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PREDICTION OF PCCP FAILURE BASED ON HYDROPHNE
DETECTING
Yuan Zhang, Yibo Li
College of Precision Instruments and Optoelectronic Engineering
Tianjin University , Weijin Road 72#
Tianjin, 300072, China
Emails:[email protected]
Submitted: May 12,2013 Accepted: Aug.03,2013 Published:Sep.05,2013
Abstract: Prestressed Concrete Cylinder Pipe (PCCP) is a widely used water pipe all over the world.
A major cause of PCCP failure is the internal wire break, which will emit acoustic signal. In this
paper, a hydrophone-based PCCP real-time monitoring and failure-prediction system was proposed.
By applying wavelet energy normalization analysis to signal feature extraction and Support Vector
Machine (SVM) to signal recognition, a high prediction accuracy of 98.33% was achieved. The
result showed that the hydrophone-based PCCP failure prediction system is much more effective
and economic in real application compared with electromagnetic method and acoustic fiber optical.
Index terms: Wire break signal, acoustic, PCCP, hydrophone, wavelet analysis, SVM
Yuan Zhan and Yibo Li, PREDICTION OF PCCP FAILURE BASED ON HYDROPHNE DETECTING
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I INTRODUCTION
Prestressed Concrete Cylinder Pipe (PCCP) is a large-diameter water pipe widely used in the
world. Figure 1 illustrates the structure of PCCP, which primarily consists of five parts: the
internal concrete core, a thin steel cylinder, external concrete, highly prestressed wires and
external mortar layer [1][2]. Highly prestressed wire is winded on the circular surface of the
concrete core by certain tensile stress. When the size of inner concrete core is fixed, the PCCP
can bear different inner pressure and external loads by adjusting the prestressed wire diameter
and screw pitch. Therefore, the PCCP’s bearing capacity mainly depends on the wire winded
in it. Once the wire breaks due to artificial destruction or natural corrosion, the PCCP will
face threat of rupture[3], which brings about not only great economic loss but also potential
casualties [4][5][6]. Therefore the prediction of wire break in the PCCP is of great
significance.
Figure 1 Internal structure of the PCCP
Conventionally PCCP is inspected manually via visual observation or sounding [7]. Recently
new methods including Remote Field Eddy Current/Transformer Coupling (RFEC/TC) [8][9],
Acoustic Fiber Optical (AFO), and hydrophone-based acoustic inspection are implemented in
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the PCCP failure detection[10][11][12]. RFEC/TC is an off-line inspection method with rather
low efficiency. In addition, the water in the PCCP has to be evacuated before the RFEC/TC
inspection, which will consume large human and material resources. AFO is a real-time
inspection method with quite high accuracy. However, AFO is only applicable to newly built
pipelines since the interior surface of old PCCP is unavailable for AFO installation, and it is
also expensive to lay fibers for AFO. Hydrophone-based inspection, an economic method
compared with AFO, is not only accurate due to the high sensitivity of the hydrophone to
acoustic signal but also convenient to install the hydrophone into the wells or holes that are
reserved and present on the outside surface of the PCCP when constructed. Due to its distinct
advantages, the hydrophone-based inspection has become a promising PCCP failure
prediction method with great economic potential.
In this paper, a hydrophone-based PCCP failure prediction method is proposed and fully
developed. Acoustic signal is sampled using a data acquisition device produced by the
National Instruments (NI) Corporation [13]. Signal features are extracted via wavelet
decomposition method. SVM is used to differentiate real wire break signal from other
interfering signals. The accuracy is up to 98.33%.
