The temperature variation results in significant impedance variations, particularly a frequency shift in the impedance, which may lead to erroneous diagnostic results of real structures,
Trang 1Incorporating Effective Frequency Shift for Compensating
Temperature Effects
KI-YOUNGKOO,1SEUNGHEEPARK,2,* JONG-JAE LEE3ANDCHUNG-BANGYUN1,* 1
Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology
Guseong-dong, Yuseong-gu, Daejeon, Korea 2
Department of Civil and Environmental Engineering, Sungkyunkwan University, Cheoncheon-dong, Jangan-gu
Suwon, Gyeonggi-do, Korea 3
Department of Civil and Environmental Engineering, Sejong University, Gunja-dong, Gwangjin-gu, Seoul, Korea
ABSTRACT: This study presents an impedance-based structural health monitoring (SHM) technique considering temperature effects The temperature variation results in significant impedance variations, particularly a frequency shift in the impedance, which may lead to erroneous diagnostic results of real structures, such as civil, mechanical, and aerospace structures In order to minimize the effect of the temperature variation on the impedance measurements, a previously proposed temperature compensation technique based on the cross-correlation between the reference-impedance data and a concurrent impedance data is revisited In this study, cross-correlation coefficient (CC ) after an effective frequency shift (EFS), which is defined as the frequency shift causing two impedance data to have the maximum correlation, is utilized To promote a practical use of the proposed SHM strategy,
incor-porated with the current hardware system Validation of the proposed technique is carried out
on a lab-sized steel truss bridge member under a temperature varying environment It has been found that the CC values have shown significant fluctuations due to the temperature variation, even after applying the EFS method Therefore, an outlier analysis providing the optimal decision limits under the inevitable variations has been carried out for more systematic damage detection It has been found that the threshold level shall be properly selected considering the daily temperature range and the minimum target damage level for detection
It has been demonstrated that the proposed strategy combining the EFS and the outlier analysis can be effectively used in the automated continuous SHM of critical structural members under temperature variations
effects, effective frequency shift, cross-correlation coefficients, outlier analysis, steel truss members
INTRODUCTION
STRUCTURALhealth monitoring (SHM) has become
an important issue in many fields, such as civil,
mechanical, and aerospace engineering In recent years,
the electromechanical impedance method, which utilizes
piezoelectric materials as collocated actuator-sensors,
has emerged as a new SHM technique (Giurgiutiu and
Rogers, 1997; Giurgiutiu et al., 1999; Park et al., 2000,
2003a, 2005, 2006a; Soh et al., 2000; Tseng et al., 2000;
Zagrai and Giurgiutiu, 2001; Bhalla et al., 2002) In this
technique, a piezoelectric sensor is surface-mounted to
the host structure by means of a high strength epoxy
adhesive and its electrical impedance is extracted across
a high frequency-band, typically in the order of kHz The real part of this signature is used as a representation
of the local dynamic parameters of the structure in the vicinity of the sensor Damage to the structure in the vicinity of the sensor is expected to alter this signature thereby giving an indication of the imminent damage However, there are many impediments to the practical application of the technique for SHM of real structures, such as bridges, buildings, and airplanes The main challenge lies in achieving continuous monitoring of the impedance response of the piezoelectric sensor over sufficiently long periods; several days, months, or years
To this end, the development in terms of hardware and software systems has been pursued From the viewpoint
of hardware systems, the low-cost, portable, and wireless
*Authors to whom correspondence should be addressed E-mail: ycb@kaist.ac.kr
and shparkpc@skku.edu
Figures 1–18 appear in color online: http://jim.sagepub.com
JOURNAL OFINTELLIGENTMATERIALSYSTEMS ANDSTRUCTURES, Vol 20—March 2009 367
1045-389X/09/04 0367–11 $10.00/0 DOI: 10.1177/1045389X08088664
ß SAGE Publications 2009 Los Angeles, London, New Delhi and Singapore
Trang 2telemetry requirements resulted in an on-board active
sensor system (Grisso and Inman, 2005; Mascarenas
et al., 2006; Park et al., 2006b) The on-board active
sensor system interrogates a structure utilizing a
self-sensing macro-fiber composite (MFC) patch and the
low-cost impedance measuring chip, and all the
