IMPEDANCE-BASED TECHNIQUE AND GUIDED WAVE METHOD
FOR DAMAGE ASSESSMENT USING SMART MATERIALS
Yong Hong 1,a, Byeong-hee Han1,b, Gao-Ping Wang1,c, Dong-Pyo Hong 2,d, Young-Moon Kim 3,e
1
Department of Precision Mechanical Engineering, Chonbuk National University Jeonjusi Jeonbuk 561756 South Korea
2
Department of Precision Mechanical Engineering, The Research Center of Industrial Technology,
Chonbuk National University Jeonjusi Jeonbuk 561-756 South Korea.
3
Department of Architectural Engineering, Chonbuk National University Jeonjusi Jeonbuk 561-756
South Korea.
a
[email protected], [email protected], [email protected], [email protected],
e
[email protected]
ABSTRACT
The paper mainly presents an impedance-based technique and also a guided wave method to detect and localize the same
incipient damages in structures, respectively. The impedance-based technique utilizes the direct and converse electromechanical impedance properties of bonded piezoceramic (PZT) patches which serve as actuator-sensors. The interaction
between a PZT and its host structure can be described by using a simple 1-D vibration model. A longitudinal wave is applied to
the structure by the special arrangement of the PZT pairs, Park et al. [1]. The guided wave method needs high-frequency wave
propagation for achieving the necessary time and space resolution to detect and localize the incipient damages instead of the
electro-impedance obtained by the efficient impedance analyzer. To check the time-of-flight of the wave the damage is
localized. Results of several experiments presented show high sensitivity and reliability of the guided wave method, Giurgiutiu
et al. [2]. Based on the electro-impedance based technique and the guided wave method, a large number of experiments are
conducted. Additionally, the applications of the wavelet transform to detect incipient damages are also presented by means of
several simulated examples. The numerical method requires only the response of the damaged structure. When the suitable
wavelet is selected, the ability of wavelet to detect and localize the damages is verified.
Introduction
The aging of large structures is a major concern for engineers and scientists, and the rapid development of the economy gives
rise to much higher and stricter criteria and requirements for SHM (Structural Health Monitoring). The NDE technique
(Nondestructive Evaluation) is especially a major concern. A large number of technologies for NDE have been developed,
such as MA (Modal Analysis), wave propagation, time domain, eddy-current methods and ultrasonic, magnetic field methods,
etc. The application ranges from aircrafts to infrastructures, i.e. pipeline systems, bridges and buildings, etc. The piezoceramic
sensors (PZT) that simultaneously act as an actuator and sensor are widely used for SHM. In the high frequency range, the
electro-impedance-based technique with using a PZT is very sensitive for the evaluation of the incipient and small damage,
such as bolt loosening, cracks and holes.
We present the performance of the electro-impedance-based technique for detecting real-time damage on the sample of a
plate with bolts and nuts. A large amount of experiments are executed and several conditions are imposed to simulate realtime damage, i.e. the location of the loosening bolts, and the loosening extent of the bolts. The different indices are discussed
and executed to efficiently quantify the damage conditions. The theory behind this technique and the experimental
investigations is presented in this paper. The analytical results strongly show the sensibility and reliability of this technique.
E/m impedance method
The interaction between a PZT and its host structure can be described by using a simple 1-D model, as shown in Fig. 1. The
PZT is normally bonded directly to the surface of the structure with using a high-strength adhesive to ensure a better
mechanical interaction. The bonded PZT is considered as a thin bar that is undergoing axial vibration in response to an
applied alternating voltage. One end of the bar is fixed and the other end is connected to the host structure, which is
represented by a single-degree-of-freedom system. This assumption regarding the interaction at two discrete points is
consistent with the mechanism of force transfer from the bonded PZT sensor to the structure. The model of the principle is
shown as in Fig. 1.
Figure 1. Degree of freedom model of structure where piezoelectric sensors attached
Guided Wave Technique
In order to find the damage location, a time domain approach using multiple piezoelectric sensors and actuators is investigated.
