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Damage detection in beam-like structure based on wavelet packet

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  • Islamic Azad University Malekan Branch

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Modern and efficient methods of structural damage detection focus on signal processing and have drawn researchers' attention in recent years. These methods mainly are based on Wavelet Packet Transforms (WPT). The WPT is an extension of the Wavelet Transform, which provides a complete level-by-level decomposition of signal. The wavelet packets are alternative bases formed by the linear combinations of the usual wavelet functions. Therefore, the WPT enables the extraction of features from the signals that combine the stationary and non-stationary characteristics with an arbitrary time-frequency resolution. In this study, a damage detection index called Wavelet Packet Energy Rate Index (WPERI) is proposed for the diagnosing of damage in beam-like structures with two different damage scenarios. For this purpose, the measured vibration signals of an experimental model of the beam were decomposed into the wavelet packet components and the wavelet energy rate index which were computed to indicate the structural damages. It will be shown that, the advantage of this method is applying minimum number of sensors which therefore makes this method practical and economical in comparison with other methods, for example Continues Wavelet Transform and Discrete Wavelet Transform. Also, in spite of low signal to noise ratio, the damage location and intensity will be identified correctly.
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Scientific Research and Essays Vol. 6(7), pp. 1537-1545, 4 April, 2011
Available online at http://www.academicjournals.org/SRE
ISSN 1992-2248 ©2011 Academic Journals
Full Length Research Paper
Damage detection in beam-like structure based on
wavelet packet
M. Koohdaragh1, M. A. Lotfollahi-Yaghin2*, M. M. Ettefagh3, A. Mojtehedi2
and B. Beyghbabaye1
1Faculty of Civil Engineering, Islamic Azad University, Malekan Branch, Iran.
2Faculty of Civil Engineering, University of Tabriz, Iran.
3Faculty of Mechanical Engineering, University of Tabriz, Iran.
Accepted 13 October, 2010
Modern and efficient methods of structural damage detection focus on signal processing and have
drawn researchers’ attention in recent years. These methods mainly are based on Wavelet Packet
Transforms (WPT). The WPT is an extension of the Wavelet Transform, which provides a complete
level-by-level decomposition of signal. The wavelet packets are alternative bases formed by the linear
combinations of the usual wavelet functions. Therefore, the WPT enables the extraction of features
from the signals that combine the stationary and non-stationary characteristics with an arbitrary time-
frequency resolution. In this study, a damage detection index called Wavelet Packet Energy Rate Index
(WPERI) is proposed for the diagnosing of damage in beam-like structures with two different damage
scenarios. For this purpose, the measured vibration signals of an experimental model of the beam were
decomposed into the wavelet packet components and the wavelet energy rate index which were
computed to indicate the structural damages. It will be shown that, the advantage of this method is
applying minimum number of sensors which therefore makes this method practical and economical in
comparison with other methods, for example Continues Wavelet Transform and Discrete Wavelet
Transform. Also, in spite of low signal to noise ratio, the damage location and intensity will be
identified correctly.
Key words: Wavelet packet transform, damage, signal, sensor.
INTRODUCTION
During the service life of all structures such as beams,
large-scale frames, long-span bridges and high-rise build-
ings, local damage of their key positions may have been
continually accumulated, and finally results in sudden
failure of structures. Therefore damage identification of
the structures is very vital to protect against disastrous
collapses. A classification system of damage
identification commonly defines four levels of damage
assessment: (1) the presence of damage; (2) the location
of the damage; (3) quantification of the severity of the
damage; and (4) prediction of the remaining serviceability
of the structure (Doebling and Farrar, 1998). The effect of
*Corresponding author. E-mail: lotfollahi@tabrizu.ac.ir.
damage on the structural behaviour is the variation of its
stiffness that has great influences on dynamic properties
of structure. This subject is very significant in variation of
natural frequencies and modal shapes and these
differences make it possible to explore the changes of
damages. There are various methods for examination
and distinction of these differences, but each of them has
advantages and disadvantages. One of the methods is
based on the Fourier analysis, that transforms the signal
from a time-based or space-based domain to a
frequency-based one. Unfortunately, the time or space
information may be lost during performing this
transformation and it is sometimes impossible to
determine when or where a particular event takes place
(Ren and Roeck, 2002).
