Nghiên cứu thực nghiệm về chẩn đoán lỗi cảm biến cho việc giám sát sức khỏe kết cấu bằng kỹ thuật giao diện áp điện

the coupled interface-host 
structure ( )Z  , as described below: 
 (1) 
where ˆ (1 )E Exx xxY i Y is the complex Young’s 
modulus of the PZT patch at a zero electric 
field; ˆ (1 )T Txx xxi   is the complex dielectric 
constant at zero stress; d3x is the piezoelectric 
coupling constant in the x-direction at zero 
stress; and wa, la, and ta are the width, length, 
and thickness of the PZT patch, respectively. 
The parameters  and  are structural damping 
loss factor and dielectric loss factor of 
piezoelectric material, respectively. The SM 
impedance of the coupled interface-host 
structure system ( )Z  can be computed from 
the following equation [21]: 
(2) 
Equation (2) shows that the SM impedance 
of the coupled interface-host structure system is 
characterized by the masses, damping, and 
stiffness of both the interface (ki, ci, mi) and the 
host structure (ks, cs, ms). Thus, the change in 
these parameters caused by structural damages 
can be represented by the change in the EM 
impedance obtained from the PZT sensor. By 
quantifying the variations of EM impedance 
signals, the structural damage occurred in the 
host structure can be detected. 
To successfully implement a damage 
detection job, it is important to confirm the 
operation of the PZT sensor. In a realistic 
situation, the sensor and its bonding layer can 
be degraded under the effects of overloading 
conditions, material deteriorations, and 
environmental changes. The sensor breakage/ 
quality degradation will cause changes in 
piezoelectric properties. Also, the bonding 
layer’s defects will affect the force transmission 
from the PZT to the interface structure. As a 
result, observable changes in the measured EM 
impedance could be inaccurately interpreted as 
the occurrence of structural damages. 
1
2
33 31 11
1 ˆˆ( )
( ) ( ) 1
T Ea a
a a
w lV
Z i d Y
I t Z Z
  
 
  
  
 
22 2
2
( ) ( )
( )
( ) ( )
i i i s i s i s i i
s i s i s
m i c k m i c c k k i c k
Z
i m i c c k k
    

