Robust algorithms of temperature compensation for
electromechanical impedance monitoring in tendon-anchorage
Thanh-Canh Huynh1), and *Jeong-Tae Kim2)
1), 2)
Department of Ocean Engineering, PKNU, Busan 608-737, Korea
2)
[email protected]
ABSTRACT
In this study, three well-known algorithms of temperature-effect compensation for
electromechanical (EM) impedance monitoring at tendon-anchorage of prestressed
structures are examined. Firstly, the EM impedance monitoring of prestressed tendonanchorages using the mountable interface technique is visited. Secondly, three
algorithms of temperature compensation, including the principle component analysis
(PCA), the radial basis function network (RBFN) and the effective frequency shift (EFS)
are selected for the impedance-based damage diagnosis in tendon-anchorage under
temperature variation. Thirdly, impedance measurements are conducted at tendonanchorage of a lab-scale prestressed concrete (PSC) girder. A lead-zirconate-titanate
(PZT) interface is embedded at the tendon-anchorage for indirectly monitoring the
impedance response. A series of temperature variation and prestress-loss events are
simulated for the lab-scale PSC girder. Finally, the selected temperature-compensation
algorithms are employed to adjust the temperature-effect on the measured impedance
responses. The prestress-loss diagnosis results using these algorithms are compared
to evaluate their applicability for the impedance monitoring under temperature-varying
condition.
1. INTRODUCTION
Cable/tendon-anchorage is the key subsystem of prestressed structures due to
its important responsibility for transferring the prestress force into the main structures.
Damage in the tendon-anchorage is often not evident and can result in uncertain states
of whole prestressed structures. To ensure the as-built performance, the integrity and
the structural safety of the prestressed structures, appropriate damage diagnosis
techniques using state-of-the-art condition assessment technologies are needed
(Azizinamini 2012).
1)
2)
Graduate Students
Professor
Damage diagnosis in structural systems using local dynamic impedance
responses has been recognized by many researchers (Liang et al. 1994, Zagrai and
Giurgiutiu 2001, Park et al. 2015). To detect structural changes induced by damage at
local critical areas, the impedance-based method utilizes the electro-mechanical (EM)
impedance sensed by piezoceramic patchs as the local dynamic feature. Since the EM
impedance response contains the information about the structural status, damage
occurred in the structural systems can be diagnosed by quantifying the variation in the
measured impedance signals. The impedance-based method has been proved as a
promising local technique due to its practical potential for real damage detection
problems.
Recently, the impedance-based method has been applied for diagnosing the
damage occurrence in the tendon-anchorage of prestressed structures. Kim et al.
(2010) conducted the impedance monitoring on a lab-scaled prestressed tendonanchorage. Although changes in the prestress force were successfully detected, it was
shown that the effective frequency range was very significant, even over 800 kHz.
Nguyen and Kim (2012) and Huynh and Kim (2014) proposed PZT interface technique
that can emerge resonant impedance peaks below 100 kHz and reduce the need of
high performance impedance analyzers. Min et al. (2016) introduced an effective
scheme using the regression analysis for monitoring tensile force and damage in the
anchorage system. However, the temperature effect on the tensile force monitoring
results was not considered in the experimental evaluation.
Temperature-induced variability of local impedance responses should be
quantified for the impedance-based damage monitoring. To remove the temperature
effect, Park et al. (1999) used a modified root-mean-square-deviation (RMSD) index
based on the concept of effective frequency shift (EFS). Koo et al. (2009) proposed a
maximum cross-correlation (CC) index to minimize the variation in impedance
signatures caused by the variation of temperatures. Sepehry et al. (2011) and Yang et
al. (2015) used radial basis function network (RBFN) to compensate errors induced by
the temperature change or the external force. Tibaduiza et al. (2013) have applied the
principle component analysis (PCA) to compensate the experimental uncertainties such
as noise, redundancies, and temperature effect.
Previous works by the authors have shown the feasibility of implementing the
PZT interface technique in combination with the EFS-based algorithm for the
impedance-based prestress-loss diagnosis in prestressed tendon-anchorages under
varying temperatures (Huynh and Kim 2014, Huynh et al. 2015a and 2015b, Huynh and
Kim 2016). The current study aims to extend the previous studies by examining robust
algorithms of temperature-effect compensation for the EM impedance monitoring at the
tendon-anchorage. Three well-known algorithms of temperature compensation,
including the PCA, the RBFN and the EFS are selected for the impedance-based
prestress-loss diagnosis in the tendon-anchorage under temperature variation. The
prestress-loss diagnosis results using these algorithms are compared to evaluate their
applicability for the impedance monitoring under temperature-varying condition.