Zhong and Oyadiji (2007) presented a new approach
1538 Sci. Res. Essays
for crack detection in the beam-like structures when crack
is relatively small. This approach is based on finding the
difference between two sets of detail coefficients
obtained by the use of the Stationary Wavelet Transform
(SWT) of two sets of mode shape data of the beam-like
structure. In spite of detection of crack, this method has a
disadvantage, because the method can use only
stationary signal. Yan et al. (2006) suggested intelligent
damage diagnosis and its application prospects in
structural damage detection based on wavelet. Also, the
development trends of structural damage detection are
also put forward in their method. Xiang et al. (2006)
studied the model-based forward and inverse problems in
the diagnosis of structural crack location and size by
using the finite element method of a B-Spline Wavelet on
the Interval (FEM BSWI). Zhu and Law (2005) presented
a new method for crack identification of bridge under a
moving load based on wavelet analysis. Maosen and
Pizhong (2008) proposed a new technique, integrated
wavelet transform with taking synergistic advantages of
the Stationary Wavelet Transform (SWT) and the
Continuous Wavelet Transform (CWT) that, this
technique improved the robustness of abnormality
analysis of mode shapes in damage detection. Rucka
and Wilde (2006) presented a method for estimating the
damage location in beam and plate structures. In
addition, Zheng et al. (2006) suggested a damage
detection method based on a continuous wavelet
transform and applied to analyze flexural wave in a
cracked beam.
Most of the crack identification methods, which were
mentioned earlier, apply continuous wavelet transforms
based on the modal analysis and a large number of
sensors, so in practice this analysis can be very hard and
in some cases impossible. The present study aims to
devise a method of identifying the crack in a more
applicable and practical way. Hence, Wavelet Packet
Energy Rate Index is suggested, and the advantages of
the suggested method are compared with other ones.
Also, it will be shown that this index is sensitive to
increased depth of crack and this method used a low
number of sensors for detection of characteristics of
crack.
The theory of the wavelet packet transform
The Wavelet Packet Transform (WPT) is an extension of
the WT, which provides a complete level-by-level
decomposition of signal. This transform is formed by the
linear combination of the wavelet. So, the wavelet packet
transform can indicate the permanent and temporary
features of a signal with the desired frequency-time
separation (Han et al., 2005). Wavelet packets consist of
a set of linearly combined usual wavelet functions. The
wavelet packets inherit the properties such as
orthonormality and time-frequency localization from their
corresponding wavelet functions. A wavelet packet
)(
,t
i
kj
ψ
is a function with three indices where integers i, j
and k are the modulation, scale and translation
parameters, respectively:
)2(.
2
/
2)(
,kt
j
j
j
t
i
kj =
ψψ
(1)
The wavelet function is derived from the following
rebound relation:
),2()(2)(
2ktkht i
k
j=
−∞=
ψψ
(2)
)2()(2)(
12 ktkgt
k
ij =
−∞=
+
ψψ
(3)
The first wavelet function is known as the mother
function:
)()(
1tt
ψψ
= (4)
The discrete filters h(k) and g(k) are the quadrate mirror
filters associated with the scaling function and the mother
wavelet function. There are quite a few mother wavelets
reported in the literature. Most of these mother wavelets
are developed to satisfy some key properties such as the
invisibility and orthogonally. Choosing the best wavelet
function to find the location of the damage is very
important. There have been different wavelets such as
bior6.8, sym6, Gaus4, Gaus6, and db5.
In the current research, the mentioned wavelets are
discussed and as the db5 functions are better than the
other wavelets, it is proposed in this paper as the main
function (Han et al., 2005). The transform of packet
wavelet includes a complete decomposition of each
surface, so it analyzes in an area with a high frequency.