struc-tural interrogation and data analysis are pursued in near
real-time at the sensor location From the viewpoint of
software systems, the development of an automated
algorithm suitable for continuous monitoring under
significant environmental variation especially
tempera-ture effects should be accompanied with the
corres-ponding hardware system Several studies have been
reported about the temperature variation effects on the
impedance measurement (Sun et al., 1995; Park et al.,
1999a,b; Bhalla et al., 2003) Sun et al (1995) used a
temperature compensation method based on
cross-correlation to correct the horizontal shift in the
impe-dance signature pattern Park et al (1999a,b) proposed
an impedance-based health monitoring technique under
a temperature varying environment considering the root
mean square deviations (RMSD) of the measured
sign-atures after introducing proper shifts in the horizontal
and vertical directions Bhalla et al (2003) also
inves-tigated the influence of the structure–actuator
inter-actions and temperature on the impedance signatures
In this study, the change of the impedance data under
temperature variation has been investigated using an
automated continuous monitoring system In order to
minimize the effect of the temperature variation on the
impedance measurements, the temperature
compensa-tion technique previously proposed by Park et al
(1999a) is revisited In this study, the authors utilize
cross-correlation coefficient (CC) with an effective
frequency shift (EFS) which is defined as the frequency
shift causing the concurrent impedance data to have the
maximum correlation with the reference-impedance
data The proposed technique was applied to health
monitoring of a lab-sized steel truss bridge member
under a temperature varying environment It has been
found that the CC values have shown significant
fluc-tuations due to the temperature variations, even after
applying the EFS method Therefore, an outlier analysis
providing the optimal decision limits under this
inevi-table variation has been carried out for more systematic
damage detection Herein, as the damage level increases,
the threshold level should be properly selected
consi-dering the daily temperature range and the minimum
target damage level for detection, and continuous
updating of the threshold level is inevitably required
Through an experimental study using a MFC sensor to
detect artificial cuts on a steel truss member, it has been
demonstrated that the proposed strategy combining the
EFS method and the outlier analysis can be applied to
the automated continuous SHM of critical structural
members under temperature variations
IMPEDANCE-BASED STRUCTURAL HEALTH MONITORING
In general, the impedance-based SHM technique utilizes small piezoelectric sensors, such as piezoelectric ceramic (PZT) and MFC sensors, attached to a structure
as self-sensing actuators to simultaneously excite the structure with high-frequency excitations and to monitor the changes in the measured impedance signature Since the piezoelectric sensor is bonded directly to the structure
of interest, the mechanical impedance of the structure is directly correlated with the measured electrical impe-dance of the piezoelectric sensor Figure 1 presents an idealized 1-D model between the piezoelectric sensor and
a host structure Then, the electromechanical impedance function of the coupled system can be represented as
a function of frequency as (Liang et al., 1994):
Ztotalð!Þ ¼ i!C 1 2
31
Zsð!Þ
ZAð!Þ þ Zsð!Þ
ð1Þ
where C is the zero-load capacitance of the piezoelectric sensor, 31 is the electromechanical coupling coefficient
of the piezoelectric sensor, ZS is the impedance of the host structure, and ZA is the impedance of the un-bonded piezoelectric sensor
Thus, by observing changes in the electrical impe-dance measurement of the piezoelectric sensor, assess-ments can be made about the integrity of the host structure (Giurgiutiu and Rogers, 1997; Giurgiutiu
et al., 1999; Park et al., 2000, 2003a, 2005, 2006a; Soh
et al., 2000; Tseng et al., 2000; Zagrai and Giurgiutiu, 2001; Bhalla et al., 2002) However, there are still many impediments to the practical application of the techni-que for SHM of real bridge and building structures, such
as the sensitivity of the impedance measurement to the temperature variation
CONTINUOUS IMPEDANCE MONITORING SYSTEM
In recent years, the use of wireless sensors and networks is becoming increasingly popular as a research
V =nsin(wt)
Piezo-sensor
K C M
I =isin(wt+f)
Figure 1 Idealized 1-D electromechanical modeling between
a piezoelectric sensor and a host structure (Giurgiutiu and Rogers, 1997).
