This study focuses on the modeling and simulation of non-stationary transient events such as earthquake ground motions and extreme wind events characterized by time-varying amplitude and frequency features. Modeling and simulation of transient events, e.g., earthquake ground motions, hurricane/downburst wind loads, is of great importance due to limited number of available time histories of these extreme events, and the significance of these load effects on structures. Various attempts to realize numerical simulation of non-stationary random processes have been reported in the literature where non-stationarity in the frequency contents of target processes is often neglected due to modeling convenience. However, studies have shown that temporal variations in frequency may have a significant impact on structural response especially in the inelastic range. In order to address these needs that currently preclude desired level of accuracy in the response analysis, time-frequency modeling and analysis tools are introduced in this study that include the Hilbert and wavelet transforms. Following an extensive literature review concerning the simulation of non-stationary random processes, modeling and simulation of transient events utilizing time-frequency representation are presented with examples of ground motion and gust front winds. The evolutionary characteristics of transient events like earthquake ground motion, gust front winds, and transient wave fronts are first modeled utilizing a time-frequency domain framework. Application of the wavelet and Hilbert transforms in tandem revealed that the instantaneous frequency of transient signals, e.g., downburst winds and earthquakes at each of the frequency bands considered followed the Gaussian distribution. This observation served as a key role in the development of a simulation methodology for non-stationary processes that preserves both amplitude and frequency modulation features of the process. In this scheme, the stationary wavelet transform is first introduced to decompose a sample of a non-stationary random process into a set of mono-component signals. These components are then transformed to analytic signals using the Hilbert transform which yields their instantaneous amplitude and frequency. Without the customary assumption of piece-wise stationarity, or an assumed modulation function, this method helps to simulate non-stationary random processes based on a given sample realization. The univariate simulation scheme is extended to multi-variate cases by introducing the proper orthogonal decomposition (POD) of the covariance matrix of the instantaneous frequency. Several quantitative criteria are employed to assess the quality of non-stationary simulations. Examples involving the simulation of measured ground motions and downburst wind velocity data are presented to demonstrate the efficacy of the proposed scheme.
Finally, a framework for the conditional simulation of non-Gaussian non-stationary space-time random processes is presented. Focusing on time-frequency description of non-stationary random fields, the evolutionary cross-correlation structure of non-stationary random fields is established analytically in terms of wavelet coefficients. By extending kriging technique to the time-frequency domain, the proposed method facilitates conditional simulation of non-stationary random fields with known time-dependent correlation structure. Numerical examples concerning the conditional simulation of downburst wind velocities are presented to demonstrate the accuracy and efficacy of the method. This technique has immediate applications to earthquake engineering, wind engineering and ocean engineering in simulating additional time history when only measurements at limited locations are available.
This study provides emerging tools for generating input to the Monte Carlo-based simulation methods for structural response and reliability analysis, particularly for cases involving transient environmental loads.
Date Modified
2017-06-02Defense Date
2007-12-03Research Director(s)
Joseph M. PowersCommittee Members
Tracy L. Kijewski-Correa
Ahsan Kareem
David J. Kirkner
Flint O. ThomasAlternate Identifier
etd-12202007-163138Publisher
University of Notre DameProgram Name
- Civil Engineering and Geological Sciences