Earthquakes and Structures

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Important measure analysis of uncertainty parameters in bridge probabilistic seismic demands

  • Song, Shuai (School of Civil Engineering, Qingdao University of Technology) ;
  • Wu, Yuan H. (School of Civil Engineering, Taiyuan University of Technology) ;
  • Wang, Shuai (School of Civil Engineering, Taiyuan University of Technology) ;
  • Lei, Hong G. (School of Civil Engineering, Taiyuan University of Technology)
  • Received : 2020.05.13
  • Accepted : 2022.01.06
  • Published : 2022.02.25
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Abstract

A moment-independent importance measure analysis approach was introduced to quantify the effects of structural uncertainty parameters on probabilistic seismic demands of simply supported girder bridges. Based on the probability distributions of main uncertainty parameters in bridges, conditional and unconditional bridge samples were constructed with Monte-Carlo sampling and analyzed in the OpenSees platform with a series of real seismic ground motion records. Conditional and unconditional probability density functions were developed using kernel density estimation with the results of nonlinear time history analysis of the bridge samples. Moment-independent importance measures of these uncertainty parameters were derived by numerical integrations with the conditional and unconditional probability density functions, and the uncertainty parameters were ranked in descending order of their importance. Different from Tornado diagram approach, the impacts of uncertainty parameters on the whole probability distributions of bridge seismic demands and the interactions of uncertainty parameters were considered simultaneously in the importance measure analysis approach. Results show that the interaction of uncertainty parameters had significant impacts on the seismic demand of components, and in some cases, it changed the most significant parameters for piers, bearings and abutments.

Keywords

Acknowledgement

The research described in this paper was financially supported by National Natural Science Foundation of China (Grand no. 51808376) and China Postdoctoral Science Foundation (Grand no. 2019M651076). The authors also acknowledge Dr. Jing Liu for polishing the language.

