sensors
Article
Determination Method of Bridge Rotation Angle
Response Using MEMS IMU
Hidehiko Sekiya 1, *, Takeshi Kinomoto 2 and Chitoshi Miki 3
1
2
3
*
Advanced Research Laboratories, Tokyo City University, 8-15-1 Todoroki, Setagaya 158-0082, Japan
Maintenance and Transportation Division, Metropolitan Expressway Co., Ltd., 1-4-1 Kasumigaseki,
Chiyoda-ku 100-8930, Japan; [email protected]
Tokyo City University, 1-28-1 Tamazutsumi, Setagaya 158-8557, Japan; [email protected]
Correspondence: [email protected]; Tel.: +81-3-5706-3119; Fax: +81-3-5706-3786
Academic Editor: Stefano Mariani
Received: 30 August 2016; Accepted: 7 November 2016; Published: 9 November 2016
Abstract: To implement steel bridge maintenance, especially that related to fatigue damage, it is
important to monitor bridge deformations under traffic conditions. Bridges deform and rotate
differently under traffic load conditions because their structures differ in terms of length and flexibility.
Such monitoring enables the identification of the cause of stress concentrations that cause fatigue
damage and the proposal of appropriate countermeasures. However, although bridge deformation
monitoring requires observations of bridge angle response as well as the bridge displacement
response, measuring the rotation angle response of a bridge subject to traffic loads is difficult.
Theoretically, the rotation angle response can be calculated by integrating the angular velocity,
but for field measurements of actual in-service bridges, estimating the necessary boundary conditions
would be difficult due to traffic-induced vibration. To solve the problem, this paper proposes
a method for determining the rotation angle response of an in-service bridge from its angular
velocity, as measured by a inertial measurement unit (IMU). To verify our proposed method, field
measurements were conducted using nine micro-electrical mechanical systems (MEMS) IMUs and
two contact displacement gauges. The results showed that our proposed method provided high
accuracy when compared to the reference responses calculated by the contact displacement gauges.
Keywords: bridge health monitoring; micro-electro-mechanical systems; inertial measurement unit;
rotation angle response; angular velocity; free vibration
1. Introduction
In steel bridge maintenance, countermeasures for fatigue damage are important because such
damage is hard to detect and may cause sudden brittle failure. In order to conduct appropriate
maintenance for fatigue damage in a steel bridge, it is important to monitor bridge deformation, which
consists of the displacement response and the rotation angle response, against traffic loads because
such deformation is the primary source of the stress concentrations that cause fatigue damage [1–3].
Figure 1 shows an example of fatigue damage at a web gap plate, which is typical fatigue damage
in steel bridge. Concentrations of stress that lead to the fatigue damage at a web gap plate are
thought to be caused by either the rotation angle response of the upper flange due to reinforced
concrete (RC) slab deflection or the relative displacement between main girders, as shown in Figure 2.
Therefore, when such fatigue damage is prevented or repaired, in the case of the former, the RC slab
stiffness should be strengthened, whereas in the case of the latter, the main girder stiffness should be
strengthened. Thus, gaining an understanding of bridge deformations enables the implementation of
appropriate and timely maintenance and reinforcement needed to prevent fatigue damage.
Sensors 2016, 16, 1882; doi:10.3390/s16111882
www.mdpi.com/journal/sensors
Sensors 2016, 16, 1882
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enables
the
implementation
Sensors
2016,
16,implementation
1882
enables
the
prevent fatigue
fatigue damage.
damage.
prevent
of appropriate
appropriate and
and timely
timely maintenance
maintenance and
and reinforcement
reinforcement needed
needed
to
2 of 13
of
to
Figure 1.
1. Example
Example of
of fatigue
fatigue damage
damage at
at aaasteel
steelbridge
bridgeweb
webgap
gapplate.
plate.
Figure
Figure
1.
damage
at
steel
bridge
web
gap
plate.
Figure2.
2.Example
Exampleof
ofthe
therotation
rotationangle
angleresponse
responsedue
dueto
toreinforced
reinforcedconcrete
concrete(RC)
(RC)slab
slabdeflection
deflection and
and
Figure
Figure
2.
Example
of
the
rotation
angle
response
due
to
reinforced
concrete
(RC)
slab
deflection
and
relative
displacement
between
main
girders.
relative
relative displacement
displacement between
between main
main girders.
girders.
Herein, due
due to their
their compact
compact and inexpensive
inexpensive nature,
nature, the
the use of
of micro-electro-mechanical
micro-electro-mechanical
Herein,
Herein,
due tototheir
compact andand
inexpensive nature,
the use of use
micro-electro-mechanical
system
system
(MEMS)
sensors
to
measure
responses
against
the
external
forces
of traffic
traffic loading,
loading, wind
wind
system
(MEMS)
sensors
to
measure
responses
against
the
external
forces
of
(MEMS) sensors to measure responses against the external forces of traffic loading, wind force, and
force,
and
seismic
force
are
proposed
[4–9].
Unlike
strain
gauges,
which
have
often
been
used
to
force, and
seismic
force are [4–9].
proposed
[4–9].
Unlike
strainwhich
gauges,
which
used to
seismic
force
are proposed
Unlike
strain
gauges,
have
oftenhave
beenoften
usedbeen
to measure
measure responses
responses against
against the external
external forces
forces [1],
[1], MEMS
MEMS sensors
sensors can
can be
be easily
easily attached
attached to
to the
the
measure
responses
against the externalthe
forces [1], MEMS
sensors
can be easily attached
to the painted
surfaces
painted
surfaces
of
steel
bridges
using
magnets.
Furthermore,
unlike
fixed
reference-based
painted
surfacesusing
of steel
bridges
using magnets.
unlike measuring
fixed reference-based
of
steel bridges
magnets.
Furthermore,
unlike Furthermore,
fixed reference-based
tools such
measuring
tools
such
as
linear
variable
differential
transformers
(LVDTs)
[10], laser
laser Doppler
measuring
tools differential
such as linear
variable (LVDTs)
differential
(LVDTs)
[10],
as
linear variable
transformers
[10],transformers
laser Doppler
vibrometers
(LDVs)Doppler
[11,12],
vibrometers (LDVs)
(LDVs) [11,12],
[11,12], and
and vision-based
vision-based systems
systems [13–15],
[13–15], MEMS
MEMS sensors
sensors do
do not
not require
require fixed
fixed
vibrometers
and vision-based systems [13–15], MEMS sensors do not require fixed reference points, which are
reference
points,
which
are
often
unavailable
in
large
civil
infrastructures
[16].