Trang 3topic for SHM system In particular, development of
a self-contained wireless sensor incorporating on-board
actuating/sensing, power generation, on-board data
processing/damage diagnostic, and radio frequency
(RF) technologies is strongly required With the current
trend of SHM heading towards unobtrusive
self-contained sensors, the approaches integrating MEMS
and RF telemetry-based active sensing systems on the
electromechanical impedance-based damage detection
technique have been investigated untiringly by several
researchers (Grisso and Inman, 2005; Mascarenas et al.,
2006; Park et al., 2006b) Grisso and Inman (2005)
developed an autonomous on-board wireless
impe-dance-based SHM system The on-board sensor system
interrogates a structure utilizing a PZT patch and the
low-cost impedance method, and all the structural
interrogation and data analysis are pursued in near
real-time at the sensor location Moreover, a wireless
telemetry that alerts the end user of any harmful changes
in the structure is combined Conventional impedance
analyzers, such as HP4294A for the electromechanical
impedance method are too expensive and too bulky,
which is not attractive for real world applications
To overcome these limitations, Mascarenas et al
(2006) devised an active sensor node, as displayed in
Figure 2, which consists of AD5933, a microcontroller
(ATmega128L), and a radio frequency (RF) transmitter
(XBee) AD5933 developed by Analog Device is a new
impedance measuring device of low cost, portable, and
readily combined with a wireless telemetry, as shown in
Figure 3, which costs only 150$ A PZT patch
inter-rogates a host structure by using a self-sensing technique
of the AD5933 All the processes including structural
interrogation, data acquisition, signal processing, and
damage diagnostic are performed at the sensor location
by the microcontroller And only damage diagnostic
result implying ‘damage’ or ‘no damage’ will be
tran-smitted to the end-user through the RF data
transmis-sion Finally, the LED light shows ‘green’ or ‘red’ color
according to ‘intact’ or ‘damage’ state, respectively
Park et al (2006b) validated the feasibility of the active sensing node through two kinds of example studies for corrosion detection on an aluminum beam and loose bolt inspection on a bolt-jointed structure
In this context, this study presents an automated continuous impedance monitoring system As a current laboratory test setup, commercial equipments including impedance analyzers and temperature measurement systems are supported via General Purpose Interface Bus (GPIB) which is the most common interface for measurement and control systems, and RS232C which is
a standard for serial binary data communication The impedance analyzer HP4294A is connected to a laptop computer through local area network (LAN), so that GPIB commands may be instructed and measurements may be received via telnet protocol A computer program developed in MATLABÕ language performs all the tasks of the continuous impedance monitoring: (1) scheduling and execution of each measurement task, (2) measuring the impedance and temperature through equipment automations, (3) displaying real time mea-surements and diagnosis results on the screen, and
Structure
P Z T AD5933
Active sensing node
Wireless sensor Network system
On-line wireless SHM (MFC + AD5933 + ATMega128L + XBee)
station
LED Indoor: 30 m
Outoor: 100 m 2.4GHz data link Tx
(RF)
Rx (RF)
Figure 2 An active sensor node for wireless impedance-based SHM system (Mascarenas et al., 2006).
Figure 3 A miniaturized impedance measuring device (AD5933).
