Smart Structures and Systems

  • 제31권2호
  • /
  • Pages.113-130
  • /
  • 2023
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical and experimental exploration of sobol sequence based DoE for response estimation through hybrid simulation and polynomial chaos expansion

  • Rui Zhang (School of Civil Engineering, Shandong University) ;
  • Chengyu Yang (Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Tongji University) ;
  • Hetao Hou (School of Civil Engineering, Shandong University) ;
  • Karlel Cornejo (School of Engineering, San Francisco State University) ;
  • Cheng Chen (School of Engineering, San Francisco State University)
  • 투고 : 2022.03.12
  • 심사 : 2022.10.15
  • 발행 : 2023.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

Hybrid simulation (HS) has attracted community attention in recent years as an efficient and effective experimental technique for structural performance evaluation in size-limited laboratories. Traditional hybrid simulations usually take deterministic properties for their numerical substructures therefore could not account for inherent uncertainties within the engineering structures to provide probabilistic performance assessment. Reliable structural performance evaluation, therefore, calls for stochastic hybrid simulation (SHS) to explicitly account for substructure uncertainties. The experimental design of SHS is explored in this study to account for uncertainties within analytical substructures. Both computational simulation and laboratory experiments are conducted to evaluate the pseudo-random Sobol sequence for the experimental design of SHS. Meta-modeling through polynomial chaos expansion (PCE) is established from a computational simulation of a nonlinear single-degree-of-freedom (SDOF) structure to evaluate the influence of nonlinear behavior and ground motions uncertainties. A series of hybrid simulations are further conducted in the laboratory to validate the findings from computational analysis. It is shown that the Sobol sequence provides a good starting point for the experimental design of stochastic hybrid simulation. However, nonlinear structural behavior involving stiffness and strength degradation could significantly increase the number of hybrid simulations to acquire accurate statistical estimation for the structural response of interests. Compared with the statistical moments calculated directly from hybrid simulations in the laboratory, the meta-model through PCE gives more accurate estimation, therefore, providing a more effective way for uncertainty quantification.

키워드

과제정보

The study has been partially supported by the Ministry of Science and Technology of the People's Republic of China under Grant No. 2018YFE0206100. The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organizations.

참고문헌

  1. Abbiati, G., Marelli, S., Bursi, O.S., Sudret, B. and Stojadinovic, B. (2015), "Uncertainty propagation and global sensitivity analysis in hybrid simulation using polynomial chaos expansion", Proceedings of the Fourth International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering.
  2. Abbiati, G., Marelli, S., Sudret, B. and Stojadinovic, B. (2018), "Hybrid simulation of mechanical systems with uncertain parameters based on surrogate modeling", Proceedings of the 11th National Conference on Earthquake Engineering, Los Angeles, CA, USA, June.
  3. Airouche, A., Bechtoula, H., Aknouche, H., Thoen, B.K. and Benouar, D. (2014), "Experimental identification of the six DOF CGS, Algeria, shaking table system", Smart Struct. Syst., Int. J., 13(1), 137-154. https://doi.org/10.12989/sss.2014.13.1.137
  4. Avci, M., Botelho, R.M. and Christenson, R. (2020), "Real-time hybrid substructuring of a base isolated building considering robust stability and performance analysis", Smart Struct. Syst., Int. J., 25(2), 155-167. https://doi.org/10.12989/sss.2020.25.2.155
  5. Bernal, D. (1992), "Instability of buildings subjected to earthquakes", J. Struct. Eng., 118(8), 2239-2260. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:8(2239)
