Variations in the Dynamic Properties of Structures:
The Wigner-Ville Distribution

  &

Time Frequency Representations of Seismic Signals

1906 San Francisco Earthquake 100th Anniversary Conference

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I presented these posters at the 1906 Centennial Conference (Official Conference Website).

During the EERI opening reception (Monday evening), I gave a brief overview of time-frequency methods, and discussed their applications to seismic records. Then on Tuesday, during the afternoon poster session, I described the application of these techniques in more detail. As always, please feel free to e-mail me if you have any questions.



TIME-FREQUENCY REPRESENTATIONS OF SEISMIC SIGNALS
Samuel Case Bradford, Thomas H Heaton

Presented during EERI / 8NCEE Opening Night Reception and Poster Session (17 April 2006).

Introduction
A Fourier Transform of a building record contains information regarding frequency content of a signal, but it cannot resolve the exact onset of changes in frequency -- all temporal resolution is contained in the phase of the transform. The spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. To overcome this restriction, several classes of Time-Frequency representations have been proposed, including wavelet methods and quadratic time-frequency distributions such as the Wigner-Ville distribution.


Poster: bradford_poster
(A0 size, ~33" x 47")



VARIATIONS IN THE DYNAMIC PROPERTIES OF STRUCTURES:
THE WIGNER-VILLE DISTRIBUTION

Samuel Case Bradford, Jing Yang, Thomas H Heaton

Presented in EERI poster session,
T49: Experimental and Analytical Simulation of Structures,
(18 April 2006, 4:00PM), at the 1906 centennial conference.

Abstract
The Wigner-Ville Distribution (WVD) is a promising method for analyzing frequency variations in seismic signals, including those of interest for structural monitoring. Nonlinearities in the force displacement relationship will temporarily decrease the apparent natural frequencies of structures during strong to moderate excitation, and earthquake damage can permanently change building stiffnesses. A Fourier Transform of a building record contains information regarding frequency content, but it can not resolve the exact onset of changes in natural frequency -- all temporal resolution is contained in the phase of the transform. The spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Time-frequency transformations such as the WVD allow for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. We develop a mathematical foundation for analyzing the evolution of frequency content in a signal, and apply these techniques to synthetic records from linear and nonlinear FEM analysis (including plastic rotation and weld fractures). Our analysis techniques are then applied to earthquake records from damaged buildings.


Paper:bradford_1906.pdf
Poster: bradford_poster2.png
(~51" x 36")



case@caltech.edu
Last modified: Fri May 5 15:46:35 PDT 2006