Geology Reference
In-Depth Information
Table 6. Actual and identified parameters for the 15-story shear building due to structural damage
Parameter
Actual
values
Identified values
Noise-free
2% noise
4% noise
6% noise
k
14
*
D
14
k
15
D
15
38480
700
16800
168
38469 (0.03%)
695.36(0.66%)
16797 (0.02%)
166.34(0.99%)
38415 (0.17%)
690.72 (1.33%)
16761 (0.23%)
164.68 (1.98%)
38291 (0.49%)
676.87 (3.30%)
16694 (0.63%)
159.71 (4.94%)
38118 (0.94%)
698.75 (4.57%)
16610 (1.13%)
155.89 (7.21%)
k
1
**
D
1
k
D
2
k
D
3
51600
645
63400
634
72700
727
51596 (0.01%)
643 (0.31%)
63392 (0.02%)
632 (0.32%)
72688 (0.02%)
724 (0.41%)
51223 (0.73%)
660.80 (2.46%)
62935 (0.73%)
656.15 (3.49%)
72157 (0.75%)
754.73 (3.81%)
50652 (1.84%)
678.68 (5.22%)
62230 (1.85%)
682.05 (7.58%)
71335 (1.88%)
787.71 (8.35%)
50272 (2.57%)
687.95 (6.66%)
61760 (2.59%)
696.09 (9.79%)
70786 (2.63%)
805.91 (10.85%)
Note: The numbers in parentheses indicates % error in identified parameter.
* Case 1: Damage in columns of fourteenth floor.
** Case 2: Damage in columns of first floor.
The modeling of continuous dynamic systems us-
ing bond graphs is carried out using finite-mode
bond graphs as described before. This example
demonstrates the health assessment of a reinforced
concrete high-rise building using the finite-mode
bond graphs. It may be recalled here that the
modal analysis technique is used to model the
continuous system with an equivalent discretized
multi-degree-of-freedom system. The bond graph
and temporal causal graph models of the building
are shown in Figure 6. The bond graph and TCG
graph model the structural components and the
sensor as well. The structure is taken to be sub-
jected to a simulated Kanai-Tajimi random ground
acceleration at the support points and the response
measurement is taken as the displacement at the
tip point of the structure. The input acceleration
and simulated displacement measurements with
5% noise are shown in Figure 10.
The structure properties used in simulating the
sensor measurements are taken as
h
= 75.00 m,
E
= 2.0
×
1010 N/m
2
and mass density of 2500
kg/m
3
. The structure is taken to have a uniform
cross sectional area of 8.00 m outer diameter and
7.20 m inner diameter. A modal viscous damping
of 5% damping ratio is assumed for all modes.
The first 5 modes are considered in the health
assessment analysis. The free vibration analysis
was carried out analytically (Blevins, 1979).
Damage in the structural components is mod-
eled as a reduction of 20% in the stiffness of the
structure. The sensor fault is modeled as either bias
of 0.02 m or drift function of 0.002
t
, at
t
= 5.0
s. Figure 10 shows the input load and simulated
noisy measurements (5% noise level). Possible
damage scenarios are taken as changes in modal
stiffness and damping in all modes. It should be
noted here that the transformer index (TF = the
participation factor) is a positive quantity for
odd modes and is negative for even modes. For
the case of structural damage, the identification
algorithm detects damage and isolates it to be in
the modal stiffness or modal damping. Similarly,
the identification algorithm successfully isolates
the sensor fault (bias or drift) to be the sensor.
In this example, damage detection and
qualitative damage isolation are carried out. It is
possible to perform damage quantification using
the least-squares method to quantify the modal
parameters. To do this, additional sensors should
be placed for collecting required measurements
for the quantification process. Given that changes
in the modal parameters of the structure provide
a measure of the structural damage at the global
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