  6. Blatman, G. and Sudret, B. (2010), "An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis", Probabil. Eng. Mech., 25(2), 183-197. https://doi.org/10.1016/j.probengmech.2009.10.003
  7. Blatman, G. and Sudret, B. (2011), "Adaptive sparse polynomial chaos expansion based on least angle regression", J. Computat. Phys., 230(6), 2345-2367. https://doi.org/10.1016/j.jcp.2010.12.021
  8. Blanning, R.W. (1975), "The construction and implementation of metamodels", Simulation, 24(6), 177-184. https://doi.org/10.1177/003754977502400606
  9. Bourinet, J.M. (2016), "Rare-event probability estimation with adaptive support vector regression surrogates", Reliabil. Eng. Syst. Safety, 150, 210-221. https://doi.org/10.1016/j.ress.2016.01.023
  10. Casciati, S. and Hamdaoui, K. (2008), "Experimental and numerical studies toward the implementation of shape memory alloy ties in masonry structures", Smart Struct. Syst., Int. J., 4(2), 153-169. https://doi.org/10.12989/sss.2008.4.2.153
  11. Cha, Y.J., Agrawal, A.K., Friedman, A., Phillips, B., Ahn, R., Dong, B., Dyke, S.J., Spencer, B.F., Ricles, J. and Christenson, R. (2014), "Performance validations of semiactive controllers on large-scale moment-resisting frame equipped with 200-kN MR damper using real-time hybrid simulations", J. Struct. Eng., 140(10), p. 04014066. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000982
  12. Chae, Y., Ricles, J.M. and Sause, R. (2014), "Large-scale real-time hybrid simulation of a three-story steel frame building with magneto-rheological dampers", Earthq. Eng. Struct. Dyn., 43(13), 1915-1933. https://doi.org/10.1002/eqe.2429
  13. Chen, P.C. and Chen, P.C. (2020), "Robust stability analysis of real-time hybrid simulation considering system uncertainty and delay compensation", Smart Struct. Syst., Int. J., 25(6), 719-732. https://doi.org/10.12989/sss.2020.25.6.719
  14. Chen, C., Ricles, J.M., Marullo, T.M. and Mercan, O. (2009), "Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm", Earthq. Eng. Struct. Dyn., 38(1), 23-44. https://doi.org/10.1002/eqe.838
  15. Chen, C., Ricles, J.M., Karavasilis, T.L., Chae, Y. and Sause, R. (2012), "Evaluation of a real-time hybrid simulation system for performance evaluation of structures with rate dependent devices subjected to seismic loading", Eng. Struct., 35, 71-82. https://doi.org/10.1016/j.engstruct.2011.10.006
  16. Chen, C., Xu, W., Guo, T. and Chen, K. (2017), "Analysis of actuator delay and its effect on uncertainty quantification for real-time hybrid simulation", Earthq. Eng. Eng. Vib., 16(4), 713-725. https://doi.org/10.1007/s11803-017-0409-6
  17. Chen, P.C., Hsu, S.C., Zhong, Y.J. and Wang, S.J. (2019), "Real-time hybrid simulation of smart base-isolated raised floor systems for high-tech industry", Smart Struct. Syst., Int. J., 23(1), 91-106. https://doi.org/10.12989/sss.2019.23.1.091
  18. Chen, M., Guo, T., Chen, C. and Xu, W. (2020), "Data-driven arbitrary polynomial chaos expansion on uncertainty quantification for real-time hybrid simulation under stochastic ground motions", Experim. Techniq., 44, 751-762. https://doi.org/10.1007/s40799-020-00381-w
  19. 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. Safety, 52, 78-89. https://doi.org/10.1016/j.strusafe.2014.09.002
  20. Chowdhury, R. and Rao, B.N. (2009), "Assessment of high dimensional model representation techniques for reliability analysis", Probabil. Eng. Mech., 24(1), 100-115. https://doi.org/10.1016/j.probengmech.2008.02.001
  21. Darby, A.P., Blakeborough, A. and Williams, M.S. (1999), "Real-time substructure tests using hydraulic actuators", J. Eng. Mech., 125, 1133-1139. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:10(1133)
  22. Dermitzakis, S.N. and Mahin, S.A. (1985), "Development of Substructuring Techniques for On-Line Computer Controlled Seismic Performance Testing", Report UCB/EERC-85/04, Earthquake Engineering Research Center, University of California, Berkeley, CA, USA.