2. THEORIES OF IMPEDANCE MONITORING AT TENDON-ANCHORAGE
2.1 Impedance Monitoring using Mountable PZT Interface
On the demand to be integrated with the wireless sensing technology
(Mascarenas et al. 2007, Hong et al. 2012, Kim et al. 2014) and to predetermine the
sensitive frequency band for the impedance monitoring, Huynh and Kim (2014)
proposed the mountable PZT interface technique to indirectly monitor the EM
impedance response of the prestressed tendon-anchorage system. The interface
device is an aluminum beam-like structure mounted on the surface of the bearing plate.
The interface structure has a flexible beam section in the middle and the fixed-fixed
boundary by two outside contact bodies. A PZT sensor is attached on the interface to
monitor the changes in the stress field of the bearing plate that can be induced by the
prestress-loss events.
In practice, the electric current I() is measured and then it is utilized to calculate
EM impedance, as described below (Liang et al., 1994):
V  w l
Z ( )   i a a
I 
ta
1
 T
 
1
d32xYˆxxE  
ˆ33 
Z a ( ) Z s ( )  1

 
(1)
where YˆxxE  (1  i )YxxE is the complex Young’s modulus of the PZT patch at zero electric
field; ˆxxT  (1  i ) xxT is the complex dielectric constant at zero stress; d3x is the
piezoelectric coupling constant in 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. Eq. (1) shows that the EM impedance, Z(ω), is a combining function of
the structural mechanical (SM) impedance of the piezoelectric patch, Za(ω), and that of
the host structure (e.g., the interface), Zs(ω). The SM impedance is a function of mass,
damping, and stiffness (Liang et al. 1994). Thus, the change in structural parameters
(m, k and c) caused by environmental conditions and damage can be represented by
the change in the EM impedance.
2.2 Damage Quantification Approach
To quantify the change in the EM impedance, the RMSD index can be utilized
(Sun et al., 1995). RMSD index is calculated as:
RMSD  Z , Z *  
N
  Z * i   Z i 
i 1
2
N
  Z  
i 1
i
2
(2)
where Z i  and Z * i  are the impedances measured before and after damage for the
i th frequency, respectively; and N denotes the number of frequency points in the sweep.
The correlation coefficient deviation (CCD) index can also be used to quantify the
change of the whole impedance signatures (Zagrai and Giurgiutiu, 2001). The CCD
index is calculated, as follows:
CCD  1 
1


E  Re( Z i )  Re( Z )   Re( Z i* )  Re( Z * ) 
 Z
*
Z
(3)
where E[.] is the expectation operation; Re( Zi ) signifies the real parts of the EM
impedances of the ith frequency before and after damage; Re( Z ) signifies the mean
values of impedance signatures (real part) before and after damage; and  Z signifies
the standard deviation values of impedance signatures before and after damage.
Note that the asterisk (*) denotes the damaged state.
The upper control limit (UCL) of the damage index is adopted to deal with the
uncertain conditions occurred in the decision-making alarming damage occurrence as:
UCL    3
(4)
where  and  are mean and standard deviation of the damage index data at
undamaged condition, respectively. In Eq. (4), the UCL is determined by three standard
deviations of the mean, which is corresponding to 99.7% confidence level (Hong et al.
2012).
3. TEMPERATURE-EFFECT COMPENSATION ALGORITHMS
3.1 PCA-based algorithm
PCA linearly transforms an original dataset of variables into a substantially
smaller one of uncorrelated variables which can describe most of the information of the
original data set (Jlooiffe 1986, Worden and Farrar 2007, Min et al. 2015). From
previous experimental studies, it was shown that each resonant peak in an impedance
signal has the different nature under the changes in temperature (Huynh et al. 2016).
