On the Gaussian and Non-Gaussian Characteristics of Nonstationary Seismic Ground Motions
Publication: Journal of Structural Engineering
Volume 148, Issue 6
Abstract
In earthquake engineering, seismic ground motions are most often modelled as a nonstationary Gaussian process. A few studies indicated that seismic ground motions should be treated as a nonstationary non-Gaussian process, by showing that the kurtosis coefficient of the historical ground motion records is much greater than three. These findings and conclusions are queried in the present study, which analyzes a large number of historical ground motion records. Our results indicate that while the mixture marginal distribution of the acceleration of the records is non-Gaussian with a heavy distribution tail, the mixture marginal distribution of the standardized record, defined by the time-varying record to its standard deviation, is only mildly non-Gaussian. We point out that the mixture marginal distribution of a nonstationary Gaussian process may not be Gaussian. The implication of these observations in simulating records is explained. The sampled nonstationary Gaussian/non-Gaussian records are used to compare the responses of single-degree-of-freedom systems. The results indicate that the error introduced by adopting the Gaussian assumption is small, suggesting that the ground motions could be assumed to be a nonstationary Gaussian process with sufficient accuracy, especially if structures that are not very stiff are considered.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models or code generated or used during the study are available from the corresponding author upon reasonable request.
Acknowledgments
We gratefully acknowledge the financial support received from the Natural Sciences and Engineering Research Council of Canada (RGPIN-2016-04814, for HPH), and the University of Western Ontario.
References
Alamilla, J., L. Esteva, J. García-Pérez, and O. Díaz-López. 2001. “Simulating earthquake ground motion at a site, for given intensity and uncertain source location.” J. Seismolog. 5 (4): 475–485. https://doi.org/10.1023/A:1012062620566.
Ancheta, T. D., et al. 2003. NGA-West2 database. Berkeley, CA: Pacific Earthquake Engineering Research Center. https://doi.org/10.1193/070913EQS197M.
Benjamin, J. R., and C. A. Cornell. 2014. Probability, statistics, and decision for civil engineers. Mineola, NY: Dover.
Chopra, A. K. 2012. Dynamics of structures: Theory and applications to earthquake engineering. 4th ed. Hoboken, NJ: Prentice Hall.
Clough, R. W., and J. Penzien. 2003. Dynamics of structures. 3rd ed. Berkeley, CA: Computers & Structures, Inc.
Cui, X. Z., and H. P. Hong. 2021. “A time frequency representation model for seismic ground motions.” Bull. Seismol. Soc. Am. 111 (2): 839–856. https://doi.org/10.1785/0120200123.
Deodatis, G. 1996. “Non-stationary stochastic vector processes: Seismic ground motion applications.” Probab. Eng. Mech. 11 (3): 149–167. https://doi.org/10.1016/0266-8920(96)00007-0.
Fan, F.-G., and G. Ahmadi. 1990. “Nonstationary Kanai-Tajimi models for El Centro 1940 and Mexico City 1985 earthquakes.” Probab. Eng. Mech. 5 (4): 171–181. https://doi.org/10.1016/0266-8920(90)90018-F.
Goda, K., and H. P. Hong. 2006. “Optimal seismic design for limited planning time horizon with detailed seismic hazard information.” Struct. Saf. 28 (3): 247–260. https://doi.org/10.1016/j.strusafe.2005.08.001.
Goda, K., H. P. Hong, and C. S. Lee. 2009. “Probabilistic characteristics of seismic ductility demand of SDOF systems with Bouc-Wen hysteretic behavior.” J. Earthquake Eng. 13 (5): 600–622. https://doi.org/10.1080/13632460802645098.
Grigoriu M. 1995. Applied non-Gaussian processes: Examples, theory, simulation, linear random vibration, and MATLAB solutions. Hoboken, NJ: Prentice Hall.
Grigoriu M. 1998. “Simulation of stationary non-Gaussian translation processes.” J. Eng. Mech. 124 (2): 121–126. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:2(121).