The rebound relation between the components of ith and
i+1th surfaces are as follows:
)()()( 2
1
12
1tftftf i
j
i
j
i
j+
++= (5)
)()(
12
1tHftf i
j
j
j=
+ (6)
)()(
2
1tGftf i
j
i
j=
+ (7)
The amount of H, G is gained as follows:
−∞=
=
k
tkhH )2({.} (8)
−∞=
=
k
tkgG )2({.} (9)
After decomposition in "j" surface, the function of f(t) is
indicated as follows:
)()(
2
1
tftf
j
i
i
j
=
=
(10)
The )(tf i
jfunctions of linear combination of wavelet
packet functions are gained as follows:
)().()( ,, ttctf i
kj
k
i
kj
i
j
ψ
−∞=
=
(11)
where the wavelet packet coefficients )(
,tci
kj can be
obtained from:
dtttfc i
kj
i
kj ).()( ,,
+∞
=
ψ
(12)
Providing that the wavelet packet functions are
orthogonal:
0)().( ,, =tt n
kj
m
kj
ψψ
(13)
Each component in the WPT tree can be viewed as the
output of a filter tuned to a particular basis function; thus,
the whole tree can be regarded as a filter bank. At the top
of WPT tree (lower level), the WPT yields a good
resolution in the time domain but a poor resolution in the
frequency domain. At the bottom of the WPT tree (higher
level), the WPT results in a good resolution in the
frequency domain yet a poor resolution in the time
domain.
In this study, the wavelet packet energy index is
proposed to identify the locations and severity of
damage. To do that, the signal energy i
f
Eat j level is first
defined as:
dttftfdttfE n
j
m n
m
jf
j j
j).()()(
2
1
2
1
2
= =
==
(14)
Substituting Equation (14) into (17) and using the
orthogonal condition Equation (16) yields:
=
=
j
i
j
j
i
f
fEE
2
1 (15)
Koohdaragh et al. 1539
Finally:
dttfE i
jf j
2
)(
=
(16)
Equation (15) shows that, the overall energy of the signal
can be decomposed to wavelet packet energy
components in different frequency bands. Finally, the
WPERI is proposed as follows, to identify the location
and intensity of the crack (Han et al., 2005)
=
=
j
i
j
i
j
i
j
j
ia
f
a
f
b
f
fE
EE
E
2
1)(
)()(
)(
(17)
Where, a
fi
j
E)(
is the component signal energy i
j
f
E at
j level without damage, b
fi
j
E)( is the component signal
energy i
j
f
Eat j level with some damage.
It is postulated that structural damage would affect the
wavelet packet component energies and subsequently
would alter this damage indicator. It is desirable to select
the WPERI, that is sensitive to the changes in the signal
characteristics (Zeng et al., 2005).
Damage identification procedures
A damage identification procedure based on the
proposed WPERI is described here. Two assumptions
were adopted in this study:
(1) The reliable undamaged and damaged structural
models are available;
(2) The structure is excited by the same impulse load and
acts at the same location.
Vibration signals measured from the structure by sensors
are first processed using the WPT. The level of wavelet
packet decomposition is determined through a trial and
error sensitivity analysis, using the undamaged and
damaged structural models. Then the wavelet packet
energy rates of signals are calculated (Benffey, 1993). If
n stands for the total number of all sensors distributing in
structure, a total of n WPERIs can be obtained, after
performing the wavelet packet decomposition. When the
mean values and the standard deviations of these
WPERIs are expressed as WPERI
µ
and WPERI
σ
, the
one-side
(
)
α
1 upper confidence limit for the WPERI
1540 Sci. Res. Essays
Figure 1. Flowchart of damage identification processing.
