Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A novel reliability analysis method based on Gaussian process classification for structures with discontinuous response

  • Zhang, Yibo (School of Mechanical Engineering and Automation, Northeastern University) ;
  • Sun, Zhili (School of Mechanical Engineering and Automation, Northeastern University) ;
  • Yan, Yutao (School of Mechanical Engineering and Automation, Northeastern University) ;
  • Yu, Zhenliang (School of Mechanical Engineering and Automation, Northeastern University) ;
  • Wang, Jian (School of Mechanical Engineering and Automation, Northeastern University)
  • Received : 2019.10.18
  • Accepted : 2020.05.01
  • Published : 2020.09.25
⟨ Previous Next ⟩

Abstract

Reliability analysis techniques combining with various surrogate models have attracted increasing attention because of their accuracy and great efficiency. However, they primarily focus on the structures with continuous response, while very rare researches on the reliability analysis for structures with discontinuous response are carried out. Furthermore, existing adaptive reliability analysis methods based on importance sampling (IS) still have some intractable defects when dealing with small failure probability, and there is no related research on reliability analysis for structures involving discontinuous response and small failure probability. Therefore, this paper proposes a novel reliability analysis method called AGPC-IS for such structures, which combines adaptive Gaussian process classification (GPC) and adaptive-kernel-density-estimation-based IS. In AGPC-IS, an efficient adaptive strategy for design of experiments (DoE), taking into consideration the classification uncertainty, the sampling uniformity and the regional classification accuracy improvement, is developed with the purpose of improving the accuracy of Gaussian process classifier. The adaptive kernel density estimation is introduced for constructing the quasi-optimal density function of IS. In addition, a novel and more precise stopping criterion is also developed from the perspective of the stability of failure probability estimation. The efficiency, superiority and practicability of AGPC-IS are verified by three examples.

Keywords

Acknowledgement

The financial supports of this research are from the National Natural Science Foundation of China (Grant NO. 51775097 and Grant NO. 51875095). The authors gratefully acknowledge their supports.

