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Structural reliability analysis using temporal deep learning-based model and importance sampling

  • Nguyen, Truong-Thang (Faculty of Building and Industrial Construction, Hanoi University of Civil Engineering) ;
  • Dang, Viet-Hung (Faculty of Building and Industrial Construction, Hanoi University of Civil Engineering)
  • Received : 2022.01.08
  • Accepted : 2022.09.20
  • Published : 2022.11.10

Abstract

The main idea of the framework is to seamlessly combine a reasonably accurate and fast surrogate model with the importance sampling strategy. Developing a surrogate model for predicting structures' dynamic responses is challenging because it involves high-dimensional inputs and outputs. For this purpose, a novel surrogate model based on cutting-edge deep learning architectures specialized for capturing temporal relationships within time-series data, namely Long-Short term memory layer and Transformer layer, is designed. After being properly trained, the surrogate model could be utilized in place of the finite element method to evaluate structures' responses without requiring any specialized software. On the other hand, the importance sampling is adopted to reduce the number of calculations required when computing the failure probability by drawing more relevant samples near critical areas. Thanks to the portability of the trained surrogate model, one can integrate the latter with the Importance sampling in a straightforward fashion, forming an efficient framework called TTIS, which represents double advantages: less number of calculations is needed, and the computational time of each calculation is significantly reduced. The proposed approach's applicability and efficiency are demonstrated through three examples with increasing complexity, involving a 1D beam, a 2D frame, and a 3D building structure. The results show that compared to the conventional Monte Carlo simulation, the proposed method can provide highly similar reliability results with a reduction of up to four orders of magnitudes in time complexity.

Keywords

Acknowledgement

This work was financially supported by the Hanoi University of Civil Engineering (Vietnam).