1 2 3 4 5 6 7 8 9 1 0 1 1
L = 8 2 0 m m
h = 1 0 m m
b = 2 0 m m
1 2 3 4 5 6 7 8 9 1 0 1 1
L = 8 2 0 m m
1
2
3
4
5
6
7
8
9
L = 8 2 0 m m
Figure 2. The experimental beam with its cross-section and crack positions.
can be obtained from;
)(
n
ZUL WPERI
WPERIWPERI
σ
µ
α
α
+= (18)
Where
α
Z is the value of a standard normal distribution
with zero mean and unit variance, such that the
cumulative probability is )1(100
α
. This limit can be
considered as a threshold value for alarming of possible
abnormality in the damage indicator WPERI. One special
advantage of this damage identification is that, the setting
of the threshold value is based on the statistical
properties of the damage indicator which was measured
with sensors. Any indicator that exceeds the threshold
would cause damage alarming. The location of sensors
whose WPERI values exceed the threshold will indicate
where possible damage occurs (Ang and Tang, 1975).
The flowchart in Figure 1 illustrates the considered
processes schematically.
THE EXPERIMENTAL SETUP
Three Box-section aluminium beams with span length of 820 mm,
as shown in Figure 2, are used to evaluate the proposed damage
assessment index. The properties of the beams are as follows:
Koohdaragh et al. 1541
Table 1. Characteristics of local and intensity damage in all of the undamaged and damaged beams.
Specimen Location of damage Number of elements Intensity of damage
(percent of cutting relative to the height of the beam)
D0 Safe - -
D1 1/2 L 6 20
D2 1/2 L 6 30
D3 1/4 L 3 30
D4 1/4 L 3 40
Figure 3. Beam dynamic measurements in the laboratory.
Figure 4. Acceleration–time history for two specimens.
mass density 3
/2700 mkg=
ρ
, elastic modulus 2
/70 mGNE =,
cross section area 2
200mmA =, and the inertia moment of cross
section 44 67.6666,67.1666 mmImmI yx == . Undamaged beam
and two damaged ones with different locations and intensity of
damage were considered. All beams were divided into 11 segments
as shown in Figure 2. Also, intensity of all damages was calculated
based on percent of element cutting (crack) relative to the height of
the beam as shown in Table 1. Dynamic tests and measurements
have been carried out on all the beams in the laboratory as shown
in Figure 3. The excitation is provided by an impact hammer applied
at node 11th. An accelerometer is used to measure the dynamic
responses. The sampling frequency for all signals is 3000 Hz. The
acceleration responses of beams at the same node (node 11th) are
shown in Figure 4. It is shown that damage cannot be seen in the
acceleration-time responses.
It should be mentioned that, applying one sensor for identification
1542 Sci. Res. Essays
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11
location
(
D
1
)
WPERI
Location (D1
)
Figure 5. Histogram of wavelet packet energy rate index for specimen D1.
0
5
10
15
20
25
30
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11
location(D2)
WPERI
L
ocation
(
D2)
Figure 6. Histogram of wavelet packet energy rate index for specimen D2.
0
10
20
30
40
50
60
70
1 2 3 4 5 6 7 8 9 10 11
location
(
D
3
)
WPERI
Location (D3)
Figure 7. Histogram of wavelet packet energy rate index for specimen D3.
of crack is one of the main advantage of this method. That is, the
beam exited in the 11th point and the response is extracted in 1st
point. Then, the beam was exited in the 11th point and the sensor
moved to the 2nd point and this processing continues. Therefore,
the location of load is fixed but the position of sensor (one sensor)
changes in the length of beam.
RESULTS AND DISCUSSION
For the tested beams, the decomposition level is chosen
to be 5 where a total of 32 component energies are
generated because when scale and level of
decomposition are less than 4, the identification of
damage will be impossible. After decomposing the
signals, the WPERIs
(
)
j
f
E of every node are calculated
using Equation (4). The histograms of results are shown
in Figures 5 to 8. As it can be seen in the stated figures,
the suggested index is in maximum amount in the
cracked position but in other positions, the index has low
Koohdaragh et al. 1543
0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10 11
location(D4)
WPERI
Location (D4)
Figure 8. Histogram of wavelet packet energy rate index for specimen D4.
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9 10 11
location
(
D
1
)
Location (D1)
Figure 9. Histogram after considering crack threshold for specimen D1.