Therefore,
the
reference
points, in
which
unavailable
inTherefore,
large civiltheinfrastructures
[16].
Therefore,
often
unavailable
large are
civiloften
infrastructures
[16].
increased use of
MEMS
sensorsthe
in
increased use
use of MEMS
MEMS sensors
sensors in
in full-scale
full-scale civil
civil infrastructures
infrastructures has
has recently
recently been
been anticipated.
anticipated.
increased
full-scale
civil of
infrastructures
has recently
been anticipated.
In order
order to
to monitor
monitor bridge
bridge deformations
deformations against
against actual
actual traffic
traffic loads,
loads, bridge
bridge displacement
displacement
In
In
order to
monitor bridge
deformations against
actual traffic
loads, bridge
displacement
measurements
are
essential,
and
many
studies
have
explored
methods
for
conducting
such
measurements are
are essential,
essential, and
and many
many studies
studies have
have explored
explored methods
methods for
for conducting
conducting such
such
measurements
measurements using
using accelerometers
accelerometers [17–21].
[17–21]. However, in
in order to
to accurately
accurately monitor
monitor bridge
bridge
measurements
measurements
using accelerometers
[17–21]. However,
However, in order
order to accurately
monitor bridge
deformation
against
traffic
loads,
it
is
necessary
not
only
to
measure
the
bridge
displacement
deformationagainst
againsttraffic
traffic
loads,
is necessary
not toonly
to measure
thedisplacement
bridge displacement
deformation
loads,
it isitnecessary
not only
measure
the bridge
response,
response,
but
also
to
measure
the
bridge
rotation
angle
response.
If
a
bridge
structure
is composed
composed
response,
also tothe
measure
the bridge
rotation
angleIfresponse.
If a bridge
structure is
but
also tobut
measure
bridge rotation
angle
response.
a bridge structure
is composed
of only one
of only
only one
one material,
material, the
the bridge
bridge rotation
rotation angle
angle response
response can
can be
be approximately
approximately extrapolated
extrapolated from
from the
the
of
material,
the bridge rotation
angle response
can be approximately
extrapolated from the displacement
displacement
responses
at
multiple
points.
However,
in
a
mixed
structure,
such
as
a
steel-concrete
displacement
responses
at multiple
points.
However,
in a mixed
such as
a steel-concrete
responses
at multiple
points.
However,
in a mixed
structure,
such asstructure,
a steel-concrete
girder
bridge, it is
girder
bridge,
it
is
difficult
to
extrapolate
the
bridge
rotation
at
the
joints
between
an
upper flange
flange
girder bridge,
it is difficult
to extrapolate
rotation an
at the
joints
between
upper
difficult
to extrapolate
the bridge
rotation atthe
thebridge
joints between
upper
flange
and ananRC
deck using
and
an
RC
deck
using
the
displacement
responses
measured
at
that
location
because
of
differences
anddisplacement
an RC deck using
the displacement
responses
measured
locationbetween
becausethe
of stiffness
differences
the
responses
measured at that
location
because at
of that
differences
of
between the
the stiffness
stiffness of
of steel
steel and
and RC.
RC. Therefore,
Therefore, the
the rotation
rotation angle
angle response
response at
at joints
joints composed
composed of
of
between
steel and RC. Therefore, the rotation angle response at joints composed of different materials should
different materials
materials should
should be
be measured
measured at
at aa point
point where
where we
we want
want to
to obtain
obtain rotation
rotation angle
angle response
response
different
be
measured at a point
where we
want to obtain
rotation angle
response
data.
data.
data.Hou et al. [22] proposed a method that can be used to determine bridge displacement responses
Hou et
et al.
al. [22]
[22] proposed
proposed aa method
method that
that can be
be used
used to
to determine
determine bridge
bridge displacement
displacement
usingHou
inclinometers,
and the results
provided in can
that study
indicate
that the proposed
method is
responses
using
inclinometers,
and
the
results
provided
in
that
study
indicate
that
the
proposed
responses
using
inclinometers,
and
the
results
provided
in
that
study
indicate
that
the
highly accurate. However, it is thought that since an in-service bridge would be constantly proposed
vibrating
method
is
highly
accurate.
However,
it
is
thought
that
since
an
in-service
bridge
would
be
method
is highly
accurate.
However,
it is thought
that since
an in-service
bridge
be
due
to vehicle
traffic,
and it would
be difficult
to accurately
measure
the rotation
anglewould
response
constantly vibrating
vibrating due to
to vehicle traffic,
traffic, and
and it
it would
would be
be difficult
difficult to
to accurately measure
measure the
the
constantly
using
an inclinometerdue
becausevehicle
the measured data
would
be subject
to trafficaccurately
acceleration-generated
bridge vibration.
rotation angle could be calculated from gravitational acceleration changes caused by the MEMS
accelerometer tilt [23]. However, since an in-service bridge is always vibrating due to traffic loads,
changes in the measured acceleration would include changes in the gravitational acceleration and
acceleration generated by bridge vibration, and it would be difficult to separate the acceleration
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types.Sensors 2016, 16, 1882
In theory, a bridge rotation angle response can be calculated from the integration of its angular
velocity, as
measured
an inertial
measurement
unit measurements,
(IMU). However,
integration
In another
studyby
considering
gravitational
acceleration
it was the
thought
that the process
rotation
angle
could
be
calculated
from
gravitational
acceleration
changes
caused
by
the
MEMS
would require numerical integration of the initial condition, which would be difficult
to achieve on
accelerometer
tilt
[23].
However,
since
an
in-service
bridge
is
always
vibrating
due
to
traffic
loads,
an in-service bridge that is constantly vibrating due to vehicle traffic. Furthermore, since sensor
changes in the measured acceleration would include changes in the gravitational acceleration and
noise and quantization errors, due to the analog-to-digital (A/D) conversion process, are inevitably
acceleration generated by bridge vibration, and it would be difficult to separate the acceleration types.
included in
the angular
measured
bycan
anbe
IMU
(particularly
at low frequencies),
In theory,
a bridgevelocity
rotation angle
response
calculated
from the integration
of its angularand those
errorsvelocity,
can be expected
to degrade
the integrated
results
[21]. However, the integration process
as measured
by an inertial
measurement
unit (IMU).
require numerical
the initial
condition,
whichangle
would responses,
be difficult tofield
achieve
on
Inwould
the present
study, inintegration
order toofanalyze
bridge
rotation
measurements
an
in-service
bridge
that
is
constantly
vibrating
due
to
vehicle
traffic.
