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same except for the initial values for the structural parameters selected in order to examine the
sensitivity of the method to these assumed values. The initial values of the structural parameters for
Cases 1 to 4 are given in TableS.l in bracket together with the identified results. Cases A to D in Table
3.1 are the cases using the different number of sampling points L but with the same initial value. For
all the cases, the convergence indices are set as 10~ 6 . For Casel, the convergence curve, which is
defined as the variation of the identified value normalized by the actual value with the iterative time, is
depicted in Fig.3.3 and Fig.3.4 for building damping and stiffness parameters, respectively.
It is seen from Table 3.1 that the stiffness parameters identified by the dynamic compound inverse
method are almost the same as the true values for all the cases including Case D where the sample
points of only 200 are used. For the damping parameters, the maximum relative estimation error is less
than 0.1%. It can be also seen that even for very poor initial values selected as in Case 4, the true
structural parameters can be still identified. Thus, one may conclude that the accuracy of the identified
method is not sensitive to initial values of the structural parameters selected. From the convergence
curves shown in Fig.3.3 and Fig.3.4, it is clearly demonstrated that with the increase of iteration times
the estimated parameters converge rapidly to the true values. Moreover, the input ground motion
identified is found to be nearly the same as the real input acceleration.
Case
L
Cl
Ci
C3
ki
k 2
k*
TABLE3.1
IDENTIFICATION RESULTS FROM NOISE-FREE BUILDING RESPONSES
2
3 4 A B C
4000 4000 4000 2000 1000 500
4370.9(1000) 4370.9(-1) 4370.9(-0.32) 4370.9 4370.9 4369.7
291.37(1000) 291.37(-1) 291.37(1000) 291.37 291.37 291.35
145.60(1000) 145.59(-1) 145.58(1.2) 145.59 145.59 145.48
4728337(1000) 4728370(1) 4728308(0.03) 4728306 4728306 4728482
315210(1000) 315208(1) 315208(-1234) 315208 315208 315216
157581(1000) 157581(1) 157581(23232) 157581 157581 157584
1
4000
4370.9(1)
291.36(1)
145.59(1)
4728307(1)
315208(1)
157581(1)
L: Number of sampling points used
D
200
4369.5
291.39
145.57
4728495
315219
157586
\
-.r
c,
t
80 100 120 140
Iteration times
Fig.3.3 Convergence curve for damping
coefficients
Q 20 40 60 80 100 120 140
Iteration times
Fig.3.4 Convergence curve for stiffness
coefficients
Noise-polluted Cases
To assess the capacity of the dynamic compound inverse method against measurement noise in the
responses, the numerically generated zero-mean Gaussian white noise is added to the measured
responses in two ways. In the first way, which is denoted as NCI (noise easel), the identical noise
process is added to the displacement, velocity and acceleration responses of the same floor with the
noise level controlled by the root-mean-square ratio between the noise process and the response time-