As the result, some resonant ranges may contain much more information of
temperature effect than the others. In other words, there are several frequency ranges
which produce more significant magnitudes of the damage indices than others under
the temperature change. In this study, the PCA algorithm is applied to identify the
principle components (PCs) of the damage indices which are computed using
subranges of collected impedance signals. To develop the PCA model, it is important to
arrange the computed damage indices in a matrix form [DI]mxn which contains the
damage indices of n resonant frequency ranges and m impedance samples. When the
matrix [DI] is obtained, the covariance matrix [C] can be constructed, as follows:
C  
1
T
 DI   DI 
m 1
(5)
The covariance matrix [C]nxn is a square symmetric nxn matrix which measures
the degree of linear relationships within the matrix [DI]. The subspaces in the PCA are
defined by decomposing the covariance matrix, as follows:
C    A   A
T
(6)
where [A] is the matrix whose columns are the eigenvectors, and [] is the diagonal
matrix whose diagonal terms are the eigenvalues. Then, the columns of [A] are sorted
according to the eigenvalues by descending order. This process gives the PCs of the
original dataset in order of significance. By selecting only a reduced number r < n of the
PCs, a reduced transformation matrix [AR] ([A] sorted and reduced) can be considered
as the PCA model. Then, the original dataset [DI] can be geometrically transformed to
the new matrix [Z] which describes the projection of [DI] over the orientations of the
PCs, as follows:
 Z    DI  AR 
(7)
In case of using full PCs [A] in Eq. (7), the original data can be invertiblely
recovered as [DI] = [Z][A]T. In case of using reduced PCs [AR], with the given [Z], the
original data can be partially recovered by projecting the matrix [Z] back onto the
original n-dimensional space, as follows:
 DI R    Z  AR 
T
  DI  AR  AR 
T
(8)
The residual matrix [DIE], the error when not using all the PCs, can be obtained
by subtracting the original data to that projected back as:
 DI E    DI    DI R    DI   I    AR  AR 
T

(9)
Since only few first PCs govern most of the variability in the damage indices, we
could minimize the temperature effect on the damage indices by removing these PCs
when constructing the PCA model. In other words, the residual matrix [DIE] in Eq. (9)
contain the damage indices after compensating the temperature effect.
3.2 RBFN-based algorithm
RBFN is recognized as a powerful curve-fitting tool due to its strong nonlinear
processing and approximating features. Sepehry et al. (2011) proposed a method using
the ANN based radial basic function (RBF) to minimize the temperature effect on the
damage index of impedance-based diagnoses. In this study, to avoid the temperature
effect-induced false diagnosis, the RFBN-based technique is implemented to
approximate the reference for each impedance measurement at a particular
temperature. The RBFN architecture has three layers consisting of an input layer, a
hidden layer with a non-linear RBF activation function and a linear output layer, as
illustrated in Fig. 1. The input layer contains the swept frequency of the impedance
measurement and the temperature data, while the output layer is defined by the real
impedance response. The hidden layer includes the RBF neurons which non-linearly
transform the input vector to the hidden space by taking the weights of its input values.
The RBF activation function of the RBF neuron j is typically taken to be Gaussian
function that is defined as follows:
 1
2
x

c
(10)

j
 2 2
 j

in which x is the input vector, cj is the center vector of neuron j and the j is the
variance of the Gaussian function. The output of the RBFN is a linear combination of
the outputs from the RBF neurons calculated as:
 j  Exp 
N
d   j wj
(11)
j 1
where N is the number of RBF neurons, d is the output of the network and wj is the
weight of the neuron j. In order to obtain the well-approximated impedance signatures,
the RBFN needs to be trained with the appropriate values of the center vector c j, the
variance j, and the output weights wj. More detailed information about the learning
algorithm for the RBFN can be found in the related publications (Chen et al. 1991,
Sepehry et al. 2011, Yang et al. 2015).
Real
Impedance
Output Layer
Linear Weights
….
Radial Basic
Functions
Hidden Layer
Weights
Frequency &
Temperature
Input Layer
Fig. 1 RBFN architecture used to predict the impedance baseline
3.3 EFS-based algorithm
By utilizing the concept of EFS, Koo et al. (2009) proposed an EFS-based
temperature-effect compensation method for minimizing false impedance-based
diagnoses. The EFS-based technique compensates the temperature effect by shifting
an effective frequency () to give the minimum correlation coefficient deviation (CCD)
between the baseline impedance signature, Zo(), and the current impedance
signature after temperature change, Z1(). The CCD index after the EFS (CCDEFS) is
calculated, as follows:

 
 E  Re( Z o (i ))  Re( Z o )   Re( Z1 (i   ))  Re( Z1 ) 




CCDEFS  min 1 


 
Z o Z1



(12)
in which E[.] is the expectation operation; Re( Z o (i )) and Re(Z1 (i )) signifies the real
parts of the EM impedances of the ith frequency; Re( Z o ) and Re( Z1 ) signify the mean
values of impedance signatures (real part); and  Zo and  Z1 are the standard
deviation values. A loop routine is needed until the value of the minimum CCD is
obtained.
