. (2017a). “Locating design point in structural reliability analysis by introduction of a control parameter and moving limited regions.” Int. J. Mech. Sci., Vol. 126, pp. 196–202, DOI: 10.1016/j.ijmecsci.2017.04.003.
Wang, L. P. and Grandhi, R. V. (1996). “Safety index calculation using intervening variables for structural reliability analysis.” Comput. Struct., Vol. 59, Issue 6, pp. 1139–1148, DOI: 10.1016/0045-7949 (96)00291-X.
Yang, D. (2010). “Chaos control for numerical instability of first order reliability method.” Commun. Nonlinear Sci. Numer. Simulat., Vol. 15, No. 10, pp. 3131–3141, DOI: 10.1016/j.cnsns.2009.10.018.
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Shayanfar, M.A., Barkhordari, M.A. & Roudak, M.A. A Modification to HL-RF Method for Computation of Structural Reliability Index in Problems with Skew-distributed Variables. KSCE J Civ Eng 22, 2899–2905 (2018). https://doi.org/10.1007/s12205-017-1473-1
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DOI: https://doi.org/10.1007/s12205-017-1473-1