References

  1. Alibrandi, U., Alani, A.M. and Ricciardi, G. (2015), "A new sampling strategy for svm-based response surface for structural reliability analysis", Probabilistic Eng. Mech., 41, 1-12. https://dx.doi.org/10.1016/j.probengmech.2015.04.001
  2. Au, S.K. (2016), "On mcmc algorithm for subset simulation", Probabilistic Eng. Mech., 43, 117-120. http://dx.doi.org/10.1016/j.probengmech.2015.12.003
  3. Au, S.K. and Beck, J.L. (1999), "A new adaptive importance sampling scheme for reliability calculations", Structural Safety, 21(2), 135-158. https://dx.doi.org/10.1016/S0167-4730(99)00014-4
  4. 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://dx.doi.org/10.1016/S0266-8920(01)00019-4
  5. Barkhori, M., Shayanfar, M.A., Barkhordari, M.A. and Bakhshpoori, T. (2018), "Kriging-aided cross-entropy-based adaptive importance sampling using gaussian mixture", J. Sci. Technol. Transactions Civil Eng., 43, 81-88. https://dx.doi.org/10.1007/s40996-018-0143-y
  6. Basudhar, A. and Missoum, S. (2008), "Adaptive explicit decision functions for probabilistic design and optimization using support vector machines", Comput. Struct., 86(19-20), 1904-1917. https://dx.doi.org/10.1016/j.compstruc.2008.02.008
  7. Basudhar, A., Missoum, S. and Sanchez, A.H. (2008), "Limit state function identification using support vector machines for discontinuous responses and disjoint failure domains", Probabilistic Eng. Mech., 23(1), 1-11. https://dx.doi.org/10.1016/j.probengmech.2007.08.004
  8. Beachkofski, B.K. and Grandhi, R.V. (2002), "Improved distributed hypercube sampling", Proceedings of the 43rd AIAA/ASME/ASCE/ASC Structures, Structural Dynamics, and Materials Conference, Denver, USA, April.
  9. Doh, J., Yang, Q. and Raghavan, N. (2020), "Reliability-based robust design optimization of polymer nanocomposites to enhance percolated electrical conductivity considering correlated input variables using multivariate distributions", Polymer, 186, 122060. http://dx.doi.org/10.1016/j.polymer.2019.122060
  10. 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://dx.doi.org/10.1016/j.strusafe.2011.01.002
  11. 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://dx.doi.org/10.1016/j.probengmech.2005.07.002
  12. En, X.N., Zhang, Y.M. and Huang, X.Z. (2019), "Time-variant reliability analysis of a continuous system with strength deterioration based on subset simulation", Adv. Manufact., 7(2), 188-198. https://dx.doi.org/10.1007/s40436-019-00252-7
  13. Fang, Y.F. and Teea, K.F. (2017), "Structural reliability analysis using response surface method with improved genetic algorithm", Struct. Eng. Mech., 62(2), 139-142. https://dx.doi.org/10.12989/sem.2017.62.2.139
  14. Fei, C.W. and Bai, G.C. (2013), "Nonlinear dynamic probabilistic analysis for turbine casing radial deformation using extremum response surface method based on support vector machine", J. Comput. Nonlinear Dynam., 8(4), 041004. http://dx.doi.org/10.1115/1.4023589
  15. Gao, H.Y., Guo, X.L. and Hu, X.F. (2012), "Crack identification based on kriging surrogate model", Struct. Eng. Mech., 41(1), 25-41. https://dx.doi.org/10.12989/sem.2012.41.1.025
  16. Garcia-Fernandez, A.F., Tronarp, F. and Sarkka, S. (2019), "Gaussian process classification using posterior linearization", IEEE Signal Processing Letters, 26(5), 735-739. https://dx.doi.org/10.1109/LSP.2019.2906929
  17. Gaspar, B., Teixeira, A.P. and Soares, C.G. (2014), "Assessment of the efficiency of kriging surrogate models for structural reliability analysis", Probabilistic Eng. Mech., 37, 24-34. https://dx.doi.org/10.1016/j.probengmech.2014.03.011
  18. Guan, X.L. and Melchers, R.E. (2001), "Effect of response surface parameter variation on structural reliability estimates", Struct. Safety, 23(4), 429-444. https://dx.doi.org/10.1016/S0167-4730(02)00013-9
  19. Jagan, J., Samui, P. and Kim, D. (2019), "Reliability analysis of simply supported beam using grnn, elm and gpr", Struct. Eng. Mech., 71(6), 739-749. https://dx.doi.org/10.12989/sem.2019.71.6.739