  23. Fang, H. and Horstemeyer, M.F. (2006), "Global response approximation with radial basis functions", Eng. Optimiz., 38(04), 407-424. https://doi.org/10.1080/03052150500422294
  24. Gao, X., Castaneda, N. and Dyke, S.J. (2013), "Real time hybrid simulation: from dynamic system, motion control to experimental error", Earthq. Eng. Struct. Dyn., 42(6), 815-832. https://doi.org/10.1002/eqe.2246
  25. Gaspar, B., Teixeira, A.P. and Soares, C.G. (2014), "Assessment of the efficiency of Kriging surrogate models for structural reliability analysis", Probabil. Eng. Mech., 37, 24-34. https://doi.org/10.1016/j.probengmech.2014.03.011
  26. Goda, K., Hong, H.P. and Lee, C.S. (2009), "Probabilistic characteristics of seismic ductility demand of sdof systems with bouc-wen hysteretic behavior", J. Earthq. Eng., 13(5), 600-622. https://doi.org/10.1080/13632460802645098
  27. Goel, R.K. and Chopra, A.K. (2004), "Evaluation of modal and FEMA pushover analyses: SAC buildings", Earthq. Spectra, 20(1), 225-254. https://doi.org/10.1193/1.1646390
  28. Guo, T., Xu, W. and Chen, C. (2014), "Analysis of decimation techniques to improve computational efficiency of a frequency-domain evaluation approach for real-time hybrid simulation", Smart Struct. Syst., Int. J., 14(6), 1197-1220. https://doi.org/10.12989/sss.2014.14.6.1197
  29. Hakuno, M., Shidawara, M. and Hara, T. (1969), "Dynamic destructive test of a cantilever beam, controlled by an analog-computer", Proceedings of the Japan Society of Civil Eengineers, Vol. 1969, No. 171, pp. 1-9. https://doi.org/10.2208/jscej1969.1969.171_1
  30. Hashemi, M.J. and Mosqueda, G. (2014), "Innovative substructuring technique for hybrid simulation of multistory buildings through collapse", Earthq. Eng. Struct. Dyn., 43(14), 2059-2074. https://doi.org/10.1002/eqe.2427
  31. Hayati, S. and Song, W. (2017), "An optimal discrete-time feedforward compensator for real-time hybrid simulation", Smart Struct. Syst., Int. J., 20(4), 483-498. https://doi.org/10.12989/sss.2017.20.4.483
  32. Hurtado, J.E. and Alvarez, D.A. (2001), "Neural-network-based reliability analysis: a comparative study", Comput. Methods Appl. Mech. Eng., 191(1-2), 113-132. https://doi.org/10.1016/S0045-7825(01)00248-1
  33. Ibarra, L.F., Medina, R.A. and Krawinkler, H. (2005), "Hysteretic models that incorporate strength and stiffness deterioration", Earthq. Eng. Struct. Dyn., 34(12), 1489-1511. https://doi.org/10.1002/eqe.495
  34. Iman, R.L., Davenport, J.M. and Zeigler, D.K. (1980), Latin hypercube sampling (program user's guide), OSTI 5571631.
  35. Isukapalli, S.S., Roy, A. and Georgopoulos, P.G. (1998), "Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems", Risk Anal., 18(3), 351-363. https://doi.org/10.1111/j.1539-6924.1998.tb01301.x
  36. Jin, R., Chen, W. and Sudjianto, A. (2002), "On sequential sampling for global metamodeling in engineering design", In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Vol. 36223, pp. 539-548. https://doi.org/10.1115/DETC2002/DAC-34092
  37. Krawinkler, H. and Seneviratna, G.D.P.K. (1998), "Pros and cons of a pushover analysis of seismic performance evaluation", Eng. Struct., 20(4-6), 452-464. https://doi.org/10.1016/S0141-0296(97)00092-8
  38. Lee, S.K., Park, E.C., Min, K.W., Lee, S.H., Chung, L. and Park, J.H. (2007), "Real-time hybrid shaking table testing method for the performance evaluation of a tuned liquid damper controlling seismic response of building structures", J. Sound Vib., 302(3), 596-612. https://doi.org/10.1016/j.jsv.2006.12.006
  39. Lignos, D.G. and Krawinkler, H. (2011), "Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading", J. Struct. Eng., 137(11), 1291-1302. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000376
  40. Lignos, D.G., Moreno, D.M. and Billington, S.L. (2014), "Seismic retrofit of steel moment-resisting frames with high-performance fiber-reinforced concrete infill panels: Large-scale hybrid simulation experiments", J. Struct. Eng., 140(3), p. 04013072. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000877
  41. Lin, Y.C., Sause, R. and Ricles, J. (2013), "Seismic performance of a large-scale steel self-centering moment-resisting frame: MCE hybrid simulations and quasi-static pushover tests", J. Struct. Eng., 139(7), 1227-1236. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000661
  42. Mahin, S.A., Shing, P.S.B., Thewalt, C.R. and Hanson, R.D. (1989), "Pseudodynamic test method-current status and future directions", J. Struct. Eng., 115(8), 2113-2128. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:8(2113)
  43. Marelli, S. and Sudret, B. (2015), "UQLab user manual-Polynomial chaos expansions", In: Chair of Risk, Safety &Uncertainty Quantification, ETH Zurich, 0.9-104 edition, pp. 97-110.
