DOI QR코드

DOI QR Code

An evolutionary approach for structural reliability

  • 투고 : 2018.02.04
  • 심사 : 2019.04.01
  • 발행 : 2019.08.25

초록

Assessment of failure probability, especially for a complex structure, requires a considerable number of calls to the numerical model. Reliability methods have been developed to decrease the computational time. In this approach, the original numerical model is replaced by a surrogate model which is usually explicit and much faster to evaluate. The current paper proposed an efficient reliability method based on Monte Carlo simulation (MCS) and multi-gene genetic programming (MGGP) as a robust variant of genetic programming (GP). GP has been applied in different fields; however, its application to structural reliability has not been tested. The current study investigated the performance of MGGP as a surrogate model in structural reliability problems and compares it with other surrogate models. An adaptive Metropolis algorithm is utilized to obtain the training data with which to build the MGGP model. The failure probability is estimated by combining MCS and MGGP. The efficiency and accuracy of the proposed method were investigated with the help of five numerical examples.

키워드

참고문헌

  1. Alvarez, D.A., Uribe, F. and Hurtado, J.E. (2018), "Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory", Mech. Syst. Signal Process, 100, 782-801. https://doi.org/10.1016/j.ymssp.2017.07.040.
  2. Au, S.K. and Beck, J.L. (1999), "A new adaptive importance sampling scheme for reliability calculations", Struct. Safety, 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", Probabilistic Eng. Mech., 16(4), 263-277. https://doi.org/10.1016/S0266-8920(01)00019-4.
  4. Au, S.K. and Beck, J.L. (2003), "Subset simulation and its application to seismic risk based on dynamic analysis", J. Eng. Mech., 129(8), 901-917. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:8(901).
  5. Breitung, K. and Hohenbichler, M. (1989), "Asymptotic approximations for multivariate integrals with an application to multinormal probabilities", J. Multivariate Anal., 30(1), 80-97. https://doi.org/10.1016/0047-259X(89)90089-4.
  6. Bucher, C. and Most, T. (2008), "A comparison of approximate response functions in structural reliability analysis", Probabilistic Eng. Mech., 23(2), 154-163. https://doi.org/10.1016/j.probengmech.2007.12.022.
  7. Changcong, Z., Zhenzhou, L., Feng, Z. and Zhufeng, Y. (2015), "An adaptive reliability method combining relevance vector machine and importance sampling", Struct. Multidisciplinary Optimization, 52(5), 945-957. https://doi.org/10.1007/s00158-015-1287-z.
  8. Ching, J., Au, S.K. and Beck, J.L. (2005), "Reliability estimation for dynamical systems subject to stochastic excitation using subset simulation with splitting", Comput. Method Appl. Mech. Eng., 194(12-16), 1557-1579. https://doi.org/10.1016/j.cma.2004.05.028.
  9. Chojaczyk, A., Teixeira, A., Neves, L., Cardoso, J. and Soares, C.G. (2015), "Review and application of Artificial Neural Networks models in reliability analysis of steel structures", Struct. Safety, 52, 78-89. https://doi.org/10.1016/j.strusafe.2014.09.002.
  10. Chojaczyk, A., Teixeira, A., Neves, L.C., Cardoso, J. and Soares, C.G. (2015), "Review and application of artificial neural networks models in reliability analysis of steel structures", Struct. Safety, 52, 78-89. https://doi.org/10.1016/j.strusafe.2014.09.002.
  11. Dai, H., Zhang, H., Wang, W. and Xue, G. (2012), "Structural Reliability Assessment by Local Approximation of Limit State Functions Using Adaptive Markov Chain Simulation and Support Vector Regression", Comput. Aid Civil Infrastruct. Eng., 27(9), 676-686. https://doi.org/10.1111/j.1467-8667.2012.00767.x.
  12. Der Kiureghian, A., Lin, H. and Hwang, S. (1987), "Second-Order Reliability Approximations", J. Eng. Mech., 113(8), 1208-1225. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:8(1208).
  13. Echard, B., Gayton, N. and Lemaire, M. (2011), "AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation", Struct. Safety, 33(2), 145-154. https://doi.org/10.1016/j.strusafe.2011.01.002.
  14. Echard, B., Gayton, N., Lemaire, M. and Relun, N. (2013), "A combined importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models", Raliability Eng. Syst. Safety, 111, 232-240. https://doi.org/10.1016/j.ress.2012.10.008.
  15. Elhewy, A.H., Mesbahi, E. and Pu, Y. (2006), "Reliability analysis of structures using neural network method", Probabilistic Eng. Mech., 21(1), 44-53. https://doi.org/10.1016/j.probengmech.2005.07.002.
  16. Fang, Y. and 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.