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11
location (D2)
Location (D2)
Figure 10. Histogram after considering crack threshold specimen D2.
amounts. So, it can be used to identify the position of the
cracks. Furthermore, the present method not only
identifies the crack position but also is sensitive to the
crack depth.
With assuming 02.0
=
α
, the one-sided 98%
confidence upper limit
α
WPERI
UL for the WPERIs can be
calculated from Equation (5). For every damaged beam,
the histogram can be drawn when the
α
WPERI
UL value is
subtracted from the WPERI values. The histograms of
result are shown in Figures 9 to 12. As it can be seen in
the figures, the crack threshold is clearly visible and in
crack-free positions, this index is zero. For instance in
Figure 12, wavelet packet energy rate index in 6st nod
shows the exact position of the crack.
1544 Sci. Res. Essays
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6 7 8 9 10 11
location (D3)
Location (D3)
Figure 11. Histogram after considering crack threshold specimen D3.
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11
location
(
D
4
)
L
ocation
(
D4)
Figure 12. Histogram after considering crack threshold specimen D4.
CONCLUSION
Based on the analysis results of the simulated beam, it is
demonstrated that the proposed WPT-based energy rate
index is a good candidate index, that is sensitive to local
structural damage. These calculations are rather
straightforward and not time-consuming; hence, on-line
implementation is possible if the reference information is
available. The selection of scale and the level of suitable
decomposition are very important in wavelet packet
analysis.
As a result, if the scale and level of decomposition is
less than 4, the identification of damage will be
impossible. Also, increase in the depth of the crack raises
the suggested index based on the wavelet packet, but
does not have a linear relationship with high damage in
the structure. In addition, the last and main point which
can be concluded from this research is a possibility of
using minimum sensor for crack detection in comparing
with other methods. Therefore, this method is practicable
and applicable.
REFRENCES
Ang AHS, Tang WH (1975). Probability Concepts in Engineering
Planning and Design, vol. I. John Wiley & Sons, Inc., New York, pp.
258-300.
Benffey JP (1993). An Introduction to Reliability and Quality
Engineering. Longman Scientific & Technical, Longman Group UK
Limited, London, pp. 122-132.
Doebling SW, Farrar CR, Prime MB (1998). A summary review of
vibration-based damage identification methods, Shock and Vibration
Digest., 30 (2): 91-105.
Han JG, Ren WX, Sun ZS (2005). Wavelet packet based damage
identification of beam structures. Int. J. Solids Struct., 42: 6610-6627.
Maosen C, Pizhong Q (2008). Integrated wavelet transform and its
application to vibration mode shapes for the damage detection of
beam-type structures. Smart Mater. Struct., IOP. 17(5): 222-232.
Ren WX, Roeck G (2002a). Structural damage identification using
modal data, I: Simulation verification. J. Structural Eng. ASCE., 128
(1): 87-95.
Rucka M, Wilde K (2006). “Crack identification using wavelets on
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Xiang JW, Chen XF, Li B, He YM, He ZJ (2006). “Identification of a
crack in a beam based on the finite element method of a B-spline
wavelet on the interval.” J. Sound Vibration., 296(4-5): 1046-1052.
Yan YJ, Cheng L, Wu ZY, Yam LH (2006) “Development in vibration-
based structural damage detection technique.” Mechanical Syst.
Signal Processing., 21(5): 2198-2211.
Zeng SS, Wei XR, Jian GH (2005). Wavelet packet based damage
identification of beam structures. Int. J. Solids Struct., 42: 6610-6627.
Koohdaragh et al. 1545
Zheng L, Shuman X, Jun W, Xianyune S (2006). “Damage detection of
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Zhong S, Oyadiji SO (2007). Crack detection in simply supported
beams without baseline modal parameters by stationary wavelet
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... Under the heading of crack identification using the CWT and DWT, WPT methods have also been employed in damage detection subjected to moving loads. Many researchers have conducted damage identification, location, and quantification using wavelet packet decomposition [91][92][93][94][95]. Some have used the WPT for damage detection in beam-like bridges subjected to an impact load or cyclic combined loading [96,97]. ...
