Hilbert-Huang-transform based modelling and simulation of nonstationary processes and applications to earthquake engineering.

摘要

The Hilbert-Huang-Transform method is extended in developing a theoretical basis for spectral representation of univariate and multivariate nonstationary random processes based on the sample records. Three simulation methods are developed, namely, IMF Recombination Method, Improved Wen-Yeh Method, and Fixed Frequency Method. Relation between Hilbert Marginal Spectrum and Fourier Energy Spectrum and relation between Hilbert spectrum and evolutionary spectrum are derived. Unlike most existing methods, these methods do not need assumptions of piece-wise stationarity or any analytical function forms of the spectra which are unknown a priori. Applications to spectral characterization and simulation of earthquake ground motions show that the Hilbert spectra give a clear description of the time-varying spectral content of the motions and the simulated samples represent an accurate statistical image of the records. The response spectra compare well with those of the records and retain the jagged look.; The methods are further applied to generation of Uniform Hazard Earthquake Response Spectrum and Ground Motions. A record-based methodology is proposed and demonstrated by an example at Los Angeles. The resulting UHRS compare well with those of USGS and SAC. The method does not rely on theories or empirical models, such as the rupture models, attenuation relation, Fourier spectrum and it preserves the variability across the ensemble. It uses only free-field records from the local region with similar seismicity environment and does not scale the records, consequently, the UHGM are truly site-dependent. It considers the strikes of the major faults near the site and the difference between the fault normal and fault parallel directions, and provides UHRS and three-component UHGM in three orthogonal directions.