Stochastic Model for Earthquake Ground Motion Using Wavelet Packets

Abstract

For performance-based design, non-linear dynamic structural analysis for various types of input ground motions is required. Stochastic (simulated) ground motions are sometimes useful as input motions, because unlike recorded motions they are not limited in number and because their properties can be varied systematically to understand the impact of ground motion properties on structural response. Here a stochastic ground motion model with time and frequency nonstationarity is developed using wavelet packets. Wavelet transform is a tool for analyzing time-series data with time and frequency nonstationarity, as well as simulating such data. Wavelet packet transform is an operation that decomposes time-series data into wavelet packets in the time and frequency domain, and its inverse transform reconstructs a time-series from wavelet packets. The characteristics of a nonstationary ground motion therefore can be modeled intuitively by specifying the amplitudes of wavelet packets at each time and frequency. In the proposed model, 13 parameters are sufficient to completely describe the time and frequency characteristics of a ground motion. These parameters can be computed from a specific target ground motion recording or by regression analysis based on a large database of recordings. The simulated ground motions produced by the proposed model reasonably match the target ground motion recordings in several respects including the spectral acceleration, inelastic response spectra, duration, bandwidth, and time and frequency nonstationarity. In addition, the median and logarithmic standard deviation of the spectral acceleration of the simulated ground motions match those of the published empirical ground motion prediction. These results suggest that the syntheti c ground motions generated by the proposed model can be used for the non-linear dynamic structural analysis as the input ground motions.