Advanced
Vibration
Measurement
System
for
Infrastructures using Laser Doppler Vibrometers
__________________________________________________________________________________________________________
TAKESHI MIYASHITA*, HIRONORI ISHII, KEITA KUBOTA, YOZO
FUJINO, NORIYUKI MIYAMOTO,
ABSTRACT:
A subjective visual inspection of infrastructures mainly has been conducted as
conventional maintenance technique. Therefore, the development of quantitative
maintenance techniques is required. This paper introduces three studies of advanced
vibration measurement for infrastructures using Laser Doppler Vibrometers.
INTRODUCTION
In Japan, continuous investments in infrastructures have formed a huge stock. However,
since the infrastructures were constructed rapidly and emphatically in high economic
growth period, the number of the degraded ones comes to increase rapidly. Therefore, the
development of quantitative and efficient maintenance techniques is required.
Laser Doppler Vibrometer (LDV) is an optical instrument employing laser technology
to measure velocity. The characteristics of LDV are the followings: first, in comparison
with conventional transducers such as accelerometers, non-contact and long distance
measurement is possible without adding mass or stiffness to an object. Second,
resolution of velocity is very high, and frequency bandwidth is very wide. Third, by
attaching a scanning unit of mirror in front of the laser sensor head, measurement on
multiple points is made possible. This paper introduces three studies of advanced
vibration measurement using LDVs in order to monitor infrastructures.
1. UNDERSTANDING OF HIGH-SPEED TRAIN
VIBRATION OF A RAILWAY STEEL BRIDGE1), 2)
INDUCED
LOCAL
At a railway steel box girder bridge, damage was observed on the web of a main girder at
the bottom end of a welded vertical stiffener. The objective of this study is to clarify the
cause of the damage
Bridge for measurement
The investigated bridge is a pair of steel mono-box girders with 4 spans as shown in Figs.1.
The stiffeners were not welded to the lower flange in the sections where positive moment
affects the main girder. In bridges which have similar detail, damage was observed on the
* Department of Civil and Env. Eng., Nagaoka University of Technology
Address: 1603-1 kamitomioka, Nagaoka, Niigata, 940-2188 JAPAN
E-mail: mtakeshi@vos.nagaokaut.ac.jp
163
web of a main girder at the bottom end of a welded vertical stiffener. The parts of the
bridge of similar detail were retrofitted such as in Fig.1(b) using a T-shape member
installed between the web and the lower flange using high tension bolts.
4@40 000
M
F
M
M
M
2600
E D E C E D E C E D E C E D
2000
@1 600
600
Damage
2000
2000
600
Center Line
of end span
2000
Not welded
Sec.D
(with Simple
cross frame)
Sec.C
(with Cross frame)
Sec.E
(without
cross frame)
࡮Damaged detail
࡮Retrofited detail
(a) Detailof bridge(b) Detail of Retrofitting (Sec.E)
Figure 1: The focused bridge for measurement
Measurement using conventional sensors
Accelerometers and strain gauges were installed in the bridge for measurement of train
induced vibration. Since it is suspected that the cause of high local stresses was local
vibration of the web or lower flange of the main girder, accelerometers were installed on
both the web and the lower flange of the main girder. The strain gauges were installed on
the main girder web 20mm away from the toe of welding. Furthermore, the strain gauges
were installed on the lower flange on the main girder as shown in Fig.2.
Measurement results
Figs.3 show examples of the field data. Fig.3(a) shows that there is one large waveform
caused by trains passing on the bridge and there are 17 cycles corresponding to each
vehicle passing the cross section. It is shown that the dominant frequency is 3.0 Hz. This
phenomenon is known as “speed effect by cyclic loading” 3) which depends on the interval
that bogies or train vehicles pass at constant speed. Fig.3(b) shows the presence of high
frequency local vibration, and the frequencies of these vibrations are 20Hz - 30Hz.