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Wavelet packet transform (WPT) is a mathematical tool which is an extension of wavelet transform. This tool has been used to estimate wavelet packet energy rate index (WPERI) to indicate the structural damage in simple structures that are subjected to known input loads. In this study, a novel approach is attempted in the form of WPT being used to detect damage in a glass fiber reinforced polymer (GFRP) cantilever type beam from the response under the ambient excitation. An effectiveness of the proposed damage diagnostic tool is verified by changing the parameters such as scale, level of decomposition to identify the location and size of damage.
... ________________________________________ 1 Research Scholar, rprakashiitm@gmail.com 2 Professor, mssiva@iitm.ac.in 3 Proprietor, dhanush@techpassiontech.com To deal this problem, wavelet packet transform has been proposed which is an extension of wavelet transform and it has ability to capture high frequency components through level by level decomposition of a signal. Jian-Gang et al. [3] and Koohdaragh et al. [4] estimated a quantity called wavelet packet energy rate index (WPERI) to indicate the structural damage in simple structures that are subjected to known input loads (mainly impulse loads). ...
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Wavelet packet transform (WPT) is a mathematical tool which is an extension of wavelet transform and it allows complete level by level decomposition of a signal. This tool has been used to estimate wavelet packet energy rate index (WPERI) to indicate the structural damage in simple structures that are subjected to known input loads. However, in many practical situations, it is difficult to introduce a known excitation, especially in large structures. Therefore, damage detection tools would require a methodology by which it is possible to detect damage from the ambient excitation. In this study, a novel approach is attempted in the form of WPT being used to detect damage in a glass fiber reinforced polymer (GFRP) cantilever type beam from the response under the ambient excitation. An effectiveness of the proposed damage diagnostic tool is verified by changing the parameters such as scale, level of decomposition to identify the location and size of the damage
... ________________________________________ 1 Research Scholar, rprakashiitm@gmail.com 2 Professor, mssiva@iitm.ac.in 3 Proprietor, dhanush@techpassiontech.com To deal this problem, wavelet packet transform has been proposed which is an extension of wavelet transform and it has ability to capture high frequency components through level by level decomposition of a signal. Jian-Gang et al. [3] and Koohdaragh et al. [4] estimated a quantity called wavelet packet energy rate index (WPERI) to indicate the structural damage in simple structures that are subjected to known input loads (mainly impulse loads). ...
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Wavelet transform (WT) analysis is a mathematical tool which has been widely used for structural damage detection applications in many industries like mechanical, aerospace, civil structures etc. Advantage of WT is that it breaks down a signal into a series of local basis functions on the space / time axis and allows the identification of local features of a signal from the scale and position of the wavelets. A wavelet based structural damage identified by variation of wavelet coefficients with known excitation has been studied earlier [1] and the abnormality analysis of mode shapes in damage detection with a relatively high signal to noise ratio explained [2]. It is difficult to introduce a known excitation in a practical situation. Therefore, damage detection tools would require a methodology by which it is possible to detect damage without having to impart a known excitation. In this study, an innovative approach is attempted in the form of WT being used to detect damage of glass fiber reinforced polymer (GFRP) cantilever type beam using the ambient excitation. By using wavelet filter passed through the obtained response signal, it is possible to obtain the wavelet coefficients pertaining a particular structure. The difference in the wavelet coefficient between the healthy and damaged specimen is used as an indicator of damage at the appropriate location. It is also possible to size the damage using this technique. A photograph of the experimental set-up is shown in Figure 1. The response signals are recorded over a short duration from accelerometers at various positions along length of a GFRP healthy and a specimen with a predefined damage. Wavelet error coefficients obtained from different sensors positions show that significant peak is attained at the defect location (see Figure 2). In the ongoing study, different methods that currently exist in literature are compared with the method proposed above to assess the effectiveness the proposed damage diagnostic tool with the existing ones. The results of the same will be presented at the time of the conference. Also, parameters such as positions of the sensors and size and location of damage will be varied in the experimental study to validate the tool.
