Geology Reference
In-Depth Information
Table 5. Numerical values for mass, stiffness and damping coefficient for the 15-story building
Floor No.
1
2
3
4
5
6
7
8
Mass (kg)
Stiffness
×
10
3
(N/m)
Damping (N s/m)
103.2
64.5
645
97.2
63.4
634
97.2
72.7
727
95.3
72.1
721
100.2
68.7
687
108.1
52.3
523
76.6
48.5
600
80.0
51.5
650
Floor No.
9
10
11
12
13
14
15
Mass (kg)
Stiffness
×
10
3
(N/m)
Damping (N s/m)
90.0
48.1
700
90.0
68.7
687
108.1
52.3
523
76.6
48.5
600
80.0
51.5
650
90.0
48.1
700
70.0
16.8
168
the columns of the fourteenth floor due to devia-
tion of displacement measurements x
14
. Similar
analyses with 2%, 4% and 6% noise level are also
carried out and the identification algorithm detects
and isolates the damage to be in the fourteenth
floor. Herein, the Z-test is used to detect the dam-
age. The parameters
N N
9.1.1.2 Faults in Sensors
Damage in sensors is performed by simulating
sensor measurements of the fourteenth floor
displacement as bias (0.02 m) or drift (0.002
t
)
functions from the true measurements at
t
= 5.0
s (Figure 9). The diagnosis algorithm correctly
detects the fault to be in the sensor at the four-
teenth floor, since no other damage cause provides
similar damage signatures. To quantify the bias
value, the two measurements at the fourteenth
floor are subtracted. Notwithstanding that the
bias function contains noise, the average value,
however, was found to be about 0.019 m which
is close to the correct value. Alternatively, the
true and measured data can be denoised before
computing the bias value. For the noise-free case,
the difference leads to correctly quantifying the
bias value to be 0.02 m.
Further numerical analyses with faults simu-
lated in the sensor measuring the displacement
response of the first floor were also conducted.
The health assessment algorithm successfully
detects, isolates, and quantifies the correct damage
to be in the first floor sensor.
1
, ,
α
were taken as 50,
5 and 1.0, respectively. The quantitative identifi-
cation scheme described in Section 7 leads to
identifying the stiffness and damping parameters
of the last two floors, see Table 6. For noise-free
measurements, the identified stiffness and damp-
ing parameter of the last two floors contain very
small errors. For 2% noise measurements, the
reduction in the stiffness was identified close 19%.
The accuracy of the identified parameters was
seen to decrease for higher values of noise (see
Table 6). Denoising of sensor measurements will
definitely improve the accuracy of the identified
parameters.
It was found that the time step of the ground
acceleration of 0.01 s provides inaccurate results.
Therefore, interpolation of the ground acceleration
at smaller time period of 0.005 s was performed.
Similar analyses with damage simulated as reduc-
tion in the stiffness of the first floor columns were
also conducted and the health assessment algo-
rithm was found to detect and isolate the damage
successfully. Some of these results are provided
in Table 6. Note that
s
= 6 in this case.
9.2 Health Assessment of a High-
Rise Building under Simulated
Kanai-Tajimi Acceleration
In the previous example discrete structures were
modeled using one-to-one bond graph elements.
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