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* Reference Channel
128 Sensors
Case 1
72 Sensors 40 Sensors
Case 2 Case 3
Figure 3. Sensor Locations.
sensors, case 2 uses 72 sensors and Case 3 uses 40 sensors.
Cross correlation functions were calculated as the inverse Fourier transform of the cross
spectral density function, and treated as free response data. For these calculations the reference
channel shown in Fig. 3 was selected. Frames of 512 points with 50% overlapping
were used to determine cross spectral density functions. A representative cross spectral
density and cross correlation function are shown in Fig. 4. Note that this structure may
have many closed spaced modes at very low frequencies, as is typical of large flexible
structures'such as cable stayed or suspension bridges.
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Figure 4. Representative Cross Spectral Density and Cross Correlation Functions.
The ERA was used to identify the modal parameters
from the cross correlation functions.
Figure 5 shows a typical singular values plot
obtained with the ERA. In most structures a
sharp drop in the values will occur, indicating
a finite number of singular values appropriate
for effective modeling of the structure (Juang
and Pappa, 1985: Caicedo et al, 2001). In this
case, this sharp drop is not present due to the
closely spaced modes. Here, the correct natural
frequencies and mode shapes are selected
by examining the identified damping ratio.
Only modes with damping ratios between 2.5
and 3.5% are accepted.
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Singular Value No.
Figure 5. Singular Values.
Table 1 provides the identified natural frequencies and the error in the frequency with respect
to the corresponding analytical value. Negative values indicates that the identified
natural frequency was higher than the analytical value. Vertical responses are analyzed independently
of transverse responses for this initial study, and thus torsional modes are not