Furthermore,
since
sensor
noise
were first conducted on an actual in-service bridge using nine MEMS IMUs and two contact
and quantization errors, due to the analog-to-digital (A/D) conversion process, are inevitably included
displacement gauges. Next, based on the characteristics of the bridge rotation angle response, a
in the angular velocity measured by an IMU (particularly at low frequencies), and those errors can be
method
was proposed by which we could calculate the bridge rotation angle response from the
expected to degrade the integrated results [21].
measured In
angular
velocity.
by comparing
the rotation
angle field
calculated
from the
the present
study, inFinally,
order to analyze
bridge rotation
angle responses,
measurements
weremeasured
angular
using
proposed
with
theMEMS
rotation
determined
from two contact
firstvelocity
conducted
on anthe
actual
in-servicemethod
bridge using
nine
IMUsangle
and two
contact displacement
gauges.
Next,
based
on
the
characteristics
of
the
bridge
rotation
angle
response,
a
method
was obtained
displacement gauges, the effectiveness of the proposed method was verified. The results
by which
we could
calculate
theto
bridge
rotation
angle response from the measured angular
using proposed
our proposed
method
were
found
be highly
accurate.
velocity. Finally, by comparing the rotation angle calculated from the measured angular velocity using
the proposed method with the rotation angle determined from two contact displacement gauges,
2. Experimental
Section
the effectiveness of the proposed method was verified. The results obtained using our proposed
method were found to be highly accurate.
2.1. Description of Test Bridge and Measuring Instrument Used in This Study
2. Experimental Section
Field measurements of an actual in-service bridge were performed in order to analyze the
Description
of Test
Bridge andcharacteristics
Measuring Instrument
in ThisaStudy
bridge2.1.
rotation
angle
response
and Used
propose
method to determine rotation angle
Field measurements
of an actual
bridge were
performed
in order
to analyze the structure
from measured
angular velocity.
Thein-service
test bridge,
which
is a mixed
steel-concrete
bridge
rotation
angle
response
characteristics
and
propose
a
method
to
determine
rotation
angle
equipped with three traffic lanes, is a 38-m-long single-span bridge (see Figure
3) equipped
with
from measured angular velocity. The test bridge, which is a mixed steel-concrete structure equipped
five main 1.9-m-high girders (hereafter, G1 to G5) supporting RC deck plates. The total width of the
with three traffic lanes, is a 38-m-long single-span bridge (see Figure 3) equipped with five main
structure
is 14.25 m. The bridge is managed by the Metropolitan Expressway Co., Ltd. (Tokyo,
1.9-m-high girders (hereafter, G1 to G5) supporting RC deck plates. The total width of the structure
Japan)isand
located
within
the Tokyo
Metropolitan
14.25ism.
The bridge
is managed
by the
MetropolitanArea.
Expressway Co., Ltd. (Tokyo, Japan) and is
We
began
by the
installing
a MEMS IMU
located
within
Tokyo Metropolitan
Area.at the longitudinal center of the lower flange of G4 using
We
began
by
installing
a
MEMS
IMU
at the
longitudinal
center
lowerlocation
flange of in
G4 order
using to verify
a magnet. Two contact displacement gauges
were
also fixed
at of
thethesame
a magnet. of
Twothe
contact
displacement
also fixedfrom
at the same
location in order
to verify
the
the accuracy
rotation
angle gauges
valueswere
obtained
the measured
angular
velocity.
This
accuracy of the rotation angle values obtained from the measured angular velocity. This experimental
experimental setup is shown in Figure 4. The method used to determine the bridge rotation angle
setup is shown in Figure 4. The method used to determine the bridge rotation angle values from the
valuescontact
from displacement
the contact displacement
responses
is shown in Figure 5.
gauge responsesgauge
is shown
in Figure 5.
Figure 3. Cont.
Figure 3. Cont.
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Figure
3. Test bridge used in our field measurements (units: mm): (a) top view; (b) front view at the
Figure 3. Test bridge used in our field measurements (units: mm): (a) top view; (b) front view at the
Figure 3. Test
bridge used girder;
in our field measurements
mm):
(a)
top view;
longitudinal
center
view(units:
at the
themain
maingirder
girder
edge.(b) front view at the
longitudinal
centerofofmain
main girder;and
and (c)
(c) front
front view
at
edge.
longitudinal center of main girder; and (c) front view at the main girder edge.
Figure 4. Installation of micro-electro-mechanical system (MEMS) inertial measurement unit (IMU)
Figure 4. Installation of micro-electro-mechanical system (MEMS) inertial measurement unit (IMU)
and two
contact displacement
gauges.
Figure
4. Installation
of micro-electro-mechanical
system (MEMS) inertial measurement unit (IMU)
and two
contact displacement
gauges.
and two contact displacement gauges.
In order to precisely detect vehicle entry and exit times using the measured acceleration
In ordereight
to precisely
detectwere
vehicle
entry and
exitvertical
times using
the measured
accelerationedges
responses,
responses,
MEMS IMUs
attached
to the
stiffeners
on both longitudinal
of
In order to precisely detect vehicle entry and exit times using the measured acceleration
eight
MEMS
IMUs
wereThese
attached
the allowed
vertical stiffeners
on both
longitudinal
of thevehicles
four main
the four
main
girders.
IMUstoalso
us to determine
the
travel lanesedges
used when
responses, eight MEMS IMUs were attached to the vertical stiffeners on both longitudinal edges of
girders.
IMUs
also The
allowed
us to
determine
the travel
usedatwhen
vehicles
passed of
over
passed These
over the
bridge.
MEMS
IMU
experimental
setuplanes
located
the vertical
stiffener
thethe
the four main girders. These IMUs also allowed us to determine the travel lanes used when vehicles
exit side
of G5
is shown
Figure 6. Thesetup
specifications
of the MEMS
and of
contact
displacement
bridge.
The
MEMS
IMUinexperimental
located at
verticalIMUs
stiffener
the exit
side of G5 is
passed
over
the
bridge.
