TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3331 ~ 33
3
7
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.4933
3331
Re
cei
v
ed O
c
t
ober 1
6
, 201
3; Revi
se
d Novem
b
e
r
29, 2013; Accept
ed De
cem
b
e
r
18, 2013
Application of Inclinometer in Arch Bridge Dynamic
Deflection Measurement
Xianlong He
*
1
, Xueshan Yang
2
, Lizhe
n
Zhao
3
1,2
Key
Lab
orat
or
y
of Earth
q
u
a
ke Eng
i
n
eeri
n
g and En
gi
neer
ing Vi
bratio
n, In
stitute of Engi
neer
ing
Mecha
n
ics, CE
A, Harbin 1
5
0
0
80, Chi
na, Ph:
+
8613
78
477
29
17;
3
Institute of Disaster Preventi
o
n Scienc
e an
d T
e
chnolog
y, H
e
Bei Sh
an
he, 065
20
1, Chin
a,
Ph:+
8613
78
56
266
23.
Corresp
on
din
g
author, e-mai
l
: hxl
4
1
28@
16
3.com*
1
, 5242
45
186
@qq.com
2
,
hxl
1
2
0
6
26@
1
63.com
3
A
b
st
r
a
ct
Dyna
mic defl
e
ction
meas
ure
m
e
n
t is an i
m
p
o
rtant co
mp
on
ent to the bri
d
g
e
loa
d
i
ng ex
pe
riment or
hea
lth
mo
nitor
i
ng. Us
ing
h
i
gh
-precisi
on
inc
l
i
n
o
m
eters
to
te
st the dy
na
mic
defl
e
ctio
n is
a
go
od
metho
d
for
High-S
p
e
ed R
a
ilw
ay Brid
ge
deflect
io
n measur
e
m
ent in
this paper,
w
e
develo
p
a
kind of preci
s
io
n
incli
n
o
m
eter w
h
ich c
o
mpr
ehe
nsives th
e C
a
pacitiv
e se
nsor
techn
o
lo
gy a
n
d
the S
e
rvo s
ensor t
e
chn
o
l
o
gy
and
has
be
en
call
ed QY
inc
lino
m
eter. W
e
also
der
iv
e
a
new
theory
to calc
ul
ate d
e
f
lection
bas
ed
on
incli
nati
on. Us
i
ng
elev
en
QY incl
in
o
m
eters
an
d thre
e
C
abl
e-Dis
plac
e
m
e
n
t se
nsors,
w
e
hav
e d
o
n
e
a
comparis
on dy
na
mic deflecti
o
n
meas
ur
e
m
e
n
t
experi
m
ent o
n
an
arch
brid
ge. T
e
st result
s ind
i
cate: us
i
n
g
incli
n
o
m
eters to measur
e dy
na
mic d
e
flecti
on can
ac
hi
ev
e the sa
me
ac
curacy w
i
th Cabl
e-Dis
plac
e
m
e
n
t
sensor w
h
ic
h can ach
i
ev
e 0.1
mm a
ccur
a
cy. T
herefore, thi
s
experi
m
ent
h
a
s prove
d
Usi
ng hi
gh-
precis
i
o
n
incli
n
o
m
eters to me
asur
e dy
na
mic
defl
e
ctio
n of bridg
e
ca
n satisfy
the dyna
mic defl
e
cti
on meas
ure
m
e
n
t
requ
est of high
-spee
d railw
ay
bridg
e
. Co
mp
arin
g w
i
th
other metho
d
s of d
y
na
mic d
e
flecti
on meas
ure
m
e
n
t,
usin
g hi
gh-
pre
c
ision
inc
lin
o
m
eters to
meas
u
r
e dyn
a
m
ic
d
e
flectio
n
is very
easy to o
per
ate, and
als
o
do
no
t
nee
d find a sta
t
ic reference p
o
int.