Trang 4(4) data archiving Using the current continuous
impe-dance monitoring system, the impeimpe-dance measurement
can be carried out automatically over sufficiently long
periods
EXPERIMENTAL INVESTIGATION
Test Specimen and Test Setup
An experimental study was carried out to investigate
the feasibility of the proposed method for continuous
health monitoring using a MFC sensor on a steel truss
member under a temperature varying environment The
test specimen is a 1/8 scale model with a dimension of
150 150 530 mm3 for a vertical truss member of
Seongsu Bridge, Seoul, Korea, which caused the collapse
of the bridge in 1994 The specimen consists of two
segments with wide flange sections of different flange
thicknesses of 6 and 3 mm welded together as in Figure 5
A ‘d33-type’ MFC sensor of 28 14 0.02 mm3 was employed to detect three damage cases with an artificial cut with different lengths of 2, 4, and 8 mm sequentially inflicted at the same location on the welded zone of the specimen The MFC sensor was placed at a distance of
40 mm away from the cut on the outside surface of
a flange A thermocouple was also placed near the MFC sensor for temperature measurement The present experimental setup for the impedance-based SHM consists of a host structure, a MFC sensor, an impedance analyzer (HP4294A), a thermocouple, and a laptop computer equipped with the continuous impedance monitoring framework as shown in Figures 4 and 5 Impedance Variations due to Temperature Effects
Temperature effects on the impedance signature of the MFC sensor were investigated Figure 6(a) shows the measured impedance data on the intact structure during
a period over 10 days The temperature varied in a range
530 mm
6 mm Thermo-coupler
Thermo-coupler
Cut
Cut
40 mm
50 mm
150 mm
144 mm
3 mm
Figure 5 Test specimen, MFC sensor, and thermocouple.
Test specimen
Temperature measurement (TC-31K)
Impedance analyzer (HP4294A)
LAN connection
Labtop computer
(1) Scheduled excution (2) Automated measurement (3) Displaying real-time results (4) Data archiving
A continuous SHM program developed using MATLAB®
RS232C
Telnet protocol
to send GPIB commands and to receive measurements
Send commands and receive measurement
Figure 4 An automated continuous impedance monitoring system.
Trang 5of 10.3–26.08C during the period Figure 6(b) shows
similar results for a damage case with a cut of 4 mm in
the middle of the welded zone of a flange, where the
temperature variation was in the range of 15.9–31.38C
The results show that the temperature variations caused
significant variations in the impedance signatures in
both the vertical and the horizontal axes Thus, the
impedance changes due to the temperature variations
could lead to erroneous diagnostic results about the
integrity of the structure Therefore, a damage-feature
selection strategy robust to the ambient temperature
variation is required in the impedance-based SHM for
real applications
Effective Frequency Shift by Correlation Analysis
As mentioned earlier, the impedance and temperature
measurements were carried out continuously during
a long period The total number of the measurements for
the baseline (intact) state is 700 Figure 7(a) shows the
first and the 338th impedance signatures (both for the
intact cases) measured at 22.6 and 10.38C, respectively Considerable variation with both vertical and horizontal shifts can be observed between two impedance signa-tures and the CC is found to be very small as 0.099
To compensate the impedance variation due to the temperature change of 12.38C, an EFS by the cross-correlation analysis is introduced in this study Herein, the EFS ( ~!) for an impedance data y(!) is defined as the shift corresponding to the maximum cross-correlation with the reference impedance data x(!) as:
max
~
~
!
1=NPN i¼1ðxð!iÞ xÞðy ið!i!Þ ~ yÞ
XY
ð2Þ where x and y are the mean values of two impedance signatures of x(!) and y(!); and X and Y are the standard deviations Note that the EFS method may compensate the vertical shifts as well by subtracting the mean values from the original signatures Figure 7(b) shows the normalized impedance signature ^x338ð!Þ of
50
100
150
200
250
300
350
400
50 100 150 200 250 300 350 400
Frequency (Hz) × 10 4
Frequency (Hz) × 10 4 Figure 6 Impedance variations due to temperature variations in a range of 10.3–31.38C (a) Intact cases, (b) Damage cases with a 4 mm cut.
× 10 4 90
100
110
120
130
140
Test#1 at 22.6 °C Test#338 at 10.3 °C
−2 0 2 4 6
Test#338 at 10.3°C
Frequency (Hz)
× 10 4 Frequency (Hz)
Figure 7 Impedance data for two intact measurements (a) Original impedance signatures, (b) Normalized impedance signatures after EFS (Reference: Test #1).
