Detection and localization of small

damages in a real bridge by local excitation

using piezoelectric actuators

P. Rathish Kumar, Toshiyuki Oshima,

Tomoyuki Yamazaki, Shuichi Mikami &
Yasunouri Miyamouri

Journal of Civil Structural Health

Monitoring

ISSN 2190-5452

J Civil Struct Health Monit

DOI 10.1007/s13349-012-0020-5

1 23
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1 23
 Author's personal copy
J Civil Struct Health Monit
DOI 10.1007/s13349-012-0020-5

ORIGINAL PAPER

Detection and localization of small damages in a real bridge

by local excitation using piezoelectric actuators
P. Rathish Kumar • Toshiyuki Oshima •
Tomoyuki Yamazaki • Shuichi Mikami •
Yasunouri Miyamouri

Received: 18 October 2011 / Accepted: 20 June 2012

 Springer-Verlag 2012

Abstract Detection, localization and estimation of small detect damage at the earliest possible stage is an important
damage using piezoelectric actuators for local excitation is task of maintenance. One of the possible ways to do this is
the main idea of this study. The theoretical background of to monitor regularly changes in the dynamic characteris-
an algorithm based on power spectral density (PSD) tics. If the mass, geometric dimensions and bearing con-
method suiting multiple damage detection is developed and ditions are consistent, the change in the stiffness or
verified experimentally with the field data obtained from a discontinuities in the material due to a defect can cause
composite steel bridge. The method is based on only the change in the dynamic characteristics [1, 2]. This idea can
output data from the accelerometers without the need for be implemented in a bridge monitoring system for esti-
measuring the excitation force. Some damage scenarios mating the damage condition and the remaining capacity
were introduced to the test structure by releasing bolts from useful in the asset management of the infrastructure [3–5].
the members connecting the lower lateral members and the Many damage detection schemes rely on analyzing
main longitudinal girder. The results indicate that the PSD response measurements from sensors placed on the struc-
method could identify the location and monitor small ture [6–9]. Damage detection methods, such as acoustics or
damage growth in structural members. ultrasonic methods, magnetic field methods, radiograph,
Eddy current methods and thermal field methods, are either
Keywords Power spectral density  Damage detection  visual or involve localized experimental methods [10, 11].
Modal parameters  Vibration data  Small damage and It is difficult to apply these methods to detect damage in
health monitoring large structures or inaccessible members. Therefore, there is
a need for more global damage detection methods that can
be applied to a complex structure. During the past decade, a
1 Introduction significant amount of research has been done in the area of
damage detection using the dynamic response of a structure.
Structural damage detection, identification of location and Research efforts have been made to detect structural dam-
size of the structural damage leads to improved safety and age directly from dynamic response measurements in the
offer the possibility of extending the service life of a time domain, e.g., the random decrement technique [12, 13]
structure by repairing the structural components when/ or from frequency response function (FRF) [14]. In addi-
where necessary. The ability to monitor a structure and tion, methods have been proposed to detect damage using
system identification techniques [15, 16].
The basic idea of damage or fault detection based on
P. R. Kumar (&)
Department of Civil Engineering, National Institute changes in the dynamic response is that the occurrence of
of Technology, Warangal, Andhra Pradesh, India damage or loss of integrity in a structural system leads to a
e-mail: drrateesh@gmail.com change in response due to dynamic forces caused by
changes in the dynamic properties of the structure (Eigen
T. Oshima  T. Yamazaki  S. Mikami  Y. Miyamouri
Department of Civil Engineering, Kitami Institute frequencies, modal damping rates, mode shapes and/or
of Technology, Kitami, Hokkaido, Japan transfer functions). Extensive research work was carried