II ACOUSTICAL SIGNAL PROPAGATION AND IDENTIFICATION
a. Acoustic signal propagation in PCCP
PCCP is a typical cylinder waveguide, in which three families of guided waves: longitudinal,
torsional and flexural modes can propagate [14][15]. Longitudinal mode is axial-symmetric,
and studies have shown that L(0,1) mode and 1α mode exist in water-filler pipes surrounded
by any medium, whereas occurrence of 2α mode and 3α mode depends mainly on the
surrounded medium of the pipe [16][17]. L(0,1) mode wave has been demonstrated to suffer
strong attenuation due to leakage and scattering when encountering pipe joints and fittings
[14-16]. The attenuation of flexural mode F(1,1) wave is also large if the mode phase velocity
is greater than the longitudinal bulk velocities in the soil. Compared to L(0,1) and F(1,1)mode
Yuan Zhan and Yibo Li, PREDICTION OF PCCP FAILURE BASED ON HYDROPHNE DETECTING
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wave,α mode wave experiences less attenuation due to its predominantly axial water-borne
displacements. It is predicted that α mode has the most chance to be the dominant mode in
the signal received over long propagation distance since α mode signal can propagate a long
time without much energy loss into the soil or pipe wall [16]. Based on this prediction, the
maximum spacing distance between sensors can be 260m within which acoustic signal still
propagate[18].
b. Signal feature extraction
Wavelet analysis is a time-frequency analysis method developed by Morlet in the 1980th and
it’s especially suitable for instable signals[19][20]. Wavelet decomposition is widely used in
signal feature extraction[21][22][23].The results of wavelet decomposition are coefficients
that include several details representing the high-frequency information and one
approximation representing the low-frequency information[24]. The wavelet decomposition
can be used for feature extraction by introducing the energy-mode concept. Suppose the
sampling rate of signal is fs, if a j layer wavelet is used to decompose the signal, the signal
can be decompose into j+i unequal frequency bands.
The jth layer wavelet coefficients can be expressed in cdk (k=1,2,3...j), which represent the
high frequency bands information, and caj which represent the low frequency energy
information. The time domain energy of signal x(t) can be reached by
dttxtx ∫+∞
∞−= 22 )()( (1)
According to the Parseval energy integration theory, x(t) in equation (1) can be connected
with the wavelet transform coefficients cdk and caj,, then we can get the following equation
∑=
=
+=jk
kjk cacdE
1
22 (2)
According to the equation (2), the wavelet transform coefficients cdk and caj have energy
calculation function.
The feature vector extraction based on wavelet decomposition method can be accomplished
according to the following steps:
First, decompose the signal by using wavelet analysis
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Second, choose n frequency bands which are sensitive to energy and calculate each band’s
energy and normalize each band. Suppose E1,E2,E3....Ej are the energy in accordance with cdk
(k=1,2,3...j), and Ej+1is the energy in accordance with caj. Then we can get the following
equations
2
∑=m
mkk cdE ,(k=1,2,3,...j) (3)
m is the vector element number of cdk
2
1 ∑=+m
jj caE (4)
∑+=
=
= 1
1
'jk
kk
kk
E
EE (5)
Third, choose the above normalized energy as the feature vector of the signal, that is
],...,,[ '1
'2
'1 += jEEEE (6)
c SVM method
SVM (Support Vector Machine) is a classification and regression statistical theory proposed
by V.Vapnik in the AT&T Bell lab [25][26]. It’s widely used in signal recognition and
classification [27][28][29][30].The main concept of SVM lies in two notions: first, SVM is
used under the condition of liner separable cases. For the linear inseparable cases, non-linear
mapping algorithm is applied to transform the low-dimension input linear inseparable samples
into high-dimension feature space, making it possible to use liner algorithm to analyze the
non-linear characteristics of samples; second, when structural risk minimization theory is
applied in constructing the optimal split hyperplane among feature space, the studying
machine can get global optimization.