The
experimental setup located at the vertical stiffener of the
gauges
listed
Tables
1 MEMS
and 2. IMU
shown
inare
Figure
6.inThe
specifications
of the MEMS IMUs and contact displacement gauges are listed
exit
of 1G5
is 2.
shown in Figure 6. The specifications of the MEMS IMUs and contact displacement
inside
Tables
and
gauges are listed in Tables 1 and 2.
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Figure 5. Rotation angle displacement using two contact displacement gauges.
Figure 5.
5. Rotation
Rotation angle
angle displacement
displacement using
using two
two contact
contact displacement
Figure
displacement gauges.
gauges.
Figure 6. Installation of sensor to detect vehicle exit at main girder five (G5).
Figure 6. Installation of sensor to detect vehicle exit at main girder five (G5).
Figure 6. Installation of sensor to detect vehicle exit at main girder five (G5).
Table 1. Specifications of MEMS IMUs.
Table 1. Specifications of MEMS IMUs.
1. SpecificationsSampling
of MEMS IMUs.
MeasurementTableFrequency
IMU
Resolution
Noise Density
Measurement
Frequency
Sampling
Range
Bandwidth
Frequency
IMU
Resolution
Noise Density
Measurement
Frequency
Sampling
Range
Bandwidth
Frequency
M-G550-PC (SEIKO
IMU
Resolution
Noise Density
Range
Bandwidth
Frequency
133 (−3
dB)
M-G550-PC
EPSON Co.,(SEIKO
Ltd.
±300 [°/s]
100 [Hz]
0.0125 [(°/s)/LSB]
0.004 [(°/s)/√Hz]
133[Hz]
(−3 dB)
M-G550-PC
(SEIKO
EPSON
Co., Ltd.
±300 [°/s]
0.01250.0125
[(°/s)/LSB]
0.004
(Suwa, Japan))
133 (−3 dB) 100 [Hz]
0.004[(°/s)/√Hz]
◦
[Hz]
EPSON
Co., Ltd.
±300 [ /s]
100 [Hz]
◦ /s)/LSB]
◦ /s)/√Hz]
(Suwa,
Japan))
[Hz]
[(
[(
M-G550-PC
(SEIKO
(Suwa,
Japan))
148 (−3dB)
M-G550-PC
EPSON
Co.,(SEIKO
Ltd. (SEIKO±29.4 [m/s2]
981 [μm/(s2√Hz)]
500 [Hz]
1226 [μm/s2]
M-G550-PC
148[Hz]
(−3dB)
148 (−3dB) 500 [Hz]
2
2√Hz)]
2]
22]]
EPSON
Co.,
Ltd.
±29.4
[m/s
]
981981
[μm/(s
1226
[μm/s
√
EPSON
Co.,
Ltd.
500
[Hz]
±
29.4
[m/s
1226
[µm/s
(Suwa, Japan))
[Hz][Hz]
[µm/(s2 Hz)]
Japan))
(Suwa,(Suwa,
Japan))
Table 2. Contact displacement gauges.
Table 2. Contact displacement gauges.
Nonlinearity
Sampling
Capacity
Sensitivity [×10–6
Contact Displacement Gauge
Nonlinearity
Sampling
Capacity
Sensitivity
[×10–6 Nonlinearity
[mm]
Strain/mm]
[mm]
Frequency
[Hz]
Capacity
Sensitivity
Sampling
Contact
Displacement
Gauge
Contact
Displacement
Gauge
–6
[mm]
Strain/mm]
[mm]
Frequency
[mm]
[×10 Strain/mm]
[mm]
Frequency [Hz] [Hz]
CDP-50 (Tokyo Sokki Kenkyujo
0–50
200
0.1% RO
100
CDP-50
(Tokyo
SokkiSokki
Kenkyujo
Co.,CDP-50
Ltd.
(Tokyo,
Japan))
(Tokyo
Kenkyujo
0–50
200
0.1%
0–50
200
0.1%
RO RO
100 100
Co., Ltd.
(Tokyo,
Japan))
Co., Ltd. (Tokyo, Japan))
2.2. Analysis of Bridge Rotation Angle Response under Traffic Loads
2.2. Analysis
Response under
under Traffic
Traffic Loads
Loads
2.2.
Analysis of
of Bridge
Bridge Rotation
Rotation Angle
Angle Response
By comparing the bridge displacement and bridge rotation angle responses under traffic load
By comparing
comparing
thetime
bridge
displacement
and
rotation
angle
responses
under
traffic
load
By
the
bridge
and bridge
bridge
rotation
angle angle
responses
under
traffic
load
conditions
in both the
anddisplacement
frequency domains,
the bridge
rotation
response
under
traffic
conditions
in
both
the
time
and
frequency
domains,
the
bridge
rotation
angle
response
under
traffic
conditions
both the time and frequency domains, the bridge rotation angle response under traffic
loads
can beinanalyzed.
loadsThe
can25
besanalyzed.
analyzed.
loads
can
be
displacement response measured by the contact displacement gauges at the lower
The
25ssdisplacement
displacement
response
measured
by
the
contact
displacement
gauges
the
lower
25
response
contact
displacement
at other
the at
lower
flangeThe
center
of
G4 is shown
in measured
Figure
7. by
In the
order
to eliminate
anygauges
effects
thanflange
the
flange
center
of
G4
is
shown
in
Figure
7.
In
order
to
eliminate
any
effects
other
than
the
center of G4 is
shown in
Figure
7. In the
order
to eliminateresponse
any effects
other after
than the
theapplication
displacement
displacement
response,
Figure
7 shows
displacement
obtained
of
displacement
response,
Figure
7
shows
the
displacement
response
obtained
after
the
application
of
response,
Figure
7
shows
the
displacement
response
obtained
after
the
application
of
a
10
Hz
low-pass
a 10 Hz low-pass filter, which was selected because the main frequency range of the bridge
a
10
Hz
low-pass
filter,
which
was
selected
because
the
main
frequency
range
of
the
bridge
filter, which was
selected
the main frequency
range
theFigure
bridge 7displacement
traffic
displacement
under
trafficbecause
load conditions
is below 10
Hz of
[21].
shows someunder
deflections
displacement
under
traffic
load
conditions
is
below
10
Hz
[21].
Figure
7
shows
some
deflections
caused by the weight of vehicles travelling on the bridge. Vehicle passage times, which depend on
caused by the weight of vehicles travelling on the bridge. Vehicle passage times, which depend on
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load
conditions
is below 10 Hz [21]. Figure 7 shows some deflections caused by the weight of vehicles
travelling
on the
bridge.
passage
which
depend
the vehicle
speed
and the
bridgetimes,
span a
the vehicle
speed
andVehicle
the bridge
spantimes,
length,
ranged
fromon1.454
to 2.062
s. Based
on those
the
vehicle
speed
and
the
bridge
span
length,
ranged
from
1.454
to
2.062
s.