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out on the development of non-destructive damage assess- over continuous frequency range including eigenvalue
ment methods and on the translation of changes in the modal frequencies will be compared before and after damage
characteristics with damage in a structure [17–21]. using the proposed method. Spectral function data can then
In this paper, a method based on changes in the power be analyzed using statistical procedures to determine the
spectral density (PSD) is presented. The algorithm is used to damage location, as explained in detail in the next section.
detect damage, locate its position and monitor the increase
in damage at multiple locations using only the measured 2.1 Concept of power spectral density
data without the need for any modal identification or
numerical models. This method is applied to the experi- For a continuous time series, x(t), defined on the interval of
mental data extracted from a composite steel bridge with 0 to T, the discrete Fourier transform (DFT), X(f), is defined
steel longitudinal and cross girders after inducing some as [1]:
defects to the structural connections joining the longitudinal ZT
girder. The damage was introduced to the bridge through Xðf Þ ¼ xðtÞei2pft dt ð1Þ
the release of some bolts connecting the lower laterals to
0
one of the main longitudinal girder of the bridge. pffiffiffiffiffiffiffi
A comprehensive bridge monitoring system is one that where i ¼ 1 and f = cyclic frequency (Hz).
has a self-monitoring system where sensors feed measured This function is complex and its magnitude is typically
responses (accelerations, strains, etc.) into a local com- plotted in engineering units (EU), such as m/s2 or g, versus
puter. In turn, this computer would apply a damage iden- frequency. The power spectrum is then defined as:
tification algorithm to this data to determine if the bridge
jXðf Þj2 ¼ Xðf ÞXðf Þ ð2Þ
has significantly deteriorated to the point where structural
safety maybe jeopardized. The local computer could then where X* denotes a complex conjugate of X(f). The power
contact a central monitoring facility (via cellular phone) to spectrum is a real-valued frequency domain function with
notify the appropriate maintenance or safety officials of the units of (EU)2. The PSD, Gx(f) is defined as:
bridge’s current condition.
In this paper, the implementation of piezoelectric actu- 2 h i
Gx ðf Þ ¼ E jXðf Þj2 ð3Þ
ators as a local excitation source for large structures such as T
steel bridges is presented. The advantage of using piezo- where E[ ] indicates an ensemble average for a specific f
electric actuators over shakers, hammers or ambient over n samples of X(f). Again, this is a real-valued fre-
vibrations is also shown in experimental results. quency domain function and has the units of (EU)2. From
the definition of PSD, it is noteworthy that PSD is calcu-
lated from the measured response of the structure such as
2 Damage identification algorithm the acceleration response without the need for measuring
the excitation force. However, the excitation forces used
Modal parameters, such as mode shapes, resonant fre- for the undamaged and damaged structure must have the
quencies and damping, are the functions of physical same amplitude and vibration waveform. Therefore, it is
properties of the structure (mass, stiffness and boundary not necessary to measure the excitation force in order to
conditions). Damage will change the physical properties of use the ambient vibrations as an excitation source for the
the structure, which in turn alter the modal parameters. continuous health monitoring of structures. On the other
Many techniques have been proposed in the area of non- hand, the problem of obtaining two equal excitation forces
destructive damage detection using changes in the modal from the ambient vibration data is under research stages.
parameters. However in many structures, only few modes
are available which may decrease the accuracy of detecting 2.2 Proposed algorithm and research significance
and localizing damage using these techniques. The basic
premise of the proposed damage identification technique is Let Gi(f) denote the PSD magnitude measured at channel
that for each modal response, the magnitude of spectral number i at frequency value f. The absolute difference in
function can be estimated. Then, any change in the modal PSD magnitude before and after damage can then be
response due to the occurrence of damage will, in turn, defined as:
change the spectral function magnitude. In order to over-
Di ðf Þ ¼ jGi ðf Þ  Gi ðf Þj ð4Þ
come the problem of the limited number of identified
eigenvalue parameters, spectral function information esti- where Gi(f) and Gi ðf Þ represent PSD magnitude for the
mated from the various accelerometer measurements at all undamaged and damaged structures, respectively. When
frequencies within the measured range and all responses the change in PSD is measured at different frequencies in

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the measurement range from f1 to fm, a matrix [D] can be In order to monitor the frequency of damage detection at
formulated as follows: any node, a new matrix [C] is formulated. This matrix
2 3 represents the ratio of a particular change in PSD to the
D1 ðf1 Þ D1 ðf2 Þ . . .. . . D1 ðfm Þ
6 D2 ðf1 Þ D2 ðf2 Þ . . .. . . D2 ðfm Þ 7 maximum change in that row. As explained earlier based
6 7 on the maximum locations and no damage locations in
6   . . .. . .  7
D¼6 6 
7 ð5Þ matrix [M], the values in the [C] matrix shall be unity or
6  . . .. . .  7 7
4   . . .. . .  5 zero. For example, in the matrix [C], C3(f1), C1(f2) and
Dn ðf1 Þ Dn ðf2 Þ . . .. . . Dn ðfm Þ C4(f3), etc. correspond to 1 as they are elements of
maximum change of PSD in those rows. Similarly, C4(f1),
where n represents the number of measuring points. In C3(f2) and C2(f3), etc. correspond to 0s at damage locations.
matrix [D], every column represents the changes in PSD at Similar procedure is followed in other locations and other
different measuring channels but at the same frequency columns also and the matrix is as shown below:
value. The summation of PSD changes over different 2h i h i h i3
frequencies is used as the indicator of damage occurrence M1 ðf1 Þ
½1 M1 ðf3 Þ
. . .. . . M1 ðfm Þ

