Structural Engineering and Mechanics

  • 제34권6호
  • /
  • Pages.779-799
  • /
  • 2010
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A new high-order response surface method for structural reliability analysis

  • Li, Hong-Shuang (School of Aeronautics, Northwestern Polytechnical University) ;
  • Lu, Zhen-Zhou (School of Aeronautics, Northwestern Polytechnical University) ;
  • Qiao, Hong-Wei (School of Aeronautics, Northwestern Polytechnical University)
  • 투고 : 2009.01.20
  • 심사 : 2010.01.15
  • 발행 : 2010.04.20
⟨ 이전 논문 다음 논문 ⟩

초록

In order to consider high-order effects on the actual limit state function, a new response surface method is proposed for structural reliability analysis by the use of high-order approximation concept in this study. Hermite polynomials are used to determine the highest orders of input random variables, and the sampling points for the determination of highest orders are located on Gaussian points of Gauss-Hermite integration. The cross terms between two random variables, only in case that their corresponding percent contributions to the total variation of limit state function are significant, will be added to the response surface function to improve the approximation accuracy. As a result, significant reduction in computational cost is achieved with this strategy. Due to the addition of cross terms, the additional sampling points, laid on two-dimensional Gaussian points off axis on the plane of two significant variables, are required to determine the coefficients of the approximated limit state function. All available sampling points are employed to construct the final response surface function. Then, Monte Carlo Simulation is carried out on the final approximation response surface function to estimate the failure probability. Due to the use of high order polynomial, the proposed method is more accurate than the traditional second-order or linear response surface method. It also provides much more efficient solutions than the available high-order response surface method with less loss in accuracy. The efficiency and the accuracy of the proposed method compared with those of various response surface methods available are illustrated by five numerical examples.