Our idea is from the pulse-echo method which is often used in ultrasonic inspection. Instead of ultrasonic transducers, multiple
piezoelectric sensors and actuators are used for the feasibility study on identifying damage location. The piezoelectric sensoractuator is basically a thin PZT patch. In this case, we have to be careful about the wave form generated by the PZT. The
wave speed can be calculated from the length of the test piece and the time difference between the initial echo and the back
echo. Thus, we can assess the damage location by tracking the flaw echo. The longitudinal wave equation can be expressed
as:
2
∂ 2 u ( x, t )
2 ∂ u ( x, t )
=
c
∂t 2
∂x 2
(1)
c= E/ρ
(2)
where u( x , t) is the displacement at position x and time t, c is the longitudinal wave speed, E is the Young’s modulus,
and ρ is the mass density. The longitudinal wave speed calculated by Equation (2) can be used to check the validity of the
wave speed obtained by the experiment.
Experiment
1. E/m Impedance and Guided Wave Measurement System
The experimental setup is comprised of an impedance analyzer HP4192A, PZT sensors and a notebook computer with
software, GPIB interface cables and two plate specimens. A 0.3mm thickness is selected for the experimental investigations to
efficiently generate the longitudinal elastic wave for the rectangular PZT sensors of 25mm length and 4mm width.
In general, one PZT sensor that is bonded on the surface of the structure dominantly generates the traverse or bending wave;
however, the longitudinal wave is required for the damage detection along with the plates in the experiments. Fig. 2 shows the
arrangement of the PZT sensors. PZT1 is bonded on one side of the end of the plate, while PZT1" is bonded on the back side
of the plate that corresponds to PZT1. Therefore, the transverse or bending component of the waves that are generated by
PZT1 and PZT1" counteract each other; however, the longitudinal component that is generated is intensified along the plate.
a. E/M impedance Method
b. Guided Wave Method
Figure 2. The measurement system and the PZT sensors
2. Experimental Specimens for E/m Impedance and Guided Wave Measurement
a. Specimen 1 - Single lap joints with 2-row bolts
b. Specimen 2 - Two L-angle Al beam connected by 6 bolts
c. Specimen 3 - Plate with 25 Bolts
d. Specimen 4 - Crack simulated beam with 1m length
Figure 3. Specimens for E/M impedance method test
Figure 4. Specimen 5 and 6 for guided wave test and analysis
Results Analysis
1. E/M Impedance Analysis Results
Original impedance spectrum.
Figure 5. The E/M impedance spectrum graph
Selection of Frequency range
The electro-impedance-based technique demonstrates high sensibility in the high frequency range. To obtain the most
appropriate range to acquire the admittance signatures, the pair of PZT1, 1" is scanned through a wide range from 10kHz to
1,000kHz. The real part of the admittance that corresponds to 100~150 kHz includes 20~30 dominant peaks. According to the
literature, the signatures, which include several peaks, indicate high sensibility to the change that is caused by a small amount
of damage. Except for those that are relative to 100~150kHz, the admittance signatures that are relative to 10~40kHz show
random irregular variations and those that are relative to 160~1,000kHz show ordinary signals without dominant peaks.
Several sampling intervals, i.e. 5Hz, 10Hz, 20Hz, 50Hz, are investigated to obtain the admittance signatures. The smaller the
interval is, the more accurate the signature is without distortion over a longer period of time. By comparing the fidelity of the
signatures with the time cost, the interval of 20Hz is found to be the optimal choice for the experiments
Specimen 1. Statistical Analysis of Damages for Single lap joint Strip with 2-row bolts
The experiments are conducted using the specimen 3 in Figure. 3 over 100~150 kHz, and the data is processed by displaying
the real part of the electro-impedance. Several damage indices are tried: Root Mean Square Deviation (RMSD), Mean
Absolute Percentage Deviation (MAPD), Correlation Coefficient (CC) and Covariance (Cov). For the damages, i.e. the location
of bolt loosening and the extent of bolt loosening at the same location, the RMSD is found to have a strongly linear relation
between the damaged and healthy conditions. In this case, the damaged conditions of the Specimen 1 are analyzed with using
the index of the RMSD, CC and Cov.
Figure 6. Measured with specimen 1 data under 100~180kHz(x-axis data labeled with bolt number - torque(Nm))
Specimen 2. Statistical Analysis of Damages for Two L-angle Al beam connected by 6 bolts
In this case, the damaged conditions of the Specimen 1 are analyzed using the index of the RMSD, CC and Cov.