and the increase in damage. In other words, the damage 6 hM3 ðf1 Þi h i M4 ðf3 Þ M2 ðfm Þ 7
6 M2 ðf1 Þ M2 ðf2 Þ 7
indicator is calculated from the sum of rows of matrix [D] as: 6 M ðf Þ ½0 . . .. . . ½1 7
6 3 1 M1 ðf2 Þ
h i h i 7
8P 9 6 M3 ðf3 Þ M3 ðf2 Þ 7
> D1 ðf Þ > 6 ½1 ½ 0  . . .. . . 7
>
> >
> 6 h i M4 ðf3 Þ hM2 ðfm Þi 7
> Pf > C¼6 7:
>
> >
> 6 ½0 M4 ðf2 Þ
½ 1  . . .. . . M4 ðfm Þ 7
>
> D 2 ðf Þ >
> 6 M1 ðf2 Þ M2 ðfm Þ 7
> f > 6 
<
:
= 6   . . .. . . 0 7 7
Total change ¼ : ð6Þ 6  7
>
> : >
> 4h i h  i h  i . . .. . . h  i 5
>
> >
> Mn ðf1 Þ Mn ðf2 Þ Mn ðf3 Þ Mn ðfm Þ
. . .. . . M2 ðfm Þ
>
>P : >
> M3 ðf1 Þ M1 ðf2 Þ M4 ðf3 Þ
>
> >
>
: Dn ðf Þ >
> ;
f
ð8Þ

However, this was found to be a weak indicator of damage Now, the total of maximum changes in PSD can be
localization. A statistical decision-making procedure was calculated from the sum of the rows of matrix [M] as:
hence adopted to determine the location of damage. The first 8P 9
>
> M1 ðf Þ > >
step in this procedure is the picking of the changes in PSD at >
> f >
>
>
> P >
>
each frequency value in each column of matrix [D]. Among >
> M 2 ðf Þ >
>
> f
< >
=
the values in the first column of the matrix [D], there can be :
SM ¼ : ð9Þ
one maximum, more than one maximum in the case of >
> : >
>
>
> >
>
identical damage at more locations or even zero >
> P : >
>
>
> >
>
corresponding to no change in PSD before and after : Mn ðf Þ >
> ;
f
damage. Accordingly, assuming that M3(f1) is the maximum
change in the first column corresponding to D3(f1) and let us The total number of instances of detecting the damage at
say the maximum change at M4(f1) is zero meaning no different nodes is calculated from the sum of the rows of
damage(no change in PSD) at that channel location. So, like matrix [C] as:
this there will be different values for different elements in the 8P 9
>
> C1 ðf Þ > >
first column corresponding to frequency (f1). Similarly, in the >
>P f >
>
>
> >
>
other columns also the maximum changes of PSD at different >
> C 2 ðf Þ >
>
>
< f >
=
frequencies can be identified. If the third channel at first :
frequency, first at second frequency, fourth at third frequency SC ¼ : ð10Þ
>
> : >
>
are maximum values and fourth channel at first frequency, >
> >
>
>
> : >
>
>P
> >
>
third at second frequency and second at third frequency are not >
: C n ðf Þ >
;
having any damage, then the new matrix [M] can be written as: f
2 3
M1 ðf1 Þ M1 ðf2 Þ M1 ðf3 Þ . . .. . . M1 ðfm Þ Damage bolts at locations connecting{SM} and {SC}.
6 M2 ðf1 Þ M2 ðf2 Þ 0 . . .. . . M2 ðfm Þ 7 In order to reduce the effect of noise or measurement
6 7
6 M3 ðf1 Þ 0 M ðf Þ . . .. . . M3 ðfm Þ 7 errors, a value of one or two times standard deviation of the
6 3 3 7
M¼6 6 0 M4 ðf2 Þ M4 ðf3 Þ . . .. . . M4 ðfm Þ 7 7: ð7Þ elements in vector {SM} will be subtracted from the vector
6    . . .. . .  7 {SM}. Any resulting negative values will be removed. The
6 7
4    . . .. . . 0 5 same procedure will be applied to the vector {SC} as
Mn ðf1 Þ Mn ðf2 Þ Mn ðf3 Þ . . .. . . Mn ðfm Þ follows:

