Nonstationary ARMA modeling of seismic motions

Abstract Discrete time-varying autoregressive — moving average (ARMA) models are used to describe realistic earthquake ground motion time histories. Both amplitude and frequency nonstationarities are incorporated in the model. An iterative Kalman filtering scheme is introduced to identify the time-varying parameters of an ARMA model from an actual earthquake record. Several model verification tests are performed on the identified model. Applications of these identification and verification procedures are given and show that the proposed models and identification algorithms are able to capture accurately the nonstationary features of real earthquake accelerograms, especially the time-variation of the frequency content. The well-known Kanai-Tajimi earthquake model is covariance equivalent with a subset of the low order ARMA(2,1) model. Using the results and methodology of this study, the parameters of a time-varying Kanai-Tajimi earthquake model can be estimated from a target earthquake record or they can be directly associated with characteristic earthquake features such as predominant frequency and frequency bandwidth.

[1]  M. Shinozuka,et al.  Auto‐Regressive Model for Nonstationary Stochastic Processes , 1988 .

[2]  R. M. Oliver,et al.  Simulating and analyzing artificial nonstationary earthquake ground motions , 1982 .

[3]  C. Page.  Instantaneous Power Spectra , 1952 .

[4]  W. J. Hall,et al.  Procedures and Criteria for Earthquake-Resistant Design , 1975 .

[5]  Pol D. Spanos,et al.  Simulation of Stationary Random Processes: Two-Stage MA to ARMA Approach , 1990 .

[6]  S. C. Liu.  Evolutionary power spectral density of strong-motion earthquakes , 1970 .

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

[8]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Ahmet S. Cakmak,et al.  Modelling earthquake ground motions in California using parametric time series methods , 1985 .

[10]  Konstantinos Papadimitriou.  Stochastic Characterization of Strong Ground Motion and Applications to Structural Response , 1990 .

[11]  W. Gersch,et al.  Time Series Methods for the Synthesis of Random Vibration Systems , 1976 .

[12]  G. Kitagawa.  Changing spectrum estimation , 1983 .

[13]  Ahmet S. Cakmak,et al.  Simulation of earthquake ground motions using autoregressive moving average (ARMA) models , 1981 .

[14]  H. G. Natke,et al.  System identification techniques , 1986 .

[15]  Andrejs Jurkevics,et al.  Representing and simulating strong ground motion , 1978 .

[16]  P-T. D. Spanos,et al.  ARMA Algorithms for Ocean Wave Modeling , 1983 .

[17]  Vitelmo V. Bertero,et al.  Uncertainties in Establishing Design Earthquakes , 1987 .

[18]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[19]  Norman A. Abrahamson,et al.  The SMART I Accelerograph Array (1980-1987): A Review , 1987 .

[20]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[21]  Armen Der Kiureghian,et al.  Seismic hazard analysis : improved models, uncertainties and sensitivities , 1988 .

[22]  G. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

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