Fig. 2 shows an ideal scenario for the impedance monitoring with the EFS-based
temperature compensation. For the intact state under temperature variation, the
temperature change (T) causes approximately the same frequency shift (T) of the
resonant impedance peaks (see Fig. 2(a)). Meanwhile, the damage state under
temperature change induces the different frequency shift (d+T) of the resonant peaks
(see Fig. 2(b)). After the EFS compensation, consequently, the CCDEFS index of the
damage state could be much more significant than that of the intact state under the
temperature variation. By this way, the structural damage under varying temperature
conditions could be alarmed.
Intact State at T+T
Intact State after EFS
T+T
T
T
CCDEFS  0
Temp. Compensation
by EFS
Impedance
Impedance
T+T
T
Frequency
Frequency
(a) Intact state under temperature variation
Damage State after EFS
Damage State at T+T
T+T
d +T,
T
Temp. Compensation
by EFS
Frequency
Impedance
Impedance
Impedance
Impedance
T+T
CCDEFS > 0
T
Frequency
(b) Damage state under temperature variation
Fig. 2 EFS-based temperature compensation of impedance monitoring
4. EXPERIMENTAL TESTS ON TENDON-ANCHORAGE
4.1 Test-setup of PSC girder
Lab-scale experiments were conducted on a 6.4-meter PSC girder instrumented
with a mountable PZT interface at the tendon-anchorage, as shown in Fig. 3(a). The
PSC girder was eccentrically prestressed by a 7-wire straight tendon. The prestress
forces were introduced into the tendon by a stressing jack. A load cell was installed at
the left end to measure the applied prestress force. The tendon was first pre-tensioned
to 138.3 kN (14.1 ton) for the intact state. As shown in Fig. 3(b), the aluminum interface
was designed and surface-bonded onto the bearing plate of the right anchorage. For
the temperature measurement, a K-type thermocouple wire was setup on the top
surface of the PSC girder, see Fig. 3(c). The PZT patch on the interface was excited by
a harmonic excitation voltage with 1V-amplitude, and the impedance signature was
measured by an impedance analyser HIOKI 3532. A static data logger (Kyowa EDX-1
00A) was used to acquire temperature from the K-type thermocouple wire.
4.2 Impedance Testing Scenarios
For the first test scenario, the laboratory temperature was controlled to vary
between 6.72oC to 22.33oC by heaters while the tendon force was set fixed as 138.3
kN (PS1). A series of tests were performed for seven consecutive days including two
days for heating and five days for continuously auto-monitoring, see Fig. 4. The
impedance analyzer was set for automatically measuring every 10 minutes with the
swept frequency within 10 ~ 55 kHz (901 interval points, 50 Hz frequency interval).
Totally, 669 tests were conducted on the PSC girder under the temperature variation.
The second test scenario was performed after the first one. The room temperature
was controlled almost constant at 19.5oC by air conditioners in the laboratory (Huynh et
al. 2016). While the laboratory temperature was handled to nearly constant, a set of
prestress-loss events was simulated to the PSC girder from which the impedance
responses of the PZT interface were measured for detecting the prestress-loss. Five
prestressing levels: PS1= 138.3 kN, PS2 = 128.5 kN, PS3 = 117.7 kN, PS4 = 108.9 kN,
and PS5 = 99.1 kN were set for the test structure. By each prestressing level, five sets
of impedance were sampled. Totally, 25 tests were acquired from the PZT interface
under the near-constant temperature.
Anchor
Block
Stressing
Jack
Load Cell
Indicator
Bearing
Plate
PZT
Interface
Thermocouple
Wire
Support
Top ofofPSC
Girder
(a) PSC
girder
(b) Anchorage
zone
(c) Top
PSC
girder
Anchorage Zone
PSC Girder
Fig. 3 Experimental setup in PSC girder (Huynh and Kim 2016)
25
Test # 1 Test #114
Temperature ( oC)
Test #363
Test #501
20
15
10
Heater on
5
2015/01/28
01/29
Heater off
01/30
01/31
02/01
02/02
02/03
02/04
Time
Fig. 4 Time histories of temperature variation simulated in the laboratory
4.3 Impedance Responses of Tendon-Anchorage
Fig. 5 shows the 669 impedance samples in 10-55 kHz measured from the intact
tendon-anchorage for temperatures 6.72oC ~ 22.33oC (the first test scenario). It is
worth noting that the impedance samples corresponding to temperatures 18.5 oC ~
22oC were not measured due to the quick drop of the laboratory temperature after
turning the heaters off, see Fig. 4. As observed from Fig. 5, the temperature variation
caused significant horizontal and vertical shifts of the impedance signals. The
impedance signals were zoomed in for the frequency range of 26.5-27.5 kHz, as
plotted in Fig. 5. Noticing that the impedance amplitude varied significantly when the
temperature changed.