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8P 9 8 9
M1 ðf Þ  r > >
> SMD2ð1Þ  SCD2ð1Þ >
>
>
> > >
> >
> f
> >
> >
> SMD2ð2Þ  SCD2ð2Þ >
>
>
>
> P >
> < =
>
> M ðf Þ  r >
> :
>
> 2 >
> Damage indicator 2 ¼ : ð14Þ
>
< f >
= >
> : >
>
: >
> >
>
SMD1 ¼ or >
> : >
>
>
> : >
> : ;
>
> >
> SMD2ðnÞ  SCD2ðnÞ
>
> : >
>
>
> >
>
>
> P >
> These damage indicators 0, 1 and 2 will be used to
>
: M n ðf Þ  r >
;
f
determine the damage location. On the other hand, the total
8P 9 change in PSD (Eq. 6) will be used to detect the occurrence
> M1 ðf Þ  2r >
>
> >
> of damage and assess the damage extent. The above
>
>
f
P >
>
>
> >
> algorithm could locate damage at more than one point as
>
> M 2 ðf Þ  2r >
>
>
> f >
> against the earlier approaches [22], where damage could be
< : =
SMD2 ¼ ð11Þ detected only at one single location, i.e., at maximum
>
> : >
> damage.
>
> >
>
>
> : >
>
>
> >
>
>
> P >
>
: Mn ðf Þ  2r >
> ;
f
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi, 3 Utilizing tunable piezoelectric actuators on bridges
P n P
n
where r¼ ðSMðiÞ  SMÞ2 ðn  1Þ; SM ¼
i¼1 i¼1
 Dynamic shakers and impulse hammers have been used
SMðiÞ n; extensively as excitation sources for structural dynamic
applications, especially in civil engineering applications.
8P 9 On the other hand, employing piezoelectric actuators [2]
> C1 ðf Þ  k >
>
> >
> for large civil infrastructures such as bridges or buildings
>
>
f
P >
>
>
> >
> have not been much reported in the literature because of
>
> C2 ðf Þ  k >
>
>
> f >
> their small force amplitude. In this research work, pie-
< : =
SCD1 ¼ or zoelectric actuators were used as a local excitation source
>
> : >
> to excite a localized area of the structure rather than
>
> >
>
>
> : >
>
>
> >
> exciting the structure in a global sense. The main
>
> P >
> Cn ðf Þ  k >
: >
; advantages of using piezoelectric actuators over conven-
f tional excitation methods, such as dynamic shakers,
8P 9
> C1 ðf Þ  2k > hammers or ambient vibration can be summarized as
>
> >
>
>P
>
f >
> follows:
>
> >
>
>
> C2 ðf Þ  2k >
>
>
> >
> • The actuator is very small (6 9 8 910 cm including a
< f : =
SCD2 ¼ ð12Þ magnetic holder), very light (about 1 kg including the
>
> : >
> magnetic holder) and can be handled easily. Conse-
>
> >
>
>
> : >
> quently, the actuator can be permanently fixed to any
>
> >
>
>
> P >
>
: Cn ðf Þ  2k >
> ; structural element and remotely operated for continu-
f ous health monitoring of structure.
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  • Actuators provide local excitation that can be employed
Pn  2 P
where k ¼ i¼1 SCðiÞ  SC ðn  1Þ; SC ¼ ni¼1 to excite only a localized region of the whole system.
 This employment of the local excitation facilitates the
SCðiÞ n: The damage indicators 1 and 2 are defined as extraction of features that are sensitive to local
the scalar product of {SMD} and {SCD} as shown in the structural response rather than the global behavior of
expressions (13) and (14). the structure. As a result, actuators are very efficient in
8 9
> SMD1ð1Þ  SCD1ð1Þ > mitigating the environmental and operation effects,
>
> >
>
>
> SMD1ð2Þ  SCD1ð2Þ > > which tend to be a global phenomenon.
>
< >
=
: • Piezoelectric actuators can excite the structure at
Damage indicator 1 ¼ ; ð13Þ
>
> : >
> different and high frequencies and, therefore, activate
>
> >
>
>
> : >
> various higher modes of the structure to detect small
: ;
SMD1ðnÞ  SCD1ðnÞ damages in bridges.