  44. Martin, J.D. and Simpson, T.W. (2005), "Use of kriging models to approximate deterministic computer models", AIAA Journal, 43(4), 853-863. https://doi.org/10.2514/1.8650
  45. 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
  46. Mooney, C.Z. (1997), Monte Carlo Simulation, Vol. 116, Sage publications.
  47. Mosqueda, G., Stojadinovic, B. and Mahin, S.A. (2007), "Real-time error monitoring for hybrid simulation. Part I: methodology and experimental verification", J. Struct. Eng., 133(8), 1100-1108. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:8(1100)
  48. Mosqueda, G., Stojadinovic, B. Hanley, J. Sivaselvan, M. and Reinhorn, A.M. (2008), "Hybrid seismic response simulation on a geographically distributed bridge model", J. Struct. Eng., 134(4), 535-543. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:4(535)
  49. Nakashima, M. (2001), "Development, potential, and limitations of real-time online (pseudo-dynamic) testing", Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 359(1786), 1851-1867. https://doi.org/10.1098/rsta.2001.0876
  50. Nakashima, M. (2020), "Hybrid simulation: An early history", Earthq. Eng. Struct. Dyn., 49(10), 949-962. https://doi.org/10.1002/eqe.3274
  51. Nakashima, M., Kato, H. and Takaoka, E. (1992), "Development of real-time pseudo dynamic testing", Earthq. Eng. Struct. Dyn., 21(1), 79-92. https://doi.org/10.1002/eqe.4290210106
  52. Nakashima, M., Matsumiya, T., Suita, K. and Liu, D. (2006), "Test on full-scale three-storey steel moment frame and assessment of ability of numerical simulation to trace cyclic inelastic behaviour", Earthq. Eng. Struct. Dyn., 35(1), 3-19. https://doi.org/10.1002/eqe.528
  53. Nakata, N. and Stehman, M. (2014), "Compensation techniques for experimental errors in real-time hybrid simulation using shake tables", Smart Struct. Syst., Int. J., 14(6), 1055-1079. https://doi.org/10.12989/sss.2014.14.6.1055
  54. Nakata, N., Spencer Jr, B.F. and Elnashai, A.S. (2007), "Multi-dimensional mixed-mode hybrid simulation control and applications", Newmark Structural Engineering Laboratory. University of Illinois at Urbana-Champaign.
  55. Nakata, N., Dyke, S., Zhang, J., Mosqueda, G., Shao, X., Mahmoud, H., Head, M.H., Bletzinger, M., Marshall, G.A., Ou, G. and Song, C. (2014), Hybrid Simulation Primer and Dictionary. https://datacenterhub.org/resources/8102
  56. Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. Div., 85(3), 67-94. https://doi.org/10.1061/JMCEA3.0000098
  57. Niederreiter, H. (1992), Random number generation and quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics.
  58. Ramos, M.D.C., Mosqueda, G. and Hashemi, M.J. (2016), "Large-scale hybrid simulation of a steel moment frame building structure through collapse", J. Struct. Eng., 142(1), 04015086. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001328
  59. Schellenberg, A., Mahin, S.A. and Fenves, G.L. (2007), "A software framework for hybrid simulation of large structural systems", In: Structural Engineering Research Frontiers, pp. 1-16. https://doi.org/10.1061/40944(249)3
  60. Shao, X., Reinhorn, A.M. and Sivaselvan, M.V. (2011), "Real-time hybrid simulation using shake tables and dynamic actuators", J. Struct. Eng., 137(7), 748-760. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000314
  61. Shao, X., van de Lindt, J., Bahmani, P., Pang, W., Ziaei, E., Symans, M., Tian, J. and Dao, T. (2014), "Real-time hybrid simulation of a multi-story wood shear wall with first-story experimental substructure incorporating a rate-dependent seismic energy dissipation device", Smart Struct. Syst., Int. J., 14(6), 1031-1054. https://doi.org/10.12989/sss.2014.14.6.1031
  62. Shen, S.D., Pan, P., Li, W.F., Miao, Q.S. and Gong, R.H. (2019), "Test on the anchoring components of steel shear keys in precast shear walls", Smart Struct. Syst., Int. J., 24(6), 783-791. http://doi.org/10.12989/sss.2019.24.6.783
  63. Silva, C.E., Gomez, D., Maghareh, A., Dyke, S.J. and Spencer Jr, B.F. (2020), "Benchmark control problem for real-time hybrid simulation", Mech. Syst. Signal Process., 135, 106381. https://doi.org/10.1016/j.ymssp.2019.106381
  64. Sivaselvan, M.V. and Reinhorn, A.M. (2000), "Hysteretic models for deteriorating inelastic structures", J. Eng. Mech., 126(6), 633-640. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:6(633)
  65. Sobol, I.M. (1993), "Sensitivity estimates for nonlinear mathematical models", Math. Model. Comput. Exp., 1(4), 407414.