Fig. 6 shows real impedance signatures in 10-55 kHz for the healthy state PS1 and
four damage cases PS2 ~ PS5 under the near-constant temperature about 19.5oC. A
resonant frequency range of 25-35 kHz was zoomed in and also plotted in Fig. 6. As
observed from the figure, the resonant peaks tended to sensitively shift left according to
the decrement of prestress force. This indicates that modal stiffness of the PZT
interface decreased with the prestress-loss of the PSC girder.
1000
800
600
400
300
200
100
0
21
200
20.5
0
10
15
20
26.5-27.5 kHz
1200
Impedance
RealReal
(Ohm)
Impedance (Ohm)
400
Real Impedance (Ohm)
Real Impedance (Ohm)
1200
25
30
02/04
20
Frequency
Frequency
(kHz)
02/02
35
19.5
(kHz)
40
15/01/29
01/31
45
Time
50
1000
800
600
400
200
0
28
27.5
02/04
27
02/02
26.5
55
01/31
26
Frequency (kHz)
o
15/01/29
Time
o
Fig. 5 Impedance signals in 10-55 kHz and 26.5-27.5 kHz at 6.72 C ~ 22.33 C
900
900
Real Impedance (Ohm)
700
600
138.3 kN
128.5 kN
117.7 kN
108.9 kN
99.1 kN
500
400
300
700
600
400
300
200
100
100
15
20
25
30
35
Frequency (kHz)
40
45
50
55
138.3 kN
128.5 kN
117.7 kN
108.9 kN
99.1 kN
500
200
0
10
PS1 =
PS2 =
PS3 =
PS4 =
PS5 =
800
Real Impedance (Ohm)
PS1 =
PS2 =
PS3 =
PS4 =
PS5 =
800
0
25
30
Frequency (kHz)
35
Fig. 6 Impedance signals in 10-55 kHz and 25-35 kHz at various prestress forces
5. PERFORMANCE EVALUATION OF SELECTED ALGORITHMS
5.1 Temperature Compensation by PCA-based Algorithm
Once the impedance signals were measured from the PZT interface, the
frequency range of 10-55 kHz was first divided into seven narrow subranges with the
same frequency interval of 5 kHz. They are Range 1 of 11-16 kHz, Range 2 of 16-21
kHz, Range 3 of 21-26 kHz, Range 4 of 26-31 kHz, Range 5 of 31-36 kHz, Range 6 of
36-41 kHz and Range 7 of 41-46 kHz. The frequency interval was determined so that
each subrange contains one clear resonant peak. Next, the CCD index of the seven
subranges were computed for the intact and damage cases, as shown in Fig. 7.
Intact PS1, 6.72~22.33 oC
Prestress-loss PS1~PS5, 18.80~19.96 oC
140
Range 1
Range 2
Original CCD Index (%)
120
Range 3
Range 4
Range 5
Range 6
Range 7
600 669
Test Number
675
100
80
60
40
20
0
1
100
200
300
400
500
680
685
690
694
Fig. 7 Original CCD index of 7 frequency ranges under intact and prestress-loss cases
-0.5
0
0.5
1
-0.5
0
0.5
1
-0.5
0
0.5
1
-0.5
0
0.5
1
-0.5
0
0.5
1
-0.5
0
0.5
1
-0.5
0
0.5
1
90
80
70
Variance (%)
PC1
PC2
PC3
PC4
PC5
PC6
PC7
100
1
0
-1
-1
1
0
-1
-1
1
0
-1
-1
1
0
-1
-1
1
0
-1
-1
1
0
-1
-1
1
0
-1
-1
60
50
40
30
20
10
0
Fig. 8 PCs of original CCD indices
Intact PS1, 6.72~22.33 oC
CCD Index After Removing PC1, PC2 (%)
100
Range 1
Range 2
80
PC1
PC2
PC3
PC4
PC5
Prestress-loss PS1~PS5, 18.80~19.96 oC
Range 3
Range 4
Range 5
Range 6
Range 7
600 669
Test Number
675
60
40
20
0
-20
-40
-60
1
100
200
300
400
500
680
685
690
694
Fig. 9 CCD index of 7 frequency ranges after removing PC1 and PC2
The matrix [CCD]669x7 that contains the CCD values of 7 ranges and 669
impedance samples (under the intact state) was constructed by using Test 114 at
12.63 oC as the impedance reference. Using Eqs. (5) and (6), the PCs of the CCD
matrix were computed, as plotted in Fig. 8. Next, the original CCD data was
transformed into the new coordinate system (PC1~PC7). The PCA transformation
ensures that the axis PC1 has the most variation, the axis PC2 is the second-most, and
the axis PC7 is the least, see Fig. 8. Using Eqs. (7)~(9), PC 1 and PC2 were removed
from the PCA model, then the CCD matrix was projected back to the original coordinate
system, as shown in Fig. 9.