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• The ability to generate vibration by the actuators at any 4 Steel bridge: description and experimental setup
specific time allows undesired vibrations induced from
wind, traffic or other sources to be avoided. The experimental work in this research was performed on a
• The same excitation force (equal magnitude and the composite steel bridge with concrete piers and deck. The
same waveform) can be produced on both the undam- details of the span of the bridge inspected are shown in
aged and damaged structures, which is a crucial need Fig. 2a, b. This portion consists of four main longitudinal
for the application of several damage identification girders spanning 30 m and spaced at 8.5 m in the trans-
techniques. verse direction.
Two piezoelectric actuators attached to the web are used
The main procedure of using the actuators and their
to excite the chosen main girder of bridge in the out of
basic characteristics are explained here. A wave function
plane direction. The details of the location of the actuators
generator is used to adjust the required excitation fre-
are shown in Figs. 2c and 3. The plan of the steel girder in
quency range, the time in which the actuator reaches the
the portion between the two piers inspected is shown in
maximum frequency and the excitation waveform in a
Fig. 3 along with the positions of the accelerometers. The
sine sweep excitation form. Then, the adjusted waveform
sectional side view elevation of the cross girder of the
is transferred to the power supplier, which in turn pro-
bridge is shown in Fig. 4.
vides the actuator (Fig. 1) with the adjusted power. The
G1–G4 represents the longitudinal main girders, while
actuator is fixed to the structure by a magnetic holder.
16 channels in all Ch1–16 are used to evaluate the response
This magnetic holder is suitable for fixing the actuator to
at different portions of the bridge as shown in Fig. 3.
steel structures; however, a thin steel plate must be
The locations of the accelerometer position are chosen
mounted on the surface of concrete structures to attach
as an array in such a way that they correspond to the
the magnetic holder. A steel spring is fixed over the
locations in the vicinity of damage and excitation, so that
actuator to control the excitation force amplitude as
any minor changes in the bridge could be easily detected.
shown in Fig. 1. The produced force amplitude is constant
All the connections of the bridge girder were with bolts
but the excitation frequency gradually increases over time
and hence the removal of the bolts one by one of the
until it reaches its maximum value after the designated
lower laterals to the main girder was adopted to introduce
time. It should also be noted that because the actuator is
damage to the longitudinal main girder (G2) in the
pressed but not glued to the test structure, the actuator
present case. As explained earlier, two actuators, located
provides pressure force only.
at approximately the middle part on the web of the main
girder in the horizontal direction as shown in Fig. 2c,
were used for excitation. The excitation forces used for
the undamaged and the damaged structures were sweep,
equal in amplitude and had the same vibration waveform.
This was verified, but, the excitation force was not
measured as the method is based on the measured output
and not on the excitation force. The actuator force
amplitude was estimated to be around 200 N by mea-
suring the displacement in the spring that presses the
actuator. Although this force amplitude was very small
compared with the shaker force or ambient vibration, it
was sufficient to excite the web of the main girder even at
the farthest accelerometer. The acceleration response is
collected at various locations (channels 1–16). Acceler-
ometers were mounted at each of the nodal points as
shown in Fig. 3. For this study, 20 s time histories were
sampled at a rate of 6,500 Hz, producing 130,000 time
points. A matrix of response data sets was recorded
before and after damage. For each damage case, five
separate time histories were recorded. Totally, three cases
are examined including two damages and one under no
damage condition. The damage to the beam is introduced
in the form of removal of bolts. The three cases consid-
Fig. 1 Piezoelectric actuator components ered are

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Fig. 2 a, b Details of the bridge and the portion inspected. c Details of the two actuators fixed to web of the main beam