  17. Gandomi, A.H., Alavi, A.H., Arjmandi, P., Aghaeifar, A. and Seyednour, R. (2010), "Genetic programming and orthogonal least squares: a hybrid approach to modeling the compressive strength of CFRP-confined concrete cylinders", J. Mech. Mater. Struct., 5(5), 735-753. http://dx.doi.org/10.2140/jomms.2010.5.735.
  18. Gao, L., Xiao, M., Shao, X., Jiang, P., Nie, L. and Qiu, H. (2012), "Analysis of gene expression programming for approximation in engineering design", Struct. Multidisciplinary Optimization, 46(3), 399-413. https://doi.org/10.1007/s00158-012-0767-7.
  19. Gaspar, B., Naess, A., Leira, B.J. and Soares, C.G. (2014), "System reliability analysis by Monte Carlo based method and finite element structural models", J. Offshore Mech. Arctic Eng., 136(3), 031603-031603. https://doi.org/10.1115/1.4025871.
  20. Giovanis, D.G., Papaioannou, I., Straub, D. and Papadopoulos, V. (2017), "Bayesian updating with subset simulation using artificial neural networks", Comput. Method Appl. Mech. Eng., 319, 124-145. https://doi.org/10.1016/j.cma.2017.02.025.
  21. Goda, K. and Atkinson, G.M. (2010), "Intraevent spatial correlation of ground-motion parameters using SK-net data", Bullet. Seismologic. Soc. America, 100(6), 3055-3067. https://doi.org/10.1785/0120100031.
  22. Haario, H., Saksman, E. and Tamminen, J. (2001), "An adaptive Metropolis algorithm", Bernoulli, 223-242. https://doi.org/10.2307/3318737
  23. Hasofer., A.M. and Lind, M.C. (1974), "An exact and invariant first order reliability format", J. Eng. Mech., 100, 111-121.
  24. Hohenbichler, M. and Rackwitz, R. (1988), "Improvement of second-order reliability estimates by importance sampling", J. Eng. Mech., 114(12), 2195-2199. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:12(2195).
  25. Hornik, K., Stinchcombe, M. and White, H. (1989), "Multilayer feedforward networks are universal approximators", Neural Networks, 2(5), 359-366. https://doi.org/10.1016/0893-6080(89)90020-8.
  26. Huang, X., Chen, J. and Zhu, H. (2016), "Assessing small failure probabilities by AK-SS: an active learning method combining Kriging and subset simulation", Struct. Safety, 59, 86-95. https://doi.org/10.1016/j.strusafe.2015.12.003.
  27. Hurtado, J. and Alvarez, D. (2003), "Classification Approach for Reliability Analysis with Stochastic Finite-Element Modeling", J. Struct. Eng., 129(8), 1141-1149. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:8(1141).
  28. Hurtado, J.E. and Alvarez, D.A. (2001), "Neural-network-based reliability analysis: a comparative study", Comput. Method Appl. Mech. Eng., 191(1-2), 113-132. https://doi.org/10.1016/S0045-7825(01)00248-1.
  29. Kaymaz, I. (2005), "Application of kriging method to structural reliability problems", Struct. Safety, 27(2), 133-151. https://doi.org/10.1016/j.strusafe.2004.09.001.
  30. Kmiecik, M. and Soares, C.G. (2002), "Response surface approach to the probability distribution of the strength of compressed plates", Marine Struct., 15(2), 139-156. https://doi.org/10.1016/S0951-8339(01)00024-7.
  31. Koza, J.R. (1992), Genetic programming: On the Programming of Computers by Means of Natural Selection, The MIT Press, MA, USA.
  32. Li, H., Lu, Z. and Yue, Z. (2006), "Support vector machine for structural reliability analysis", Appl. Math. Mech., 27(10), 1295-1303. https://doi.org/10.1007/s10483-006-1001-z.
  33. Li, L. (2012), Sequential Design of Experiments to Estimate a Probability of Failure, Supelec, France.
  34. Liu, H., Ong, Y.S. and Cai, J. (2017), "A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design", Struct. Multidisciplinary Optimization, 1-24. https://doi.org/10.1007/s00158-017-1739-8.
  35. Liu, P.L. and Der Kiureghian, A. (1991), "Optimization algorithms for structural reliability", Struct. Safety, 9(3), 161-177. https://doi.org/10.1016/0167-4730(91)90041-7
  36. Liu, X., Wu, Y., Wang, B., Ding, J. and Jie, H. (2017), "An adaptive local range sampling method for reliability-based design optimization using support vector machine and Kriging model", Struct. Multidisciplinary Optimization, 55(6), 2285-2304. https://doi.org/10.1007/s00158-016-1641-9.
  37. Matheron, G. (1973), "The intrinsic random functions and their applications", Adv. Appl. Probability, 439-468. https://doi.org/10.2307/1425829.
  38. McCulloch, W.S. and Pitts, W. (1943), "A logical calculus of the ideas immanent in nervous activity", Bullet. Math. Biophys., 5(4), 115-133. https://doi.org/10.1007/BF02478259.
  39. Metropolis, N., Rosenbluth, A.W., Ronsenbluth, M.N., Teller, A.H. and Teller, E. (1953), "Equations of state calculations by fast computing machines", J. Chem. Phys., 21, 1087-1092. https://doi.org/10.1063/1.1699114.
