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Damage Detection Based on Electromechanical Impedance Principle and
Principal Components
Conference Paper · February 2013
DOI: 10.1007/978-1-4614-6585-0_28
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Chapter 28
Damage Detection Based on Electromechanical Impedance Principle
and Principal Components
Mario Anderson de Oliveira, Jozue Vieira Filho, Vicente Lopes Jr., and Daniel J. Inman
Abstract This paper presents a novel time domain approach for Structural Health Monitoring (SHM) systems based
on Electromechanical Impedance (EMI) principle and Principal Component Coefficients (PCC), also known as loadings.
Differently of typical applications of EMI applied to SHM, which are based on computing the Frequency Response Function
(FRF), in this work the procedure is based on the EMI principle but all analysis is conducted directly in time-domain.
For this, the PCC are computed from the time response of PZT (Lead Zirconate Titanate) transducers bonded to the monitored
structure, which act as actuator and sensor at the same time. The procedure is carried out exciting the PZT transducers using
a wide band chirp signal and getting their time responses. The PCC are obtained in both healthy and damaged conditions and
used to compute statistics indexes. Tests were carried out on an aircraft aluminum plate and the results have demonstrated
the effectiveness of the proposed method making it an excellent approach for SHM applications. Finally, the results using
EMI signals in both frequency and time responses are obtained and compared.
Keywords SHM • Damage detection • Time-domain analysis • Electromechanical impedance • Principal component
coefficients
28.1 Introduction
Researches in Structural Health Monitoring (SHM) have been conducted in the last years focusing the importance of
economic and security aspect for mechanical, aerospace and civil structures. As a consequence, the SHM systems have
become an important way to increase the safety and reduce maintenance costs in a variety of such systems [1, 2]. Typically,
conventional inspection tests are based on either visual inspection or other types of Non-Destructive Evaluation (NDE)
methods [3]. Visual inspection methods are very limited because they depend of the visual acuity and experience of the
inspector. On the other hand, other types of NDE can be used to detect small cracks that would be imperceptible to the
human eye. Among several NDE techniques, Electromechanical Impedance (EMI) and Lamb wave based methods have been
exploited on academic and industrial researches. Both techniques are notable by using the small and lightweight piezoelectric
M.A. de Oliveira ()
Department of Electrical and Electronic, Federal Institute of Education, Science and Technology of Mato Grosso,
Campus Cuiabá, Cuiabá, Mato Grosso, Brazil
Department of Electrical Engineering, Universidade Estadual Paulista, Ilha Solteira, São Paulo, Brazil
e-mail: mario.oliveira@cba.ifmt.edu.br
J. Vieira Filho
Department of Electrical Engineering, Universidade Estadual Paulista, Ilha Solteira, São Paulo, Brazil
e-mail: jozue@dee.feis.unesp.br
V. Lopes Jr
Department of Mechanical Engineering, Universidade Estadual Paulista, Ilha Solteira, São Paulo, Brazil
e-mail: vicente@dem.feis.unesp.br
D.J. Inman
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA
e-mail: daninman@umich.edu
R. Allemang et al. (eds.), Topics in Modal Analysis, Volume 7: Proceedings of the 31st IMAC, A Conference
on Structural Dynamics, 2013, Conference Proceedings of the Society for Experimental Mechanics Series 45,
DOI 10.1007/978-1-4614-6585-0 28, © The Society for Experimental Mechanics 2014
307
308
M.A. de Oliveira et al.
wafer active sensor bonded to the structure to be monitored. When the structure is excited through PZTs in an appropriate
frequency range it is possible to identify structural damages by analyzing their responses and computing some statistical
indexes [4]. For that, both methodologies need to previously know the response signal from the structure in healthy condition
(baseline). Thus, the development of new techniques and methods of prognosis and identification of structural failures can
provide more efficiency and also cost reduction in different applications [5, 6]. With the growing demand for new services
in the area of structural analysis, researches in SHM have been developed in order to extrapolate the academic world and
reach the most sophisticated practical SHM systems.
Thus, this paper proposes a novel method for damage detection based on EMI principle applied to SHM using the Principal
Component Coefficients (PCC). Differently of traditional EMI which use the Frequency Response Function (FRF), this
approach uses the response signals in time-domain to calculate the PCC. A chirp signal is used to excite the structure through
PZT transducers and the same transducers are used as a sensor to get the response from the structure. The Root Mean Square
Deviation (RMSD) indexes are directly calculated from the PCC. The proposed method was applied to an aircraft aluminum
plate, and the results were compared with the traditional EMI technique based on FRF.
