Abstract
A technique for fitting the multi-dimensional time-varying autoregressive model to a set of three components of earthquake ground motion and for generating the three dimensional nonstationary stochastic process from the fitted model are proposed. From section 2 to section 3, Levinson-Durbin's recursive algorithm for fitting the time-invariant autoregressive model to an observed data sequence of a stationary process, generalized Levinson-Szego's algorithm for solving general prediction problems and Monden-Yamada-Arimoto's fast recursive algorithm for tracking both orders and parameters of time-varying autoregressive models based on Akaike's information criterion are introduced. Section 4 gives a verification of efficiency of Monden-Yamada-Arimoto's algorithm through the computer simulations. In section 5, a technique for generating the three dimensional simulated earthquake ground motion is presented. Descriptions of multi-dimensional time-varying transfer function and power spectral density function using the fitted autoregressive parameters are given in section 6. In section 7, a numerical example of the fitting problem to actual earthquke records is presented. The time-varying parameters of the autoregressive model fitted to the velocity records of El-centro 1940 earthquake, the sample wave forms generated from the fitted model, the velocity response spectra computed with the sample wave forms, the time-varying power spectral density function and the time-varying transfer function are illustrated in this section. This paper shows an approach to gain an optimal time-varying autoregressive model fitting to actual earthquake records without any assumptions on orders and parameters of the model.