Figure 7. Measured data with specimen 2 under 70~175kHz(x-axis data labeled with bolt number - torque(Nm))
Specimen 3. Statistical Analysis of Simulated Damages for the Location of Bolt Loosening
In this case, the damaged conditions of the Specimen 3 are analyzed using the index of the RMSD. For each stage of damage,
the admittance signatures are obtained by the pairs of PZT1, 1" and PZT2, 2". Eleven arbitrarily selected damages, which are
located at the holes that are numbered 1, 3, 5, 7, 9, 11, 13, 15, 18, 21 and 25, are investigated.
Figure. 8 a., b. presents the RMSD values for the damaged signatures that are obtained by PZT1, 1" and PZT2, 2",
respectively, for the bolt loosening by 0 N.m in the frequency range of 100~150kHz. It's observed from Figure. 8 a. that even
when the farthest bolt, number 25, is subjected to a small bolt loosening damage, the RMSD value reaches a relatively high
value of 10%. The result efficiently verifies that PZT sensors have a high sensitivity to detect a small damage that is located at
a far distance. Figure. 8 b. also provides similar verification for the high sensitivity of PZT sensors. Figure. 8 a. shows that the
RMSD values gradually decrease when the simulated damage moves away from the pair of PZT1, 1", and Figure. 8 b.
indicates that the RMSD values gradually increase when the simulated damage approaches the pair of PZT2, 2" with each
step. The trends of increase and decrease of the RMSD show a considerably uniform linear relation.
Figure. 8 c., d. presents the RMSD values for the damaged signatures with the bolt loosening by 1 N.m in the frequency range
of 100~150kHz. Figure. 8 c., d. indicates that the RMSD values have the same variation trend as that of Figure. 8 c., d.
however, the magnitude is relatively smaller. For example, the farthest bolt, number 25, is subjected to a small bolt loosening
damage by 0N.m and the RMSD value reaches a value of 5%, but Figure. 8 c. has a value of 10% at the same location. The
theory behind this phenomenon is that the different torques of 1N.m and 0N.m apply different normal stresses to the vicinity of
the bolts. Therefore the elastic wave propagation along the plate that is generated by the PZT sensors is influenced and the
energy dissipation of the wave is presented in different extents. It can be said again that the gentle variation of the bolt
loosening conditions between 1N.m and 0N.m can be efficiently detected, and therefore the sensitivity and reliability of PZT
sensors for such an incipient damage are validated once again.
From all of the figures above, it is shown that the closest bolt, that is, bolt 1 that is relative to PZT1, 1" and bolt 25 that is
relative to PZT2,2", has a much greater RMSD value than all of the other bolts. This phenomenon reflects the energy
dissipation of the wave propagation along the plate.
a. RMSD(%) of PZT 1, 1" with 0 Nm Torque
b. RMSD(%) of PZT 2, 2" with 0 Nm Torque
c. RMSD(%) of PZT 1, 1" with 1 Nm Torque
d. RMSD(%) of PZT 2, 2" with 1 Nm Torque
Figure 8. Measured data with specimen 3 - RMSD versus Damage Location
60.00
3
50.00
2.5
40.00
2
Frequency
Real Part Impedance(Ω)
Specimen 4. Analysis of Simulated Damages for the specimen with a crack
30.00
0-3
0-6
0-9
0-12
0-15
0-18
0-21
1.5
20.00
1
10.00
0.5
0
0.00
10
20
30
40
50
60
Frequency (KHz)
70
80
90
100
10
11
12
13
14
15
Mode number
a. Peak frequency shift of the plate with a crack
b. Peak frequency shift of the plate with a crack
Figure 9. Measured data with specimen 4
With respect to simulated damage, i.e. the size of the crack, the peak frequency shift is used to numerically estimate the
damaged conditions. Figure. 9 a. shows the impedance response of the healthy plate. And therefore the impedance response
over 100 kHz is excluded, because the response has non-uniform tendency relative to that indicated below 100 kHz. By
comparison, the 10, 11, 12, 13, 14, 15 modes are selected to provide the reference for the frequency peak shift ∆F.
(3)
ΔF = f H − f D
In Eq. 3, fH represents the peak frequency for the health status of the beam, and fD the peak frequency for the damaged status.