28.2 Theoretical Base
28.2.1 Principal Component Analysis
The main characteristic of Principal Component Analysis (PCA) is its capability to reduce amount of data. However, PCA
is considered a factorial method because the reduction of variables do not happen by simply selecting some variables, but by
construction of new synthetic variables obtained by linear combination of initial variables by means of factors. The new set
of variables occurs with the least possible loss of information, and this also seeks to eliminate some variables that have little
information about the original data. The use of the Principal Component Analysis (PCA) applied to SHM can be found in
several works in the literature. In [7], PCA algorithm was used as a preprocessing module to reduce the data dimensionality
and eliminate the unwanted noises on EMI based method. In [8] the authors used PCA to distinguish changes in the measured
features due to environmental variations. In [9] the authors used PCA to eliminate environmental factors in damage detection
applied to an outlier. In [10] the authors proposed PCA to reduce dimensionality in damage identification problem, more
specifically detecting and locating impacts in a part of a commercial aircraft wing flap. In [11], PCA was used in a vibration
problem for data reduction in a time-series obtained from a benchmark structure.
The calculation of Principal Components (PC) is described as follows. Given a data set represented by the matrix X D
Œxi1 xi2 : : : xij where i D 1; 2; 3; : : :; M; j D 1; 2; 3; : : : ; N which M is the total number of observations and N number of
variables, we form the covariance matrix .C/ with dimension N N as following Eq. (28.1) [12],
CD
M
X
Xi XTi
(28.1)
iD1
where T represents transposition. If C is a square matrix and I represent the identity matrix, then the scalars œ1 ; œ2 ; : : : ; œN
must satisfy the Eq. (28.2),
jC œIj D 0
(28.2)
where, œ is known as eigenvalues of C. Considering the covariance matrix C and œ as an eigenvalues of C, thus eigenvector
.E/ can be calculated according to Eq. (28.3)
CE D œE
(28.3)
where, the dimension of E is N N as well. The strategy to obtain the PC (Z) is to form the linear combinations of
original variables. For this, they are determined taking the elements of X and calculating the coefficients of Z according to
Eq. (28.4) [13].
ZDXE
(28.4)
28 Damage Detection Based on Electromechanical Impedance Principle and Principal Components
Fig. 28.1 Circuit used to excite
PZT and get response signal
309
Rs
Vy(t)
Vx(t)
I(t)
Z
PZT
The Principal Component Coefficients (PCC) quantify the influence of each variable xi;1 ; xi;2 ; : : : ; xi;j have on the each
principal components .zi;1 ; zi;2 ; : : : ; zi;j / (Eq. 28.4). In the PCC matrix (W), the rows correspond to variables, columns to
component. The PCC of each variable above the component principal can be calculated from the Eq. (28.5) [12],
ei;j
WD p
Var.xi;j /
(28.5)
where ei;j represents an element of eigenvector matrix E and Var (xi;j ) represents the variance of xi;j . In this work, the PCC
will be used as input to calculate the RMSD indexes.
28.2.2 Electromechanical Impedance Principle
The technique based on the Electromechanical Impedance (EMI) applied to SHM was originally proposed by Liang et al.
[14] and improved by several other authors. Currently, EMI has been studied in several fronts and application including
signal processing, statistics methods and new circuits for excitation/reception of signals from the set PZT/structure. Its basic
principle considers a PZT bonded to a structure which is excited in an appropriated frequency range (acting as an actuator)
to generate a response based on the structure condition (acting as a sensor). In general, the results from these measurements
are used to determine the Frequency Response Function (FRF) in both healthy and damaged conditions and then statistical
indexes are computed to detect structural damage [4].
The proposed method is based on the basic idea of the EMI, but the analysis is carried out in time-domain without
computing the FRF. The time-domain analysis based on the electromechanical impedance principle is recent and it was
proposed by Vieira Filho et al. [15], in which the authors proposed to detect damages using multilevel wavelet decomposition.
Posteriorly, the authors proposed a new method in which the time response of the PZT provides information on the
electromechanical impedance variation when a monitored structure is damaged [16]. The results showed that the EMI does
not need to be computed and damage could be detected using only the time response from the PZT. Time-domain applications
can be carried out considering the excitation circuit of the couple PZT/structure as presented in Fig. 28.1 [17].
From Fig. 28.1, the module of electromechanical impedance jZj is given by Eq. (28.6)
jZj D
Vy
Rs
.Vx Vy /P
(28.6)
where, P represents peak, I(t) represents the current through the PZT, Vx , and Vy represent excitation and response voltages,
respectively. Rs is used to limit the current through the PZT. From Eq. (28.6), it is possible to determine structural damages
using only the response signals from the couple PZT/structure because these signals are correlated with the mechanical
impedance of structure. In this work the damage detection is carry out using the measurement response signal in time-domain
.Vy / to procedure the calculation of PCC. This analysis provides a damage detection system fast and efficient.