Based
on
those
times,
length,
ranged
from 1.454
2.062 s. Based0.5
ontothose
times,
a deflection
frequency of approximately 0.5a
deflection
frequency
of to
approximately
0.7 Hz
could
be calculated.
deflection
frequency
of
approximately
0.5
to
0.7
Hz
could
be
calculated.
to 0.7 Hz could be calculated.
Figure 7. Displacement response obtained using the contact displacement gauge at G4.
Figure 7. Displacement response obtained using the contact
contact displacement
displacement gauge
gauge at
at G4.
G4.
The bridge rotation angle response for 25 s calculated from the displacement responses
The bridge
bridgerotation
rotation angle
response
for
25 s calculated
the displacement
responses
The
response
for 25
s calculated
thefrom
responses
measured
measured
by the twoangle
contact
displacement
gauges from
at G4
isdisplacement
shown in Figure
8. One
of the
measured
by
the
two
contact
displacement
gauges
at
G4
is
shown
in
Figure
8.
One
of the
bydisplacement
the two contact
displacement
gauges
G4 is7.
shown
in 8a
Figure
8. One
of the displacement
responses
responses
is shown
in at
Figure
Figure
shows
the normal
rotation angle
response
displacement
responses
is shown
in Figure
7. Figure
8a shows
the normal
rotation angle response
is
shown
in Figure
7. Figure
8a shows
the normal
rotation
angle response
direction.
direction.
direction.
Figure
Normal
direction
rotation
angle
response
and
rotation
angle
response
obtained
using
Figure
8. 8.
Normal
direction
of of
rotation
angle
response
and
rotation
angle
response
obtained
using
Figure 8. Normal direction of rotation angle response and rotation angle response obtained using
two
contact
displacement
gauges
(a) normal
direction
of rotation
angle response;
and (b)
two
contact
displacement
gauges
at G4:at(a)G4:
normal
direction
of rotation
angle response;
and (b) rotation
two contact displacement gauges at G4: (a) normal direction of rotation angle response; and (b)
angle
response.
rotation
angle response.
rotation angle response.
The
displacement
response
Figure
7 and
rotation
angle
response
Figure
showed
The
displacement
response
inin
Figure
7 and
thethe
rotation
angle
response
in in
Figure
8b8b
showed
The displacement response in Figure 7 and the rotation angle response in Figure 8b showed
similar
shapes,
particularly
around
the
12
s
mark.
In
addition,
it
can
be
seen
that
when
the
bridge
similar shapes, particularly around the 12 s mark. In addition, it can be seen that when the bridge
similar shapes, particularly around the 12 s mark. In addition, it can be seen that when the bridge
displacement
response
in Figure
7 is vibrating
about
the zero-axis,
bridgeangle
rotation
angle
displacement
response
in Figure
7 is vibrating
about the
zero-axis,
the bridgethe
rotation
in Figure
8b in
displacement response in Figure 7 is vibrating about the zero-axis, the bridge rotation angle in
Figure
8b
is
also
rotating
about
the
zero-axis.
In
other
words,
it
is
thought
that
when
no
vehicle
is also rotating about the zero-axis. In other words, it is thought that when no vehicle is traveling on is
Figure 8b is also rotating about the zero-axis. In other words, it is thought that when no vehicle is
on the
bridge,
the bridge
is the
rotating
about the zero-axis.
thetraveling
bridge, the
bridge
rotation
angle isrotation
rotatingangle
about
zero-axis.
traveling on the bridge, the bridge rotation angle is rotating about the zero-axis.
Details
of the
displacement
response
spectrum
in 7Figure
and theangle
rotation
angle
Details
of the
displacement
response
spectrum
shownshown
in Figure
and the7rotation
response
Details of the displacement response spectrum shown in Figure 7 and the rotation angle
response
spectrum
shown
in
Figure
8b
are
shown
together
in
Figure
9.
spectrum shown in Figure 8b are shown together in Figure 9.
response spectrum shown in Figure 8b are shown together in Figure 9.
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Figure 9.
9. Detailed
at at
G4:G4:
(a) displacement
response
spectrum;
and
Figure
Detailedbridge
bridgeresponse
responsespectrum
spectrum
(a) displacement
response
spectrum;
(b) rotation
angle
response
spectrum.
and
(b) rotation
angle
response
spectrum.
The displacement response spectrum in Figure 9a and the rotation angle response spectrum in
The displacement response spectrum in Figure 9a and the rotation angle response spectrum in
Figure 9b also show similar shapes, particularly at the frequencies below 1.0 Hz, which is due to
Figure 9b also show similar shapes, particularly at the frequencies below 1.0 Hz, which is due to
forced displacement. As can be seen in Figure 9a, the displacement response spectrum shows a
forced displacement. As can be seen in Figure 9a, the displacement response spectrum shows a natural
natural vibration frequency at 2.6 Hz. In addition, while the rotation angle response spectrum peak
vibration frequency at 2.6 Hz. In addition, while the rotation angle response spectrum peak shown in
shown in Figure 9b is not as well-defined, it also shows a 2.6 Hz natural vibration frequency. In the
Figure 9b is not as well-defined, it also shows a 2.6 Hz natural vibration frequency. In the frequency
frequency range of 4 Hz to 10 Hz, neither spectrum shows other well-defined higher order mode
range of 4 Hz to 10 Hz, neither spectrum shows other well-defined higher order mode peaks that
peaks that depend on vibration. Therefore, it can be said that, based on our comparison between the
depend on vibration. Therefore, it can be said that, based on our comparison between the displacement
displacement and rotation angle response spectra, as with the displacement response [21], the
and rotation angle response spectra, as with the displacement response [21], the rotation angle response
rotation angle response is largely classified into forced displacement and free vibration
is largely classified into forced displacement and free vibration displacement responses.
displacement responses.
3. Calculation Method for Determining Bridge Rotation Angle from Measured Angular Velocity
3. Calculation Method for Determining Bridge Rotation Angle from Measured Angular Velocity
As described above, the rotation angle response is largely classified into forced displacement
As described
above, the rotation
angleInresponse
largely
forcedon
displacement
and free
vibration displacement
responses.
addition,iswhen
noclassified
vehicle isinto
travelling
the bridge,
and
free
vibration
displacement
responses.