Given an input set liRx ni ,...2,1},{ =∈ that compose of two types of modes. If xi belongs to
the first type, then yi is 1, otherwise yi is -1. Here liy }1,1{ −⊂ is the SVM. Then the training
set can be expressed by liyx ii ,...,3,2,1},,{ = . The goal of SVM is to construct a target
function which can separate the two modes to extremity based on the risk structure
Yuan Zhan and Yibo Li, PREDICTION OF PCCP FAILURE BASED ON HYDROPHNE DETECTING
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minimization theory. Under the linear separable condition, a hyperplane that is able to classify
the samples can be expressed as below:
0=+⋅ bxω (7)
Here “ ⋅ ” is dot product, ω is a normal vector of the hyperplane, b is the offset.
The hyperplane is reached by the following second-optimization
2
21)(min ωωφ = (8)
which meets the constraint condition
.,...,3,2,1,1)( nibxy ii =≥+⋅ω (9)
Under the condition of large feature number, the second-optimization problem can be changed
into dual problem.
)(21)(max
1,1jiji
n
jiji
n
ii xxyyW ⋅−= ∑∑
==
αααα (10)
ii
n
ii xy∑
=
=1
* αω (11)
ii xwyb ⋅−=* (12)
Which meets the following constraint condition
niy ii
n
ii ,...3,2,1,0,0
1=≥=∑
=
αα (13)
Here the ),...,,( 21 nαααα = is the Lagrange multiplier, *ω is the normal vector of the
hyperplane, *b is the offset of the hyperplane. KKT condition plays an important role in
such problem solution and analysis, which is shown in the equation (14)
nibxyii ,...,3,2,1,0}1)({ ==−+⋅ωα (14)
According to equation (14), the samples with 0=iα have no effect to the classification,
while samples with 0>iα are available in the classification process. The final classification
function is:
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*
1
)()( bxxyxf ii
n
ii +⋅= ∑
=
α (15)
III METHODOLOGIES
Since wire break is one of the primary causes of PCCP failure, precise prediction of PCCP
failure depends on correct identification of PCCP wire break signal. In our approach,
hydrophones were placed along the PCCP pipeline used to detect the wire break signal.
However, in real monitoring system, interferential signals, such as the walking noise of
human being along the pipe, external interference noise of tapping due to construction, repair,
and the internal surging noise in the pipeline caused by air or unstable pressure inside the pipe,
can easily disturb or mix with wire break signal since the SNR of the interfering signals itself
is undesirable. Figure 2 shows the flow chart of the working process.
Abrupt acoustical signal received by
hydrophone
Data pre‐procesing
Wavelet feature extraction
SVM parameter selection
SVM classificationWire break
Warning signal
Continue regular work
No
Figure 2 Flow chart of the system working process
For the purpose of distinguishing the wire break signal from other interferential signals,
frequency-based feature extraction is an option since different types of acoustical signals were
dominated in different frequencies. Our research adopted wavelet analysis because wavelet
Yuan Zhan and Yibo Li, PREDICTION OF PCCP FAILURE BASED ON HYDROPHNE DETECTING
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transform is good at scoping every detailed part of the original signal in both time-domain and
frequency-domain. By decomposing a signal into several sub- frequency bands, the energy
distribution in different bands can be utilized as eigenvectors of PCCP failure signal in feature
extraction.
After feature extraction, SVM was applied to the linear inseparable interfering noise and wire
break signal for classification. Since SVM is a structural-based risk minimization
classification tool, cross-validation was used for parameters optimization, which will enhance
the prediction accuracy tremendously. First, the original sample was divided into K average
groups, with one group as testing set, while the other K-1 groups as training set each time for
K times. The classification rates of the K models acquired are indicators of the property of the
model.
IV EXPERIMENT
a. System introduction
Figure 3 Experiment system display
Figure 3 is a sketch of the experiment system. The diameter of PCCP in this experiment is
1.4m. Hydrophone is inserted into PCCP through the joint well in the pipelines with sealing
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measures. In real PCCP, the joint wells along the pipeline can be used for hydrophone
installation. The inner structure of hydrophone facilitates its high sensitivity to acoustic signal
in water. In the experiment, sensitivity of the hydrophone to broadband (1HZ-100KHZ)
acoustic signal is -170dB. Since the aimed acoustic signal in this experiment are all within the
human’s ear limitation (20HZ~20KHZ), hydrophone is capable of receiving the desired signal.
