Structural Engineering and Mechanics

  • 제76권6호
  • /
  • Pages.675-685
  • /
  • 2020
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Decomposable polynomial response surface method and its adaptive order revision around most probable point

  • Zhang, Wentong (School of Civil and Environmental Engineering, Harbin Institute of Technology) ;
  • Xiao, Yiqing (School of Civil and Environmental Engineering, Harbin Institute of Technology)
  • 투고 : 2019.09.21
  • 심사 : 2020.08.13
  • 발행 : 2020.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

As the classical response surface method (RSM), the polynomial RSM is so easy-to-apply that it is widely used in reliability analysis. However, the trade-off of accuracy and efficiency is still a challenge and the "curse of dimension" usually confines RSM to low dimension systems. In this paper, based on the univariate decomposition, the polynomial RSM is executed in a new mode, called as DPRSM. The general form of DPRSM is given and its implementation is designed referring to the classical RSM firstly. Then, in order to balance the accuracy and efficiency of DPRSM, its adaptive order revision around the most probable point (MPP) is proposed by introducing the univariate polynomial order analysis, noted as RDPRSM, which can analyze the exact nonlinearity of the limit state surface in the region around MPP. For testing the proposed techniques, several numerical examples are studied in detail, and the results indicate that DPRSM with low order can obtain similar results to the classical RSM, DPRSM with high order can obtain more precision with a large efficiency loss; RDPRSM can perform a good balance between accuracy and efficiency and preserve the good robustness property meanwhile, especially for those problems with high nonlinearity and complex problems; the proposed methods can also give a good performance in the high-dimensional cases.

키워드

과제정보

The research described in this paper was financially supported by the National Key Research and Development Program of China [grant numbers 2016YFC0701107].