Gurley, K., and A. Kareem. 1999. “Applications of wavelet transforms in earthquake, wind and ocean engineering.” Eng. Struct. 21 (2): 149–167. https://doi.org/10.1016/S0141-0296(97)00139-9.
Gusev, A. A. 1996. “Peak factors of Mexican accelerograms: Evidence of a non-Gaussian amplitude distribution.” J. Geophys. Res. Solid Earth 101 (B9): 20083–20090. https://doi.org/10.1029/96JB00810.
Hong, H. P. 2021. “Response and first passage probability of linear elastic SDOF systems subjected to nonstationary stochastic excitation modelled through S-transform.” Struct. Saf. 88 (Jan): 102007. https://doi.org/10.1016/j.strusafe.2020.102007.
Hong, H. P., and X. Z. Cui. 2020. “On the estimation of power spectral density and lagged coherence of time transformed nonstationary seismic ground motions and their use to simulate synthetic records.” J. Earthquake Eng. 2020 (Sep): 1–18. https://doi.org/10.1080/13632469.2020.1811176.
Hong, H. P., X. Z. Cui, and D. Qiao. 2021. “An algorithm to simulate nonstationary and non-Gaussian stochastic processes.” J. Infrastruct. Preserv. Resilience 2 (1): 1–15. https://doi.org/10.1186/s43065-021-00030-5.
Hong, H. P., and P. Hong. 2007. “Assessment of ductility demand and reliability of bilinear single-degree-of-freedom systems under earthquake loading.” Can. J. Civ. Eng. 34 (12): 1606–1615. https://doi.org/10.1139/L07-077.
Kafali, C., and M. Grigoriu. 2003. “Non-Gaussian model for spatially coherent seismic ground motions.” In Proc., ICASP9. Amsterdam, Netherlands: ISO Press.
Karlin, S. 2014. A first course in stochastic processes. Cambridge, MA: Academic Press.
Lee, C. S., and H. P. Hong. 2010. “Statistics of inelastic responses of hysteretic systems under bidirectional seismic excitations.” Eng. Struct. 32 (8): 2074–2086. https://doi.org/10.1016/j.engstruct.2010.03.008.
Liang, J., S. R. Chaudhuri, and M. Shinozuka. 2007. “Simulation of nonstationary stochastic processes by spectral representation.” J. Eng. Mech. 133 (6): 616–627. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:6(616).
Ma, F., H. Zhang, A. Bockstedte, G. C. Foliente, and P. Paevere. 2004. “Parameter analysis of the differential model of hysteresis.” J. Appl. Mech. 71 (3): 342–349. https://doi.org/10.1115/1.1668082.
Newmark, N. M., and E. Rosenblueth. 1971. Fundamentals of earthquake engineering. Englewood Cliffs, NJ: Prentice-Hall.
Percival, D. B., and A. T. Walden. 1993. Spectral analysis for physical applications. Cambridge, MA: Cambridge University Press.
Pousse, G., L. F. Bonilla, F. Cotton, and L. Margerin. 2006. “Nonstationary stochastic simulation of strong ground motion time histories including natural variability: Application to the K-net Japanese database.” Bull. Seismol. Soc. Am. 96 (6): 2103–2117. https://doi.org/10.1785/0120050134.
Priestley, M. B. 1965. “Evolutionary spectra and non-stationary processes.” J. R. Stat. Soc. 27 (2): 204–229. https://doi.org/10.1111/j.2517-6161.1965.tb01488.x.
Radu, A., and M. Grigoriu. 2018. “A site-specific ground-motion simulation model: Application for Vrancea earthquakes.” Soil Dyn. Earthquake Eng. 111 (Aug): 77–86. https://doi.org/10.1016/j.soildyn.2018.04.025.
Rezaeian, S., and A. Der Kiureghian. 2010. “Simulation of synthetic ground motions for specified earthquake and site characteristics.” Earthquake Eng. Struct. Dyn. 39 (10): 1155–1180. https://doi.org/10.1002/eqe.997.