Trang 6Test #338 after an EFS along with the normalized
reference signature ^x1ð!Þof Test #1 as:
^
x1ð!Þ ¼ðx1ð! !Þ ~ x1Þ
X 1X 338
^
x338ð!Þ ¼ðx338ð! !Þ ~ x338Þ
X 1X 338
Excellent match between two signatures for the intact
case can be observed, and the maximum correlation
coefficient between two signatures after the EFS is
found to be as high as 0.986 Figure 8(a) shows two
impedance signatures for the same damage case with a
cut of 2 mm, measured at 25.88C (Test #763) and 20.28C
(Test #805) In the present case, the EFS was evaluated
by taking the signature of Test #763 as the reference
The maximum CC between two measurements increases
from 0.139 to 0.983 as the EFS introduces as in
Figure 8(b) Figures 9 and 10 show similar results for
damage cases with a cut of 4 and 8 mm, respectively
It has been found that the maximum CC for the same damage case increases remarkably after an EFS Cross-correlation-based Damage Detection using Effective Frequency Shift
The feasibility of the cross-correlation-based damage detection method using the proposed EFS was investi-gated for three damage cases with an artificial cut with different lengths of 2, 4, and 8 mm Narrow cuts with a width of 0.5 mm were sequentially inflicted in the middle
of the welded zone of a flange as shown in Figure 5 After a cut of 2 mm was inflicted, a series of impedance measurements was carried out under temperature variations in the range of 16.1–28.58C Typically, an impedance measurement at 22.68C (Test #951) for a case with a 2 mm cut is compared with the baseline (intact) impedance measurement at the same temperature (Test
#1) in Figure 11(a) A big difference can be observed between two impedance signatures, and the CC values
110
120
130
140
150
160
Test#763 at 25.8°C Test#805 at 20.2 °C
CC = −0.139
−2 0 2 4 6
Test#805 at 20.2 °C
Frequency (Hz) × 10 4
Frequency (Hz) × 10 4
Max CC = 0.983
Figure 8 Impedance data for two damage cases with a 2 mm cut (a) Original impedance signatures, (b) Normalized impedance signatures after EFS (Reference: Test #763).
90
100
110
120
130
140
150
160
170
180
190
Test#1116 at 22.6°C Test#1155 at 31.3 °C
−2 0 2 4 6 8
Frequency (Hz) × 10 4
Frequency (Hz) × 10 4
Test#1116 at 22.6 °C Test#1155 at 31.3°C
Figure 9 Impedance data for two damage cases with a 4 mm cut (a) Original impedance signatures, (b) Normalized impedance signatures after EFS (Reference: Test #1116).
Trang 7obtained are as low as 0.055 Figure 11(b) shows the
normalized impedance signature of Test #951 after an
EFS along with the normalized reference signature
(Test #1), which indicates that the maximum correlation
coefficient increased remarkably to 0.920 However, the
value is smaller than the maximum CC for two intact
cases (i.e., 0.986) shown in Figure 7(b) Figures 12 and
13 show similar results for larger damage cases with a 4
and 8 mm cut, respectively The maximum CCs with the
intact case (Test #1) after the EFS are found to be 0.851
(for a 4 mm cut) and 0.680 (for an 8 mm cut), which are
significantly smaller than the previous intact and small
damage cases
Figure 14(a) shows the CCs after the EFS for all
measurement cases with a cut of 2, 4, and 8 mm The
EFSs were evaluated by taking the signature of an intact
case (Test #1) as the reference It can be clearly observed
that the maximum correlation coefficient after the
EFS drops very rapidly with increasing damage level,
which indicates the effectiveness of the present CC-based damage detection method using the EFS For the purpose of comparison, three other damage measures for the impedance-based SHM were addition-ally considered: (a) maximum CCs without EFSs, (b) RMSD with EFSs, and (c) RMSD without EFSs Results of the additional analyses are displayed in Figures 14(b), 15(a) and 15(b) The RMSD values were evaluated as:
RMSDð%Þ ¼Xn
i¼1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
½ReðZi, 1Þ ReðZi, 0Þ2
½ReðZi, 0Þ2
s
100 ð4Þ
where Zi,0 is the impedance function at !i for the baseline case, Zi,1is a concurrent impedance at !i, and
n is the number of frequency points A large value of RMSD means stronger indication of damage occurrence
in the concurrent case with respect to the baseline case
100
150
200
250
300
350
Test #1466 at 28.4 °C Test #1522 at 21.7 °C
−2 0 2 4 6
3.15 Frequency (Hz) × 10 4
Frequency (Hz) × 10 4
CC = 0.013
Test#1522 at 21.7°C
Max CC = 0.983
Figure 10 Impedance data for two damage cases with an 8 mm cut (a) Original impedance signatures, (b) Normalized impedance signatures after EFS (Reference: Test #1466).