키워드

참고문헌

  1. APDL (2007), ANSYS Parametric Design Language Guide, ANSYS Inc.
  2. Au, S.K. and Beck, J.L. (1999), "A new adaptive importance sampling scheme for reliability calculations", Struct. Saf., 21(2), 135-158. https://doi.org/10.1016/S0167-4730(99)00014-4
  3. Au, S.K. and Beck, J.L. (2001), "Estimation of small failure probabilities in high dimensions by subset simulation", Probabilist. Eng. Mech., 16, 263-277. https://doi.org/10.1016/S0266-8920(01)00019-4
  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. Chang, C.H., Yung, Y.K. and Yang, J.C. (1993), "Monte Carlo simulation for correlated variables with marginal distributions", J. Hydraul. Eng-ASCE, 120(3), 313-331.
  6. Chen, K.Y. (2007), "Forecasting systems reliability based on support vector regression with genetic algorithm", Reliab. Eng. Syst. Safe., 92(4), 423-432. https://doi.org/10.1016/j.ress.2005.12.014
  7. Das, P.K. and Zhneg, Y. (2000), "Cumulative formation of response surface and its use in reliability analysis", Probabilist. Eng. Mech., 15, 309-315. https://doi.org/10.1016/S0266-8920(99)00030-2
  8. Deng, J. (2006), "Structural reliability analysis for implicit limit state function using radial basis function network", Int. J. Solids Struct., 43(11-12), 3255-3291. https://doi.org/10.1016/j.ijsolstr.2005.05.055
  9. Deng, J., Gu, D.S., Li, X. and Yue, Z.Q. (2005), "Structural reliability analysis for implicit limit state functions using artificial neural network", Struct. Saf., 27(1), 25-48. https://doi.org/10.1016/j.strusafe.2004.03.004
  10. Der Kiureghian, A. and Liu, P.L. (1986), "Structural reliability under incomplete probability information", J. Eng. Mech., 112, 85-104. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:1(85)
  11. Ditleven, O. and Madsen, H.O. (1996), Structural Reliability Methods, Wiley, New York.
  12. Gavin, H.P. and Yau, S.Y. (2008), "High-order limit state function 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
  13. Guan, X.L. and Melchers, R.E. (2001), "Effect of response surface parameter variation on structural reliability estimates", Struct. Saf., 23(4), 429-444. https://doi.org/10.1016/S0167-4730(02)00013-9
  14. Hasofer, A.M. and Lind, N.C. (1974), "An exact and invariant first order reliability format", J. Eng. Mech. Div., 100, 111-121.
  15. Hurtado, J.E. (2007), "Filtered importance sampling with support margin: A powerful method for structural reliability analysis", Struct. Saf., 29(1), 2-15. https://doi.org/10.1016/j.strusafe.2005.12.002
  16. Hurtado, J.E. and Alvarez, D.A. (2001), "Neural-network-based reliability analysis: a comparative study", Comput. Meth. Appl. Mech. Eng., 191(1), 113-132. https://doi.org/10.1016/S0045-7825(01)00248-1
  17. Hurtado, J.E. and Alvarez, D.A. (2003), "Classification approach for reliability analysis with stochastic finiteelement modeling", J. Struct. Eng-ASCE, 129(8), 1141-1149. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:8(1141)
  18. Kaymaz, I. (2005), "Application of kriging method to structural reliability problems", Struct. Saf., 27(2), 133-151. https://doi.org/10.1016/j.strusafe.2004.09.001
  19. 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
  20. Kim, S. and Na, S. (1997), "Response surface method using vector projected sampling points", Struct. Saf., 19(1), 3-19. https://doi.org/10.1016/S0167-4730(96)00037-9
  21. Lee, S.H. and Kwak, B.M. (2006), "Response surface augmented moment method for efficient reliability analysis", Struct. Saf., 28(1), 261-272. https://doi.org/10.1016/j.strusafe.2005.08.003
  22. Li, H.S., Lu, Z.Z. and Yue, Z.F. (2006), "Support vector machine for structural reliability analysis", Appl. Math. Mech., 27(10), 1295-1303. https://doi.org/10.1007/s10483-006-1001-z
  23. Liu, P.L. and Der Kiureghian, A. (1986), "Multivariate distribution models with prescribed marginals and covariances", Probabilist. Eng. Mech., 1(2), 105-112. https://doi.org/10.1016/0266-8920(86)90033-0
  24. Liu, P.L. and Der Kiureghian, A. (1991), "Optimization algorithms for structural reliability", Struct. Saf., 9, 161-177. https://doi.org/10.1016/0167-4730(91)90041-7
  25. Melcher, R.E. (1994), "Structural system reliability assessment using directional simulation", Struct. Saf., 16(1-2), 23-37. https://doi.org/10.1016/0167-4730(94)00026-M
  26. 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
  27. NESSUS 8.2 (2005), Southwest Research Institute.
  28. Papadrakakis, M. and Lagaros, N.D. (2002), "Reliability-based structural optimization using neural networks and Monte Carlo simulation", Comput. Meth. Appl. Mech. Eng., 191(32), 3491-3507. https://doi.org/10.1016/S0045-7825(02)00287-6
  29. Rackwitz, R. (2001), "Reliability analysis-a review and some perspectives", Struct. Saf., 23, 365-395. https://doi.org/10.1016/S0167-4730(02)00009-7
  30. Rackwitz, R. and Fiessler, B. (1978), "Structural reliability under combined load sequences", Comput. Struct., 9, 489-494. https://doi.org/10.1016/0045-7949(78)90046-9
  31. Rahman, S. and Xu, H. (2004), "A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics", Probabilist. Eng. Mech., 19, 393-408. https://doi.org/10.1016/j.probengmech.2004.04.003
  32. Rajashekhar, M.R. and Ellingwood, B.R. (1993), "A new look at the response surface approach for reliability analysis", Struct. Saf., 12(3), 205-220. https://doi.org/10.1016/0167-4730(93)90003-J
  33. Rosenblatt, M. (1952), "Remarks on a Multivariate Transformation", Anal. Math. Stat., 23, 470-472. https://doi.org/10.1214/aoms/1177729394
  34. Vapnik, V.N. (1995), The Nature of Statistical Learning Theory, Springer-Verlag, New York.
  35. Vapnik, V.N. (1999), "An overview of statistical learning theory", IEEE T. Neural Networ., 10, 988-998. https://doi.org/10.1109/72.788640
  36. Wang, L. and Grandhi, R.V. (1996), "Safety index calculation using intervening variables for structural reliability analysis", Comput. Struct., 59(6), 1139-1148. https://doi.org/10.1016/0045-7949(96)00291-X
  37. Zhao, Y.G. and Ono, T. (1999), "A general procedure for first/second-order reliability method (FORM/SORM)", Struct. Saf., 21, 95-112. https://doi.org/10.1016/S0167-4730(99)00008-9
  38. Zhao, Y.G. and Ono, T. (2000), "New point estimates for probability moments", J. Eng. Mech., 126(4), 433-436. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:4(433)
  39. Zhao, Y.G. and Ono, T. (2001), "Moment method for structural reliability", Struct. Saf., 23, 47-75. https://doi.org/10.1016/S0167-4730(00)00027-8
  40. Zhao, Y.G. and Ono, T. (2004), "On the problems of the fourth moment method", Struct. Saf., 26, 343-347. https://doi.org/10.1016/j.strusafe.2003.10.001
  41. Zhao, Y.G., Alfredo, H.S. and Ang, H.M. (2003), "System reliability assessment by method of moments", J. Struct. Eng., 129(10), 1341-1349. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:10(1341)

피인용 문헌

  1. Structural reliability analysis of multiple limit state functions using multi-input multi-output support vector machine vol.8, pp.10, 2016, https://doi.org/10.1177/1687814016671447
  2. Capabilities of stochastic response surface method and response surface method in reliability analysis vol.49, pp.1, 2014, https://doi.org/10.12989/sem.2014.49.1.111
  3. Reliability-based design optimization via high order response surface method vol.27, pp.4, 2013, https://doi.org/10.1007/s12206-013-0227-3
  4. A surrogate-based iterative importance sampling method for structural reliability analysis pp.07488017, 2018, https://doi.org/10.1002/qre.2352
  5. A comparative study of three collocation point methods for odd order stochastic response surface method vol.45, pp.5, 2013, https://doi.org/10.12989/sem.2013.45.5.595
  6. Reliability index for non-normal distributions of limit state functions vol.62, pp.3, 2010, https://doi.org/10.12989/sem.2017.62.3.365
  7. Decomposable polynomial response surface method and its adaptive order revision around most probable point vol.76, pp.6, 2010, https://doi.org/10.12989/sem.2020.76.6.675