In
addition,
when
no
vehicle
is
travelling
on
therotation
bridge,
the bridge rotation angle rotates about the zero-axis. Using these characteristics, the bridge
the
bridge
rotation
angle
rotates
about
the
zero-axis.
Using
these
characteristics,
the
bridge
rotation
angle response is determined from the measured angular velocity. The basic concept of our proposed
angle response
is described.
determined
from
the vehicle
measured
basicusing
concept
of our
method
will now be
First,
precise
entryangular
and exitvelocity.
times are The
detected
acceleration
proposed
method
will
now
be
described.
First,
precise
vehicle
entry
and
exit
times
are
detected
responses recorded by MEMS IMUs at the vertical stiffeners on both longitudinal edges of the main
using acceleration
recorded
by MEMS
IMUsatatits
the
vertical
stiffeners
on both
longitudinal
girders.
Second, by responses
assuming that
the bridge
is rotating
free
vibration
frequency
before
and after
edges
of
the
main
girders.
Second,
by
assuming
that
the
bridge
is
rotating
at
its
free
vibration
the vehicle travels over the bridge, the initial and terminal conditions of the rotation angle response
frequency
before
and
after
the
vehicle
travels
over
the
bridge,
the
initial
and
terminal
conditions
of
can be estimated. Finally, the angular velocity of the bridge during vehicular passage is integrated into
the rotation
rotationangle
angleresponse
response
can the
be initial
estimated.
Finally, estimates
the angular
velocityabove.
of the bridge during
the
using
and terminal
produced
vehicular
passage
is
integrated
into
the
rotation
angle
response
using
the
initialangle
and response
terminal
The procedure used by the proposed method to determine the bridge rotation
estimates
produced
above.
from the angular velocity measured by the IMUs (see Table 1) is shown in Figure 10. It consists of the
The procedure
used by the proposed method to determine the bridge rotation angle response
following
steps:
from the angular velocity measured by the IMUs (see Table 1) is shown in Figure 10. It consists of the
following
steps:
Free and
forced vibration regions are separated by precisely detecting vehicle entry and exit times.
1.
When multiple vehicles are running on the bridge, the time the first vehicle enters the bridge is
1. Free and forced vibration regions are separated by precisely detecting vehicle entry and exit
the vehicle entry time and the time the last vehicle exits the bridge is the vehicle exit time.
times. When multiple vehicles are running on the bridge, the time the first vehicle enters the
2.
The
angular
is transformed
from
thethe
time
the the
frequency
domain
through
bridge
is the velocity
vehicle entry
time and the
time
lastdomain
vehicleto
exits
bridge is
the vehicle
exit
atime.
Fourier transform.
3.
1.0isHz
are removed
in the
order
to domain
eliminate
of forced
displacement
2. Frequencies
The angular below
velocity
transformed
from
time
tothe
theeffect
frequency
domain
through a
during
vehicular
passage.
Although
the
proper
high-pass
filter
cut-off
frequency
depends on
Fourier transform.
bridge length
travellinginspeed,
the spanthe
lengths
bridges
3. the
Frequencies
belowand
1.0 vehicle
Hz are removed
ordersince
to eliminate
effect of
of most
forcedgirder
displacement
in
Japan
are
more
than
30
m
and
the
maximum
allowed
speed
on
expressways
in
Japan
is
during vehicular passage. Although the proper high-pass filter cut-off frequency depends on
100
travelling
time should
be above
1.2since
s, andthe
thespan
frequency
should
be below
Hz [21].
the km/h,
bridge the
length
and vehicle
travelling
speed,
lengths
of most
girder0.9
bridges
in
Japan are more than 30 m and the maximum allowed speed on expressways in Japan is
100 km/h, the travelling time should be above 1.2 s, and the frequency should be below 0.9 Hz
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In addition,
4.
4.
5.
5.
6.
6.
7.
7.
of 13
the natural frequency of this test bridge in Figure 9 is 2.6 Hz, the8cut-off
frequency of the high-pass filter used in this study is 1.0 Hz.
[21]. In addition, since the natural frequency of this test bridge in Figure 9 is 2.6 Hz, the cut-off
The angular velocity in the frequency domain, which does not have the effect of forced
frequency of the high-pass filter used in this study is 1.0 Hz.
displacement
during vehicular passage, is transformed to the time domain through an inverse
The angular velocity in the frequency domain, which does not have the effect of forced
Fourier
transform.
displacement
during vehicular passage, is transformed to the time domain through an inverse
The
angular
velocity under free vibration conditions obtained in Step 4, which excludes the
Fourier transform.
effects
of vehicular
forced
displacement,
is numerically
integrated
to obtain
the excludes
rotation angle,
The angular
velocity
under
free vibration
conditions obtained
in Step
4, which
the
thereby
estimate
of the initial
and terminal
rotationtoangle
conditions
under
free
effects producing
of vehicularan
forced
displacement,
is numerically
integrated
obtain
the rotation
angle,
vibration
conditions.
thereby producing an estimate of the initial and terminal rotation angle conditions under free
vibration
conditions.
The
total angular
velocity, which includes the angular velocity under both free and forced
The totalconditions,
angular velocity,
which includes
the angular
velocity
under
both angle.
free andThe
forced
vibration
is numerically
integrated
to obtain
the total
rotation
lower
vibration
conditions,
is
numerically
integrated
to
obtain
the
total
rotation
angle.
The
lower
and
and upper limits of the integration are the times when the same vehicle enters and exits the
upperrespectively.
limits of the The
integration
are the times
the same
vehicle
enters
and
exits free
the bridge,
bridge,
initial rotation
anglewhen
is defined
as the
rotation
angle
under
vibration
respectively.
The
initial
rotation
angle
is
defined
as
the
rotation
angle
under
free
vibration
conditions estimated in Step 5.
conditions estimated in Step 5.
Because of measurement errors in the measured angular velocity, which are caused by sensor
Because of measurement errors in the measured angular velocity, which are caused by sensor
noise and the limitations of A/D conversion, the integrated rotation angle does not satisfy the
noise and the limitations of A/D conversion, the integrated rotation angle does not satisfy the
terminal conditions at this point. To satisfy those conditions, the drift component is subtracted
terminal conditions at this point. To satisfy those conditions, the drift component is subtracted
from the integrated rotation angle.
from the integrated rotation angle.
