Structural Engineering and Mechanics

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Capabilities of stochastic response surface method and response surface method in reliability analysis

  • Jiang, Shui-Hua (State Key Laboratory of Water Resources and Hydropower Engineering Science, Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering (Ministry of Education), Wuhan University) ;
  • Li, Dian-Qing (State Key Laboratory of Water Resources and Hydropower Engineering Science, Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering (Ministry of Education), Wuhan University) ;
  • Zhou, Chuang-Bing (State Key Laboratory of Water Resources and Hydropower Engineering Science, Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering (Ministry of Education), Wuhan University) ;
  • Zhang, Li-Min (Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology)
  • Received : 2013.02.27
  • Accepted : 2013.12.10
  • Published : 2014.01.10
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Abstract

The stochastic response surface method (SRSM) and the response surface method (RSM) are often used for structural reliability analysis, especially for reliability problems with implicit performance functions. This paper aims to compare these two methods in terms of fitting the performance function, accuracy and efficiency in estimating probability of failure as well as statistical moments of system output response. The computational procedures of two response surface methods are briefly introduced first. Then their capabilities are demonstrated and compared in detail through two examples. The results indicate that the probability of failure mainly reflects the accuracy of the response surface function (RSF) fitting the performance function in the vicinity of the design point, while the statistical moments of system output response reflect the accuracy of the RSF fitting the performance function in the entire space. In addition, the performance function can be well fitted by the SRSM with an optimal order polynomial chaos expansion both in the entire physical and in the independent standard normal spaces. However, it can be only well fitted by the RSM in the vicinity of the design point. For reliability problems involving random variables with approximate normal distributions, such as normal, lognormal, and Gumbel Max distributions, both the probability of failure and statistical moments of system output response can be accurately estimated by the SRSM, whereas the RSM can only produce the probability of failure with a reasonable accuracy.

