Structural Engineering and Mechanics

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Reliability index for non-normal distributions of limit state functions

  • Ghasemi, Seyed Hooman (Department of Civil Engineering, Islamic Azad University) ;
  • Nowak, Andrzej S. (Department of Civil Engineering, Auburn University)
  • Received : 2015.08.09
  • Accepted : 2017.02.24
  • Published : 2017.05.10
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Abstract

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are non-normal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.

Keywords

References

  1. Ashtari, P. and Ghasemi, S.H. (2013), "Seismic design of structures using modified non-stationary critical excitation", J. Earthq. Struct., 4(4), 383-396. https://doi.org/10.12989/eas.2013.4.4.383
  2. Ayyub, B., Akpan, U., Koko, T. and Dunbar, T. (2015), "Reliability-based optimal design of steel box structures. I: theory", ASCE-ASME J. Risk Uncert. Eng. Syst., Part A: Civil Eng., 1(3), 04015009. https://doi.org/10.1061/AJRUA6.0000829
  3. Basler, E. (1961), Untersuchungen uber den Sicherheitsbegriff von Bauwerken, Schweizer Archiv fur angewandte Wissenschaft und Technik.
  4. Chowdhury, R. and Rao, B.N. (2011), "Multicut high dimensional model representation for reliability analysis", Struct. Eng. Mech., 38(5), 651-674. https://doi.org/10.12989/sem.2011.38.5.651
  5. Cornell, C.A. (1969), "A probability based structural code", ACI J., 66, 974-985.
  6. Der Kiureghian, A. and Song, J. (2008), "Multi-scale reliability analysis and updating of complex systems by use of linear programming", Reliab. Eng. Syst. Saf., 93, 288-297. https://doi.org/10.1016/j.ress.2006.10.022
  7. Dimovski, I.H. (1990), Convolutional Calculus (Mathematics and its Applications), 2nd Edition, Kluwer Academic, Dordrecht, Boston.
  8. Ditlevsen, O. and Madsen, H.O. (1996), Structural Reliability Methods, John Wiley &Sons Inc., New York.
  9. Fang, Y., Chen, J. and Tee, K.F. (2013), "Analysis of structural dynamic reliability based on the probability density evolution method", Struct. Eng. Mech., 46(6), 201-209.
  10. Hall, P. (2013), The Bootstrap and Edgeworth Expansion, Springer, New York.
  11. Hasofer, A.M. and Lind, N. (1974), "An exact and invariant first-order reliability format", J. Eng. Mech., ASCE, 100(EM1), 111-121.
  12. Ghasemi, S.H. (2014), "Target reliability analysis for structures", Doctoral Dissertation, Auburn University, Auburn, USA.
  13. Ghasemi, S.H. and Ashtari, P. (2014), "Combinatorial continuous non-stationary critical excitation in M.D.O.F structures using modified envelope functions", Earthq. Struct., 7(6), 859-908.
  14. Ghasemi, S.H., Nowak, A.S. and Ashtari, P. (2013), "Estimation of the resonance-response factor regarding to the critical excitation methods", Proceedings of the 11th International Conference on Structural Safety & Reliability, ICOSSAR 2013, New York, USA.
  15. Ghasemi, S.H. and Nowak, A.S. (2016a), "Reliability analysis for serviceability limit state of bridges concerning deflection criteria", Struct. Eng. Int., 26(2), 168-175. https://doi.org/10.2749/101686616X14555428758722
  16. Ghasemi, S.H. and Nowak, A.S. (2016b), "Mean maximum values of non-normal distributions for different time periods", Int. J. Reliab. Saf., 10(2), 99-109. https://doi.org/10.1504/IJRS.2016.078381
  17. Ghasemi, S.H., Nowak, A.S. and Parastesh, H. (2016a), "Statistical parameters of in-a-lane multiple truck presence and a new procedure to analyze the lifetime of bridges", Struct. Eng. Int., 26(2), 150-159. https://doi.org/10.2749/101686616X14555428758849
  18. Ghasemi, S.H., Jalayer, M., Pour-Rouholamin, M., Nowak, A.S. and Zhou, H. (2016b), "A state-of-the-art model to evaluate space headway based on reliability analysis", J. Tran. Eng., 142(7), 04016023. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000851
  19. Jalayer, M. and Zhou, H. (2016), "Evaluating the safety risk of roadside features for rural two-lane roads using reliability analysis", Accid. Anal. Prevent., 93, 101-112. https://doi.org/10.1016/j.aap.2016.04.021
  20. Janssen, H. (2013), "Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence", Reliab. Eng. Syst. Saf., 109, 123-132. https://doi.org/10.1016/j.ress.2012.08.003
  21. Leira, B.J. (2013), Optimal Stochastic Control Schemes within a Structural Reliability Framework, Springer.
  22. Li, H.S., Lu, Z.Z. and Qiao, H.W. (2010), "A new high-order response surface method for structural reliability analysis", Struct. Eng. Mech., 34(6), 779-799. https://doi.org/10.12989/sem.2010.34.6.779
  23. Lewis, E.F. (1996), Reliability Engineering, John Wiley & Sons Inc., New York, USA.
  24. Okasha, N.M., Frangopol, D.M. and Orcesi, A.D. (2012), "Automated finite element updating using strain data for the lifetime reliability assessment of bridges", Reliab. Eng. Syst. Reliab., 99(1), 139-150. https://doi.org/10.1016/j.ress.2011.11.007
  25. Moubray, J.M. (2002), Reliability-centred Maintenance, Butterworth-Heinemann, Oxford, United Kingdom.
  26. Nowak, A.S. and Collins, K.R. (2013), Reliability of Structures, CRC Press, New York.
  27. Rackwitz, R. and Fiessler, B. (1978), "Structural reliability under combined random load sequences", J. Comput. Struct., 9(5), 89-494. https://doi.org/10.1016/0045-7949(78)90062-7
  28. Shi, X., Teixeira, A.P., Zhang, J. and Soares, C.G. (2014), "Structural reliability analysis based on probabilistic response modelling using the maximum entropy method", Eng. Struct., 70(1), 106-116. https://doi.org/10.1016/j.engstruct.2014.03.033
  29. Weisstein, E.W. (2014a), "Convolution theorem", From Math World A Wolfram Web Resource, http://mathworld.wolfram.com/ConvolutionTheorem.html.
  30. Weisstein, E.W. (2014b), "Normal sum distribution", From Math World A Wolfram Web Resource, http://mathworld.wolfram.com/NormalSumDistribution.html.
  31. Yanaka, M., Ghasemi, S.H. and Nowak, A.S. (2016), "Reliability-based and life-cycle-cost oriented design recommendations for prestressed concrete bridge girders", Struct. Concrete, 18(1), 836-847 .
  32. Zhu, B. and Frangopol, D. (2015), "Effects of postfailure material behavior on system reliability", ASCE-ASME J. Risk Uncert. Eng. Syst., Part A: Civil Eng., 1(1), 04014002. https://doi.org/10.1061/AJRUA6.0000808

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