A semi-analytic method to estimate the response spectrum of the synthetic acceleration records with evolutionary spectrum

Document Type : Article


1 Department of Civil Engineering, Engineering School, Shahed University, Tehran, P.O. Box 33191-18651, Iran

2 Department of Civil Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-4313, Iran


In this paper, we introduce a semi-analytic procedure for deriving the response spectrum of the synthetic acceleration records generated using the Double Frequency Model (DFM). DFM is a filtered white noise method for fully non-stationarity synthetic acceleration records. The proposed semi-analytic procedure is based on the theory of the first passage problem, which precludes time and computationally extensive methods e.g. Monte Carlo simulations. Assuming a slowly-varying envelope and evolutionary transfer functions, the procedure for estimating the elastic response of a structure is implemented in both time and frequency domains. Comparing the results of our model with previous models and approximations, we conclude that for a set of 10000 realizations of the DFM model, the semi-analytic model produces less than 10% error for 92% of the realizations. The accuracy of estimations is higher in the short-period compared to the long-period ranges of the response spectrum. Comparing the accuracy of approximations used to arrive at peak factors, results show that Michaelov et al's approximation executed in the frequency domain yields the best results compared to Poisson or Vanmarcke’s procedures.


1           References

[1]           Rezaeian, S. and Der Kiureghian, A., "A stochastic ground motion model with separable temporal and spectral nonstationarities", Earthquake Eng. Struct. Dyn.,  37(13), pp. 1565-1584 (2008).
[2]           Stafford, P., Sgobba, S., and Marano, G., "An energy-based envelope function for the stochastic simulation of earthquake accelerograms", Soil Dyn. Earthquake Eng.,  29(pp. 1123-1133 (2009).
[3]           Maechling, P. J., Silva, F., Callaghan, S., and Jordan, T. H., "SCEC Broadband Platform: System architecture and software implementation", Seismol. Res. Lett.,  86(1), pp. 27-38 (2014).
[4]           Sun, X., Hartzell, S., and Rezaeian, S., "Ground‐Motion Simulation for the 23 August 2011, Mineral, Virginia, Earthquake Using Physics‐Based and Stochastic Broadband Methods", Bull. Seismol. Soc. Am.,  105(5), pp. 2641-2661 (2015).
[5]           Kramer, S. L., Geotechnical earthquake engineering vol. 80: Prentice Hall Upper Saddle River, NJ, (1996).
[6]           Li, Y., Conte, J. P., and Barbato, M., "Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems", Earthquake Eng. Struct. Dyn.,  45(8), pp. 1271-1291 (2016).
[7]           Kiureghian, A. D. and Crempien, J., "An Evolutionary Model for Earthquake Ground Motion", Struct. Saf.,  6(pp. 235-246 (1989).
[8]           Beresnev, I. and Atkinson, G., "FINSIM: A FORTRAN program for simulating stochastic acceleration", Seismol. Res. Lett.,  69(pp. 27-32 (1998).
[9]           Motazedian, D. and Atkinson, G., "Stochastic finite-fault modeling based on a dynamic corner frequency", Bull. Seismol. Soc. Am.,  95(3), pp. 995-1010 (2005).
[10]         Papadimitriou, K., "Stochastic characterization of strong ground motion and application to structural response," Pasadena, CA EERL 90-03, 1990.
[11]         Pousse, G., Bonilla, L., Cotton, F., and Margerin, L., "Non stationary stochastic simulation of strong ground motion time histories including natural variability: Application to the K-net Japanese database", Bull. Seismol. Soc. Am.,  96(6), pp. 2103–2117 (2006).
[12]         Yamamoto, Y. and Baker, J. W., "Stochastic model for earthquake ground motion using wavelet packets", Bull. Seismol. Soc. Am.,  103(6), pp. 3044-3056 (2013).
[13]         Shinozuka, M. and Deodatis, G., "Stochastic process models for earthquake ground motion", Probabilist. Eng. Mech.,  3(3), pp. 114-123 1988/09/01/ (1988).
[14]         Chen, J., Kong, F., and Peng, Y., "A stochastic harmonic function representation for non-stationary stochastic processes", Mech. Syst. Signal. Pr.,  96(pp. 31-44 2017/11/01/ (2017).
[15]         Rezaeian, S. and Der Kiureghian, A., "Simulation of synthetic ground motions for specified earthquake and site characteristics", Earthquake Engineering & Structural Dynamics,  39(10), pp. 1155-1180 (2010).
[16]         Waezi, Z. and Rofooei, F. R., "On the Evolutionary Characteristics of the Acceleration Records Generated From Linear Time-Variant Systems ", Sci. Iranica,  26(6), pp. 2817-2831 (2017).