References

  1. Billah, A.H.M.M. and Alam, M.S. (2015), "Seismic fragility assessment of highway bridges: A state-of-the-art review", Struct. Infrastruct. Eng., 11(6), 804-832. https://doi.org/10.1080/15732479.2014.912243.
  2. Borgonovo, E. (2007), "A new uncertainty importance measure", Reliab. Eng. Syst. Safe., 92(6), 771-784. https://doi.org/10.1016/j.ress.2006.04.015.
  3. Borgonovo, E. and Plischke, E. (2016), "Sensitivity analysis: A review of recent advances", Europ. J. Oper. Res., 248(3), 869-887. https://doi.org/10.1016/j.ejor.2015.06.032.
  4. Botev, Z.I., Grotowski, J.F. and Kroese, D.P. (2010), "Kernel density estimation via diffusion", Ann. Statist., 38(5), 2916-2957. https://doi.org/10.1214/10-AOS799.
  5. California Department of Transportation (CALTRANS) (2010), Seismic Design Criteria, California, U.S.A.
  6. Chen, J. and Wan, Z. (2019), "A compatible probabilistic framework for quantification of simultaneous aleatory and epistemic uncertainty of basic parameters of structures by synthesizing the change of measure and change of random variables", Struct. Safe., 78, 76-87. https://doi.org/10.1016/j.strusafe.2019.01.001.
  7. Chun, M.H., Han, S.J. and Tak, N.I. (2000), "An uncertainty importance measure using a distance metric for the change in a cumulative distribution function", Reliab. Eng. Syst. Saf., 70(3), 313-321. https://doi.org/10.1016/S0951-8320(00)00068-5.
  8. Cui, L., Lu, Z. and Zhao, X. (2010), "Moment-independent importance measure of basic random variable and its probability density evolution solution", Sci. China Technol. Sci., 53(4), 1138-1145. https://doi.org/10.1007/s11431-009-0386-8.
  9. Dong, H.H., Du, X.L., Han, Q., Hao, H., Bi, K.M. and Wang, X.Q. (2017), "Performance of an innovative self-centering buckling restrained brace for mitigating seismic responses of bridge structures with double-column piers", Eng. Struct., 148, 47-62. https://doi.org/10.1016/j.engstruct.2017.06.011.
  10. Dukes, J., Mangalathu, S., Padgett, J.E. and DesRoches, R. (2018), "Development of a bridge-specific fragility methodology to improve the seismic resilience of bridges", Earthq. Struct., 15(3), 253-261. https://doi.org/10.12989/eas.2018.15.3.253.
  11. Eem, S.H. and Jung, H.J. (2018), "Seismic fragility assessment of isolated structures by using stochastic response database", Earthq. Struct., 14(5), 389-398. https://doi.org/10.12989/eas.2018.14.5.389.
  12. Feng, K., Lu, Z., Pang, C. and Yun, W. (2018), "An efficient computational method of a moment-independent importance measure using quantile regression", Mech. Syst. Signal Pr., 109, 235-246. https://doi.org/10.1016/j.ymssp.2018.02.044.
  13. Flage, R., Aven, T. and Berner, C.L. (2018), "A comparison between a probability bounds analysis and a subjective probability approach to express epistemic uncertainties in a risk assessment context-a simple illustrative example", Reliab. Eng. Syst. Safe., 169, 1-10. https://doi.org/10.1016/j.ress.2017.07.016.
  14. Gokkaya, B.U., Baker, J.W. and Deierlein, G.G. (2016), "Quantifying the impacts of modeling uncertainties on the seismic drift demands and collapse risk of buildings with implications on seismic design checks", Earthq. Eng. Struct. D., 45(7), 1661-1683. https://doi.org/10.1002/eqe.2740.
  15. Helton, J.C. and Davis, F.J. (2003), "Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems", Reliab. Eng. Syst. Safe., 81(1), 23-69. https://doi.org/10.1016/s0951-8320(03)00058-9.
  16. Iervolino, I. (2017), "Assessing uncertainty in estimation of seismic response for PBEE", Earthq. Eng. Struct. D., 46(10), 1711-1723. https://doi.org/10.1002/eqe.2883.
  17. Iman, R.L. and Hora, S.C. (1990), "A robust measure of uncertainty importance for use in fault tree system analysis", Risk Anal., 10(3), 401-406. https://doi.org/10.1111/j.1539-6924.1990.tb00523.x.
  18. Jalayer, F. and Ebrahimian, H. (2020), "Seismic reliability assessment and the nonergodicity in the modelling parameter uncertainties", Earthq. Eng. Struct. D., 49, 434-457. https://doi.org/10.1002/eqe.3247.
  19. Jeon, J.S., Mangalathu, S., Song, J. and DesRoches, R. (2017), "Parameterized seismic fragility curves for curved multi-frame concrete box-girder bridges using bayesian parameter estimation", J. Earthq. Eng., 23(6), 1-26. https://doi.org/10.1080/13632469.2017.1342291.
  20. Kwag, S., Oh, J., Lee, J.M. and Ryu, J.S. (2017), "Bayesian-based seismic margin assessment approach: Application to research reactor", Earthq. Struct., 12(6), 653-663. https://doi.org/10.12989/eas.2017.12.6.653.