800 800
M
M
1000
2000
AX2L
Sec.Ԙ
ԙ
Ԛ
ԛ
Ԝ
2000
:strain gage
:Accelerometer
1000 1000
CL
5 sections were
measured
Vertical
Stiffner
2000
1000
2600
M
60
F
600
4@40 000
M
AX3C
S01R
SX2LI㧔inside㧕
SX2LO㧔outside㧕
X: the number of section
0
-10
-20
0
5
10
15
Time [s]
20
1
3.00Hz
3.00 Hz
0.8
0.6
0.4
0.2
0
0 10 20 30 40 50 60
Frequency [Hz]
60
40
20
0
-20
-40
-60
0
Acceleration [m/s2]
10
Stress [MPa]
Stress [MPa]
20
Acceleration [m/s2]
Figure 2: Measurement using conventional sensors
5
10
15
Time [s]
20
6
5 3.00Hz
32.80Hz
4
3
2
1
0
0 10 20 30 40 50 60
Frequency [Hz]
(a) Nominal stress of lower flange
(b) Acceleration of lower flange
Figure 3: The results of measurementby conventional sensors
164
The relation between vibration and train speed
Fig.4 shows the relation between the dominant frequency of acceleration of the main girder
and train speed of 39 trains. This figure shows that the dominant frequency of vibration of
the main girder depends on the train speed and it agrees with “speed effect by cyclic
loading”. Fig.5 shows the relation between the dominant frequency of acceleration of the
lower flange and train speed. This figure shows that the dominant frequency depends on
train speed, similar to the vibration of the main girder and that the frequency is an integer
multiple of the frequency of the main girder.
Train Speed [km/h]
Frequency [Hz]
3.2
Measurement
fb=V/90
3
2.8
2.6
2.4
1st Peak
2nd Peak
3rd Peak
300
280
260
240
10
220
11
12
13
200
230
240
250
260
270
280
25
Train speed [km/h]
30
35
40
Frequency [Hz]
Figure 4: Train speed and frequencies of
main girder
Figure 5: Train speed and frequencies of
lower flange
2
Acceleration [m/s ]
The relation between local vibration and local stresses
Fig.6 shows the relation between local vibration and local stresses. This figure shows that
there is a strong correlation between local stresses and the lower flange vibration Thus, it
was confirmed that the cause of high local stresses is local vibration of the lower flange.
The vibration-mode inducing local stresses can be seen in Fig.7 based on the investigation
of the phase between stress and acceleration.
6.0
5.0
4.0
3.0
2.0
1.0
0.0
Lower flange
Web
0OO 0OO
OO
OO
1.0
2.0
0OO
OO
OO
0.0
0OO
OO
OO
3.0
Stress [MPa]
Figure 7: Local mode shape
causing local stress
Figure 6: Correlation between
stress and acceleration
The relation between local vibration and train speed
Fig.8 shows the relation between the Fourier spectral amplitude and the frequency of the
lower flange vibration. This figure shows that there are 2 peaks of different frequencies. A
peak occurs at 28.7Hz and another one is at 32.8Hz. These 2 peaks identify the natural
frequencies of local vibration. Fig.9 shows the relation between the Fourier spectral
amplitude of the lower flange vibration and the train speed in each mode. It is shown that
each mode has each peak at a certain speed and that the frequency at each peak is an
integer multiple of the frequency of the main girder. Thus, it was confirmed that the
vibration is larger when the natural frequency of local vibration is an integer multiple of
the frequency of the main girder induced by cyclic loading.