  20. Kapoor, A., Grauman, K., Urtasun, R. and Darrell, T. (2009), "Gaussian processes for object categorization", J. Comput. Vision, 88(2), 169-188. https://doi.org/10.1007/s11263-009-0268-3.
  21. Krejsa, M., Janas, P. and Krejsa, V. (2013), "Using doproc method in structural reliability assessment", Appl. Mech. Mater., 300-301, 860-869. http://dx.doi.org/10.4028/www.scientific.net/AMM.300-301.860
  22. Krejsa, M., Janas, P. and Krejsa, V. (2016), "Application of the doproc method in solving reliability problems", Appl. Mech. Mater., 821, 717-724. http://doi.org/10.4028/www.scientific.net/AMM.821.717
  23. Li, X., Gong, C., Gu, L., Gao, W., Jing, Z. and Su, H. (2018), "A sequential surrogate method for reliability analysis based on radial basis function", Struct. Safety, 73, 42-53. https://dx.doi.org/10.1016/j.strusafe.2018.02.005
  24. Napa-Garcia, G.F., Beck, A.T. and Celestino, T.B. (2017), "Reliability analyses of underground openings with the point estimate method", Tunnelling Underground Space Technol., 64, 154-163. http://dx.doi.org/10.1016/j.tust.2016.12.010
  25. Nguyen, T.N.A., Abdesselam, B. and Phung, S.L. (2019), "A scalable hierarchical gaussian process classifier", IEEE Transactions on Signal Processing, 67(11), 3042-3057. https://dx.doi.org/10.1109/TSP.2019.2911251
  26. Niutta, C.B., Wehrle, E.J., Duddeck, F. and Belingardi, G. (2018), "Surrogate modeling in design optimization of structures with discontinuous responses", Struct. Multidisciplinary Opt., 57(5), 1857-1869. https://dx.doi.org/10.1007/s00158-018-1958-7
  27. Pan, Q.J. and Dias, D. (2017), "An efficient reliability method combining adaptive support vector machine and monte carlo simulation", Structural Safety, 67, 85-95. https://dx.doi.org/10.1016/j.strusafe.2017.04.006
  28. Peng, L.F., Su, G.S. and Zhao, W. (2014), "Fast analysis of structural reliability using gaussian process classification based dynamic response surface method", Appl. Mech. Mater., 501-504, 1067-1070. https://dx.doi.org/10.4028/www.scientific.net/AMM.501-504.1067
  29. Qin, S., Hu, J., Zhou, Y.L., Zhang, Y. and Kang, J. (2019), "Feasibility study of improved particle swarm optimization in kriging metamodel based structural model updating", Struct. Eng. Mech., 70(5), 513-524. https://dx.doi.org/10.12989/sem.2019.70.5.513
  30. Rodrigues, F., Pereira, F.C. and Ribeiro, B. (2014), "Gaussian process classification and active learning with multiple annotators", Proceedings of the 31st International Conference on Machine Learning, Beijing, China, June.
  31. Roudak, M.A. and Karamloo, M. (2019). "Establishment of non-negative constraint method as a robust and efficient first-order reliability method", Appl. Math. Modell., 68, 281-305. http://dx.doi.org/10.1016/j.apm.2018.11.021
  32. Shayanfar, M.A., Barkhordari, M.A., Barkhori, M. and Rakhshanimehr, M. (2017), "An adaptive line sampling method for reliability analysis", J. Sci. Technol. Transactions Civil Eng., 41(3), 275-282. https://dx.doi.org/10.1007/s40996-017-0070-3
  33. Su, G., Jiang, J., Yu, B. and Xiao, Y. (2015), "A gaussian process-based response surface method for structural reliability analysis", Struct. Eng. Mech., 56(4), 549-567. https://dx.doi.org/10.12989/sem.2015.56.4.549
  34. Sun, S., Zhong, P., Xiao, H. and Wang, R. (2015), "Active learning with gaussian process classifier for hyperspectral image classification", IEEE Transactions on Geoscience and Remote Sensing, 53(4), 1746-1760. https://dx.doi.org/10.1109/TGRS.2014.2347343
  35. Sun, S., Zhong, P., Xiao, H. and Wang, R. (2017), "Lif: a new kriging based learning function and its application to structural reliability analysis", Reliability Eng. Syst. Safety, 157, 152-165. https://dx.doi.org/10.1016/j.ress.2016.09.003
  36. Vahedi, J. Ghasemi, M.R. and Miri, M. (2018), "Structural reliability assessment using an enhanced adaptive kriging method", Struct. Eng. Mech., 66(6), 677-691. https://dx.doi.org/10.12989/sem.2018.66.6.677