Keywords

References

  1. Ang, A.H.S. and Tang, W.H. (2007), Probability concepts in engineering: emphasis on applications to civil and environmental engineering, 2nd Edition, John Wiley and Sons, New York, NY, USA.
  2. Basaga, H.B., Bayraktar, A. and Kaymaz, I. (2012), "An improved response surface method for reliability analysis of structures", Struct. Eng. Mech., 42(2), 175-189. https://doi.org/10.12989/sem.2012.42.2.175
  3. Box, G.E.P. and Wilson, K.B. (1951), "On the experimental attainment of optimum conditions (with discussion)", J. R. Stat. Soc. B, 13(1), 1-45.
  4. Bucher, C.G. and Bourgund, U. (1990), "A fast and efficient response surface approach for structural reliability problems", Struct. Saf., 7(1), 57-66. https://doi.org/10.1016/0167-4730(90)90012-E
  5. Cameron, R. and Martin, W. (1947), "The orthogonal development of nonlinear functional in series of Fourier Hermite functional", Ann. Math., 48(2), 385-392. https://doi.org/10.2307/1969178
  6. Cheng, J., Li, Q.S. and Xiao, R.C. (2008), "A new artificial neural network-based response surface method for structural reliability analysis", Probabilist. Eng. Mech., 23(1), 51-63. https://doi.org/10.1016/j.probengmech.2007.10.003
  7. Cheng, J. and Li, Q.S. (2009), "Application of the response surface methods to solve inverse reliability problems with implicit response functions", Computat. Mech., 43(4), 451-459. https://doi.org/10.1007/s00466-008-0320-0
  8. Das, P. K. and Zheng, Y. (2002), "Cumulative formation of response surface and its use in reliability analysis", Probabilist. Eng. Mech., 15(4), 309-315.
  9. Der Kiureghian, A., Lin, H.Z. and Hwang, S.J. (1987), "Second order reliability approximations", J. Eng. Mech., 113(8), 1208-1225. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:8(1208)
  10. Ditlevsen, O. and Madsen, H.O. (1996), Structural Reliability Methods, John Wiley and Sons, New York, NY, USA.
  11. Duprat, F. and Sellier, A. (2006), "Probabilistic approach to corrosion risk due to carbonation via an adaptive response surface method", Probabilist. Eng. Mech., 21(3), 207-216. https://doi.org/10.1016/j.probengmech.2005.11.001
  12. Eldred, M.S., Webster, C.G. and Constantine, P. (2008), "Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos", Proceedings of the 10th AIAA nondeterministic approaches conference, Schaumburg, IL, AIAA-2008-1892.
  13. Faravelli, L. (1989), "Response surface approach for reliability analysis", J. Eng. Mech., 115(12), 2763-2781. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:12(2763)
  14. Gavin, H.P. and Yau, S.C. (2008), "High-order limit state functions in the response surface method for structural reliability analysis", Struct. Saf., 30(2), 162-179. https://doi.org/10.1016/j.strusafe.2006.10.003
  15. Gomes, H.M. and Awruch, A.M. (2004), "Comparison of response surface method and neural network with other methods for structural reliability analysis", Struct. Saf., 26(1), 49-67. https://doi.org/10.1016/S0167-4730(03)00022-5
  16. Hasofer, A.M. and Lind, N.C. (1974), "Exact and invariant second moment code format", J. Eng. Mech., 100(1), 111-121.
  17. Huang, S.P., Liang, B. and Phoon, K.K. (2009), "Geotechnical probabilistic analysis by collocation-based stochastic response surface method- An EXCEL add-in implementation", Georisk, 3(2), 75-86.
  18. Isukapalli, S.S. (1999), "Uncertainty analysis of transport transformation models", Ph. D. Dissertation, The State University of New Jersey, New Brunswick, New Jersey, USA.
  19. Jiang, S.H., Li, D.Q., Zhang, L.M. and Zhou C.B. (2013), "Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method", Eng. Geol., 168, 120-128.
  20. Kaymaz, I. and McMahon, C.A. (2005), "A response surface method based on weighted regression for structural reliability analysis", Probabilist. Eng. Mech., 20(1), 11-17. https://doi.org/10.1016/j.probengmech.2004.05.005
  21. Kim, S.H. and Na, S.W. (1997), "Response surface method using vector projection sampling points", Struct. Saf., 19(1), 3-19. https://doi.org/10.1016/S0167-4730(96)00037-9
  22. Li, D.Q., Chen, Y.F., Lu, W.B. and Zhou, C.B. (2011), "Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables", Comput. Geotech., 38(1), 58-68. https://doi.org/10.1016/j.compgeo.2010.10.006
  23. Li, D.Q., Wu, S.B., Zhou C.B. and Phoon, K. K. (2012), "Performance of translation approach for modeling correlated non-normal variables", Struct. Saf., 39: 52-61. https://doi.org/10.1016/j.strusafe.2012.08.001
  24. Li, D.Q., Jiang, S.H., Chen, Y.F. and Zhou, C.B. (2013a), "Reliability analysis of serviceability performance for an underground cavern using a non-intrusive stochastic method", Environ. Earth. Sci., DOI:10.1007/s12665-013-2521-x.
  25. Li, D.Q., Jiang, S.H., Cheng, Y. G. and Zhou, C.B. (2013b), "A comparative study of three collocation point methods for odd order stochastic response surface method", Struct. Eng. Mech., 45(5), 595-611. https://doi.org/10.12989/sem.2013.45.5.595
  26. Li, D.Q., Phoon, K.K., Wu, S.B., Chen, Y.F. and Zhou C.B. (2013c), "Impact of translation approach for modelling correlated non-normal variables on parallel system reliability", Struct. Infrastruct. E., 9(10), 969-982. https://doi.org/10.1080/15732479.2011.652968
  27. Li, H. and Zhang, D.X. (2007), "Probabilistic collocation method for flow in porous media: comparisons with other stochastic method", Water Resour. Res., 43(W09409), DOI:10.1029/2006 WR005673.
  28. 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
  29. Lin, K., Qiu, H.B., Gao, L. and Sun, Y.F. (2009), "Comparison of stochastic response surface method and response surface method for structure reliability analysis", Second International Conference on Intelligent Computation Technology and Automation, Changsha, China, October.
  30. Mao, N., Al-Bittar, T. and Soubra, A.H. (2012), "Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek-Brown failure criterion", Int. J. Rock Mech. Min., 49(1), 45-58. https://doi.org/10.1016/j.ijrmms.2011.11.005
  31. Melchers, R.E. (1989), "Importance sampling in structural systems", Struct. Saf., 6(1), 3-10. https://doi.org/10.1016/0167-4730(89)90003-9
  32. Melchers, R.E. (1999), Structural reliability analysis and prediction, 2nd Edition, John Wiley and Sons, Chichester.
  33. Milani, G. and Benasciutti, D. (2010), "Homogenized limit analysis of masonry structures with random input properties: polynomial Response surface approximation and Monte Carlo simulations", Struct. Eng. Mech., 34(4), 417-447. https://doi.org/10.12989/sem.2010.34.4.417
  34. Nataf, A. (1962), "Determination des distributions de probabilite dont les marges sont donnees", Comptes Rendus de l'Academie des Sciences, 225, 42-43.
  35. Nguyen, X.S., Sellier, A., Duprat, F. and Pons, G. (2009), "Adaptive response surface method based on a double weighted regression technique", Probabilist. Eng. Mech., 24(2), 135-143. https://doi.org/10.1016/j.probengmech.2008.04.001
  36. Roussouly, N., Petitjean, F., Salaun, M. (2013), "A new adaptive response surface method for reliability analysis", Probabilist. Eng. Mech., 32, 103-115. https://doi.org/10.1016/j.probengmech.2012.10.001
  37. Sudret, B. (2008), "Global sensitivity analysis using polynomial chaos expansion", Reliab. Eng. Syst. Safe., 93(7), 964-979. https://doi.org/10.1016/j.ress.2007.04.002
  38. Tang, X.S., Li, D.Q., Chen, Y.F., Zhou, C.B. and Zhang, L.M. (2012), "Improved knowledge-based clustered partitioning approach and its application to slope reliability analysis", Comput. Geotech., 45, 34-43. https://doi.org/10.1016/j.compgeo.2012.05.001
  39. Tatang, M.A., Pan, W., Prinn, R.G. and McRae, G.J. (1997), "An efficient method for parametric uncertainty analysis of numerical geophysical models", J. Geophys. Res., 102(D18), 21925-21932. https://doi.org/10.1029/97JD01654
  40. Xiu, D.B. and Karniadakis, G.E. (2003), "Modeling uncertainty in flow simulations via generalized polynomial chaos", J. Comput. Phys., 187(1), 137-167. https://doi.org/10.1016/S0021-9991(03)00092-5

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