165
32.80Hz
28.65Hz
4
8
1st Peak
2nd Peak
3rd Peak
2
0
25
30
35
28.65Hz
32.80Hz
2
Acceleration [m/s ]
2
Acceleration [m/s ]
6
4
Figure 8: Fourier spectral amplitude
and peak frequencies of lower flange
32.80/(268.4/90)=11
28.65/(258.0/90)=10
32.80/(246.2/90)=12
2
0
220
40
Frequency [Hz]
6
230
240
250
260
270
280
Train Speed [km/h]
Figure 9: Train speed and Fourier
spectral amplitude of lower flange
Measurement using LDVs
The measurement system consists of three scanning type LDVs at three sections and
one single point type LDV. The single point type LDV always measures a reference
point and is used to calculate the phase between measurement points for the
identification of mode shapes. Using LDV, measurements of ambient vibration was
conducted. During ambient vibration measurement, measurements were conducted
before and after retrofitting the bottom part of the vertical stiffeners as shown in Fig.1(b).
The objective of the measurement is to identify natural frequencies and mode shapes at
the sections before and after retrofitting.
Identification of mode shapes using LDVs
Figs.10 show identified mode shapes based on the ambient vibration measurement
Figs.10(a), (c) and (b), (d) show the mode shapes before and after attaching the stiffener
for retrofitting respectively. Notice that although natural frequencies of both modes of
Figs.10(a), (c) are the same 29.3 Hz, the mode shapes are different. In Figs.10(b), (d),
the natural frequency after retrofitting increases a little.
Vertical
Lateral
Longitudinal
(a) Before retrofitting (29.35 Hz)
(b) After retrofitting (29.35 Hz)
(c) Before retrofitting (32.75 Hz)
(d) After retrofitting (33.35 Hz)
Figure 10: Identified mode shape from ambient vibration data using LDV
166
2.
DEVELOPMENT
OF
THREE-DIMENSIONAL
MEASUREMENT SYSTEM USING LDVS4), 5)
VIBRATION
The objective of this study is to develop vibration measurement system using three
LDVs, which makes possible to measure three-dimensional behavior of an object high
accurately and spatially high densely. Since developed system can clarify the
three-dimensional local deformation of structures caused by train/traffic-induced
vibration, it can contribute to the preventive maintenance and the improvement of
functionality in existing infrastructures.
Problem in one-dimensional vibration measurement using LDV
When only one LDV is used and the laser beam is perpendicular to the measurement
surface, the velocity component perpendicular to the surface can be measured with very
high accuracy. However, if the laser beam is not perpendicular to the surface, the
accuracy of the velocity decreases depending on the laser beam angle.
To investigate this problem, a simple experiment was conducted. Figs.11 show the
experimental set up. First, a steel plate with an attached accelerometer was hit by a
hammer. Then, a LDV measured the velocity of the plate from the direction making an
angle of 45q with respect to the normal axis.
Fig.12 shows the comparison. The solid blue line is the velocity computed from the
acceleration and the thin red dot line is the velocity from the LDV. Comparing these
two velocities, their amplitudes are different, because the laser beam angle is not
perpendicular to the surface. In order to obtain the vibration component perpendicular to
the surface, compensation on laser beam angle is necessary such as Eq. (1).
Vm V cos T
(1)
where Vm is the velocity perpendicular to the surface, V is the velocity measured by
the LDV and T is the laser beam angle of the LDV.
The green thick dot line in Fig.12 is the velocity compensated by Eq. (1). Comparing
the solid and thick dotted lines, their amplitudes agree well. Therefore, when only one
LDV is used, it is necessary to install the LDV perpendicular to the surface to conduct
accurate measurements. However, during field measurement using LDV, it is difficult
to satisfy such a condition.
