Simulation of Seismic Motions by Stochastic ARMA Identification Based on ACF, PACF, and AIC Criterion
DOI:
https://doi.org/10.22399/ijcesen.4592Keywords:
ARMA model, Stochastic simulation, Earthquake ground motion, Near-field, seismic recordsAbstract
This study presents a stochastic approach for simulating earthquake ground motions using time-varying ARMA models with parameters fitted to real accelerograms. The ARMA model identification relies on the autocorrelation function (ACF), partial autocorrelation function (PACF), and the Akaike Information Criterion (AIC) to ensure optimal model order selection. The maximum likelihood technique is applied for parameter estimation. Near-field earthquakes recorded on dense soils in Algeria Boumerdes (2003) are synthesized using a moving time-window technique. Random sets of synthetic earthquakes are generated for each event to establish statistically valid structural response spectra. Key damage predictors, including peak linear displacement, ductility demand, and hysteretic energy, are computed from the mean and variance of response spectral ordinates and compared with spectra based on single earthquake records. Results show that low-order ARMA (2,1) models, excited by Gaussian white noise and amplitude-modulated with a simple envelope function, reliably reproduce both the nonstationary amplitude and frequency content of real earthquake records. This highlights the effectiveness of the proposed methodology for seismic motion simulation and structural damage assessment.
References
[1] Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.
[2] Bouhadad, Y., Meghraoui, M., & Ayadi, A. (2004). Seismicity and active tectonics in Northern Algeria. Journal of Seismology, 8(3), 303–320.
[3] Box, G.E.P., Jenkins, G.M., Reinsel, G.C., & Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley, New York, USA.
[4] Box, G.E.P., & Jenkins, G.M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco, USA.
[5] Box, G.E.P., Jenkins, G.M., & Reinsel, G.C. (1994). Time Series Analysis: Forecasting and Control (3rd ed.). Prentice Hall, Englewood Cliffs, NJ, USA.
[6] Brillinger, D.R. (1981). Time Series: Data Analysis and Theory. McGraw-Hill, New York, USA.
[7] Chopra, A.K. (2012). Dynamics of Structures: Theory and Applications to Earthquake Engineering (4th ed.). Prentice Hall, New Jersey, USA.
[8] Clough, R.W., & Penzien, J. (2003). Dynamics of Structures (3rd ed.). Computers and Structures Inc., Berkeley, California, USA.
[9] CGS (2003). Report on the Boumerdes Earthquake. National Center for Seismic Engineering, Algeria.
[10] Deodatis, G. (1996). Simulation of ergodic multivariate stochastic processes. Journal of Engineering Mechanics (ASCE), 122(8), 778–787.
[11] Laouami, M., et al. (2004). Seismic characterization and recording of the Boumerdes shocks (2003). Algerian Journal of Geophysics, 12(2), 45–58.
[12] Lay, T., & Wallace, T.C. (1995). Modern Global Seismology. Academic Press, San Diego, USA.
[13] Papoulis, A., & Pillai, S.U. (2002). Probability, Random Variables and Stochastic Processes (4th ed.). McGraw-Hill, New York, USA.
[14] USGS / ISC (1980). Chlef (El Asnam) earthquake, 10 October 1980. USGS Earthquake Catalog.
[15] Park, Y. T., Ang, H.-S., and Wen, Y. K. (1984). Seismic damage analysis and damage-limited design of reinforced concrete buildings. Structural Research Series No. 516, Department of Civil Engineering, University of Illinois, Urbana, IL.
[16] Pradlwarter, H. J. (1987). Estimation of modulating functions of earthquake records. In Proceedings of the U.S.–Austria Workshop on Stochastic Structural Dynamics, Florida Atlantic University, Boca Raton, FL.
[17] Riddell, R., and Newmark, N. M. (1979). Force–deformation models for nonlinear behavior. Journal of the Structural Division, ASCE, 105(12), 2773–2790.
[18] Turkstra, C. J., Tallin, A. G., Brahimi, M., and Kim, H. J. (1987). The use of ARMA models to measure damage potential in seismic records. National Center for Earthquake Engineering Research (NCEER), Report No. NCEER-88-0032.
[19] Zarah, T. F., and Hall, W. J. (1984). Earthquake energy absorption in SDOF structures. Journal of the Structural Division, ASCE, 110(8), 1757–1772.
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