[17]         Waezi, Z. and Rofooei, F. R., "Stochastic Non-Stationary Model for Ground Motion Simulation Based on Higher-Order Crossing of Linear Time Variant Systems", J. Earthquake Eng., pp. 1-28 (2016).
[18]         Waezi, Z., Rofooei, F. R., and Hashemi, M. J., "A Multi-Peak Evolutionary Model for Stochastic Simulation of Ground Motions Based on Time-Domain Features", J. Earthquake Eng., pp. 1-37 (2018).
[19]         Alderucci, T., Muscolino, G., and Urso, S., "Stochastic analysis of linear structural systems under spectrum and site intensity compatible fully non-stationary artificial accelerograms", Soil Dyn. Earthquake Eng.,  126(p. 105762 2019/11/01/ (2019).
[20]         Kiureghian, A. D. and Fujimura, K., "Nonlinear stochastic dynamic analysis for performance‐based earthquake engineering", Earthquake Eng. Struct. Dyn.,  38(5), pp. 719-738 (2009).
[21]         Ferrer, I. and Sánchez-Carratalá, C. R., "Efficient estimation of the peak factor for the stochastic characterization of structural response to non-stationary ground motions", Struct. Saf.,  59(pp. 32-41 (2016).
[22]         Michaelov, G., Lutes, L. D., and Sarkani, S., "Extreme value of response to nonstationary excitation", J. Eng. Mech.,  127(4), pp. 352-363 (2001).
[23]         Barbato, M. and Vasta, M., "Closed-form solutions for the time-variant spectral characteristics of non-stationary random processes", Probabilist. Eng. Mech.,  25(1), pp. 9-17 2010/01/01/ (2010).
[24]         Barbato, M. and Conte, J. P., "Structural reliability applications of nonstationary spectral characteristics", J. Eng. Mech.,  137(5), pp. 371-382 (2011).
[25]         Clough, R. W. and Penzien, J., Dynamics of structures, 2 ed. Berkeley, CA USA: Computers & Structures, Inc., (1993).
[26]         Barbato, M. and Conte, J. P., "Time-Variant Reliability Analysis of Linear Elastic Systems Subjected to Fully Nonstationary Stochastic Excitations", J. Eng. Mech.,  141(6), p. 04014173 (2015).
[27]         Alderucci, T. and Muscolino, G., "Time–frequency varying response functions of non-classically damped linear structures under fully non-stationary stochastic excitations", Probabilist. Eng. Mech.,  54(pp. 95-109 2018/10/01/ (2018).
[28]         Yu, H., Wang, B., Gao, Z., and Li, Y., "An exact and efficient time-domain method for random vibration analysis of linear structures subjected to uniformly modulated or fully non-stationary excitations", J. Sound Vibrat.,  488(p. 115648 2020/12/08/ (2020).
[29]         Zhao, N. and Huang, G., "Efficient Nonstationary Stochastic Response Analysis for Linear and Nonlinear Structures by FFT", J. Eng. Mech.,  145(5), p. 04019023 (2019).
[30]         Xu, J. and Feng, D.-C., "Stochastic dynamic response analysis and reliability assessment of non-linear structures under fully non-stationary ground motions", Struct. Saf.,  79(pp. 94-106 2019/07/01/ (2019).
[31]         Xu, J., Ding, Z., and Wang, J., "Extreme value distribution and small failure probabilities estimation of structures subjected to non-stationary stochastic seismic excitations", Struct. Saf.,  70(pp. 93-103 2018/01/01/ (2018).
[32]         Waezi, Z. and Rofooei, F. R., "Stochastic Non-Stationary Model for Ground Motion Simulation Based on Higher-Order Crossing of Linear Time Variant Systems", J. Earthquake Eng.,  21(1), pp. 123-150 2017/01/02 (2017).
[33]         Amin, M. and Ang, A. H., "Nonstationary stochastic models of earthquake motions", J. Eng. Mech.,  94(2), pp. 559-584 (1968).
[34]         Priestley, M. B., "Evolutionary spectra and non-stationary processes", J. Roy. Stat. Soc. Ser. B. (Stat. Method.),  27(2), pp. 204-237 (1965).
[35]         Senthilnathan, A. and Lutes, L. D., "Nonstationary maximum response statistics for linear structures", J. Eng. Mech.,  117(2), pp. 294-311 (1991).
[36]         Shinozuka, M. and Yang, J.-N., "Peak structural response to non-stationary random excitations", J. Sound Vibrat.,  16(4), pp. 505-517 (1971).
[37]         Vanmarcke, E. H., "On the distribution of the first-passage time for normal stationary random processes", Journal of applied mechanics,  42(1), pp. 215-220 (1975).
[38]         Corotis, R. B., Vanmarcke, E. H., and Cornell, A. C., "First passage of nonstationary random processes", J. Eng. Mech.,  98(2), pp. 401-414 (1972).
[39]         Michaelov, G., Sarkani, S., and Lutes, L., "Spectral characteristics of nonstationary random processes—response of a simple oscillator", Struct. Saf.,  21(3), pp. 245-267 (1999).
[40]         Lutes, L. D. and Sarkani, S., Random vibrations: analysis of structural and mechanical systems. Burlington, MA 01803, USA: Butterworth-Heinemann, (2004).