  
N.T.V.Phan, V.D.Tran, T.C.Huynh / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(39) (2020) 03-10 
6 
3. Experimental sensor defect diagnosis for 
piezoelectric interface 
3.1. PZT interface-based health monitoring 
of steel bolted connection 
A bolted connection of a steel beam 
(H 200 180 8 10 mm) was selected to 
perform impedance monitoring via the 
piezoelectric interface technique. The 
connection was fastened by 8 bolts (20 mm) at 
the top and the bottom flanges, respectively 
(see Fig. 2a). All bolts were fastened by the 
torque level of 160 Nm (i.e., a healthy state). To 
acquire the EM impedance from the joint, a 
PZT interface was fabricated and mounted to 
the surface of the splice plate (see Fig. 2b). The 
material of the interface structure is aluminium. 
The flexible section of the interface has the 
width of 33 mm, the length of 30 mm, and the 
thickness of 4 mm; and the two bonded sections 
have a width of 33 mm, a length of 30 mm, and 
a thickness of 5 mm. The PZT sensor (PZT-5A) 
has the width of 25 mm, the height of 25 mm, 
and the thickness of 0.51 mm. The sensor was 
bonded to the interface via a bonding layer 
(instant adhesive Loctite 401). For impedance 
measurements, the HIOKI 3532 analyzer was 
used to generate the harmonic excitation of 1 V 
and to measure the EM impedance responses 
(see Fig. 2c). 
As described in Table 1, three testing 
scenarios were carried out for the experimental 
investigation, including the sensor debonding, 
the sensor breakage, and the structural damage 
tests. The sensor debonding test was performed 
by reducing the bonding area of the adhesive 
layer. Four debonding cases of the sensor were 
investigated, including no debonding (i.e., an 
intact state), 39.2% debonding, 66.4% 
debonding, and 84% debonding cases. The 
sensor breakage test was simulated by reducing 
the size of the PZT. Four breakage cases of the 
PZT were studied, including no breakage (i.e., 
an intact state), 36% breakage, 64% breakage, 
and 84% breakage cases. The structural damage 
test was conducted by reducing the torque of 
Bolt 2 (see Fig. 2a) from 160 Nm to 110 Nm, 
60 Nm, and 0 Nm. During the experimental 
tests, the room temperature was controlled at 
21oC to avoid any effect of temperature changes 
on the measurements. 
 (a) Bolted joint (b) PZT interface (c) Impedance analyzer 
Fig 2. Experimental setup for the lab-scaled steel beam 
Table 1. Descriptions of test scenarios 
Test 
Scenarios 
Description 
Sensor 
Debonding 
PZT’s bonding area was reduced 
by 0%, 39.2%, 66.4%, and 84% 
Sensor 
Breakage 
PZT’s area was reduced by 0%, 
36%, 64%, and 84% 
Structural 
Damage 
Bolt 2‘ torque was reduced from 160 
Nm to 110 Nm, 60 Nm, and 0 Nm 
3.2. Effect of sensor defects on impedance 
responses 
The real impedance signatures in 10-50 kHz 
measured under the sensor debonding cases are 
shown in Fig. 3a. The signatures show two 
clear resonant peaks under the intact state of the 
PZT (i.e., a perfect bonding condition). When 
the debonding level of the PZT was increased 
up to 84%, the magnitude of the resonant 
impedance peaks was reduced, as zoomed in 
N.T.V.Phan, V.D.Tran, T.C.Huynh / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(39) (2020) 03-10 7 
Fig. 3a. It is known that the imaginary part of 
impedance contains much information about the 
sensor’s health status. Hence, the effect of the 
sensor debonding on the imaginary admittance 
(i.e., an inverse of impedance) was examined in 
Fig. 3b. It is observed that the sensor debonding 
caused upward shifts in the slope of the 
imaginary admittance. 
Figure 4a shows the real impedance 
signatures in 10-50 kHz for different levels of 
the sensor breakage. Obviously, the sensor 
breakage caused upward shifts in the real 
impedance signatures, as zoomed in Fig.4a. The 
shifting effect was found to be more 
considerable for lower frequencies. The 
imaginary admittance signatures in 10-50 kHz 
were also examined for the different breakage 
levels of the PZT, as shown in Fig. 4b. It is 
obvious that the sensor breakage caused 
downward shifts in the slope of the imaginary 
admittance, as zoomed in Fig. 4b. 
For the structural damage cases, the real 
impedance signatures in 10-50 kHz were shown 
in Fig. 5a. The reduction in bolt torque caused 
leftward shifts in the real impedance at the 
resonances. The torque reduction also 
significantly modified the imaginary admittance 
signatures at the resonances, as observed in Fig. 
5b. Interestingly, the structural damage did not 
cause any shifts in the slope of the imaginary 
admittance. 
(b) Imaginary part 
Fig 3. Measured impedance signatures under the sensor debonding cases 
No Debonding
84% Debonding
Log-scale
(a) Real part 
84% Debonding
No Debonding
N.T.V.Phan, V.D.Tran, T.C.Huynh / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(39) (2020) 03-10 
 8
(b) Imaginary part 
Fig 5. Measured impedance signatures under the structural damage cases (Bolt 2 loosened) 
84% Breakage
No 
Breakage
(a) Real part 
84% Breakage
No Breakage
(b) Imaginary part 
Fig 4. Measured impedance signatures under the sensor breakage cases 
Torque 
= 0 Nm
Torque
= 160 Nm
(a) Real part 
Torque 
= 0 Nm
Torque
= 160 Nm
N.T.V.Phan, V.D.Tran, T.C.Huynh / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(39) (2020) 03-10 9
3.3. Sensor fault diagnosis using an 
impedance feature 
To diagnose and differentiate the sensor 
defects from the structural damage for the 
bolted joint, the slope of the imaginary 
admittance was extracted. For that, the slope of 
the imaginary admittance signatures was 
estimated by using the linear approximation 
method. The computed slopes were then plotted 
according to the severities of the structural 
damage (i.e., torque-loss), the sensor 
debonding, and the sensor breakage, as depicted 
in Fig. 6. The results showed that the slope of 
the imaginary impedance remained generally 
stable about 8 10-5 for the structural damage 
cases (i.e., no sensor defects). When the sensor 
was debonded, the slope of the imaginary 
admittance was rapidly increased. Particularly, 
the slope was changed from 8 10-5 to 16 10-5 
as the debonding severity rose from 0% to 84%. 
For the sensor breakage cases, the slope was 
decreased from 8 10-5 to 1.8 10-5 as the 
breakage level was changed from 0% to 84%. 
It is experimentally confirmed that the slope 
of the imaginary admittance can be used to 
diagnose the sensor defects for the impedance 
monitoring via the piezoelectric interface. 
Particularly, an increased value of the slope of 
the imaginary admittance is an indication for 
the sensor debonding while a decreased value 
of the slope is responsible for the sensor 
breakage, and stable values of the slope can be 
interpreted as no sensor defects. 
0
0.00002
0.00004
0.00006
0.00008
0.0001
0.00012
0.00014
0.00016
G
ra
d
ie
n
t 
o
f 
(1
/I
m
a
gi
n
a
ry
 Im
p
ed
a
n
ce
)
Unchanged
Sensor BreakageTorque-loss of Bolt 2 Sensor Debonding
0% 31% 63% 100% 0% 39% 66% 84% 0% 36% 64% 84% 
Fig 6. Sensor fault diagnosis using the slope of imaginary 
admittance 
4. Conclusion 
This study presented an experimental 
investigation on the effects of sensor faults on 
impedance-based SHM using the piezoelectric-
based smart interface. The experimental 
investigation showed that the sensor faults 
caused significant changes in measured EM 
impedance responses. Specifically, the sensor 
debonding caused a decrease in the magnitude 
of resonances and an increase in the slope of the 
imaginary admittance. The sensor breakage 
caused upward shifts in the patterns of the real 
EM impedance and a decrease in the slope of 
the imaginary admittance. By contrast, the 
structural damage did not cause any variations 
in the slope of the imaginary admittance. The 
slope of the imaginary admittance was then 
extracted to assess the sensor defects for the 
PZT interface. The obtained results showed that 
the presence of the sensor defects can be 
effectively distinguished from the existence of 
the structural damages by using the extracted 
impedance feature. This study provides an 
experimental background for impedance-based 
SHM practices, via the piezoelectric interface 
technique, with the presence of sensor defects. 
Acknowledgement 
This research is funded by Vietnam National 
Foundation for Science and Technology 
Development (NAFOSTED) under grant 
number 107.01-2019.332 
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