Skip to main content
Log in

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

  • Structural Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Azzalini, A. (1985). “A class of distributions which includes the normal ones.” Scand. J. Statist., Vol. 12, No. 2, pp. 171–178.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Cornell, C. A. (1969). “A probability based structural code.” J. Am. Concr. Insf., Vol. 66, Issue 12, pp. 974–985.

    Google Scholar 

  • Ditlevsen, O. and Madsen, H. O. (1996). “Structural Reliability Methods.” Wiley, Chichester.

    Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Henze, N. (1986). “A probabilistic representation of the ‘skew-normal’ distribution.” Scand. J. Statist., Vol. 13, No. 4, pp. 271–275.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Ranganathan, R. (2000). Structural reliability: analysis and design, Jico Publishing House.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Rubinstein, R. Y. (1981). Simulation and the Monte Carlo Method, Wiley, New York, NY.

    Book  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohsen A. Shayanfar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12205-017-1473-1

Keywords

Navigation