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history to be polluted. In the second way named as NC2, different noise processes are added to the
dynamic responses of the same floor. As a result, the three different noise processes are simulated and
used in NC1 while the nine different noise processes are simulated and used in NC2. Moreover, three
noise levels of 1%, 3% and 5% are considered in NCI whereas NC2 considers three noise levels of 1%,
2%, and 3%. The identification results are listed in Table 3 2 and Table 3.3 for NCI and NC2,
respectively.
TABLE3.2
IDENTIFICATION RESULTS FROM NOISE-POLLUTED BUILDING RESPONSES (NCI)
Noise Level
1%
Estimated Error
3%
Estimated Error
5%
Estimated Error
Cj
C2
C3
ki
k 2
k 3
PGA
4409.6
294.73
147.52
4727325
315159
157559
1.2097
0.93%
1.18%
1.32%
0.02%
0.02%
0.03%
0.8%
4510.6
302.29
151.58
4726698
315047
157483
1.229
3.24%
3.78%
4.11%
0.04%
0.06%
0.08%
2.41%
4642.6
310.97
155.92
4727935
314917
157365
1.248
6.26%
6.75%
7.09%
0.01%
0.10%
0.16%
4%
PGA(m/s~): Peak ground acceleration identified
TABLE3.3
IDENTIFICATION RESULTS FROM NOISE-POLLUTED BUILDING RESPONSES (NC2)
XT . T , 1% 2% 3%
iNUIbC l_,CVCi
C]
C2
C3
k,
k 2
k 3
PGA
Estimated
4276.9
283.66
144.21
4673818
312894
156761
1.1952
Error
2.11%
2.62%
0.96%
1.15%
0.74%
0.54%
0.4%
Estimated
4325.7
274.55
140.69
4569663
307930
155069
1.1796
PGA(m/T): Peak ground acceleration identified
Error
0.99%
5.75%
3.37%
3.36%
2.32%
1.61%
1.7%
Estimated
4514.2
264.94
135.52
4488512
302899
151148
1.15
Error
3.32%
9.05%
6.93%
5.07%
3.91%
4.09%
4.16%
From Table3.2, one may see that the dynamic compound inverse method can accurately identify the
stiffness coefficients even though the noise contamination in the responses reaches a 5% level. For the
damping coefficients and the peak acceleration of ground motion, the capacity of the method against
noise contamination seems to be relatively weak. The maximum identification errors of damping
coefficient are 1.32%, 4.11% and 7.09% for noise level of 1%, 3% and 5%, respectively. The
identified time history of input ground motion is shown in Fig. 3.6 for a noise level of 5% in NCI. It is
seen that the identified one is quite close to the true one, with the maximum error of the peak
acceleration of 4%. For NC2 where different noise processes are added to different types of structural
responses at the same floor, the identification errors increase moderately for damping coefficients and
input peak acceleration but considerably for stiffness coefficients when compared with NCI. The
maximum identification errors in damping coefficients are 2.62%, 5.75% and 9.05% for noise level of
1%, 2% and 3%, respectively. The maximum identification errors in stiffness coefficients are 1.15%,
3.36% and 5.07% for noise level of 1%, 2% and 3%, respectively. The estimated ground acceleration
motion for a 3% noise level in NC2 is plotted in Fig.3.7. The peak acceleration of the estimated ground
motion is found to be lower than the true peak acceleration by 4.2%.