References

  1. Afshari, S.S., Enayatollahi, F., Xu, X. and Liang, X. (2022), "Machine learning-based methods in structural reliability analysis: A review", Reliab. Eng. Syst. Saf., 219, 108223. https://doi.org/10.1016/j.ress.2021.108223.
  2. Ankireddi, S. and Y. Yang, H.T. (1996), "Simple ATMD control methodology for tall buildings subject to wind loads", J. Struct. Eng., 122(1), 83-91. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:1(83).
  3. Chau, K.W. (2007), "Reliability and performance-based design by artificial neural network", Adv. Eng. Softw., 38(3), 145-149. https://doi.org/10.1016/j.advengsoft.2006.09.008.
  4. Chojaczyk, A.A., Teixeira, A.P., Neves, L.C., Cardoso, J.B. and Soares, C.G. (2015), "Review and application of artificial neural networks models in reliability analysis of steel structures", Struct. Saf., 52, 78-89. https://doi.org/10.1016/j.strusafe.2014.09.002.
  5. Chopra, A.K. (2007), Dynamics of Structures, Pearson Education India.
  6. Cruz, C. and Miranda, E. (2017), "Dynamic tests on large cable-stayed bridge", Eng. Struct., 138, 324-3366. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:1(54).
  7. Dang, H.V., Tran-Ngoc, H., Nguyen, T.V., Bui-Tien, T., De Roeck, G. and Nguyen, H.X. (2020), "Data-driven structural health monitoring using feature fusion and hybrid deep learning", IEEE Trans. Auto. Sci. Eng., 18(4), 2087-2103. https://doi.org/10.1109/TASE.2020.3034401.
  8. de Santana Gomes, W.J. (2019), "Structural reliability analysis using adaptive artificial neural networks", ASME J. Risk Uncertain. Part B, 5(4), 041004. https://doi.org/10.1115/1.4044040.
  9. Echard, B., Gayton, N. and Lemaire, M. (2011), "AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation", Struct. Saf., 33(2), 145-154. https://doi.org/10.1016/j.strusafe.2011.01.002.
  10. Fang, Y., Chen, J. and Tee, K.F. (2013), "Analysis of structural dynamic reliability based on the probability density evolution method", Struct. Eng. Mech., 45(2), 201-209. https://doi.org/10.12989/sem.2013.45.2.201.
  11. Feng, J., Liu, L., Wu, D., Li, G., Beer, M. and Gao, W. (2019), "Dynamic reliability analysis using the extended support vector regression (X-SVR)", Mech. Syst. Signal Pr., 126, 368-391. https://doi.org/10.1016/j.ymssp.2019.02.027.
  12. Ghosh, S., Roy, A. and Chakraborty, S. (2018), "Support vector regression based metamodeling for seismic reliability analysis of structures", Appl. Math. Model., 64, 584-602. https://doi.org/10.1016/j.apm.2018.07.054.
  13. Gong, C. and Zhou, W. (2018), "Importance sampling-based system reliability analysis of corroding pipelines considering multiple failure modes", Reliab. Eng. Syst. Saf., 169, 199-208. https://doi.org/10.1016/j.ress.2017.08.023
  14. Hammersley, J. (2013), Monte Carlo Methods, Springer Science & Business Media.
  15. Hariri-Ardebili, M.A. and Pourkamali-Anaraki, F. (2018), "Support vector machine based reliability analysis of concrete dams", Soil Dyn. Earthq. Eng., 104, 276-295. https://doi.org/10.1016/j.soildyn.2017.09.016.
  16. Hochreiter, S. and Schmidhuber, J. (1997), "Long short-term memory", Neur. Comput., 9(8), 1735-1780. https://doi.org/10.1162/neco.1997.9.8.1735.
  17. Hsu, W.C. and Ching, J. (2010), "Evaluating small failure probabilities of multiple limit states by parallel subset simulation", Prob. Eng. Mech., 25(3), 291-304. https://doi.org/10.1016/j.probengmech.2010.01.003.
  18. Hung, D.V., Thang, N.T. and Dat, P.X. (2021), "Probabilistic pushover analysis of reinforced concrete frame structures using dropout neural network", J. Sci. Technol. Civil Eng. (STCE)-NUCE, 15(1), 30-40. https://doi.org/10.31814/stce.nuce2021-15(1)-03.
  19. Khatir, S., Boutchicha, D., Le Thanh, C., Tran-Ngoc, H., Nguyen, T. and Abdel-Wahab, M. (2020), "Improved ANN technique combined with Jaya algorithm for crack identification in plates using XIGA and experimental analysis", Theor. Appl. Fract Mech., 107, 102554. https://doi.org/10.1016/j.tafmec.2020.102554.
  20. Khatir, S., Tiachacht, S., Le Thanh, C., Ghandourah, E., Mirjalili, S. and Wahab, M.A. (2021), "An improved Artificial Neural Network using Arithmetic Optimization Algorithm for damage assessment in FGM composite plates", Compos. Struct., 273, 114287. https://doi.org/10.1016/j.compstruct.2021.114287
  21. Koeppe, A., Bamer, F., Hernandez Padilla, C.A. and Markert, B. (2017), "Neural network representation of a phase-field model for brittle fracture", PAMM, 17(1), 253-254. https://doi.org/10.1002/pamm.201710096.
  22. Krige, D.G. (1951), "A statistical approach to some basic mine valuation problems on the Witwatersrand", J. South. Afri. Inst. Min. Metal., 52(6), 119-139.
  23. Lagaros, N.D. and Papadrakakis, M. (2012), "Neural network based prediction schemes of the non-linear seismic response of 3D buildings", Adv. Eng. Softw., 44(1), 92-115. https://doi.org/10.1016/j.advengsoft.2011.05.033.
  24. Li, M. and Wang, Z. (2020), "Deep learning for high-dimensional reliability analysis", Mech. Syst. Signal Pr., 139, 106399. https://doi.org/10.1016/j.ymssp.2019.106399.
