Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil Engineering

Committee Chair

Ayhan Irfanoglu

Committee Member 1

Santiago Pujol

Committee Member 2

Robert L. Nowack

Committee Member 3

Mete A. Sozen


A new structural mode-identification approach, called the Phase Difference Index plot (PDI plot), is used to identify the natural modes in a building from its acceleration records response to earthquake ground motion. The phase difference index can be calculated by the Hilbert transform of displacement response curves obtained from acceleration records at two different floors in the building. The torsional mode can also be identified if two accelerometers are installed on opposite sides in a floor. To demonstrate the power of the new approach, earthquake acceleration records from ten buildings in Taiwan and the U.S. are used. After applying narrow band-pass filter (frequency bandwidth of 0.05-0.1 Hz) to the acceleration records, and then using Hilbert transform on pairs of displacement records on chosen floors (obtained from the acceleration records), the phase difference between the corresponding pair of designated floors can be calculated. The cosine of the phase difference angle of the two displacement curves is defined as the phase difference index (PDI). The phase difference index versus frequency graph forms a PDI plot. Structural behavior at chosen floors and in various frequency bands can be found by studying the PDI plot. From comparison of PDI plot and typical building mode shapes obtained based on estimated stiffness and mass distribution, the natural modes can be identified. The method has been tested for accuracy and limitations by applying it to data obtained from numerical simulations. Response of one full scale four-story model in Japan, and ten actual buildings in U.S. and Taiwan have been studied using the proposed method. It is shown that using the PDI plot method more modes of a building can be identified confidently compared to traditional frequency-domain and time-domain based methods.