Geology Reference
In-Depth Information
Table 4. Damage signatures for the MDOF building up to the first non zero direction of change
Response
quantity
Damage in structural components
Sensor faults
k 1 -
k 2 -
k 3 -
D 1 -
D 2 -
D 3 -
B 1 +
B 2 +
B 3 +
dr 1 +
dr 2 +
dr 3 +
x 1
00+
00+
000-
00+
00+
000-
+
0
0
0+
00
00
x 2
000+
00-
00-
000+
00-
00-
0
+
0
00
0+
00
x 3
0000+
000-
00-
0000+
000-
00-
0
0
+
00
00
0+
8. HYBRID QUALITATIVE-
QUANTITATIVE SYSTEM
IDENTIFICATION TECHNIQUE
1
j
1
j
1
ˆ ( )
ˆ ( )
2
µ
t
=
r t
( )
;
σ
t
=
[ ( )
r t
µ
( )]
t
N
j
i
N
j
i
N
j
N
N
2
1
1
2
i
= −
j N
1
i
= −
j N
2
(16)
The health assessment method developed here
consists of damage detection, qualitative damage
isolation, and quantitative damage identification
(Figure 8). Here, p is the external load and r is
the residual, the difference between the current
structural response x , obtained from sensor
measurements, and the undamaged structural
response x , determined using the BG model.
Note that the BG and TCG models and the dam-
age signatures are derived before the sensor data
collection. This makes the damage detection,
isolation and quantification efficient and inexpen-
sive. The steps to be discussed in the next subsec-
tions are done after the collection of the sensor
health monitoring data.
The symbol generation step follows the
comparison of the measurements from healthy
and damaged structures. If the measurement of
the damaged structure at a given point of time is
above normal, a (+) symbol is assigned, and if
below normal, a (-) symbol is assigned.
8.2 Qualitative Damage Isolation
The damage isolation step begins once damage is
detected. Having developed the damage signatures
matrix in Section 6, this step is a monitoring of
system response measurements over time and
comparison with the damage signatures matrix to
identify possible damage causes. For the MDOF
structure of Figure 4, the system measurements
are the displacements x 1 , x 2 ,…, x n . These measure-
ments are compared with those for the undamaged
structure. The damage that matches the damage
signature is the cause of damage. If multiple causes
are identified, the quantitative step in next sec-
tion is used to discriminate between them. This
qualitative approach is very fast, due to off-line
development of the damage signature beforehand,
and thus enables on-line health assessment.
8.1 Damage Detection and Symbol
Generation
The detection scheme is based on comparison of
measurements from damaged and undamaged
structures. This leads to estimating the residuals,
which, when statistically significant, imply dam-
age occurrence. Since measurements contain
noise, a statistical test (Z-test) is used to examine
if the structure is damaged or not (Biswas et al,
2003). The deviation of the residual r(t) from zero
is defined for the last N2 samples and the variance
of r(t) is estimated for a larger data points N1,
where N
>>
N
as follows:
1
2
 
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