  25. Lieu, Q.X., Nguyen, K.T., Dang, K.D., Lee, S., Kang, J. and Lee, J. (2022), "An adaptive surrogate model to structural reliability analysis using deep neural network", Exp. Syst. Appl., 189, 116104. https://doi.org/10.1016/j.eswa.2021.116104.
  26. Lim, B., Arik, S.O., Loeff, N. and Pfister, T. (2021), "Temporal fusion transformers for interpretable multi-horizon time series forecasting", Int. J. Forecast., 37(4), 1748-1764. https://doi.org/10.1016/j.ijforecast.2021.03.012.
  27. McKenna, F. (2011), "OpenSees: a framework for earthquake engineering simulation", Comput. Sci. Eng., 13(4), 58-66. https://doi.org/10.1109/MCSE.2011.66.
  28. Melchers, R. (1989), "Importance sampling in structural systems", Struct. Saf., 6(1), 3-10. https://doi.org/10.1016/0167-4730(89)90003-9.
  29. Mendoza-Lugo, M.A., Delgado-Hern'andez, D.J. and Morales-N'apoles, O. (2019a), "Reliability analysis of reinforced concrete vehicle bridges columns using non-parametric Bayesian networks", Eng. Struct., 188, 178-187. https://doi.org/10.1016/j.engstruct.2019.03.011.
  30. Nguyen-Le, D.H., Tao, Q., Nguyen, V.H., Abdel-Wahab, M. and Nguyen-Xuan, H. (2020), "A datadriven approach based on long short-term memory and hidden Markov model for crack propagation prediction", Eng. Fract. Mech., 235, 107085. https://doi.org/10.1016/j.engfracmech.2020.107085.
  31. Papaioannou, I., Papadimitriou, C. and Straub, D. (2016), "Sequential importance sampling for structural reliability analysis", Struct. Saf., 62, 66-75. https://doi.org/10.1016/j.strusafe.2016.06.002.
  32. Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., ... & Chintala, S. (2019), "Pytorch: An imperative style, high-performance deep learning library", arXiv preprint arXiv:1912.01703.
  33. 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://doi.org/10.12989/sem.2019.70.5.513.
  34. Rackwitz, R. (2001), "Reliability analysis a review and some perspectives", Struct. Saf., 23(4), 365-395. https://doi.org/10.1016/S0167-4730(02)00009-7.
  35. Robens-Radermacher, A. and Unger, J.F. (2020), "Efficient structural reliability analysis by using a PGD model in an adaptive importance sampling schema", Adv. Model. Simul. Eng. Sci., 7(1), 1-29. https://doi.org/10.1186/s40323-020-00168-z.
  36. Roy, A., Manna, R. and Chakraborty, S. (2019), "Support vector regression based metamodeling for structural reliability analysis", Prob. Eng. Mech., 55, 78-89. https://doi.org/10.1016/j.probengmech.2018.11.001.
  37. Schueller, G. (2009), "Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis-recent advances", Struct. Eng. Mech., 32(1), 1-20. https://doi.org/10.12989/sem.2009.32.1.001.
  38. Su, G., Peng, L. and Hu, L. (2017), "A Gaussian process-based dynamic surrogate model for complex engineering structural reliability analysis", Struct. Saf., 68, 97-109. https://doi.org/10.1016/j.strusafe.2017.06.003.
  39. Tran-Ngoc, H., Khatir, S., Ho-Khac, H., De Roeck, G., Bui-Tien, T. and Wahab, M.A. (2021), "Efficient Artificial neural networks based on a hybrid metaheuristic optimization algorithm for damage detection in laminated composite structures", Compos. Struct., 262, 113339. https://doi.org/10.1016/j.compstruct.2020.113339
  40. Tran-Ngoc, H., Khatir, S., Le-Xuan, T., De Roeck, G., Bui-Tien, T. and Wahab, M.A. (2020), "A novel machine-learning based on the global search techniques using vectorized data for damage detection in structures", Int. J. Eng. Sci., 157, 103376. https://doi.org/10.1016/j.ijengsci.2020.103376
  41. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, L. and Polosukhin, I. (2017), "Attention is all you need", arXiv preprint arXiv:1706.03762. Vazirizade, S.M., Nozhati, S. and Zadeh, M.A. (2017), "Seismic reliability assessment of structures using artificial neural network", J. Build. Eng., 11, 230-235. https://doi.org/10.1016/j.jobe.2017.04.001.
  42. Xiao, M., Zhang, J. and Gao, L. (2020), "A system active learning Kriging method for system reliability-based design optimization with a multiple response model", Reliab. Eng. Syst Saf., 199, 106935. https://doi.org/10.1016/j.ress.2020.106935.
  43. Zhang, J., Xiao, M. and Gao, L. (2019), "An active learning reliability method combining Kriging constructed with exploration and exploitation of failure region and subset simulation", Reliab. Eng. Syst Saf., 188, 90-102. https://doi.org/10.1016/j.ress.2019.03.002.
  44. Zhao, W., Shi, X. 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://doi.org/10.12989/sem.2016.57.4.587.
  45. Zhou, T. and Peng, Y. (2022), "Efficient reliability analysis based on deep learning-enhanced surrogate modelling and probability density evolution method", Mech. Syst. Signal Pr., 162, 108064. https://doi.org/10.1016/j.ymssp.2021.108064
  46. Zuniga, M.M., Murangira, A. and Perdrizet, T. (2021), "Structural reliability assessment through surrogate based importance sampling with dimension reduction", Reliab. Eng. Syst Saf., 207, 107289. https://doi.org/10.1016/j.ress.2020.107289