The signal acquisition device is USB 4431 developed by National Instrument Corporation,
with a 24 bits resolution , maximum 102.4ksps simultaneous sampling rate and ± 10V input
range. The user interface of data acquisition is programmed using LabView. The sampling
rate in this experiment is 44 kbps.
Besides the surging signal results from the instable pressure in the pipeline, and the wire
break signal results from PCCP inner failure, we artificially added two interfering signals:
human walking noise and hammer tapping on the pipe surface to mimic real PCCP
environments.
b. Data processing
As mentioned in 1.2, α mode is the dominant mode in water-filled pipeline with little
energy loss into soil or scattering at joint or fitting. Therefore, acoustic signal received by
hydrophone is mainly α mode acoustic signal. Figure 4 shows the time-domain wave plot
of the four signals, all of which can be considered as sudden event for the PCCP. The length
of every signal is 6000 points.
0 1000 2000 3000 4000 5000 6000-6
-4
-2
0
2
4
6
8Wire Break Signal
Samples
Ampl
itute
/V
0 1000 2000 3000 4000 5000 6000-5
0
5Internal surging interference signal
Samples
Ampl
itute
/V
0 1000 2000 3000 4000 5000 6000-15
-10
-5
0
5
10
15External tapping interference signal
Samples
Am
plitu
te/V
0 1000 2000 3000 4000 5000 6000-1.5
-1
-0.5
0
0.5
1
1.5Walking noise signal
Samples
Am
plitu
te/V
Figure 4 Time domain wave of four signals
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c. Feature extraction
Wavelet energy normalization method is applied to extract the feature from the four different
signals. In the wavelet analysis process, the Daubechies6 wavelet is used as the wavelet basis.
The signals are decomposed into 8 layers. Since the sampling rate of data collected is 44kbps,
after the wavelet decomposition process, the signal is divided into 9 bands with each band
characterized by a normalized energy. Figure 5 displays the four signals’ energy distributions
in different bands.
12
34
56
78
9
12
34
0
0.5
1
Layer
Energy distribution of four sinals in 9 frequency bands
Signal type
Nor
mal
ized
ene
rgy
Signal type 1: wire break , 2: internal surging signal, 3: external tapping signal, 4: walking
signal. Layer 1(cd1): 11000HZ~22000Hz, 2(cd2):5500~11000HZ, 3(cd3): 2750~5500HZ,
4(cd4):1375~2750Hz, 5(cd5):688~1375HZ, 6(cd6): 344~688HZ, 7(cd7): 172~344HZ, 8(cd8):
86~172HZ, 9(ca8): 0~86HZ.
Figure5 Energy distribution of four signal base on wavelet decomposition
Figure 5 is the normalized energy distribution of the four different signals. The wire break
signal has rather average distribution in each band. While the internal surging signal
dominates in the low frequency band ca8(0~86HZ). The external tapping signal has
concentrated energy in cd5(688~1375HZ) and cd6(344~688HZ). The walking signal
dominates in the cd8(86~172HZ) and ca8(0~86HZ).From the energy distribution histogram,
obvious and clear difference of the four signals can be quantified by a series feature vector
which consists of 9 dimensions of elements. Since frequency is a fundamental characteristic
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of acoustic signal, different types of signals may dominate in different frequencies, the
frequency-based feature extraction method is appropriate for the four acoustic signals.