Case 1 No damage, case D0 (Fig. 5) where NFFT specifies the DFT length that PSD uses. The
Case 2 Releasing of eight bolts at locations connecting magnitude squared of the length NFFT DFTs of the sec-
the laterals and the main longitudinal plate girders (G2) tions are averaged to form Gi(f). Then 10 is multiplied to
viz Nodes 3-2 and 4-1 (Fig. 6). This condition is the base 10 logarithm of the elements of Gi(f) to compute
damage, case D1 Gi(f) in dB. Gi(f) is length NFFT/2 ? 1 for NFFT even,
Case 3Removal of eight bolts at locations connecting (NFFT ? 1)/2 for NFFT odd. If a scalar for WINDOW is
the diagonal bracing between the main longitudinal specified, a Hanning window of that length is used. Fs is
plate girders viz No 3-1 and 4-2 (Fig. 7) in addition to the sampling frequency which does not affect the spectrum
eight bolts at No 3-2 and 4-1. This condition is damage, estimate but is used for scaling the X-axis of the plots. In
Case D2. this study, WINDOW = NFFT = 4,096 and Fs = 6,500.

5.1 Before introducing any damage

5 Damage identification algorithm applied to different
damage cases for the bridge One of the drawbacks of general vibration-based damage
identification methods is that these methods sometimes
The PSD is calculated from node point accelerations using produce false positive readings due to noise, measurement
Matlab [23, 24] standard and the Matlab Signal Processing errors or environmental changes. It is therefore very
Toolbox as: Gi(f) = PSD (x(t), NFFT, Fs, Window) esti- important to check if the results obtained from the damage
mates the PSD of a discrete-time signal vector x(t) using identification methods are due to damage or due to other
Welch’s averaged, modified periodogram method [25, 26]. changes. Because of this need, the experiment was per-
x(t) is divided into overlapping sections, then windowed by formed a number of times on the undamaged structure prior
the WINDOW parameter, then zero padded to length NFFT to the introduction of any damage. PSD data for one data

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Fig. 3 Details of the

accelerometers and actuators
fixed to the main beam G2

Fig. 4 Typical side view

elevation of the cross girder

Fig. 5 Case D0: no damage

condition

Fig. 6 Case D1: removal of

bolts at No 3-2 and 4-1

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Fig. 7 Case D2: removal of

bolts at No 3-1 and 4-2 also in
addition to bolts at No 3-2 and
4-1

(a) x 10
4 PSD at Channel 4 (b) x 10
4 PSD at Channel 5
2 2.5
Undamaged 1 Undamaged 1
1.8 X: 548.8 Undamaged 2
Undamaged 2 X: 433.6
Y: 1.909e+004
Y: 2.337e+004
1.6 2

Power Spectral Density

Power Spectral Density

X: 334 X: 550.8
1.4 X: 300.8 Y: 1.577e+004
Y: 1.207e+004 Y: 1.546e+004

1.2 1.5
X: 585.9
1 X: 334.1 Y: 1.063e+004
Y: 7863
0.8 1
X: 318.4
X: 348.3 Y: 7023 X: 564.5
0.6 Y: 7547 X: 384.8
Y: 6386
X: 613.3
X: 585.9
Y: 4913 X: 535.2 Y: 4960
X: 263.7 Y: 3522
0.4 X: 385.7 0.5 Y: 3616
Y: 2541 Y: 2234
X: 367.2
0.2 X: 597.4
Y: 4794

Y: 2485
0 0
100 150 200 250 300 350 400 450 500 550 600 650 100 150 200 250 300 350 400 450 500 550 600 650
Frequency (Hz) Frequency (Hz)

(c) PSD at Channel 6

16000
Undamaged 1 X: 550.8
Undamaged 2 Y: 1.582e+004
14000
X: 451.2
Y: 1.172e+004
Power Spectral Density

12000
X: 433.6 X: 535.2
10000 Y: 9084 Y: 1.147e+004

8000 X: 585.9
X: 566.4 Y: 6384
Y: 5952
X: 519.5
6000 X: 367.2
X: 335.9 Y: 5026
Y: 4693
Y: 4339
X: 468.8
4000 Y: 3141

2000

0
200 250 300 350 400 450 500 550 600 650
Frequency (Hz)

Fig. 8 PSD versus frequency for various undamaged cases. a PSD for undamaged structure (channel 4). b PSD for undamaged structure
(channel 5). c PSD for undamaged structure (channel 6)

set obtained from the undamaged structure are shown in frequency range of 0–650 Hz, the data in the range of
Fig. 8a–c for three important channels near the damage 100/200–650 Hz are shown for clarity in Fig. 8.
location induced in the bridge. There was almost no change The total change in PSD due to noise was determined
in PSD due to noise and measurement errors. All the curves using Eq. (6) and the results are shown in Fig. 9. The total
were coinciding. Though the PSD data were studied in the change in PSD ranged from about 50–80 dB. When the

