Geology Reference
In-Depth Information
Accordingly, the arrows carry the signs 1, -1 and
-1, respectively. The constitutive relation for the
resistor R1 is
e
such as, temperature, humidity, and pore pressure,
and (c) Chemical, such as, chloride penetration,
sulfate penetration, pH, carbonatation penetration,
rebar oxidation, steel oxidation, and timber decay.
Conventional sensors based on mechanical and
electrical transducers are able to measure most
of these parameters. Fiber-optic sensors offer
superior performance compared with conventional
sensors and have been used during the last few
years in SHM of civil structures. More details on
recent sensor technologies can be found in Ansari
(2005) and Manders et al (2006).
In general, sensor performance and reliability
degrade with time under varying environmen-
tal conditions and externally applied loadings
(Ansari, 2005, Blackshire et al, 2006, Manders
et al, 2006, Glisic & Inaudi 2007). Different
degradation mechanisms have been observed in
different types of sensors (e.g. surface-bonded
or fully-embedded) under various environmental
effects such as temperature- and moisture-cycling
(Blackshire et al, 2006, Glisic & Inaudi 2007).
Deviations in measurements could result from
damage in structural components or due to faults
in the sensors. Sensor performance is particularly
relevant in the field of road infrastructure where
the loading conditions affecting the main structure
(traffic loads, temperature cyclying, etc.) also
affect the sensor measurements. In such situa-
tions, the use of traditional system identification
methods may not provide accurate identification
of actual damage cause since these methods do
not account for sensor faults. On the other hand,
bond graphs can easily model both the physical
system and sensors (Daigle et al, 2006).
Faults in sensors could result in bias or drift
in measured values. A biased measurement devi-
ates from its true value by a constant B. Drift is
the growth of deviations over time. For a sensor
measuring the displacement response, a bias fault
implies that the actual measured displacement
d
m
is the sum of the true displacement
d
t
and the
bias
B
. The sensor is modeled as a modulated
=
/
which
is represented by an arrow connecting e2 to f2
and carries the constant 1/Rv. The constitutive
relation for the C-element C1 is
e
=
R f
v
or
f
R e
v
2
2
2
2
∫
∫
/ ( / )
β
and is rep-
resented by an arrow connecting f4 to e4 and
carries the constant
(
=
1
C
f dt
=
1
V
f dt
4
1
4
0
4
/
V β
. The constitutive
relation for the I-element is
e
1
)
0
or
=
Mf
7
7
f
∫
/
which is represented by an
arrow connecting e7 and f7 pointing towards f7
and carries the term 1/M dt. The constitutive rela-
tion for the second C-element is
e
1
M e dt
=
7
7
1
=
∫ ∫
and is represented
by an arrow connecting
f
8
to
e
8
and carries the
term
k dt
. The flow
f
7
is integrated to compute the
displacement
u
(
t
). This completes the TCG
model for the actuator.
The TCG model of the continuous systems
derived from the bond graph model of Figure
6(a) is shown in Figure 6(b). The derivation of
the TCG follows the same procedures explained
above. Again, each modal mass is represented by
a separate TCG block. The modeling of a sensor
that measures the structure tip displacement is
also included and is explained in the next section.
/ C
f dt
k
f dt
8
2
8
8
6. MODELING SENSOR FAULTS
USING BOND GRAPHS
A typical health monitoring system consists of
a network of sensors that collect measurements
data periodically or continuously during short or
long terms. For civil structures, such as bridges,
tunnels, dams, power plants, high-rise buildings
and historical monuments, the most relevant
measurement parameters are (Ansari, 2005,
Manders et al, 2006): (a) Mechanical, such as,
strain, deformation, displacement, crack opening,
stress and forces, (b) Physical or environmental,
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