d. SVM identification
0 30 60 90 1200
2
4
6
8 x 10-3 db1
samples
norm
aliz
ed e
nerg
y
0 30 60 90 1200
0.02
0.04
0.06db2
samplesno
rmal
ized
ene
rgy
0 30 60 90 1200
0.1
0.2
0.3
0.4db3
samples
norm
aliz
ed e
nerg
y
0 30 60 90 1200
0.2
0.4
0.6
0.8db4
samples
norm
aliz
ed e
nerg
y
0 30 60 90 1200
0.2
0.4
0.6
0.8db5
samples
norm
aliz
ed e
nerg
y
0 30 60 90 1200
0.2
0.4
0.6
0.8db6
samples
norm
aliz
ed e
nerg
y
0 30 60 90 1200
0.1
0.2
0.3
0.4db7
samples
norm
aliz
ed e
nerg
y
0 30 60 90 1200
0.2
0.4
0.6
0.8db8
samples
norm
aliz
ed e
nerg
y
0 30 60 90 1200
0.5
1ca8
samples
norm
aliz
ed e
nerg
y
Figure 6 Scatter plots of 120 samples including four different signals
In the classification process, a total number of 120 sets of data are analyzed. Set 1 to 30 are
wire break signals, sample 31 to 60 are internal surging signals and sample 61 to 90 are
external tapping signals and sample 91 to 120 are walking signals. Before the SVM
classification process, feature extraction of 120 samples is conducted based on wavelet energy
normalization method. After the feature extraction, each sample has 9 element feature vector
representing energy intensity in 9 different frequency bands. Figure 6 displays the energy
distribution of 120 samples in different frequency bands. From the figure, we can see
db3,db5,db6 and ca8 have quite good classification.
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1593
-10-8
-6-4
-20
24
68
10
-10-8
-6-4
-20
24
68
1030
40
50
60
70
80
90
100
log2c
SVM Parameter selection result(3D View) Best c=32 g=32 CVAccuracy=96.25%
log2g
Acc
urac
y(%
)
Figure 7 Large step SVM parameter selection result
-10-8
-6-4
-20
24
68
10
-10-8
-6-4
-20
24
68
1030
40
50
60
70
80
90
100
log2c
SVM Parameter selection result(3D View) Best c=24.2515 g=73.5167 CVAccuracy=97.5%
log2g
Acc
urac
y(%
)
Figure 8 Small step SVM parameter selection result (3D View)
In the application of SVM, cross validation is conducted before the final classification. At first,
a large step SVM parameter selection is conducted. The parameter c and g change
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from2^( -10) to 2^(10) with a step of 0.5 .The predicted accuracy is shown in Figure 7. The
approximate range of c and g is achieved, where c is 32 and g is 32. The accuracy is 96.25%.
Then a small step parameter selection is carried out. The parameter c and g change
from2^( -10) to 2^(10) with a step of 0.1 The result is shown in Figure 8. The best c is
24.2515and best g is 73.5167. The accuracy is 97.5%.
By comparison of the results shown in Figure 7 and Figure 8, the accuracy of small step is
higher than that of large step. Therefore a final optimal parameter selection is accomplished
by small step. The best c is 24.2515 and the best g is 73.5167.
After the determination of best c and g, the next step is to apply the best c and g in the SVM
model. Of the totally sampled 120 sets of data, each ten samples are chosen from the four
different types as training samples. Then a classification model is built based on the training
samples. A total of 120 samples are utilized to test the accuracy of the model built based on
SVM method. A final accuracy of 98.33%(118/120) is shown in Figure 9. We can see that
there are one internal surging signal and one walking noise signal predicted wrong. All the
wire break samples are predicted right.
0 20 40 60 80 100 1201
1.5
2
2.5
3
3.5
4
Samples
Sam
ple
labe
ls
Test labelPredict label
Figure9 Prediction result based on SVM
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V CONCLUSIONS
(1)An efficient and economic PCCP failure prediction system is proposed. Hydrophone is
used as the sensor due to its low cost, easy installation, and high sensitivity to acoustic signal
in the PCCP. The result shows that the hydrophone is proper for PCCP failure prediction.