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Change in PSD Method The total change of PSD will be used as an indicator of
90
damage detection and damage increase. On the other hand,
Total Change in Power Spectral Density (dB)

Noise
80 damage indicators 0, 1 and 2 will be used to identify the
damage location.
70

60 5.2 Introducing damage by releasing bolts at No 3-2,

50
4-1

40 The first level of model damage was introduced in the

30 bridge by releasing the torque of eight numbers of bolts
connecting the lower laterals to the main longitudinal gir-
20
der at No 3-2 and No 4-1 as shown in Fig. 6. The accuracy
10 of a good damage identification method depends upon
locating such small damages caused in the bridge, which
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 can occur in the bridge due to ambient excitations, such as
Channel Number traffic, wind, earthquakes and their combination. PSD
magnitudes in the full frequency range of 0–650 Hz were
Fig. 9 Total change in PSD due to noise
used in the proposed algorithm. Figure 10a shows the total
total change of PSD was determined using other sets of change in PSD due to the releasing of the bolts at the above
data obtained from the undamaged structure, similar and locations. It was found that the total change in PSD is much
very close values of the total change in PSD were obtained. larger than that due to noise and measurement errors

(a) Change in PSD Method

(b) 4 Change in PSD Method
x 10
Total Change in Power Spectral Density (dB)

600 2
D0-D1 D0-D1
1.8
Damage Localization Indicator 0

500
1.6

1.4
400
1.2

300 1

0.8
200
0.6

0.4
100
0.2

0 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Channel Number Channel Number

(c) Change in PSD Method (d) Change in PSD Method

12000 5000
D0-D1 D0-D1
4500
Damage Localization Indicator 2
Damage Localization Indicator 1

10000
4000

3500
8000
3000

6000 2500

2000
4000
1500

1000
2000
500

0 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0 2 4 6 8 10 12 14 16 18
Channel Number Channel Number

Fig. 10 Proposed algorithm results for damage, Case 1. a Total change in PSD. b Damage localization using damage indicator 0. c Damage
localization using damage indicator 1. d Damage localization using damage indicator 2

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Change in PSD Method (Fig. 9). Although the maximum total change of PSD is
60
D0-D1
observed at channels 3–7 (very close to the damage loca-
tions), the total change in PSD seems to be not always a
Number of Times of Damage Detection

50 good indicator of damage as there are higher peaks noticed

at other channels also. Damage indicators 1 and 2 have
40 hence been determined based on Eqs. 13 and 14 as
explained in the algorithm. It was noticed that the damage
30 indicator 2 could locate the damage more accurately. The
details of the damage localization using indicators 0, 1 and
20 2 are shown in Fig. 10b–d, respectively. Another tool to
correlate the damage location is to determine the number of
10
times damage was detected at a particular channel (Eq. 10).
The result of the number of times the damage was detected
for this damage case is plotted in Fig. 11. A comparison of
0
0 2 4 6 8 10 12 14 16 18 changes in the PSD, the damage indicators and the number
Channel Number of times the damage was detected clearly shows that the
channels close to the damage induced viz channels 1–8
Fig. 11 Number of times damage detected at each channel
showed signs of damage. It was also noted that channel 9,

(a) Change in PSD Method (b) 5 Change in PSD Method

x 10
Total Change in Power Spectral Density (dB)

4500 4.5
D1-D2 D1-D2
4000 4
Damage Localization Indicator 0

3500 3.5

3000 3

2500 2.5

2000 2

1500 1.5

1000 1

500 0.5

0 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Channel Number Channel Number

(c) x 10
5 Change in PSD Method (d) x 10
4 Change in PSD Method
2.5 8
D1-D2 D1-D2
Damage Localization Indicator 1

7
Damage Localization Indicator 2

2
6

1.5 5

1
3

2
0.5
1

0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Channel Number Channel Number

Fig. 12 Proposed algorithm results for damage, Case 2. a Total change in PSD. b Damage localization using damage indicator 0. c Damage
localization using damage indicator 1. d Damage localization using damage indicator 2

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4250
though on the same longitudinal girder being excited, 4400