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Marine structures are exposed to various destructive factors during their serviceability. Therefore, timely damage detection and repair of these structures at early stages can increase their service life and prevent economic and human losses as much as possible. In this study, a method is presented to identify the location of multiple damages in the piles of a dolphin pier. In the first step of the proposed method, based on a combination of the Wavelet Packet Energy Curvature Difference (WPECD) and the Richardson extrapolation, a damage index is introduced to accurately find the damage zone/damaged piles in the dolphin wharf. The energy curvature difference of the wavelet packet was obtained based on the vibrating signals of the structure. Using an image processing technique, in the second step of the method, the locations of damage were extracted via the WPECD method. The efficiency and capability of the proposed method was confirmed by numerical and experimental results. The exact geometry of the damages in the experimental model was initially scanned by a three-dimensional scanning device. Then, the scanned images were processed and imported into the numerical model as an input file. Finally, the results showed that the proposed method could discover multiple structural damages with acceptable accuracy.
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Introduction Structural damage and its extent can be detected by vibration-based techniques to avoid failure or to minimize maintenance. Among different damage identification techniques, modal curvature approaches are widely researched and applied one. On the contrary, wavelet transformation (WT) methods are gaining popularity in damage identification of real life buildings because of their suitability for non-stationary signals and non-dependency on baseline data. This paper presents a novel approach utilizing complex continuous wavelet to effectively locate change in physical properties of reinforced concrete (RC) buildings by virtue of variation in frequency and mode shapes due to small change in mass and stiffness. Methods In this paper, the effect of variation of mass and stiffness of a building on the modal parameters is established analytically using theequation of motion for a multi-degree freedom system under forced vibration condition. A 3-D finite element model was developed for predicting the modal frequencies and mode shapes of the scaled down six storey RC building and the effect of addition of mass on a particular level of structure on the modal parameters was studied. Further, acceleration time histories were recorded with variation in mass on 3rd story of building using wireless tri-axial accelerometers and the time histories were processed to arrive at Curvature Damage Factor and wavelet coefficients for identification of the additional load on the particular floor. Results Vibration responses from all floors of RC building in ambient and loaded conditions were analyzed for frequency response spectra (FRS). Mode shapes were drawn for unloaded case and loaded cases. It was observed that the modal frequency of building decreases with the increase in mass at floors. It is observed that CDF approach could detect the change in mass in both numerical and experimental results. However, CDF algorithm could not detect the addition of load in case 1, 2 and 3, i.e. when load was less than 25 kg, i.e. only 2.6% of floor mass (960 kg). The acquired data for the above stated load cases were analyzed using complex Gaussian ‘cgau5’ wavelet in MATLAB toolbox to determine the singularity in the signal in terms of wavelet coefficient modulus. It is observed that the WT approach is able to precisely locate the change in physical parameters of the RC model building. However, it is seen that additional load could not be detected in case where only 9 kg, i.e. 0.93% of the total floor mass, was placed on 3rd floor. Conclusions From the research work, it is observed that CDF technique is inefficient in damage detection and always demand prior baseline information, which is usually difficult to obtain in practice. However, the wavelet transform-based approach more accurately detects the location of change without relying on intact state vibration data.
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Wavelet packet transform (WPT) is a mathematical tool which is an extension of wavelet transform. This tool has been used to estimate wavelet packet energy rate index (WPERI) to indicate the structural damage in simple structures that are subjected to known input loads. In this study, a novel approach is attempted in the form of WPT being used to detect damage in a glass fiber reinforced polymer (GFRP) cantilever type beam from the response under the ambient excitation. An effectiveness of the proposed damage diagnostic tool is verified by changing the parameters such as scale, level of decomposition to identify the location and size of damage.
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This paper provides an overview of methods to detect, locate, and characterize damage in structural and mechanical systems by examining changes in measured vibration response. Research in vibration-based damage identification has been rapidly expanding over the last few years. The basic idea behind this technology is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Therefore, changes in the physical properties will cause detectable changes in the modal properties. The motivation for the development of this technology is presented. The methods are categorized according to various criteria such as the level of damage detection provided, model-based vs. non-model-based methods and linear vs. nonlinear methods. The methods are also described in general terms including difficulties associated with their implementation and their fidelity. Past, current and future-planned applications of this technology to actual engineering systems are summarized. The paper concludes with a discussion of critical issues for future research in the area of vibration-based damage identification.