(2)The wavelet method is proved to be appropriate for the feature extraction of the wire break
signal due to its fundamental frequency characteristics. The features of wire break signal and
other three signals including human walking noise, internal surging noise and external tapping
noise, show very distinct differences.
(3)SVM is proven to be an efficient and accurate method for type classification. By selecting
appropriate parameters for the SVM method, high classification precision can be achieved.
Wire break signal can be easily identified with reduced false prediction.
ACKNOWLEDGEMENTS
This work was supported by the National Natural Science Foundation of China (Grant
NO.60974110) and Tianjin tap water pipeline company.
REFERENCES
[1]S. Ge and S. K. Sinha, "Effect of Wire Breaks on Prestressed Concrete Cylinder Pipe
(PCCP) Reinforced with Steel Liners—A Case Study", in Pipelines 2012@ sInnovations in
Design, Construction, Operations, and Maintenance, Doing More with Less, pp. 1297-1306,
2012.
[2] S.-p. Sun and M. Wang ",Characteristic of prestressed concrete cylinder pipe," Municipal
Engineering Technology, 2006.
[3] J. J. Galleher and A. E. Romer, "Who Says You Need Multiple Wire Breaks for a PCCP
Pipe to Fail?", in Pipelines 2012@ sInnovations in Design, Construction, Operations, and
Maintenance, Doing More with Less, pp. 278-287, 2012.
INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL. 6, NO. 4, SEPTEMBER 2013
1596
[4] M. Higgins and P. Paulson, "Fiber optic sensors for acoustic monitoring of PCCP", in
Proceedings of the 2006 Pipeline Division Specialty Conference-Pipelines 2006: Service to
the Owner, 2006.
[5] N. D. Faber, M. R. Coghill, and J. J. Galleher, "Beyond the Wires: A Sustainable Approach
to Prestressed Concrete Cylinder Pipe Management", in Pipelines 2012@ sInnovations in
Design, Construction, Operations, and Maintenance, Doing More with Less, pp. 1214-1222,
2012.
[6] M. S. Zarghamee, D. W. Eggers, R. Ojdrovic, and B. Rose, "Risk analysis of Prestressed
concrete cylinder pipe with broken wires", Pipeline Engineering and Construction
International Conference 2003, pp. 599-609,2004.
[7] R. You and H. B. Gong, "Failure Analysis of PCCP with Broken Wires", Applied
Mechanics and Materials, vol. 193, pp. 855-858, 2012.
[8] A. Biggar, "Detecting Wire Breaks from the Outside of PCCP", in Proceedings of the
ASCE International Pipelines Conference 2010: Climbing New Peaks to Infrastructure
Reliability—Renew, Rehab, and Reinvest 2010.
[9] M. S. Zarghamee and R. P. Ojdrovic, "Risk Assessment and Repair Priority of PCCP with
Broken Wires", 2004.
[10] G. E. Bell and P. Paulson, "Measurement and Analysis of PCCP Wire Breaks, Slips and
Delaminations", Pipelines 2010: Climbing New Peaks to Infrastructure Reliability - Renew,
Rehab, and Reinvest - Proc. of the Pipelines 2010 Conference, vol. 386, pp. 1016-1024, 2010.
[11] P. Cliff Moore, "Use of Acoustic Monitoring Data for PCCP Condition Assessment",
Pipelines 2009: Infrastructure's Hidden Assets - Proceedings of the Pipelines 2009 Conference,
vol. 360, pp. 45-54, 2009.
[12] M. Higgins and P. Paulson, "Fiber optic sensors for acoustic monitoring of PCCP", in
Proceedings of the 2006 Pipeline Division Specialty Conference-Pipelines 2006: Service to
the Owner, 2006.
[13]N.Afsarimanesh & P. Z. Ahmed, “LabVIEW Based Characterization and Optimization of
Thermal Sensors”, International Journal On Smart Sensing and Intelligent Systems, vol. 4, No.