80
90
100
110
120
130
140
150
160
Test#1 at 22.6°C Test#951 at 22.6°C
−2 0 2 4 6 8
Frequency (Hz) × 10 4
Frequency (Hz) × 10 4
Test#1 at 22.6 °C Test#951 at 22.6°C
Figure 11 Impedance data for an intact case and a damage case with a 2 mm cut (a) Original impedance signatures, (b) Normalized impedance signatures after EFS (Reference: Test #1).
Trang 83.05 3.1 3.15
80
100
120
140
160
180
−2 0 2 4 6 8
Test#1 at 22.6°C Test#1116 at 22.6 °C
Frequency (Hz) × 10 4
Frequency (Hz) × 10 4
CC = −0.045
Test#1 at 22.6°C Test#1116 at 22.6 °C
Max CC = 0.851
Figure 12 Impedance data for an intact case and a damage case with a 4 mm cut (a) Original impedance signatures, (b) Normalized impedance signatures after EFS (Reference: Test #1).
80
100
120
140
160
180
Test#1340 at 22.6 °C
−2 0 2 4 6 8
Frequency (Hz) × 10 4
Frequency (Hz) × 10 4
CC = −0.101
Test#1 at 22.6 °C
Test#1340 at 22.6°C Test#1 at 22.6°C
Max CC = 0.680
Figure 13 Impedance data for an intact case and a damage case with an 8 mm cut (a) Original impedance signatures, (b) Normalized impedance signatures after EFS (Reference: Test #1).
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0
10 15 20 25 30 35
10 15 20 25 30 35
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Test no.
Test no.
8mm cut 4mm cut 2mm cut
Intact 2 mm cut 4 mm cut 8 mm cut
Figure 14 Cross-correlation coefficients for all cases with respect to Test #1 (a) After the effective frequency shift, (b) Before the effective frequency shift.
Trang 9Figures 14(b) and 15(b) present the maximum CCs
and RMSD results without applying the EFSs, while
Figures 14(a) and 15(a) show the results incorporating
the EFSs In the case of the RMSD-based method, the
EFSs correspond to the minimum RMSDs after the
shift It is noted that both CC-based and RMSD-based
methods without the EFSs did not provide good damage
diagnostic results, while both results with the EFSs
showed successful damage detections even under
tem-perature varying environment The general performance
of the CC-based and RMSD-based methods with the
respective EFSs is found to be equally good
DAMAGE DETECTION USING OUTLIER
ANALYSIS
Outlier Analysis
An automated damage diagnostic system without
requiring any a priori mathematical model of the
structure, may provide an efficient SHM tool for real
structures In order to satisfy this requirement, a
so-called ‘novelty detection’ outlier analysis method
has emerged as a robust unsupervised learning pattern
recognition tool for damage detection of structures
(Worden et al., 2000; Park et al., 2003b) The outlier
analysis aims to establish simply whether or not a new
pattern is significantly different from the previous
patterns, at the same time automatically ignoring any
negligible differences, such as random fluctuations due
to noise That is, an outlier is an observation that is
significantly different from the rest of the population
and therefore the outlier is believed to be generated by
an alternate mechanism (Barnett and Lewis, 1994)
Assuming a multivariate normal distribution (MVN)
of sample patterns, the deviation of the candidate
outlier (x), from the rest of the population can be measured by Mahalanobis square distance (MSD) measure, given by:
D& ¼ ðx&ÞT1ðx&Þ ð5Þ
where is the mean of the samples, is the covariance matrix of the samples, and D is a deviation measure For the SHM applications, and are exclusively computed from the measurement for the baseline system without including potential outliers The deviation mea-sure Dis then compared with the threshold value Dth Herein, if D4Dth, xis an outlier, which means xcame from a damaged state The basic concept of this outlier analysis is illustrated in Figure 16 The threshold value depends on both the number and the dimension of the data set To investigate the effect of the dimension and the size of the data set, a Monte Carlo method is used to
0
0
50
100
150
10 15 20 25 30 35
10 15 20 25 30 35
0 50 100 150 200 250
Test no.