Ke
y
w
ords
:
arc
h
brid
ge, dyn
a
m
ic d
e
flecti
on, incli
n
o
m
eter,
cabl
e-dis
p
lac
e
ment sensor,
me
asure d
e
flecti
o
n
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
As we
kn
ow,
dynamic
def
lection m
e
a
s
urem
ent
is v
e
ry impo
rtant
for the op
erational
safety an
d
structu
r
al
dam
age
asse
ssm
ent of
High
-Speed
Rail
way Bridg
e
[1-3], becau
se t
h
e
dynamic defl
e
ction
ha
s
cl
ose
relation
ship
with
the
l
i
ve-load
capa
city of span
and
high
-spe
ed
train d
e
railm
e
n
t [3]. There
have several
method
s to d
e
tect dyna
mi
c defle
ction
o
f
bridg
e
, mai
n
ly
inclu
d
ing: u
s
ing ca
ble-displacement sensor to
me
asu
r
e, usi
n
g
high accu
ra
cy GPS rece
iver
device to me
asu
r
e, u
s
ing
l
a
se
r device to measure
[4
]. It is an easy operation a
nd low
co
st and
high accu
ra
cy method to test dynami
c
deflectio
n by
cabl
e-di
spl
a
cement se
nsor, but this method
need
s find a static pla
c
e to install the sen
s
o
r
, can’t
been used to measure
such b
r
idg
e
which
cro
s
s
upon
t
he
river
or canyon[5]. Hi
g
h
p
r
eci
s
io
n
GPS re
ceive
r
can
be
en
use
d
to te
st
the
dynamic d
e
flection of b
r
id
ge, but
its accuracy
can o
n
ly rea
c
h cm
level [1, 6], o
n
ly been u
s
e
d
to
measure the
defle
ction
o
f
cabl
e-staye
d
an
d
su
spe
n
sio
n
b
r
idg
e
whi
c
h
have
long
span
and
signifi
cant de
flection chan
ged. Using l
a
se
r devic
e to mea
s
ure d
e
flection al
so
need
s a sta
t
ic
place to instal
l the device, so it can’t test
su
ch span
s that cro
s
s rive
r or canyon [7
].
As we
kn
o
w
, prestressed con
c
ret
e
box
beam
bridge
s an
d st
eel tru
s
s arch bea
m
bridg
e
s a
r
e
the m
a
in
pa
rt
of Hig
h
-Sp
e
e
d
Railway
. Such b
r
idg
e
s h
a
ve large stiffness and
stro
ng
ability to resi
st defo
r
matio
n
and
ca
n m
eet t
he re
qui
reme
nts of
High-Sp
eed
Railway. It maybe
has
slight dy
namic
defle
ction for some
sho
r
t sp
an of
such bri
dge
s when
Hig
h
-S
peed train ru
ns
across. T
herefore, the
p
r
eci
s
io
n of
GPS re
ceive
r
is not e
n
ough fo
r dy
namic defle
ction
measurement
of Hi
gh-S
p
e
ed
Rail
way B
r
idge.
Many
High
-Spe
ed
Rail
way Brid
ges cro
s
s riv
e
r o
r
canyo
n
. The
r
efore, using
cable
-
di
spla
ceme
nt
sen
s
or or la
se
r device to m
easure dyn
a
mic
deflectio
n
of su
ch High
-Sp
eed Rail
way Bridge
i
s
ve
ry difficult, beca
u
se th
ere are
not stati
c
pla
c
e
near th
e bri
d
ge to install t
hese devices. There h
a
s a
nother
sh
orta
ge of these method
s that
can
only test one
point’s dyna
mic defle
ctio
n at the sam
e
time [8-10]. Therefo
r
e, it is a significa
nce
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3331 – 33
37
3332
resea
r
ch
to
develop
a n
e
w dynami
c
defle
ct
ion
measurement
metho
d
fo
r the
Hig
h
-S
peed
Rail
way Bridg
e
[11-14].
In this pa
pe
r, we
develo
p
a n
e
w
dynamic defle
ction mea
s
u
r
e
m
ent metho
d
whi
c
h
basi
ng high
-pre
cisi
on in
cl
inomete
r
s to test all pos
iti
on’s dyna
mic deflection of
bridge
s [5]-[6].
Based o
n
this method, we have use
d
Q
Y
inclinom
ete
r
s to test the dynamic d
e
flection of on a
r
ch
bridg
e
su
c
c
e
ssf
ully
.
2. The Principle of QY Inclinometer
QY inc
linometer inc
l
udes t
he tec
hnology of elec
tric
c
a
pac
i
ty
dis
p
lace s
e
ns
or and
electroma
gne
tism feedba
ck sen
s
o
r
, as sho
w
n in
Figure 1. We use the
technolo
g
y of
electroma
gne
tism feedba
ck to chan
ged
the
dampin
g
coeffici
ent of pendulu
m
and develop
a
differential m
o
tion ele
c
tric
cap
a
city displ
a
ce
sen
s
o
r
to resp
on
se the
displa
cem
e
n
t
of pendulum
.
Figure 1. QY Inclinom
eter
The pri
n
ci
ple
of QY inclino
m
eter ha
s sh
own in Fig
u
re
2 and 3.