  21. Li, J., Chen, J.B. and Yang, J.Y. (2017), "PDEM-based perspective to probabilistic seismic response analysis and design of earthquake-resistant engineering structures", Nat. Hazards Rev., 18 (1), B4016002. https://doi.org/10.1061/(asce)nh.1527-6996.0000216.
  22. Li, L., Lu, Z., Feng, J. and Wang, B. (2012), "Moment-independent importance measure of basic variable and its state dependent parameter solution", Struct. Safe., 38, 40-47. https://doi.org/10.1016/j.strusafe.2012.04.001.
  23. Li, L., Liu, Y. and Lu, Z.Z. (2019), "A new dependence measure for importance analysis: Application to an environmental model", Appl. Math. Model., 74, 43-61. https://doi.org/10.1016/j.apm.2019.04.046.
  24. Mackie, K.R. and Nielson, B. (2009), "Uncertainty quantification in analytical bridge fragility curves", Technical Council on Lifeline Earthquake Engineering Conference, California, Oakland, U.S.A., June.
  25. Mangalathu, S., Jeon, J.S. and DesRoches, R. (2018), "Critical uncertainty parameters influencing seismic performance of bridges using Lasso regression", Earthq. Eng. Struct. D., 47(3), 784-801. https://doi.org/10.1002/eqe.2991.
  26. Mukherjee, D., Rao, B.N. and Meherprasad, A. (2011), "Global sensitivity analysis of unreinforced masonry structure using high dimensional model representation", Eng. Struct., 33(4), 1316-1325. https://doi.org/10.1016/j.engstruct.2011.01.008.
  27. Nielson, B.G. and DesRoches, R. (2007), "Seismic fragility methodology for highway bridges using a component level approach", Earthq. Eng. Struct. D., 36(6), 823-839. https://doi.org/10.1002/Eqe.655.
  28. Nielson, B.G. and Pang, W.C. (2011), "Effect of ground motion suite size on uncertainty estimation in seismic bridge fragility modeling", Structures Congress, Las Vegas, U.S.A., April.
  29. Padgett, J.E. and DesRoches, R. (2007), "Sensitivity of seismic response and fragility to parameter uncertainty", J. Struct. Eng., 133(9), 1710-1718. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:12(1710).
  30. Pan, Y., Agrawal, A.K. and Ghosn, M. (2007), "Seismic fragility of continuous steel highway bridges in New York State", J. Bridge Eng., 1(6), 689-699. https://doi.org/10.1061/(ASCE)1084-0702(2007)12:6(689).
  31. Pang, Y., Dang, X. and Yuan, W. (2014), "An artificial neural network based method for seismic fragility analysis of highway bridges", Adv. Struct. Eng., 17(3), 413-428. https://doi.org/10.1260/1369-4332.17.3.413.
  32. Pang, Y., Wu, X., Shen, G. and Yuan, W. (2014), "Seismic fragility analysis of cable-stayed bridges considering different sources of uncertainties", J. Bridge Eng., 19(4), 04013015. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000565.
  33. PEER (Pacific Earthquake Engineering Research Center) (2013), NGA-West2 Ground Motion Database, University of California, Berkeley, CA, U.S.A.
  34. Peng, Y., Mei, Z. and Li, J. (2014), "Stochastic seismic response analysis and reliability assessment of passively damped structures", J. Vib. Control, 20(15), 2352-2365. https://doi.org/10.1177/1077546313486910.
  35. Ramanathan, K., DesRoches, R. and Padgett, J.E. (2012), "A comparison of pre- and post-seismic design considerations in moderate seismic zones through the fragility assessment of multispan bridge classes", Eng. Struct., 45(15), 559-573. https://doi.org/10.1016/j.engstruct.2012.07.004.
  36. Razzaghi, M.S., Safarkhanlou, M., Mosleh, A. and Hosseini, P. (2018), "Fragility assessment of RC bridges using numerical analysis and artificial neural networks", Earthq. Struct., 15(4), 431-441. https://doi.org/10.12989/eas.2018.15.4.431.
  37. Ruan, W.B. and Lu, Z.Z. (2015), "Estimation of moment-independent importance measure on failure probability and its application in reliability analysis", J. Struct. Eng., 141, 05014001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001173.
  38. Saltelli, A. (2002), "Sensitivity analysis for importance assessment", Risk Anal., 22(3), 579-590. https://doi.org/10.1111/0272-4332.00040.
  39. Shang, Q., Wang, T. and Li, J. (2020), "Seismic resilience assessment of emergency departments based on the state tree method", Struct. Safe., 85, 101944. https://doi.org/10.1016/j.strusafe.2020.101944.
  40. Serdar, N. and Folic, R. (2018), "Vulnerability and optimal probabilistic seismic demand model for curved and skewed RC bridges", Eng. Struct., 176, 411-425. https://doi.org/10.1016/j.engstruct.2018.09.020.