As shown in Fig. 9, the temperature-induced variation of the CCD indices of
Ranges 1~7 significantly reduced after implementing the PCA-based algorithm. To
consider the contribution of all resonant ranges to the damage severity evaluation,
therefore, the mean values of the CCD indices along the seven subranges were
computed as the final damage index. Fig. 10 shows the control chart for decisionmaking on the prestress-loss occurrence in the PSC girder. The UCL of the final
damage index was computed as 1.61%. The small value of the UCL indicates that the
temperature effect has been well-compensated by the PCA model. It is observed from
Fig. 10 that all four prestress-loss events (PS2~PS5) were successfully detected by the
final damage index. Also, the final damage index increased when the damage severity
went up.
PC6
PC7
25
Temperature: 6.72~22.33 oC
Temperature: 18.80~19.96 oC
Damage Index (%)
20
15
PS2 =
129 kN
10
Intact
PS1 = 138 kN
5
PS3 =
118 kN
PS4 =
109 kN
PS5 =
99 kN
UCL = 1.61%
0
1
100
200
300
400
500
600 669
Test Number
675
680
685
690
694
Fig. 10 Prestress-loss monitoring results using PCA-based algorithm
5.2 Temperature Compensation by RFBN-based Algorithm
Remind that the impedance samples were measured for 901 swept frequencies
ranging from 10 to 55 kHz with 50 Hz interval. For estimating the impedance values at
the 901 swept frequencies, totally, 901 RBF networks were constructed. The 669
impedance samples (the intact case at temperatures 6.72oC ~ 22.33oC) were adopted
to train the 901 RBF networks. For each network, the input was its swept frequency
and the temperature data, and the output was the real impedance data. The good
accuracy and efficiency can be achieved using the 50 RBF neurons for each RBF
networks. K-Means clustering was used to select the center vectors for the RBF
neurons. The variance of the cluster was set at 0.5 to use for all neurons. The neuron
activation values were normalized to improve the accuracy of the function
approximation problem.
1200
1200
CCD = 0.11%
CCD = 0.20%
1000
Real Impedance (Ohm)
Real Impedance (Ohm)
1000
Measured Impedance
Estimated Impedance
800
600
400
200
0
10
Measured Impedance
Estimated Impedance
800
600
400
200
15
20
25
30
35
40
Frequency (kHz)
45
50
(a) Test 1 at 22.33 oC (trained)
55
0
10
15
20
25
30
35
40
Frequency (kHz)
45
50
55
(b) Test 114 at 12.57 oC (trained)
1200
1200
Measured Impedance
Estimated Impedance
CCD = 0.12%
Measured Impedance
Estimated Impedance
CCD = 2.74%
1000
Real Impedance (Ohm)
Real Impedance (Ohm)
1000
800
600
400
800
600
400
200
200
0
10
15
20
25
30
35
40
Frequency (kHz)
45
50
(c) Test 363 at 6.72 oC (trained)
0
10
55
15
20
25
30
35
40
Frequency (kHz)
45
50
55
(d) Test 670 at 19.49 oC (untrained)
Fig. 11 Impedance responses predicted by RBFN-based algorithm
80
Temperature: 6.72~22.33 oC
Training Data
70
Temperature: 18.80~19.96 oC
CCD Index (%)
60
50
40
30
20
10
0
Intact
PS1 = 138 kN
UCL = 2.84%
1
100
200
300
400
PS2 =
129 kN
500
600 669
Test Number
675
PS3 =
118 kN
680
PS4 =
109 kN
685
PS5 =
99 kN
690
694
Fig. 12 Prestress-loss monitoring results using RBFN-based algorithm
The performance of the trained RBF networks was evaluated by estimating the
impedance values for the 901 swept frequencies with given temperatures. Fig. 11
shows the comparisons between the measured impedance samples and the estimated
ones by the RBFNs for the temperatures 22.33 oC (Test 1), 12.57 oC (Test 114), 6.72
o
C (Test 363), and 19.49 oC (Test 670). Note that Test 670 was the untrained test and
the temperature 19.49 oC of Test 670 was the untrained temperature, as stated
previously. The correlation between two samples (measured and estimated) was
calculated using the CCD index, see Fig. 11. As observed from the figure, the
measured impedance signals and the estimated ones were well-matched each other
with very small deviations. It is found that the correlation level (CCD index) was slightly
higher for the untrained test. Despite those, these observations have proved the
reliability of using the RBFNs for the approximation of the impedance baseline at a
given temperature.