  37. Wang, F. and LI, H. (2017), "Stochastic response surface method for reliability problems involving correlated multivariates with non-gaussian dependence structure: analysis under incomplete probability information", Comput. Geotechnics, 89, 22-32. http://dx.doi.org/10.1016/j.compgeo.2017.02.008
  38. Wang, J. and Sun, Z.L. (2018), "The stepwise accuracy-improvement strategy based on the kriging model for structural reliability analysis", Struct. Multidisciplinary Opt., 58(2), 595-612. https://dx.doi.org/10.1007/s00158-018-1911-9
  39. Jian, W., Zhili, S., Qiang, Y. and Rui, L. (2017), "Two accuracy measures of the kriging model for structural reliability analysis", Reliability Eng. Syst. Safety, 167, 494-505. https://dx.doi.org/10.1016/j.ress.2017.06.028
  40. Winerstein, S.R. (1988), "Nonlinear vibration models for extremes and fatigue", J. Eng. Mech., 114(10), 1772-1790. http://dx.doi.org/10.1061/(ASCE)0733-9399(1988)114:10(1772)
  41. Xiong, F., Xiong, Y., Greene, S., Chen, W. and Yang, S. (2010), "A new sparse grid based method for uncertainty propagation", Struct. Multidisciplinary Opt., 41(3), 335-349. http://dx.doi.org/10.1007/s00158-009-0441-x
  42. Xu, J. and Wang, D. (2019), "Structural reliability analysis based on polynomial chaos, voronoi cells and dimension reduction technique", Reliability Eng. Syst. Safety, 185, 329-340. https://dx.doi.org/10.1016/j.ress.2019.01.001
  43. Yang, X., Liu, Y., Mi, C. and Wang, X. (2018), "Active learning kriging model combining with kernel-density-estimation-based importance sampling method for the estimation of low failure probability", J. Mech. Design, 140(5), 051402. https://dx.doi.org/10.1115/1.4039339
  44. Yao, W., Tang, G., Wang, N. and Chen, X. (2019), "An improved reliability analysis approach based on combined form and beta-spherical importance sampling in critical region", Struct. Multidisciplinary Opt., 60(1), 35-58. https://dx.doi.org/10.1007/s00158-019-02193-y.
  45. Yonezawa, M., Okuda, S. and Kobayashi, H. (2009), "Structural reliability estimation based on quasi ideal importance sampling simulation", Struct. Eng. Mech., 32(1), 55-69. https://dx.doi.org/10.12989/sem.2009.32.1.055
  46. Yuan, X., Lu, Z., Zhou, C. and Yue, Z. (2013), "A novel adaptive importance sampling algorithm based on markov chain and low-discrepancy sequence", Aerosp. Sci. Technol., 29(1), 253-261. https://dx.doi.org/10.1016/j.ast.2013.03.008
  47. Yun, W.Y., Lu, Z.Z. and Jiang, X. (2017), "A modified importance sampling method for structural reliability and its global reliability sensitivity analysis", Struct. Multidisciplinary Opt., 57(4), 1625-1641. https://dx.doi.org/10.1007/s00158-017-1832-z.
  48. Yun, W.Y., Lu, Z.Z. and Jiang, X. (2018), "An efficient reliability analysis method combining adaptive kriging and modified importance sampling for small failure probability", Struct. Multidisciplinary Opt., 58(4), 1383-1393. https://dx.doi.org/10.1007/s00158-018-1975-6
  49. Zhang, J.H., Xiao, M. and Gao, L. (2018), "An active learning reliability method combining kriging constructed with exploration and exploitation of failure region and subset simulation", Reliability Eng. Syst. Safety, 188, 90-102. https://dx.doi.org/10.1016/j.ress.2019.03.002
  50. Zhang, Y., Sun, Z., Yan, Y., Yu, Z. and Wang, J. (2019), "An efficient adaptive reliability analysis method based on kriging and weighted average misclassification rate improvement", IEEE Access, 7(1), 94954-94965. https://dx.doi.org/10.1109/ACCESS.2019.2928332.
  51. Zhao, H.B., Li, S.J. and Ru, Z.L. (2017), "Adaptive reliability analysis based on a support vector machine and its application to rock engineering", Appl. Math. Modell., 44, 508-522. https://dx.doi.org/10.1016/j.apm.2017.02.020
  52. Zhao, W.T., Shi, X.Y. and Tang, K. (2016), "A response surface method based on sub-region of interest for structural reliability analysis", Struct. Eng. Mech., 57(4), 587-602. https://dx.doi.org/10.12989/sem.2016.57.4.587