310
M.A. de Oliveira et al.
28.3 Methodology and Experimental Setup
The proposed method is based on the electromechanical impedance principle which uses PZT transducers attached to the
host structure. For this, from the circuit presented in the Fig. 28.1 a chirp signal from DC 0–125 kHz was used to excite
the set PZT/structure. At the same time, the response signal of structure is sampled at 1.25 Msample/s. The resistance Rs
was fixed at 1 k. The system presented in Fig. 28.2 is used to excite and receive the response signals from the structure.
The multifunctional Data Acquisition (DAQ) is controlled by LabVIEW® [17].
Practical tests were carried out using an aircraft aluminum plate as illustrated in Fig. 28.3. Firstly, five piezoelectric
transducers (S1, S2, S3, S4 and S5) were bonded to the plate. Then, six removable damages (A, B, C, D, E and F) were
simulated by using a magnet in the structure at different distances from the actuator/sensors.
The first step of the experiment consists on exciting each PZT and getting its response keeping the structure undamaged.
A couple of signals were obtained at different times for each sensor and used to calculate a simple arithmetic mean and other
ones were stored as baseline (BL). Posteriorly, damages (A, B, C, D, E and F) were simulated separately and individual
responses were acquired from each PZT sensor (S1, S2, S3, S4 and S5). Figure 28.4 presents time-domain responses from
sensor S4 in both healthy and damage (D) conditions. Note that the variation between the two signals, in healthy and damaged
conditions, is almost imperceptible. The previously described procedure is repeated for each simulated damage and healthy
condition (H), which make possible to acquire a set of response.
Afterward, the data obtained from each sensor (S1, S2, S3, S4 and S5) are grouped in eight matrices considering the
baseline (BL), all damages (A, B, C, D, E and .F)) and healthy condition .H/. As an example, Eqs. (28.7)–(28.9) show three
of these matrices.
BL D ŒxBLi;S1 xBLi;S2 xBLi;S3 xBLi;S4 xBLi;S5 (28.7)
A D ŒxAi;S1 xAi;S2 xAi;S3 xAi;S4 xAi;S5 (28.8)
H D ŒxHi;S1 xHi;S2 xHi;S3 xHi;S4 xHi;S5 (28.9)
In these equations, i D 1; 2; 3; : : :; 262144, xBLi;S1 represent signals from sensor 1 (S1) for the baseline, xAi;S3 represent
the signal from sensor 3 (S3) considering damage A, and thus for the other indexes. Summarizing, all baselines (for all
sensors) are grouped to determinate the baseline matrix BL (Eq. 28.7). Similarly, six other matrices are grouped considering
the respective signals for all damages (A, B, C, D, E and F) and another for healthy structure .H/. The matrices are organized
in five columns and 262,144 rows. Summarizing, eight matrices are formed and will be used to calculate PCC.
28.4 Results
Figure 28.5 shows a picture of the aircraft aluminum plate used in this experiment, which is 170 90 0:2 cm of size.
The PZT wafers were bonded to the plate using “super glue”. The damages were simulated using a magnet with diameter
and height around 2 cm and about 31 g weighted.
DAQ Device
Excitation x[n]
DAC
LabVIEW
USB
Rs
ADC
Response y[n]
Zin
Fig. 28.2 Schematic picture of
the measurement system
PZT
28 Damage Detection Based on Electromechanical Impedance Principle and Principal Components
Fig. 28.3 Schematic of plate
containing the PZT and damage
positions (dimensions in
centimeters)
311
90
40
S3
13
23
C
5
40
S2
20
13
S1
23
A
B
13
76
F
20
6
S5
17
E
6 D 17
S4 6
36
170
45
77
Fig. 28.4 Time signal response
for sensor S4 at healthy and
damaged conditions
BASELINE: SENSOR 4
DAMAGE D: SENSOR 4
RESPONSE VOLTAGE
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
1.9
1.91
1.92
1.93
1.94
1.95
SAMPLES
1.96
1.97
1.98
1.99
× 104
312
M.A. de Oliveira et al.
Fig. 28.5 Aircraft aluminum
plate with PZT transducers
bonded
The matrices of data organized as show in (Eqs. 28.7–28.9) were used to calculated the PCC according to (Eq. 28.5) for
all conditions (healthy and damages A, B, C, D, E and F) and for all sensors. Then, the first three principal components were
added to the RMSD indexes, in all conditions, as follows:
s
.Pa Pb /2
(28.10)
RMSD D
.Pb /2
In (Eq. 28.10), Pa and Pb represent the addition of the first three PC obtained from the analyzed structure and the baseline,
respectively. Figure 28.6 shows the results for the set of sensors.