Finally, the swept frequencies and the temperature data of the 694 tests under
the intact and prestress-loss cases were used as the input to estimate the baselines of
the 694 measured impedance samples. The CCD index was computed by comparing
the measured impedance signals with the estimated baselines over the frequency
range 10-55 kHz, as shown in Fig. 12. It is found that the temperature effect was wellcompensated on the CCD index, and the UCL of the CCD index was 2.84%. As shown
in the figure, all four prestress-loss scenarios in the PSC girder were successfully
diagnosed by the CCD index. It can be seen that the CCD index increased according to
the ascending prestress-loss severity, reflecting the natural characteristics of the
damage indices.
5.3 Temperature Compensation by EFS-based Algorithm
After measuring the impedance samples, the selecting process of appropriate
frequency range for the temperature-effect compensation was performed. Several
resonant ranges of the impedance signatures (for the intact case) within 10-55 kHz
were examined. Fig. 13 shows the CCDEFS values for five tested frequency ranges: 1247 kHz, 17-41 kHz, 23-35 kHz, 25-35 kHz, and 25-30 kHz. Test 1 at 22.33 oC was
selected as the reference impedance. It is found that the wide frequency bands have
much more significant CCDEFS values than the narrow band. As observed from Fig. 13,
the frequency range of 25-30 kHz which has very small values of the CCDEFS (less than
3%), can be selected for the temperature-effect compensation.
30
CCDEFS Index (%)
25
12-47 kHz
17-41 kHz
25-35 kHz
25-30 kHz
23-35 kHz
20
15
10
5
0
5
7
9
11
13
15
17
19
21
23
Temperature (oC)
Fig. 13 CCDEFS index of various frequency ranges (Reference: Test #1)
Fig. 14 shows the Test 1 and the Test 363 impedance signatures in 25-30 kHz
measured from the intact tendon-anchorage at 22.33 oC and 6.72 oC, respectively.
Before the EFS, a considerable CCD value, 56.4%, can be observed between two
impedance signatures. After the EFS, however, the CCD value was significantly
reduced to 2.9%. For two close temperatures of two consecutive days: Test 363 at 6.72
o
C and Test 501 at 7.19 oC, the CCD value remained the same as very small as 0.6%
for before and after the EFS, see Fig. 15. These results indicate that the temperatureeffect was mostly compensated when the narrow frequency range of 25-30 kHz was
employed.
Next, the CCDEFS index was calculated for all 694 impedance samples including
669 samples for the intact conditions (6.72 oC ~ 22.33 oC) and 25 samples for five
prestress levels (18.8 oC ~ 19.96 oC). Here, the impedance measurement at 12.63 oC
(Test 114) was set as the reference impedance. Fig. 16 shows the CCDEFS index that
was computed over the selected frequency range of 25-30 kHz. It is found that the UCL
of the CCDEFS index was significantly small at 2.1% and the CCDEFS values jumped
over the upper control limit for all prestress-loss levels. This means all prestress-loss
events occured in the PSC girder were successfully alarmed by the CCDEFS index.
Basically, the damage index supposes to rise as the damage severity increases.
However, as observed in Fig. 16, the CCDEFS index increased rapidly after the first
prestress-loss event, but remained nearly constant for the others. This implies that the
natural characteristic of the damage index was not remained after the EFS-based
temperature compensation.