  40. Pan, Q. and Dias, D. (2017), "An efficient reliability method combining adaptive support vector machine and Monte Carlo simulation", Struct. Safety, 67, 85-95. https://doi.org/10.1016/j.strusafe.2017.04.006.
  41. Parsons, R. and Canfield, S. (2002), "Developing genetic programming techniques for the design of compliant mechanisms", Struct. Multidisciplinary Optimization, 24(1), 78-86. https://doi.org/10.1007/s00158-002-0216-0.
  42. Pradlwarter, H., Schueller, G., Koutsourelakis, P. and Charmpis, D. (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.
  43. Rackwitz, R. and Flessler, B. (1978), "Structural reliability under combined random load sequences", Comput. Struct., 9(5), 489-494. https://doi.org/10.1016/0045-7949(78)90046-9.
  44. Rahman, S. and Wei, D. (2006), "A univariate approximation at most probable point for higher-order reliability analysis", J. Solid Struct., 43(9), 2820-2839. https://doi.org/10.1016/j.ijsolstr.2005.05.053.
  45. Robert, C. and Casella, G. (2004), Monte Carlo Statistical Methods, Vol. 319, Springer, Germany.
  46. Sacks, J., W. J. Welch, Mitchell, T.J. and Wynn., H.P. (1989), "Design and analysis of computer experiments", Statistical Sci., 4(4), 409-435. https://doi.org/10.1214/ss/1177012413
  47. Schueremans, L. and Van Gemert, D. (2005), "Benefit of splines and neural networks in simulation based structural reliability analysis", Struct. Safety, 27(3), 246-261. https://doi.org/10.1016/j.strusafe.2004.11.001.
  48. Schueremans, L. and Van Gemert, D. (2005). "Use of Kriging as Meta-model in simulation procedures for structural reliability", International Conference on Struct. Safety and Reliability, Rome, Italy, June.
  49. Searson, D.P., Leahy, D.E. and Willis, M.J. (2010). "GPTIPS: an open source genetic programming toolbox for multigene symbolic regression", Proceedings of the International Multiconference of Engineers and Computer Scientists, Hong Kong, March.
  50. Searson, D.P., Willis, M.J. and Montague, G. (2007), "Co-evolution of non-linear PLS model components", J. Chemometrics, 21(12), 592-603. https://doi.org/10.1002/cem.1084.
  51. Shanmugam, K. and Balaban, P. (1980), "A modified Monte-Carlo simulation technique for the evaluation of error rate in digital communication systems", IEEE Transactions on Communications, 28(11), 1916-1924. https://doi.org/10.1109/TCOM.1980.1094613.
  52. Song, H., Choi, K.K., Lee, I., Zhao, L. and Lamb, D. (2013), "Adaptive virtual support vector machine for reliability analysis of high-dimensional problems", Struct. Multidisciplinary Optimization, 47(4), 479-491. https://doi.org/10.1007/s00158-012-0857-6.
  53. Tan, X.-h., Bi, W.-h., Hou, X.-l. and Wang, W. (2011), "Reliability analysis using radial basis function networks and support vector machines", Comput. Geotech., 38(2), 178-186. https://doi.org/10.1016/j.compgeo.2010.11.002.
  54. Teixeira, A.P. and Soares, C.G. (2010), Response Surface Reliability Analysis of Steel Plates with Random Fields of Corrosion, Taylor & Francis Group, London, United Kingdom.
  55. Tvedt, L. (1990), "Distribution of Quadratic Forms in Normal Space - Application to Structural Reliability", J. Eng. Mech., 116(6), 1183-1197. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:6(1183).
  56. Valdebenito, M., Jensen, H., Hernandez, H. and Mehrez, L. (2018), "Sensitivity estimation of failure probability applying line sampling", Raliability Eng. Syst. Safety, 171, 99-111. https://doi.org/10.1016/j.ress.2017.11.010.
  57. Waarts, P. (2000), "Structural reliability using finite element methods", An appraisal of DARS: Directional Adaptive, 515.
  58. Xiang, H., Li, Y., Liao, H. and Li, C. (2017), "An adaptive surrogate model based on support vector regression and its application to the optimization of railway wind barriers", Struct. Multidisciplinary Optimization, 55(2), 701-713. https://doi.org/10.1007/s00158-016-1528-9.
  59. Yeun, Y., Kim, B., Yang, Y. and Ruy, W. (2005), "Polynomial genetic programming for response surface modeling part 2: adaptive approximate models with probabilistic optimization problems", Struct. Multidisciplinary Optimization, 29(1), 35-49. https://doi.org/10.1007/s00158-004-0461-5.
  60. Yuan, X., Lu, Z., Zhou, C. and Yue, Z. (2013), "A novel adaptive importance sampling algorithm based on Markov chain and low-discrepancy sequence", Aerospace Sci. Technol., 29(1), 253-261. https://doi.org/10.1016/j.ast.2013.03.008.
  61. Zhao, H., Ru, Z., Chang, X., Yin, S. and Li, S. (2014), "Reliability analysis of tunnel using least square support vector machine", Tunnelling Underground Space Technol., 41, 14-23. https://doi.org/10.1016/j.tust.2013.11.004.
  62. Ziha, K. (1995), "Descriptive sampling in Structural Safety", Struct. Safety, 17(1), 33-41. https://doi.org/10.1016/0167-4730(94)00038-R.