참고문헌

  1. Bucher C., Bourgund U. (1990), "A fast and efficient response surface approach for structural reliability problems", Structural Safety, 7(1), 57-66. https://doi.org/10.1016/0167-4730(90)90012-E
  2. Breitkopf P., Naceur H., Rassineux A., Villon P. (2005), "Moving least squares response surface approximation: Formulation and metal forming applications", Comput. Struct., 83(17-18), 1411-1428. https://doi.org/10.1016/j.compstruc.2004.07.011
  3. Bucher C. (2009), "Asymptotic sampling for high-dimensional reliability analysis", Probabilistic Eng. Mech., 24(4), 504-510. https://doi.org/10.1016/j.probengmech.2009.03.002
  4. Blatman G., Sudret B. (2010), "An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis", Probabilistic Eng. Mech., 25(2), 183-197. https://doi.org/10.1016/j.probengmech.2009.10.003
  5. Bourinet J.M., Deheeger F., Lemaire M. (2011), "Assessing small failure probabilities by combined subset simulation and Support Vector Machines", Struct. Safety, 33(6), 343-353. https://doi.org/10.1016/j.strusafe.2011.06.001
  6. Basaga H.B., Bayraktar A., 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
  7. Chowdhury R., Rao B.N. (2009), "Assessment of high dimensional model representation techniques for reliability analysis", Probabilistic Eng. Mech., 24(1), 100-115. https://doi.org/10.1016/j.probengmech.2008.02.001
  8. Fang Y., Tee K.F. (2017), "Structural reliability analysis using response surface method with improved genetic algorithm", Struct. Eng. Mech., 62(2), 139-142. https://doi.org/10.12989/sem.2017.62.2.139
  9. Gomes H.M., Awruch A.M. (2004), "Comparison of response surface and neural network with other methods for structural reliability analysis", Struct. Safety, 26(1), 49-67. https://doi.org/10.1016/S0167-4730(03)00022-5
  10. Gavin H.P., Yau S.C. (2008), "High-order limit state functions in the response surface method for structural reliability analysis", Struct. Safety, 30(2), 162-179. https://doi.org/10.1016/j.strusafe.2006.10.003
  11. Goswami S., Ghosh S., Chakraborty S. (2016), "Reliability analysis of structures by iterative improved response surface method", Struct. Safety, 60, 56-66. https://doi.org/10.1016/j.strusafe.2016.02.002
  12. Guimaraes H., Matos J.C., Henriques A.A. (2018), "An innovative adaptive sparse response surface method for structural reliability analysis", Struct. Safety, 73, 12-28. https://doi.org/10.1016/j.strusafe.2018.02.001
  13. He J., Gao S., Gong J. (2014), "A sparse grid stochastic collocation method for structural reliability analysis". Struct. Safety, 51:29-34. https://doi.org/10.1016/j.strusafe.2014.06.003
  14. Hadidi A., Azar B.F., Rafiee A. (2017), "Efficient response surface method for high-dimensional structural reliability analysis", Struct. Safety, 68, 15-27. https://doi.org/10.1016/j.strusafe.2017.03.006
  15. Jiang S.H., Li D.Q., Zhou C.B., Zhang L.M. (2014), "Capabilities of stochastic response surface method and response surface method in reliability analysis", Struct. Eng. Mech., 49(1), 111-128. http://dx.doi.org/10.12989/sem.2014.49.1.111
  16. Kim S.H., Na S.W. (1997), "Response surface method using vector projected sampling points", Struct. Safety, 19(1), 3-19. https://doi.org/10.1016/S0167-4730(96)00037-9
  17. Li H.S., Lu Z.Z., 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
  18. Liu P.L., Der Kiureghian A. (1986), "Multivariate distribution models with prescribed marginal and covariances", Probabilistic Eng. Mech., 1(2), 105-112. https://doi.org/10.1016/0266-8920(86)90033-0
  19. Monteiro R. (2016), "Sampling based numerical seismic assessment of continuous span RC bridges", Eng. Struct., 118, 407-420. https://doi.org/10.1016/j.engstruct.2016.03.068
  20. Nie J.S., Ellingwood B.R. (2005), "Finite element-based structural reliability assessment using efficient directional simulation", J. Eng. Mech., 131(3), 259-267. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:3(259)
  21. Pradlwarter H.J., Schueller G.I., Koutsourelakis P.S., Charmpis D.C. (2007), "Application of line sampling simulation method to reliability benchmark problems", Struct. Safety, 29(3), 208-221. https://doi.org/10.1016/j.strusafe.2006.07.009
  22. Rajashekhar M.R., Ellingwood B.R. (1993), "A new look at the response surface approach for reliability analysis", Struct. Safety, 12(3), 205-220. https://doi.org/10.1016/0167-4730(93)90003-J
  23. Rackwitz R. (2001), "Reliability analysis-A review and some perspectives", Struct. Safety, 23(4), 365-395. https://doi.org/10.1016/S0167-4730(02)00009-7
  24. Rahman S., Xu H. (2004), "A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics", Probabilistic Eng. Mech., 19(4), 393-408. https://doi.org/10.1016/j.probengmech.2004.04.003
  25. Rahman S., Wei D. (2006), "A univariate approximation at most probable point for higher-order reliability analysis", J. Solids Struct., 43(9), 2820-2839. https://doi.org/10.1016/j.ijsolstr.2005.05.053
  26. Rao B.N., Chowdhury R. (2008), "Factorized high dimensional model representation for structural reliability analysis", Eng. Comput., 25(8), 708-738. https://doi.org/10.1108/02644400810909580
  27. Roussouly N., Petitjean F., Salaun M. (2013), "A new adaptive response surface method for reliability analysis", Probabilistic Eng. Mech., 32, 103-15. https://doi.org/10.1016/j.probengmech.2012.10.001
  28. Schueller G.I. (2009), "Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis - recent advances", Struct. Eng. Mech., 32(1), 1-20. http://dx.doi.org/10.12989/sem.2009.32.1.001
  29. Vahedi J., Ghasemi M.R., Miri M. (2018), "Structural reliability assessment using an enhanced adaptive Kriging method", Struct. Eng. Mech., 66(6), 677-691. https://doi.org/10.12989/sem.2018.66.6.677
  30. Wong F.S. (1984), "Uncertainties in dynamic soil-structure interaction", J. Eng. Mech., 110(2), 308-324. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:2(308)
  31. Xu H., Rahman S. (2005), "Decomposition methods for structural reliability analysis", Probabilistic Eng. Mech., 20(3), 239-250. https://doi.org/10.1016/j.probengmech.2005.05.005
  32. Xu J., Kong F. (2018), "A new unequal-weighted sampling method for efficient reliability analysis", Reliability Eng. Syst. Safety, 172, 94-102. https://doi.org/10.1016/j.ress.2017.12.007
  33. Xu J., Kong F. (2018), "An adaptive cubature formula for efficient reliability assessment of nonlinear structural dynamic systems", Mech. Syst. Signal Process, 104, 449-464. https://doi.org/10.1016/j.ymssp.2017.10.039
  34. Xu J., Dang C. (2019), "A new bivariate dimension reduction method for efficient structural reliability analysis", Mech. Syst. Signal Process, 115, 281-300. https://doi.org/10.1016/j.ymssp.2018.05.046
  35. Xu J., Zhu S. (2019), "An efficient approach for high-dimensional structural reliability analysis", Mech. Syst. Signal Process, 122, 152-170. https://doi.org/10.1016/j.ymssp.2018.12.007
  36. Zheng Y., Das P.K. (2000), "Improved response surface method and its application to stiffened plate reliability analysis", Eng. Struct., 22(5), 544-551. https://doi.org/10.1016/S0141-0296(98)00136-9
  37. Zhao Y.G., Ono T. (2011), "Moment methods for structural reliability", Struct. Safety, 23(1), 47-75. https://doi.org/10.1016/S0167-4730(00)00027-8
  38. Zhao W., Qiu Z., Yang Y. (2013), "An efficient response surface method considering the nonlinear trend of the actual limit state", Struct. Eng. Mech., 47(1), 45-58. http://dx.doi.org/10.12989/sem.2013.47.1.045
  39. Zhang W., Xiao Y. (2019), "An adaptive order response surface method for structural reliability analysis", Eng. Comput., 36(5), 1626-1655. http://dx.doi.org/10.1108/EC-09-2018-0428