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Wavelet analysis has been extensively used in damage detection due to its inherent merits over traditional Fourier transforms, and it has been applied to identify abnormality from vibration mode shapes in structural damage identification. However, most related studies have only demonstrated its ability to identify the abnormality of retrieved mode shapes with a relatively higher signal-to-noise ratio, and its incapability of identifying slight abnormality usually corrupted by noise is still a challenge. In this paper, a new technique (so-called 'integrated wavelet transform (IWT)') of taking synergistic advantages of the stationary wavelet transform (SWT) and the continuous wavelet transform (CWT) is proposed to improve the robustness of abnormality analysis of mode shapes in damage detection. Two progressive wavelet analysis steps are considered, in which SWT-based multiresolution analysis (MRA) is first employed to refine the retrieved mode shapes, followed by CWT-based multiscale analysis (MSA) to magnify the effect of slight abnormality. The SWT-MRA is utilized to separate the multicomponent modal signal, eliminate random noise and regular interferences, and thus extract purer damage information, while the CWT-MSA is employed to smoothen, differentiate or suppress polynomials of mode shapes to magnify the effect of abnormality. The choice of the optimal mother wavelet in damage detection is also elaborately addressed. The proposed methodology of the IWT is evaluated using the mode shape data from the numerical finite element analysis and experimental testing of a cantilever beam with a through-width crack. The methodology presented provides a robust and viable technique to identify minor damage in a relatively lower signal-to-noise ratio environment.
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The change of modal characteristics directly provides an indication of structural damage. Based on changes in frequencies and mode shapes of vibration, a damage identification technique is proposed in this paper for predicting damage location and severity. The method is applied at an element level with a conventional finite-element model. The element damage equations have been established through the eigenvalue equations that characterize the dynamic behavior. Several solution techniques are discussed and compared. The influence of simulated noise in the modal data is also presented. The method has been verified by a number of damage scenarios for simulated beams and has found the exact location and severity of damage. It is demonstrated that multiplying the damaged eigenvalue equations with the undamaged or damaged mode shapes provides more equations and guarantees the damage localization. The resulting equations, however, become more sensitive to the deviation of modal data and the direct solution often yields poor results. Numerical results show that the non-negative least-squares method can lead to satisfactory results in most cases. A regularization algorithm with error-based truncation is necessary to ensure the right solutions.
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Most of vibration-based damage detection methods require the modal properties that are obtained from measured sig-nals through the system identification techniques. However, the modal properties such as natural frequencies and mode shapes are not such a good sensitive indication of structural damage. The wavelet packet transform (WPT) is a mathemat-ical tool that has a special advantage over the traditional Fourier transform in analyzing non-stationary signals. It adopts redundant basis functions and hence can provide an arbitrary time-frequency resolution. In this study, a damage detection index called wavelet packet energy rate index (WPERI), is proposed for the damage detection of beam structures. The mea-sured dynamic signals are decomposed into the wavelet packet components and the wavelet energy rate index is computed to indicate the structural damage. The proposed damage identification method is firstly illustrated with a simulated simply supported beam and the identified damage is satisfactory with assumed damage. Afterward, the method is applied to the tested steel beams with three damage scenarios in the laboratory. Despite the noise is present for real measurement data, the identified damage pattern is comparable with the tests. Both simulated and experimental studies demonstrated that the WPT-based energy rate index is a good candidate index that is sensitive to structural local damage.
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This paper presents a general summary and review of state-of-the-art and development of vibration-based structural damage detection. Various structural damage detection methods based on structural dynamic characteristic parameters are summarised and evaluated. The principle of intelligent damage diagnosis and its application prospects in structural damage detection are introduced, and the development trends of structural damage detection are also put forward. (c) 2006 Elsevier Ltd. All rights reserved.