4000
Noise
showed lower values as it was not in the close proximity of 4000 Case 1

3500
Total Change in PSD(dB)
the damage location. From this, it is very clear that the PSD 3600 Case 2
3200
algorithm could localize and detect the position of damage
2800
accurately. 2400

2100

1750
2000

1600
5.3 Damage by releasing bolts at No 3-1, 4-2

1325
1600

1250
1200
in addition to release at No 3-2, 4-1 1200
800

500

500

500
480
450
425

410
360

350

350

356

300
290

260
250
225

210
200

200

195
400

180

180

110
The second level of model damage was induced in the

75

80

76
70

66

62

66
60

56

58

52

55

54

52

60

58
0
bridge by further releasing another eight bolts at No 3-1, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4-2 in addition to the already released eight bolts as Channel
detailed in the previous section. After increasing the Fig. 14 Total change in PSD for different damage cases
damage level, the same previous remarks can be made.
The values at the previous channels have increased and the • The total change in PSD due to noise is B80 dB at all
damage was more localized at channels 4–6. The plots of channels with close values at different channels.
the total change in PSD, the damage indicators 0, 1 and 2 • After releasing the first set of bolts (Case 1), the total
corresponding to the second level of damage are plotted in change in PSD increased at the undamaged locations
Fig. 12a–d. As clearly seen from these figures, the damage (damage at one location will change the overall
at channels 4, 5 and 6 were located accurately using both stiffness of the structure) and increased remarkably at
damage indicator 2 with no false positive reading with the damaged locations (channels 3–7).
indicator 2. It was also noted that at the same locations of • After releasing some more bolts (Case 2), the total
accelerometer channel locations 4, 5 and 6, the number of change in PSD continued to increase slightly at the
times of damage detection was also higher than others undamaged locations and remarkably at the damaged
(Fig. 13). location.
As clear from Figs. 10 and 12, damage at locations close
to channels 3, 4, 5, 6 and 7 were identified accurately using
damage indicator 2 without any false positive readings. The
total changes in PSD (Eq. 6) for the two cases of damage 6 Conclusions
and for the intact structure is plotted in Fig. 14. It is clear
that the total change in PSD monitored increased damage The work presented in this paper deals with a method to
successfully. detect small damage in a real steel composite bridge. The
The following remarks can be drawn from the above method encompasses the first three steps in the process of
analysis: damage detection: existence, localization and monitoring
the damage increase. The feasibility of using piezoelectric
actuators for exciting the structure at higher frequencies
Change in PSD Method
40 and detecting small damage at multiple locations is
D1-D2 investigated. The proposed method uses only the output
Number of Times of Damage Detection

35 acceleration response at every channel without measuring

the excitation force. Therefore, local acceleration response
30
measurements due to local excitation are only needed to
25 detect and identify the localized damages.
The accuracy of damage identification methods based on
20
modal analysis is sometimes reduced when the damage
15 occurs at a node of the used mode shapes. It should also be
noted that the accuracy of damage identification methods
10 based on the changes in FRF is dependent on the mea-
surement range in which FRF is measured. The proposed
5
method improves this drawback by using PSD data in the
0 total measured frequency range.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
The proposed method has shown good results in iden-
Channel Number
tifying the changes in PSD associated with damage from
Fig. 13 Number of times damage detected at each channel the changes attributed to noise or measurement errors. The

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algorithm enabled detecting damage at multiple locations mechanical systems from changes in their vibration characteris-
accurately. tics, a literature review. Los Alamos National Laboratory Report,
LA-13070-MS
11. Farrar CR, Jauregui DA (1996) Damage detection algorithms
Acknowledgments This research is supported by the grants for applied to experimental and numerical model data from the I-40
Strategic International Cooperative Program of Japan Science and bridge. Los Alamos National Laboratory Report, LA-12979-MS
Technology Agency (JST). The authors gratefully acknowledge their 12. Kummer E, Yang JCS, Dagalakis NG (1981) Detection of fatigue
support. Special thanks to bachelor students Subokawa, Momiyama, cracks in structural members. In: 2nd American society of civil
Hashida and Masyuki for their help in conducting the experiment on engineering/EMD specialty conference, Atlanta, Georgia,
the bridge site. pp 445–460
13. Yang JCS, Chen J, Dagalakis NG (1984) Damage detection in
offshore structures by the random decrement technique. J Energy
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