1200
0.5
Test #1 at 22.33oC
Test #1 at 22.33oC
o
Test #363 at 6.72 C
0.4
Normalized Z()
CCD = 56.4 %
Real Z()
800
400
CCDEFS = 2.9 %
Test #363 at 6.72oC
0.3
0.2
0.1
0
25
26
27
28
Frequency (kHz)
29
0
30
(a) Impedance before EFS
25
26
27
28
Frequency (kHz)
29
30
(b) Normalized impedances after EFS
Fig. 14 Impedance signals in 25-30 kHz for two temperatures: 22.33 oC vs 6.72 oC
1200
0.5
o
Test #363 at 6.72oC
Test #363 at 6.72 C
o
Test #501 at 7.19 C
0.4
Normalized Z()
CCD = 0.6 %
Real Z()
800
400
CCDEFS = 0.6 %
Test #501 at 7.19oC
0.3
0.2
0.1
0
25
26
27
28
Frequency (kHz)
29
(a) Impedance before EFS
30
0
25
26
27
28
Frequency (kHz)
29
30
(b) Normalized impedances after EFS
Fig. 15 Impedance signals in 25-30 kHz for two close temperatures 6.72 oC vs 7.19 oC
6
Temperature: 6.72~22.33 oC
Temperature: 18.80~19.96 oC
CCD
EFS
Index (%)
5
4
3
UCL = 2.1%
2
1
0
PS2 =
129 kN
Intact
PS1 = 138 kN
1
100
200
300
400
500
600 669
Test Number
675
PS3 =
118 kN
680
PS4 =
109 kN
685
PS5 =
99 kN
690
694
Fig. 16 Prestress-loss monitoring results using CCDEFS (Reference: Test #114)
5.4 Comparison of PCA, RBFN and EFS algorithms
To evaluate the accuracy, the damage indices calculated previously by the three
algorithms (i.e., PCA, NRBN, and EFS) were compared with the exact damage index.
Note that Tests 670~694 (25 samples) measured during the second test scenario
under the near-constant temperature condition were utilized for the accuracy evaluation.
Fig. 17 shows the CCDPCA, CCDRBFN and CCDEFS indices computed by three examined
temperature compensation methods in comparison with the exact CCD index. Note that
the exact CCD index was computed over the whole measured frequency range of 1055 kHz. It is shown that the changing trends of the CCDPCA and CCDRBFN indices under
PS1~PS5 were well-consistent with that of the exact CCD index, meanwhile the
CCDEFS index remained nearly unchanged for PS2~PS5. It is also observed that the
magnitudes of the CCDEFS and CCDPCA indices were much smaller than that of the
CCDRBFN index, see Fig. 17. This means the RBFN-based method can produce most
accurate damage index for the impedance monitoring in the prestressed tendonanchorage. However, to conduct the RBFN-based analysis, the temperature data
needs to be sufficiently monitored and synchronized with the impedance samples.
80
PS2
CCD
PS3
PS4
PS1
PS5
PS2
PS3
110
100
Exact
RMSD
Exact
CCDEFS
90
RMSDPCA
60
CCD
80
RMSD
50
CCDRBFN
PCA
Damage Index (%)
Damage Index (%)
70
PS1
40
30
RBFN
70
60
50
40
30
20
20
10
0
670
10
675
680
685
Test Number
690
695
0
670
675
Fig. 17 CCD indices after temperature-effect compensation by three algorithms
680
685
Test Number
PS4
6. CONCLUSION
In this study, robust algorithms of temperature-effect compensation for EM
impedance monitoring at tendon-anchorage of prestressed structures were examined.
Firstly, the EM impedance monitoring of prestressed tendon-anchorages using the
mountable interface technique was visited. Secondly, three well-known algorithms of
temperature compensation, including the EFS, the PCA and the RBFN were selected
for the impedance-based damage diagnosis in tendon-anchorages under temperature
variation. Thirdly, impedance measurements were carried out at tendon-anchorage of a
lab-scale PSC girder. A series of temperature variation and prestress-loss events were
simulated for the lab-scale PSC girder. Finally, the selected temperature-compensation
algorithms were employed to adjust the temperature-effect on the measured
impedance responses. The prestress-loss diagnosis results using these algorithms
were compared to evaluate their applicability for the impedance monitoring under
temperature-varying condition.
From the performance valuation of the three algorithms, it can be concluded that
the RBFN-based algorithm can produce most accurate diagnosing results for the
impedance monitoring in the prestressed tendon-anchorage if the temperature data is
sufficiently measured. In case of lack of the temperature information, the PCA-based
method could be used as an alternative method to minimize the temperature effect on
the damage diagnosis results.
ACKNOWLEDGMENTS
This work was supported by Basic Science Research Program through the National
Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and
Technology (NRF-2013R1A1A2A10012040). The graduate student involved in this
research was also supported by the Brain Korea 21 Plus program of Korean
Government.
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