The analysis of results presented in the Fig. 28.6 is extremely difficult because there are great differences among the
RMSD indexes. So, to simplify the analysis and compare results, the RMSD indexes will be normalized considering the
healthy condition as a reference for each sensor.
28.4.1 Comparison Between PCC and EMI
In order to compare the traditional EMI based on the FRF with the proposed method, the FRF was computed according to
the system proposed in [17]. So, using the real part of EMI, the RMSD indexes were calculated as follows:
s
n
X
.En;a En;b /2
RMSD D
(28.11)
.En;b /2
1
28 Damage Detection Based on Electromechanical Impedance Principle and Principal Components
313
0.16
HEALTHY
DAMAGE A
DAMAGE B
DAMAGE C
DAMAGE D
DAMAGE E
DAMAGE F
0.14
RMSD INDEX
0.12
0.1
0.08
0.06
0.04
0.02
0
1
2
3
4
5
4
5
SENSORS
Fig. 28.6 RMSD indexes for PCC
50
45
HEALTHY
DAMAGE A
DAMAGE B
DAMAGE C
DAMAGE D
DAMAGE E
DAMAGE F
40
RMSD INDEX
35
30
25
20
15
10
5
0
1
2
3
SENSORS
Fig. 28.7 Normalized RMSD indexes for EMI
were n D 1 : : : N; En;a and En;b represent the EMI for the analyzed structure and baseline, respectively. As a way to improve
the analysis of the results, the RMSD indexes for both techniques (EMI and PCC) were normalized considering the healthy
condition as a reference for each sensor. Then, the normalized RMSD indexes for real part of EMI considering all conditions
(healthy and damages A, B, C, D, E and F) and all sensors (S1, S2, S3, S4 and S5) were obtained (Fig. 28.7).
Figures 28.8, 28.9 and 28.10 show a comparison plotting in the same picture the normalized RMSD indexes for both
techniques (EMI and PCA) considering all sensors (S1, S2, S3, S4 and S5).
Although both methods have presented excellent results for damage detection, it can be seen that the sensitivity of the
proposed method is extremely more significant than the traditional method using FRF/EMI. Of course, this is very important
because higher RMSD simplify practical SHM applications.
314
M.A. de Oliveira et al.
a
b
60
600
RMSD INDEX
RMSD INDEX
800
400
DAMAGE F
200
DAMAGE E
0
40
20
DAMAGE F
DAMAGE E
0
DAMAGE D
DAMAGE D
DAMAGE C
PCA
DAMAGE C
PCA
DAMAGE B
DAMAGE B
DAMAGE A
EMI
DAMAGE A
EMI
HEALTHY
HEALTHY
Fig. 28.8 Normalized RMSD results for: (a) sensor S1, (b) sensor S2
a
b
4
× 10
80
2
1
DAMAGE F
RMSD INDEX
RMSD INDEX
3
DAMAGE E
0
60
40
DAMAGE F
20
DAMAGE E
0
DAMAGE D
DAMAGE D
DAMAGE C
PCA
DAMAGE C
PCA
DAMAGE B
DAMAGE B
DAMAGE A
EMI
EMI
DAMAGE A
HEALTHY
HEALTHY
Fig. 28.9 Normalized RMSD results for: (a) sensor S3, (b) sensor S4
Fig. 28.10 Normalized RMSD
results for sensor S5
4000
3000
2000
1000
0
PCA
EMI
DAMAGE F
DAMAGE E
DAMAGE D
DAMAGE C
DAMAGE B
DAMAGE A
HEALTHY
28.5 Conclusion
This work presented a novel method for damage detection in structures by exploiting the electromechanical impedance
principle. The method is based on time-domain signal analysis and uses Principal Component Coefficients (PCC) to improve
the sensitivity of RMSD indexes. Experimental tests were carried out on an aircraft aluminum plate and data were analyzed
employing the traditional RMSD indexes. The results show a very sensitive approach for detecting damage when compared
with traditional EMI method based on the FRF. Also, this high sensitivity can make the proposed method conveniently in
applications for which the traditional EMI present low sensitivity such as composite materials for instance.
28 Damage Detection Based on Electromechanical Impedance Principle and Principal Components
315
Acknowledgements The authors would like to thank Capes Foundation, Ministry of Education of Brazil (DINTER 23038.034330/2008-32),
FAPESP (grant 2011/20354-6), CNPq and FAPEMIG (through the INCT-EIE).
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