Rodriguez, R. N. 1977. “A guide to the Burr type XII distributions.” Biometrika 64 (1): 129–134. https://doi.org/10.1093/biomet/64.1.129.
Rosenblueth, E. 1976. “Optimum design for infrequent disturbances.” J. Struct. Div. 102 (9): 1807–1825. https://doi.org/10.1061/JSDEAG.0004431.
Sabetta, F., and A. Pugliese. 1996. “Estimation of response spectra and simulation of nonstationary earthquake ground motions.” Bull. Seismol. Soc. Am. 86 (2): 337–352. https://doi.org/10.1785/BSSA0860020337.
Schreiber, T., and A. Schmitz. 1996. “Improved surrogate data for nonlinearity tests.” Phys. Rev. Lett. 77 (4): 635–638. https://doi.org/10.1103/PhysRevLett.77.635.
Schreiber, T., and A. Schmitz. 2000. “Surrogate time series.” Physica D 142 (3–4): 346–382. https://doi.org/10.1016/S0167-2789(00)00043-9.
Shields, M. D., and G. Deodatis. 2013. “Estimation of evolutionary spectra for simulation of non-stationary and non-Gaussian stochastic processes.” Comput. Struct. 126 (Sep): 149–163. https://doi.org/10.1016/j.compstruc.2013.02.007.
Shinozuka, M., and G. Deodatis. 1988. “Stochastic process models for earthquake ground motion.” Probab. Eng. Mech. 3 (3): 114–123. https://doi.org/10.1016/0266-8920(88)90023-9.
Shinozuka, M., and C.-M. Jan. 1972. “Digital simulation of random processes and its applications.” J. Sound Vib. 25 (1): 111–128. https://doi.org/10.1016/0022-460X(72)90600-1.
Spanos, P. D., J. Tezcan, and P. Tratskas. 2005. “Stochastic processes evolutionary spectrum estimation via harmonic wavelets.” Comput. Methods Appl. Mech. Eng. 194 (12–16): 1367–1383. https://doi.org/10.1016/j.cma.2004.06.039.
Stockwell, R. G., L. Mansinha, and R. P. Lowe. 1996. “Localization of the complex spectrum: The S transform.” IEEE Trans. Signal Process. 44 (4): 998–1001. https://doi.org/10.1109/78.492555.
Subbotin, M. T. 1923. “On the law of frequency of error.” Matematicheskii Sbornik 31 (Apr): 296–301.
Vanmarcke, E. H. 1976. “Structural response to earthquakes.” In Developments in geotechnical engineering, 287–337. New York: Elsevier.
Vlachos, C., K. G. Papakonstantinou, and G. Deodatis. 2016. “A multi-modal analytical non-stationary spectral model for characterization and stochastic simulation of earthquake ground motions.” Soil Dyn. Earthquake Eng. 80 (Jan): 177–191. https://doi.org/10.1016/j.soildyn.2015.10.006.
Yamazaki, F., and M. Shinozuka. 1988. “Digital generation of non-Gaussian stochastic fields.” J. Eng. Mech. 114 (7): 1183–1197. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:7(1183).
Yeh, C.-H., and Y. K. Wen. 1990. “Modeling of nonstationary ground motion and analysis of inelastic structural response.” Struct. Saf. 8 (1–4): 281–298. https://doi.org/10.1016/0167-4730(90)90046-R.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 148 • Issue 6 • June 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Sep 2, 2021
Accepted: Jan 19, 2022
Published online: Apr 13, 2022
Published in print: Jun 1, 2022
Discussion open until: Sep 13, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Wenliang Fan, Yuan Tian, Xiangqian Sheng, Simulation of a non-Gaussian stochastic process based on a combined distribution of the UHPM and the GBD, Probabilistic Engineering Mechanics, 10.1016/j.probengmech.2023.103438, 72, (103438), (2023).