Test no.
2 mm cut
4 mm cut
8 mm cut
Figure 15 Root mean square deviations for all cases from Test #1 (a) After the effective frequency shift, (b) Before the effective frequency shift.
Dth
Out-Dimensional decision boundary
D V
if V >Dth then x Vis outlier!
x Vcame from a damaged state.
Outlier, x V
Figure 16 Multivariate outlier analysis (novelty detection).
Trang 10arrive at a threshold value First, Xn which is a m p
(dimension of data number of observations) matrix of
the measurements is constructed as:
Xn¼ ½x1, x2, x3, , xp
xi: input measurement vector: ð6Þ
For this study, the input vector xiis taken as the CC
values calculated using Equation (2) Then, the MSD is
computed for all xias
diðxi, Þ ¼ ðxiÞT1ðxiÞ i ¼1 p ð7Þ
where and are estimated from Xn The maximum
MSD among diis selected and stored as
Di¼max
The previous steps are repeated n times to have a large
population of Di, and the probability distribution
fun-ction (PDF) of Diis empirically estimated The
thresh-old value Dthcan be established from the estimated PDF
for a prescribed confidence level, as shown in Figure 17
Damage Detection using Outlier Analysis
The optimal threshold values for more systematic
damage detection considering the fluctuations in the CC
values were investigated with a statistical confidence
level (C.L.) of 99.5% through an outlier analysis In this
analysis, all the CC values before each damage step were
utilized as the basis data to update the threshold level of
the outlier analysis The results are shown in Figure 18
As expected, it has been found that after each cut
damage of 2, 4, and 8 mm is inflicted, the CC values
dropped abruptly under the corresponding threshold
values (thr1: 0.942, thr2: 0.884, and thr3: 0.807), so that
reliable SHM and systematic damage detection may be
achieved under a temperature varying environment by
the present impedance-based method However, it is
noted that the threshold levels shall be properly selected
considering the daily temperature range and the
mini-mum target damage level for detection, and continuous
updating of the threshold level is needed as more data
are available
CONCLUSIONS
The feasibility of the impedance-based structural health monitoring (SHM) technique to diagnose the integrity of the structures has been investigated under the temperature varying environment The temperature variation resulted in a significant variation in the impedance measurement, particularly a frequency shift
in the impedance, which may lead to erroneous diagnostic results regarding the integrity of real tures including civil, mechanical, and aerospace struc-tures In order to minimize the effects of the temperature variations, a previously proposed temperature compen-sation technique based on cross-correlation between the reference-impedance data and a concurrent impedance data is revisited In this study, the cross-correlation coefficient (CC) with an effective frequency shift (EFS), which is defined as the frequency shift causing two impedance data to have the maximum correlation, was utilized To promote a practical use of the proposed SHM strategy, an automated continuous monitoring framework using MATLABÕ has been developed and incorporated with the current hardware system The proposed techniques were applied to health monitoring
of a lab-sized steel truss bridge member with the maximum temperature variation of 218C From the experimental study, it has been found that the EFS method may significantly reduce the temperature varia-tion effects on the damage detecvaria-tion However, the CC values have still shown significant fluctuations even after applying the EFS method Therefore, an outlier analysis has been also employed to determine proper threshold levels for more systematic damage detection considering the fluctuations in the CCs The results of the present experimental study demonstrated that the proposed impedance-based automated SHM technique incorpor-ating the EFS and the outlier analysis can be effectively used for diagnosing the structural integrity, even with the presence of temperature variations
1
0.8
0.6
0.4
0.2
0
1 0.8 0.6 0.4 0.2 0
0
0
−2 2 4 6 8 10 Repeat n times to get
the distribution of D i
99.5%
confidence level
Take D i = max d i
Dth i
Figure 17 Establishment of threshold through outlier analysis.
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05
10 15 20 25 30 35
Test no.
8 mm cut
4 mm cut
2 mm cut
thr1 = 0.942
thr2 = 0.884 thr3 = 0.807
Figure 18 Damage detection through the outlier analysis.