Figure
Procedure
used
in proposed
the proposed
method
to determine
angle
from
Figure
10.10.
Procedure
used
in the
method
to determine
bridge bridge
rotationrotation
angle from
measured
measured
angular
velocity.
angular velocity.
In the procedure described above, when the initial and terminal conditions of the rotation
In the procedure described above, when the initial and terminal conditions of the rotation angle
angle response in Step 3 cannot be accurately estimated, the integrated rotation angle response
response in Step 3 cannot be accurately estimated, the integrated rotation angle response results
results include the estimated error of the initial and terminal conditions. Therefore, vehicle
include the estimated error of the initial and terminal conditions. Therefore, vehicle detection in Step 1
detection in Step 1 is of crucial importance.
is of crucial importance.
Sensors 2016, 16, 1882
9 of 13
The measurement error, particularly the low frequency range measurement error, which includes
sensor noise and quantization errors due to the A/D conversion process, corrupts the integrated
results. Furthermore, since the generated angular velocity obtained over the low frequency range is
small compared to the generated angular velocity over the high frequency range, low frequency range
measurement data is easily affected by sensor noise. Therefore, it is important to use an IMU with low
sensor noise over the low frequency range so that the angular velocity can be measured over that range
√
with a high level of accuracy. The noise density of an IMU used in this study is 0.004 [(◦ /s)/ Hz].
In Figure 10, the generated angular velocity is about ±0.15 [◦ /s]. As a result, it is thought that the noise
density is sufficiently small for the generated angular velocity of a bridge-axial-orthogonal direction.
4. Results and Discussion
In order to verify the effectiveness of the method used to determine the bridge rotation angle
response from the measured angular velocity, comparisons between the rotation angle response
determined from the measured angular velocity and those determined by the two contact displacement
gauges were conducted.
4.1. Test Procedure
The test bridge and instrument installation positions are the same as those shown in Figure 3.
The field measurements were performed without traffic control using two contact displacement gauges
and nine MEMS IMUs, which included a MEMS IMU for measuring angular velocity at the longitudinal
center of the lower flange of G4 and eight MEMS IMUs for detecting vehicle entry and exit times at
the vertical stiffeners on both longitudinal edges of the four main girders. The test procedures are
as follows:
1.
2.
3.
Vehicle entry and exit times are detected by eight MEMS IMUs at the vertical stiffeners on both
longitudinal edges of the main girders.
The angle rotation response at the longitudinal center of the lower flange of G4 is determined
from the measured angular velocity at the longitudinal center of that lower flange by using the
detected vehicle entry and exit times and the proposed method.
Accuracy verification is conducted by comparing the rotation angle response determined from
the measured angular velocity and those determined by the two contact displacement gauges.
4.2. Vehicle Detection Results Using Eight MEMS IMUs
In order to apply the proposed method, precise vehicle entry and exit times must be measured.
In this study, the eight above-mentioned MEMS IMUs were used for this purpose. In addition,
the vehicle travel lane was estimated using each of the acceleration responses recorded at G2 to G5
by the eight MEMS IMUs. The determined rotation angle response using two contact displacement
gauges, and each acceleration response measured at G2 to G5 are shown in Figure 11.
The acceleration record in Figure 11b revealed that the passage of a four-axle vehicle with an entry
time of 11.372 s and an exit time of 13.434 s. It can be seen that the rotation angle response in Figure 11a
starts to increase at the vehicle entry time (11.372 s). Furthermore, since the G2 acceleration response
for the entry and exit sides showed the highest value, and the acceleration G3 response value for the
entry and exit sides showed the second highest value, the four-axle vehicle could be presumed to be
traveling on Lane 1 (see Figure 3c).
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11.Vehicle
Vehicleentry
entry
and
detection
on acceleration
at the stiffener
vertical
Figure 11.
and
exitexit
detection
timestimes
basedbased
on acceleration
recordsrecords
at the vertical
stiffener
both
longitudinal
edges
of
the
main
girder:
(a)
rotation
angle
response
obtained
using
the
both longitudinal edges of the main girder: (a) rotation angle response obtained using the two contact
two contact displacement
gauges; (b)records
acceleration
at G2; (c)
acceleration
records
at G3;
displacement
gauges; (b) acceleration
at G2;records
(c) acceleration
records
at G3; (d)
acceleration
(d) acceleration
records
at G4; andrecords
(e) acceleration
records
at G4; and
(e) acceleration
at G5. records at G5.
4.3. Verification
of the
the Rotation
Rotation Angle
Angle Response
Response Determined
Determined from
from Measured
Measured Angular
Angular Velocity
Velocity
4.3.
Verification of
By comparing
determined from
the measured
measured angular
angular velocity
velocity with
with
By
comparing the
the rotation
rotation angle
angle response
response determined
from the
that
determined
by
the
two
contact
displacement
gauges,
the
accuracy
of
the
response
determined
that determined by the two contact displacement gauges, the accuracy of the response determined
from the
byby
using
anan
entry
time
(11.372
s) and
an
from
the measured
measured angular
angularvelocity
velocitycould
couldbe
beverified.
verified.Then,
Then,
using
entry
time
(11.372
s) and
exit
time
(13.434
s)
as
the
limits
of
the
numerical
integration,
the
rotation
angle
response
was
an exit time (13.434 s) as the limits of the numerical integration, the rotation angle response was
determined from
from measured
measured angular
angular velocity.
velocity.
determined
The
rotation
angle
response
determined
thethe
MEMS
IMU
andand
thatthat
determined
by the
The rotation angle response determinedfrom
from
MEMS
IMU
determined
by two
the
contact
displacement
gauges
also
placed
at
G4
are
shown
in
Figure
12,
where
it
can
been
seen
two contact displacement gauges also placed at G4 are shown in Figure 12, where it can been seen that
that
both responses
responsesstart
starttotoincrease
increase
vehicle
entry
(11.372
s)both
and lines
bothshow
linessimilar
show similar
both
at at
thethe
vehicle
entry
timetime
(11.372
s) and
shapes.
shapes. Based on these results, the proposed method was found to be highly accurate when
compared with the reference rotation angle response produced using the two contact displacement
gauges.
Sensors 2016, 16, 1882
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Based on these results, the proposed method was found to be highly accurate when compared with
the reference
rotation
Sensors 2016,
16, 1882 angle response produced using the two contact displacement gauges.