385 [mm]
45㫦
LDV
Velocity [mm/sec]
Steel plate
Measurement
points
㪘㪺㪺㪼㫃㪼㫉㫆㫄㪼㫋㪼㫉
㪣㪛㪭㪑㩷㪋㪌㩷㪻㪼㪾㫉㪼㪼㫊
㪣㪛㪭㪑㩷㪸㫅㪾㫃㪼㩷㪺㫆㫄㫇㪼㫅㫊㪸㫋㫀㫆㫅
120
Accelerometer
300 [mm]
60
0
-60
-120
LDV
8
(a) Side view
(b) Top view
Figure11: Configurations of a LDV in
one-dimensional vibration measurement
8.1
8.2
8.3
8.4
Time [s]
Figure12: Measurements of 1D
vibration measurement using a LDV
Three-dimensional measurement principle using LDVs
The principle of three-dimensional measurement involves a geometrical transformation
of coordinatesCUshown in Fig.13. Three-dimensional vibration components of the
body are determined from measurements of the three LDVs by premultiplying by a
transformation matrix consisting of the direction cosines of the laser beam angles.
167
­Vx ½
° °
®Vy ¾
°V °
¯ z¿
ª cos D1
« cos D
2
«
¬« cos D 3
cos E1
cos J 1 º
cos J 2 »»
cos J 3 ¼»
cos E 2
cos E 3
1
­V1 ½
° °
®V2 ¾
° °
¯V3 ¿
(2)
where Vx ,Vy ,Vz are vibration components of the body in each axes, V1 ,V2 ,V3 are
vibration components measured by each LDV and D i , Ei , J i i 1, 2,3 are the laser
beam angles of each LDV.
Fundamental investigation of three-dimensional measurement
As fundamental study, three multiple points type LDVs having a scanning system
(SLDV) are set at parallel to a measurement surface. The surface was vertically
irradiated with each LDV when input voltages are 0 [V]. Therefore, laser beam angles
for the measurement points are directly obtained from mirror angles.
The developed system was applied to three-dimensional vibration measurement for a
steel railway bridge. A tri-axial accelerometer was attached on the surface of the main
girder for the purpose of validation. Fig.14 shows the setting of the SLDVs and the
measurement axes of the accelerometer. Each SLDV was set parallel to the main girder
and ground. Figs.15 show the comparison in each axes concerning time histories. These
are free vibration components after a train passes thorough the railway bridge. Since both
measurements agree well in each axis, the system can be applied to on-site measurement.
Z
Lateral
Axis1 Axis2
Longitudinal
Vz
Vy
Y
SLDV2
Axis3
SLDV1
RLDV
Vertical
V1
Vx
V3
LDV1
V2
SLDV3
LDV3
X
LDV2
1
ACC1
LDVy
0
-1
-2
10 10.1 10.2 10.3 10.4 10.5
Time [s]
4
Figure 14: Configuration of field
measurement
ACC2
LDVx
2
0
-2
-4
10 10.1 10.2 10.3 10.4 10.5
Time [s]
Acceleration [m/s2]
2
Acceleration [m/s2]
Acceleration [m/s2]
Figure 13: Three-dimensional vibration
measurement using LDVs
4
2
ACC3
LDVz
0
-2
-4
10 10.1 10.2 10.3 10.4 10.5
Time [s]
(a) Horizontal In-Plane
(b) Horizontal Out of-Plane (c) Vertical In-plane
Figure 15. verification of three-dimensional vibration measurement
3. DEVELOPMENT OF REMOTE NON-CONTACT MEASUREMENT SYSTEM
BY COMBING LASER DOPPLER VIBROMETER AND TOTAL STATION
In this Research, a non-contact measurement system which combines a LDV and a total
station (TS) was developed. This system is capable of measuring a lot of cable members
for long-span cable supported bridge applications, since it is especially suited for remote
non-contact vibration measurements.
168
100
㪘㪺㪺㪼㫃㪼㫉㫆㫄㪼㫋㪼㫉㩷
50
0
0
5
frequency [Hz]
10
Fourier Amplitude Spectral[m/s]
2
Fourier Amplitude Spectral[m/s ]
Measurement in Oshima and Tatara Bridges
The measurement was conducted by measuring the ambient vibration of the cables
using conventional accelerometers and LDV simultaneously. Typical cable vibration
frequency plots obtained from the LDV and the accelerometer data are shown in Figs.16
and 17.