  66. Song, J.K. and Pincheira, J.A. (2000), "Spectral displacement demands of stiffness-and strength-degrading systems", Earthq. Spectra, 16(4), 817-851. https://doi.org/10.1193/1.1586141
  67. Stojadinovic, B., Mosqueda, G. and Mahin, S.A. (2006), "Event-driven control system for geographically distributed hybrid simulation", J. Struct. Eng., 132(1), 68-77. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:1(68)
  68. Takizawa, H. and Jennings, P.C. (1980), "Collapse of a model for ductile reinforced concrete frames under extreme earthquake motions", Earthq. Eng. Struct. Dyn., 8(2), 117-144. https://doi.org/10.1002/eqe.4290080204
  69. Vamvatsikos, D. and Cornell, C.A. (2002), "Incremental dynamic analysis", Earthq. Eng. Struct. Dyn., 31(3), 491-514. https://doi.org/10.1002/eqe.141
  70. Villaverde, R. (2007), "Methods to assess the seismic collapse capacity of building structures: State of the art", J. Struct. Eng., 133(1), 57-66. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:1(57)
  71. Vian, D. and Bruneau, M. (2003), "Tests to structural collapse of single degree of freedom frames subjected to earthquake excitations", J. Struct. Eng., 129(12), 1676-1685. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:12(1676)
  72. Wang. T., Nakashima, M. and Pan, P. (2006), "On-line hybrid test combining with general-purpose finite element software", Earthq. Eng. Struct. Dyn., 35(12), 1471-1488. https://doi.org/10.1002/eqe.586
  73. Wang, T., McCormick, J., Yoshitake, N., Pan, P., Murata, Y. and Nakashima, M. (2008), "Collapse simulation of a four-story steel moment frame by a distributed online hybrid test", Earthq. Eng. Struct. Dyn., 37(6), 955-974. https://doi.org/10.1002/eqe.798
  74. Wang, Z., Wu, B., Bursi, O.S., Xu, G. and Ding, Y. (2014), "An effective online delay estimation method based on a simplified physical system model for real-time hybrid simulation", Smart Struct. Syst., Int. J., 14(6), 1247-1267. https://doi.org/10.12989/sss.2014.14.6.1247
  75. Wang, Z., Xu, G., Li, Q. and Wu, B. (2020a), "An adaptive delay compensation method based on a discrete system model for real-time hybrid simulation", Smart Struct. Syst., Int. J., 25(5), 569-580. https://doi.org/10.12989/sss.2020.25.5.569
  76. Wang, Z., Tan, Q., Shi, P., Yang, G., Zhu, S., Xu, G., Wu, B. and Sun, J. (2020b), "Performance validation and application of a mixed force-displacement loading strategy for bi-directional hybrid simulation", Smart Struct. Syst., Int. J., 26(3), 373-390. https://doi.org/10.12989/sss.2020.26.3.373
  77. Wiener, N. (1938), "The homogeneous chaos", Am. J. Mathe., 60(4), 897-936. https://doi.org/10.2307/2371268
  78. Wu, B. and Wang, T. (2014), "Model updating with constrained unscented Kalman filter for hybrid testing", Smart Struct. Syst., Int. J., 14(6), 1105-1129. https://doi.org/10.12989/sss.2014.14.6.1105
  79. Wu, B., Xu, G., Wang, Q. and Williams, M.S. (2006), "Operator-splitting method for real-time substructure test", Earthq. Eng. Struct. Dyn., 35(3), 293-314. https://doi.org/10.1002/eqe.519
  80. Xiu, D. and Karniadakis, G.E. (2002), "The Wiener--Askey polynomial chaos for stochastic differential equations", SIAM J. Scientif. Comput., 24(2), 619-644. https://doi.org/10.1137/S1064827501387826