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identification results of structural parameters while the averaged value x (t) obtained in stepS gives
the time history of the ground motion.
The key point of this improved method is the statistical average process in Steps 3 and 4, which
actually provides a measure to convert the dynamics of structure under earthquake excitation into a
mathematical condition that ensures the convergency of the iterative procedure. Moreover, the
statistical average process is independent from the parameter identification algonthm chosen. In this
connection, for special cases different parameter identification methods can be adopted instead of the
least-squares method.
NUMERICAL EXAMPLES
The applicability of the dynamic compound inverse method is
demonstrated in this section through a numerical example of a 3-
story shear building (see Fig.3.1) under earthquake excitation (see
Fig. 3.5) for both noise-free and noise contamination cases. The
properties of the building, as used by Yang and Agrawal (2000 j for
a high tech building, are mi=350,25,m 2 =262.29 and m 3 =175.13/0rc;
ci=4369, C2-291.3 and c 3 =145.6&Vs/m; ki=4728400, k 2 =315230
and k3-157610AW/m. The three natural frequencies of the building
"'
are computed as 3.447, 7.372 and 19.155 Hz, with the
corresponding modal damping ratios are 1%, 2.14% and 5.56%,
respectively. The peak acceleration of the input ground motion is
120cm/s 2 . The sampling time interval of the ground motion is
" s
0.02s and the time duration is 80s, resulting in a total of sampling Fig3.1 3-story shear building
points N=4000. The dynamic responses of the building are
computed by the Wilson-0 algorithm and are then taken as the measured responses in the following to
identify both the structural parameters and the ground motion. The computed (measured) relative
displacement, velocity and acceleration responses of the top floor are depicted in Fig. 3.2(a) to (c),
respectively.
Time (sec)
Time (sec)
(a) Displacement (b) Velocity (c) Acceleration
Fig.3.2. Computed dynamic responses of the top floor of the building
Noise-free Case
The measured dynamic responses without noise contamination are first used to identify the structural
parameters and the* input acceleration ground motion with the dynamic compound inverse method. The
identification results are summarized in TableS.l, in which the conditions in Cases 1 to 4 are all the