11 of 13
Figure 12. Rotation angle response obtained via MEMS IMU at G4 using the proposed method.
Figure 12. Rotation angle response obtained via MEMS IMU at G4 using the proposed method.
It can be seen that the rotation angle response determined by the two contact displacement
gauges
more
than that determined
the displacement
MEMS IMU. Itgauges
is
It can becontains
seen that
thehigh-frequency
rotation angle components
response determined
by the twofrom
contact
thought
that
this is caused by
electric noisethan
included
in the displacement
response
measured
the
contains
more
high-frequency
components
that determined
from the
MEMS
IMU. It by
is thought
contact
displacement
gauges.
that this
is caused
by electric
noise included in the displacement response measured by the contact
displacement gauges.
5. Conclusions
5. Conclusions
In the present study, by conducting field measurements of an actual in-service bridge, the
characteristics of the bridge rotation angle response were analyzed first. Next, based on the bridge
In the present study, by conducting field measurements of an actual in-service bridge, the
rotation angle response characteristics, a method for determining the bridge rotation angle response
characteristics
of the bridge
rotation
responseThen,
wereinanalyzed
first. the
Next,
based
on the
bridge
from the measured
angular
velocityangle
was proposed.
order to detect
precise
vehicle
entry
rotation
angle
response
characteristics,
a
method
for
determining
the
bridge
rotation
angle
response
and exit times and assess the vehicle travel lane, a vehicle detection system using eight MEMS IMUs
from was
the measured
angular
was proposed.
Then,
in order
detect the
precise
vehicle entry
constructed.
Finally,velocity
by determining
the bridge
rotation
angletoresponse
from
the measured
and exit
timesvelocity
and assess
travel
lane, the
a vehicle
detection
system
using
eight
MEMS
angular
usingthe
thevehicle
proposed
method,
effectiveness
of the
method
was
verified.
TheIMUs
conclusions of
the present
study are as the
follows:
was constructed.
Finally,
by determining
bridge rotation angle response from the measured angular
velocity
proposed
effectiveness
of the method
wasangle
verified.
The conclusions
 using
It wasthe
found
that, asmethod,
with thethe
displacement
response,
the rotation
response
is largely of
the present
study are
follows:
classified
intoas
the
response due to forced displacement, which consists of frequencies below 1.0
•
•
•
•
Hz, and the free vibration response. This result was achieved as a result of comparisons
It was
foundthe
that,
as with
the displacement
response,
angle response
is largely
between
bridge
displacement
response spectrum
andthe
therotation
bridge rotation
angle response
classified
into the response due to forced displacement, which consists of frequencies below 1.0 Hz,
spectrum.
and
free
Thisresponse
result was
achieved aswhich
a result
comparisons
 the
Based
onvibration
the bridgeresponse.
rotation angle
characteristics,
areof
largely
classified between
into the the
rotation
angle responses
duespectrum
to forced displacement
androtation
free vibration
responses,
bridge
displacement
response
and the bridge
angledisplacement
response spectrum.
a on
method
for determining
the bridge
rotation
angle response
from
measured
angular
Based
the bridge
rotation angle
response
characteristics,
which
arethe
largely
classified
into the
velocity
was
proposed.
rotation angle responses due to forced displacement and free vibration displacement responses,

Vehicle entry and exit times and the vehicle travelling lane could be estimated using
a method for determining the bridge rotation angle response from the measured angular velocity
acceleration responses measured by eight MEMS IMUs. This system worked by comparing the
was proposed.
maximum acceleration response values measured at the longitudinal edges of each main
Vehicle
entry and exit times and the vehicle travelling lane could be estimated using acceleration
girder.
responses
measuredrotation
by eight
MEMS
IMUs.
ThisIMU
system
worked
by comparing
maximum

The determined
angle
responses
using
and the
proposed
method werethe
found
to
be in good
agreement
withmeasured
the reference
rotation
angle responses
by the
two contact
acceleration
response
values
at the
longitudinal
edges calculated
of each main
girder.
displacement rotation
gauges. angle
This responses
outcome was
obtained
bythe
examining
resultswere
of field
The determined
using
IMU and
proposedthe
method
found to
measurements
taken
from
an
in-service
bridge
using
nine
IMUs
and
two
contact
displacement
be in good agreement with the reference rotation angle responses calculated by the two contact
gauges.
displacement gauges. This outcome was obtained by examining the results of field measurements
this an
study,
by using
vehicle
passage
time asand
thetwo
limits
of thedisplacement
numerical integration,
takenInfrom
in-service
bridge
using
nine IMUs
contact
gauges. the
rotation angle response was determined from the measured angular velocity. Further studies are
In
this study,
by using
vehicle passage
as themethod
limits of
numerical
integration,
required
to verify
the effectiveness
of thetime
proposed
for the
multiple
vehicle
travelling the
conditions.
Furthermore,
study focuses
solely
the bridge-axial-orthogonal
rotation
angle response
wasthis
determined
from
the on
measured
angular velocity.direction
Furtherrotation
studies are
required to verify the effectiveness of the proposed method for multiple vehicle travelling conditions.
Sensors 2016, 16, 1882
12 of 13
Furthermore, this study focuses solely on the bridge-axial-orthogonal direction rotation angle response.
Further studies will be required to verify the effectiveness of the proposed method for the bridge-axial
direction rotation angle response and the bridge rotation angle response at multiple points.
Acknowledgments: This research was supported by a grant from the Ministry of Education, Culture, Sports,
Science and Technology (MEXT) (Grant-in-Aid for Scientific Research (KAKENHI) (A) JP25249063) and was
carried out as part of cooperative research with the Metropolitan Expressway Co., Ltd. (Tokyo, Japan); Shutoko
Engineering Co., Ltd. (Tokyo, Japan); and the Highway Technology Research Center (Tokyo, Japan).
Author Contributions: Hidehiko Sekiya and Chitoshi Miki conceived of and designed the algorithm for the
proposed method. Hidehiko Sekiya and Takeshi Kinomoto performed the experiments. Hidehiko Sekiya analyzed
the data, and wrote the paper.
Conflicts of Interest: The authors declare they have no conflicts of interest.
Abbreviations
The following abbreviations are used in this manuscript:
IMU
MEMS
LDVT
LDV
RC
inertial measurement unit
micro-electro-mechanical systems
linear variable differential transformer
laser Doppler vibrometer
reinforced concrete
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