  41. Sfahani, M.G. and Guan, H. (2018), "An extended cloud analysis method for seismic fragility assessment of highway bridges", Earthq. Struct., 15(6), 605-616. https://doi.org/10.12989/eas.2018.15.6.605.
  42. Sobol, I.M. (2001), "Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates", Math. Comput. Simul., 55(1), 271-280. https://doi.org/10.1016/s0378-4754(00)00270-6.
  43. Soleimani, F., Mangalathu, S. and DesRoches, R. (2017), "A comparative analytical study on the fragility assessment of boxgirder bridges with various column shapes", Eng. Struct., 153, 460-478. https://doi.org/10.1016/j.engstruct.2017.10.036.
  44. Soleimani, F. (2020), "Propagation and quantification of uncertainty in the vulnerability estimation of tall concrete bridges", Eng. Struct., 202, 109812. https://doi.org/10.1016/j.engstruct.2019.109812.
  45. Song, S., Liu, J., Qian, Y., Zhang, F. and Wu, G. (2018), "Dependence analysis on the seismic demands of typical components of a concrete continuous girder bridge with the copula technique", Adv. Struct. Eng., 21(12), 1826-1839. https://doi.org/10.1177/1369433218757234.
  46. Song, S., Qian, C., Qian, Y., Bao, H. and Lin, P. (2019), "Canonical correlation analysis of selecting optimal ground motion intensity measures for bridges", KSCE J. Civil Eng., 23(7), 2958-2970. https://doi.org/10.1007/s12205-019-0929-x.
  47. Sousa, L., Silva, V., Marques, M. and Crowley, H. (2018), "On the treatment of uncertainty in seismic vulnerability and portfolio risk assessment", Earthq. Eng. Struct. D., 47(1), 87-104. https://doi.org/10.1002/eqe.2940.
  48. Suzuki, A. and Ierrvolino, I. (2020), "Intensity measure conversion of fragility curves", Earthq. Eng. Struct. D., https://doi.org/10.1002/eqe.3256.
  49. Tubaldi, E., Barbato, M. and Dall'Asta, A. (2012), "Influence of model parameter uncertainty on seismic transverse response and vulnerability of steel-concrete composite bridges with dual load path", J. Struct. Eng., 138(3), 363-374. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000456.
  50. Wang, Q., Wu, Z.Y. and Liu, S.K. (2018), "Multivariate probabilistic seismic demand model for the bridge multidimensional fragility analysis", KSCE J. Civil Eng., 22(9), 3443-3451. https://doi.org/10.1007/s12205-018-0414-y.
  51. Wu, X.Y., Wu, X.Y. and Balakrishnan, N. (2018), "Variance-based importance analysis measure for mission reliability of phased mission system", J. Stat. Comput. Simul., 88(5), 841-868. https://doi.org/10.1080/00949655.2017.1407936.
  52. Xiang, N. and Shahria, A.M. (2019), "Displacement-based seismic design of bridge bents retrofitted with various bracing devices and their seismic fragility assessment under near-fault and far-field ground motions", Soil Dyn. Earthq. Eng., 119, 75-90. https://doi.org/10.1016/j.soildyn.2018.12.023.
  53. Xiao, Q. (2014), "Evaluating correlation coefficient for Nataf transformation", Probab. Eng. Mech., 37, 1-6. https://doi.org/10.1016/j.probengmech.2014.03.010.
  54. Yilmaz, T., Banerjee, S. and Johnson, P.A. (2018), "Uncertainty in risk of highway bridges assessed for integrated seismic and flood hazards", Struct. Infrastruct. Eng., 14(9), 1182-1196. https://doi.org/10.1080/15732479.2017.1402065.
  55. Yun, W., Lu, Z., Jiang, X. and Zhang, L. (2018), "Borgonovo moment independent global sensitivity analysis by Gaussian radial basis function meta-model", Appl. Math. Model., 54, 378-392. https://doi.org/10.1016/j.apm.2017.09.048.
  56. Zanini, M.A., Faleschini, F. and Pellegrino, C. (2017), "Probabilistic seismic risk forecasting of aging bridge networks", Eng. Struct., 136, 219-232. https://doi.org/10.1016/j.engstruct.2017.01.029.
  57. Zhong, J., Gardoni, P. and Rosowsky, D. (2012), "Closed-form seismic fragility estimates, sensitivity analysis and importance measures for reinforced concrete columns in two-column bents", Struct. Infrastruct. Eng., 8(7), 669-685. https://doi.org/10.1080/15732471003686165.
  58. Zhong, J., Zhi, X.D. and Fan, F. (2018), "Sensitivity of seismic response and fragility to parameter uncertainty of single-layer reticulated domes", Int. J. Steel Struct., 18, 1607-1616. https://doi.org/10.1007/s13296-018-0057-3.
  59. Zhou, T. and Li, A. (2019), "Seismic fragility assessment of highway bridges using D-vine copulas," B. Earthq. Eng., 17(2), 927-955. https://doi.org/10.1007/s10518-018-0474-x.