At first, there was some concern that it will be difficult to determine the natural
frequency of the cables in Tatara bridge due to the influence of sag and the
contamination of the recorded data with many low-frequency vibrations. However, we
were able to get good results, verifying the effectiveness of the LDV in identifying the
natural frequency of cable elements.
30
㪣㪛㪭㩷
20
10
0
0
5
frequency [Hz]
10
1500
㪘㪺㪺㪼㫃㪼㫉㫆㫄㪼㫋㪼㫉㩷
1000
500
0
0
5
frequency [Hz]
10
Fourier Amplitude Spectral[m/s]
2
Fourier Amplitude Spectral[m/s ]
Figure 16: Comparison of the frequency plots from Oshima Bridge hanger rope
40
㪣㪛㪭㩷
30
20
10
0
0
5
10
frequency [Hz]
Figure 17: Comparison of frequency plots from a Tatara Bridge Cable
Combined LDV and TS system
When the measurement points are located far from the LDV, it is difficult to confirm the
irradiation of the LDV’s laser point during on-site measurements. To improve this
situation, the measurement system with the LDV attached to a TS, having a highly
accurate, remote measurement position identification ability, was developed. The TS
posses 1 [mm] accuracy for 100m distance, making it possible to determine the exact
position of any point (see Fig.18).
Measurement object 䋺 Hanger rope
LDV Sampling rate 䋺 1000Hz
TS Measurement time 䋺 0.8 seconds
LDV Measurement time 䋺 30 seconds
㪣㫆㫅㪾㪼㫊㫋
㪛㫀㫊㫋㪸㫅㪺㪼
㪘㪹㫆㫌㫋㩷㪏㪇㫄
㪫㪪㩷㫃㪸㫊㪼㫉㩷䋺
㪣㪛㪭㩷㫃㪸㫊㪼㫉㩷䋺
Figure 18: Combined LDV and TS system
169
2
Fourier Amplitude Spectral[m/s ]
Fourier Amplitude Spectral[m/s]
The measurement consists of the following steps: 1) The reflection tapes are attached
at the measurement points, 2) The orientation of the system is adjusted so that the
reflection level of the LDV reaches maximum level, 3) The measurement time is set, 4)
Each measurement point is identified with the TS and positional information is stored,
5) When the TS automatically aims at a measurement point using the stored position
information, the data acquisition program detects a signal and automatically records
vibration from the LDV, 6) Once the vibration measurement using LDV finishes, the TS
automatically moves to the next measurement point. Once the coordinates of the points
are identified, this system can repeat the measurements automatically.
At Kohei bridge in Hiroshima city, automatically repeated vibration measurement of
hanger ropes was conducted. The measurement of a hanger rope from a distance of
about 80m using LDV is shown in Fig.19. Moreover, the result of this hanger rope
using an accelerometer is shown in Fig.20. It is can be seen that the frequency peaks
obtained from both sensors are in good agreement. Also, we are confirming that there is
no change in the first and second natural frequencies for repeated measurements.
100
㪣㪛㪭㩷
50
0
0
10
20
Frequency [Hz]
30
Figure 19: Measurement from
about 80m distance using LDV
10000
㪘㪺㪺㪼㫃㪼㫉㫆㫄㪼㫋㪼㫉㩷
5000
0
0
10
20
Frequency [Hz]
30
Figure 20: Measurement using
accelerometer
CONCLUSIONS
This paper introduces three studies of advanced vibration measurement using LDVs for
the purpose of monitoring infrastructures: 1) Understanding of high-speed train induced
local vibration of a railway steel bridge. 2) Development of three-dimensional vibration
measurement system using LDVs. 3) Development of remote non-contact measurement
system by combing LDV and total station.
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1.
2.
3.
4.
5.
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Vibrometer, in Proceedings of Third International Conference on Bridge Maintenance, Safety and
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170