Now we compare normal peak frequency by fH and peak frequency by fD after damage. And then the difference of the peak
frequency relative to the two conditions is called ∆F.
Figure. 9 b. presents the ∆F values that are obtained with the cracks located at the distances of 100mm away from the left end
of the plate, as shown in Figure. 3 Specimen 4 and Fig. 9 b. shows that with respect to the same mode number when the
damage, i.e. the length of the crack increases, the ∆F values strongly linearly increase. However, with respect to the same
damage, when the mode number increases, the ∆F values decrease almost linearly.
2. Guided Wave Analysis Results
In our experiment, two kinds of material were used, and the parameters of the beam were the following :
(a) Al health condition (1635X25mm), (b) Cu health condition (1500X30mm), (c) Al damaged condition (1635X25mm with
10X5mm Crack)
a. Basic specimen for wave speed calculation
b. Wave propagation path of specimen with crack
Figure 10. Specimen 5 and 6 for wave speed calculations using time domain approach
Experimental results are as follows. Agilent F. G. 33250A function generator applied an excitation pulse(10V) to a pair of left
PZT in figure 10, and did sensing in a pair of right PZT. Two results are showing in a and b of figure 11, and c of figure 11
shows specimen 6 damage result of figure 4.
a. Al health condition (1635X25mm)
b. Cu health condition (1500X30mm)
c. Al damaged condition (10X5mm Crack)
Figure 11. Experimental results of excitation test and damage location
The following shows sequence of Calculating equations:
At first, the wave speed of Aluminum beam can be obtained by equation (3).
c Al − calc. =
E/ρ =
7.06 × 1010 / 2.70 × 103 = 5114 [m / s ]
(4)
Theoretical equation using first echo time( t1 ) gives the following
c Al − meas. = L / t1 = 1.635 / 0.317 × 10−3 = 5158 [ m / s ]
(5)
Second, the wave speed of Copper(Cu) beam can be obtained by equation (3).
cCu −calc. =
E/ρ =
1.1×1011 / 8.96 × 103 = 3504 [ m / s ]
(6)
Also, theoretical equation using first echo time( t1 ) gives the following
cCu − meas. = L / t1 = 1.5 / 0.430 ×10−3 = 3488 [ m / s ]
(7)
Therefore, the wave speed of Aluminum and Copper beams calculated by theoretical equation is reasonable.
Next, we considered that wave propagation path help us to find damage location, damage location can be obtained by the
following equation.
L −l −d =
c(t2 − t1 )
,
2
d = 1635 − 817.5 −
d = L−l −
c(t2 − t1 )
2
5158 × (0.313 − 0.156)
≈ 413 [mm]
2
(8)
Where, L is total length of specimen and l is one half of specimen total length, d is distance to center PZT from left PZT, t1 is
time when first echo arrives at center PZT and
t2 is time when reflection echo arrives at center PZT.
Now, we think about instrument resolution. Wave speed using first echo time t1 is 5158 [ m / s] and signal acquisition resampling frequency of Harmonie Analyzer is 51.2kHz max. Thus the sampling period of the analyzer is 19.531μ s .
Finally, resolution, Δd , is :
Δd = 5158 × 103 × 1.9531 × 10−5 = 100.7 [mm]
(9)
Remember that real damage location is at 400mm from the left PZT. Therefore, real distance of damage location is between
d − Δd , 299.3mm, and d + Δd , 500.7mm, estimated damage distance regions are not accurate. Of course, calculating
distance, 413mm, using measurement times (t1 , t2 ) is relatively accurate. If more accurate damage locations are needed,
shorter sampling periods are required.
Conclusions
We used two methods for damage estimation. One is E/M impedance method, and another is Guided wave method. E/M
impedance method could evaluate the existence and non-existence of damage and size of damage quantitatively using
statistical method. On the other hand, Guided wave method could find out position of exact damage using several PZT
sensors. If echo signal is not clear in time domain analysis, the exact damage location can be assessed using Daubechies
wavelet for mother wavelet. In addition, evaluation is possible because the use of multiple PZT sensor networking can know
the exact damage location and size.
Acknowledgments
This study was supported by NRL (National Research Laboratory) Program and by Management International Joint Research
Project of MOST (Ministry of Science and Technology), Republic of Korea.
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