Modelling and Simulation of Earthquake Ground Motion via Functional Series TARMA Models withWavelet Basis Functions

The present study explores non-stationary Functional Series Time-dependent AutoRegressive Moving Average (FS-TARMA) models with wavelet basis functions for the modelling and simulation of earthquake ground motion. FS-TARMA models constitute conceptual extensions of their conventional (stationary) counterparts, in that their parameters are time-dependent belonging to functional subspaces [1]. Wavelets, with their scaling and localization in time, comprise a promising functional basis for “fast” evolutions in the dynamics. The study focuses on the assessment of wavelet based FS-TARMA modelling and simulation for two California earthquake ground motion signals: an El Centro accelerogram recorded during the 1979 Imperial Valley earthquake, and a Pacoima Dam accelerogram recorded during the 1994 Northridge earthquake. A systematic analysis leads to a TARMA(2, 2) model for the El Centro case and a TARMA(3, 2) model for the Pacoima Dam case. Both models are formally validated and their analysis and simulation (synthesis) capabilities are demonstrated via Monte Carlo experiments focusing on important ground motion characteristics. Open image in new window Figure 1 (a) 2-D plot of the El Centro accelerogram non-parametric STFT-based time-dependent PSD estimate, and (b) 2-D plot of the TARMA (2,2)[2,2]-based parametric Melard-Tjostheim time-dependent PSD estimate.

[1]  Joel P. Conte,et al.  Nonstationary ARMA modeling of seismic motions , 1992 .

[2]  G. Kitagawa,et al.  A time varying AR coefficient model for modelling and simulating earthquake ground motion , 1985 .

[3]  Yves Grenier,et al.  Time-dependent ARMA modeling of nonstationary signals , 1983 .

[4]  Spilios D. Fassois,et al.  A polynomial-algebraic method for non-stationary TARMA signal analysis , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[5]  Theodor D. Popescu,et al.  Analysis and simulation of strong earthquake ground motions using ARMA models , 1990, Autom..

[6]  Pol D. Spanos,et al.  Wavelets : Theoretical concepts and vibrations related applications , 2005 .

[7]  Karl S. Pister,et al.  Arma models for earthquake ground motions , 1979 .

[8]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[9]  G. N. Fouskitakis,et al.  Functional series TARMA modelling and simulation of earthquake ground motion , 2002 .

[10]  Genshiro Kitagawa,et al.  A time varying coefficient vector AR modeling of nonstationary covariance time series , 1993, Signal Process..

[11]  G. Kitagawa.  Smoothness priors analysis of time series , 1996 .

[12]  Spilios D. Fassois,et al.  Parametric time-domain methods for non-stationary random vibration modelling and analysis — A critical survey and comparison , 2006 .

[13]  Y. Grenier.  Parametric Time-Frequency Representations , 1989 .

[14]  G. Kitagawa,et al.  A smoothness priors time-varying AR coefficient modeling of nonstationary covariance time series , 1985, IEEE Transactions on Automatic Control.