Yuan Zhan and Yibo Li, PREDICTION OF PCCP FAILURE BASED ON HYDROPHNE DETECTING
1597
4, pp. 726-739, 2011.
[14]R. Long, M. Lowe, and P. Cawley, "Attenuation characteristics of the fundamental modes
that propagate in buried iron water pipes", Ultrasonics, vol. 41, No. 7, pp. 509-519, 2003.
[15] R. Long, K. Vine, M. Lowe, and P. Cawley, "Monitoring acoustic wave propagation in
buried cast iron water pipes", in AIP Conference Proceedings, p. 1202, 2001.
[16] R. Long, P. Cawley, and M. Lowe, "Acoustic wave propagation in buried iron water
pipes", Proceedings of the Royal Society of London. Series A: Mathematical, Physical and
Engineering Sciences, vol. 459, No. 2039, pp. 2749-2770, 2003.
[17] B. K. Sinha, T. J. Plona, S. Kostek, and S. K. Chang, "Axisymmetric wave propagation in
fluid‐loaded cylindrical shells. I: Theory", The Journal of the Acoustical Society of America,
vol. 92, p. 1132, 1992.
[18] F. Stulen and J. Kiefner, "Evaluation of acoustic emission monitoring of buried pipelines",
in 1982 Ultrasonics Symposium, pp. 898-903, 1982.
[19] S. G. Mallat, "A theory for multiresolution signal decomposition: the wavelet
representation", Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 11, No.
7, pp. 674-693, 1989.
[20] Y. Meyer and D. H. Salinger, “Wavelets and operators” vol. 1: Cambridge university
press, 1995.
[21] L. I. Kuncheva and J. J. Rodríguez, "Interval feature extraction for classification of
event-related potentials (ERP) in EEG data analysis", Progress in Artificial Intelligence, pp.
1-8, 2013.
[22] H.Hashim, S.Ramli, N.Wahid, & M.S. Sulainman , “Recognition of psoriasis features via
Daubechies D8 wavelet technique”, International Journal On Smart Sensing and Intelligent
Systems, vol.6, No.2, pp.711-732,2013.
[23] B. Lechner, M. Lieschnegg, O. Mariani, M. Pircher, &A. Fuchs,”A wavelet-based bridge
weigh-in-motion system”, International Journal On Smart Sensing and Intelligent Systems
vol.3, No.4, pp. 573-591, 2010.
[24] I. Daubechies, "Ten lectures on wavelets vol. 61: SIAM, 1992.
INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL. 6, NO. 4, SEPTEMBER 2013
1598
[25] V. Vapnik, "The nature of statistical learning theory: springer, 2000.
[26] B. E. Boser, I. M. Guyon, and V. N. Vapnik, "A training algorithm for optimal margin
classifiers", in Proceedings of the fifth annual workshop on Computational learning theory, pp.
144-152, 1992.
[27] W. Li, P. Fu, and W. Cao, “Study on feature selection and identification method of tool
wear states based on SVM” , International Journal On Smart Sensing and Intelligent Systems,
vol.6, No.2, pp.448-465.2013.
[28] A.-M.Cretu & P.Payeur, “Biologically-inspired visual attention features for a vehicle
classification task”, International Journal On Smart Sensing and Intelligent Systems, vol.4,
No.3, pp.402-423,2011.
[29] W. Zu, J. Yuan, and W. Zhang, "Determining method for reliability distribution function
of transformer fault diagnosis based on SVM", Heilongjiang Dianli Jishu(Heilongjiang
Electric Power), vol. 35, No. 2, 2013.
[30] L. Jian, K. Weikang, S. Jiangbo, W. Ke, W. Weikui, Z. Weipu, et al., "Determination of
Corrosion Types from Electrochemical Noise by Artificial Neural Networks", Int. J.
Electrochem. Sci, vol. 8, No. pp. 2365-2377, 2013.