Parameter
k
is the stiffness of me
ch
an
ical sprin
g
, defines
b
as d
a
m
p
ing coefficie
n
t,
G
is
an ele
c
tri
c
-fe
edba
ck dam
ping
coeffici
e
n
t,
12
GB
L
L
,
1
B
L
is m
e
chanical
coupling factor,
2
L
is
the len
g
th of
pen
dulum,
g
is
an
small
electri
c
-feed
b
a
ck d
a
mpin
g
co
efficient
which
is
used
to
adju
s
t to lev
e
l of p
end
ulu
m
,
is th
e in
clination
of pe
ndulum,
c
k
is the sensitivity of electric
cap
a
cit
y
s
e
n
s
or,
X
is the d
i
spla
ce of el
ectri
c
capa
ci
ty sensor,
R
is t
he re
sist
a
n
c
e
of
coil
.
Equation (1) i
s
the motion
equatio
n of mass blo
c
k
m
.
(
1
)
1
k
is moment o
f
inertia,
13
4
k
L
Lm
,
3
L
is the equivalent l
ength of pen
dulum,
4
L
is the
length of
the movin
g
center of p
e
n
dulum
to the
ce
nter of m
a
ss bl
ock
m
,
1
is t
he ve
rtical
in
clinatio
n of
measuri
ng po
int, M is the q
uality of QY
Inclin
om
ete
r
. Solving Equa
tion (1), we can get Equation
(2):
(2)
11
02
cc
k
bk
G
i
M
g
uk
x
k
L
0
1
2
1
2
2
1
2
1
1
2
(1
)
c
u
B
sD
s
nn
kL
M
g
B
nk
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Applicatio
n of Inclinom
eter
in Arch Bri
d
g
e
Dynam
ic Deflection Me
a
s
urem
ent (Xianlon
g He
)
3333
s
is ope
rato
r.
n
is the inhe
rent
circula
r
frequ
ency of pen
d
u
lum,
1
n
k
k
.
D
is the damping
coeffici
ent wh
ich calculated
from
b
and
G
,
2
1
2
D
G
kn
R
.
m
x
G
1
g
i
R
k
0
u
1
M
g
1
1
a
b
a
b
M
g
1
F
Figure 2. The
Structure Pri
n
cipl
e of QY
Inclinom
eter
Figure 3. The
Force Balan
c
e of YQ
Inclinom
eter
If
1
D
and
22
s
n
, we ca
n get the sen
s
itivity of
sensor, ju
st like
Equation (3).
0
1
1
u
B
(3)
3. The Theor
y
of Deflec
tion Calcula
t
ion from Inclination
We defin
e the length of on
e spa
n
of brid
ge is L mete
r, and install
1
N
inclinom
eters o
n
this
s
p
an.
So we ca
n ge
t
1
N
positio
n’s in
clinatio
n data
and define th
em as Mat
r
ix (4):
1
12
N
Qq
q
q
(4)
i
q
is the
i
po
sition
’s incli
nation
data.
We defin
e the static defle
ction function
as:
1
()
()
()
s
i
n
(
)
c
o
s
(
)
N
i
i
ii
i
i
i
yx
c
f
x
f
xa
w
x
b
w
x
(
5
)
x
is a
n
y po
sitio
n
of the
bea
m.
()
i
f
x
is
define
d
a
s
the
i
mo
dal fun
c
tion
of the b
eam.
i
w
is
defined as
th
e
i
modal freq
uen
cy,
i
a
and
i
b
are
co
efficient
s
of functio
n
()
i
f
x
.
c
is
th
e co
rr
ec
te
d
coeffici
ent of deflectio
n.
As we kno
w
, there
have
not defle
ction
cha
nge
d ne
ar pi
ers. So
we
can
calcu
l
ate the
followin
g
equ
ations:
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ISSN: 23
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046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3331 – 33
37
3334
1
11
s
i
n(
)
c
os
(
)
N
i
i
NN
ii
i
i
ii
bc
aw
l
b
w
l
c
(6)
Definin
g
the inclin
ation fun
c
tion of beam
as
()
p
x
, and getting the followi
ng equ
ation:
11
()
()
c
o
s
(
)
s
i
n
(
)
NN
ii
i
i
i
i
ii
yx
p
xa
w
w
x
b
w
w
x
x
(7)
If we discrete
param
eter
x
,
we can get th
e followin
g
eq
uation:
11
()
c
o
s
(
)
s
i
n
(
)
NN
ji
i
i
j
i
i
i
j
ii
p
xa
w
w
x
b
w
w
x
(8)
So we nee
d solve 3N num
ber pa
ram
e
te
rs. We define
function:
1
2
12
1
2
1
2
1
(
,
,,
,
,
,,
,
,
,,
)
(
(
)
)
N
NN
N
j
j
j
za
a
a
w
w
w
b
b
b
p
x
q
(9)
Acco
rdi
ng the
rule of least
squ
a
re m
e
tho
d
, we ca
n get
N sets of foll
owin
g equati
ons:
0
01
,
2
,
0
i
i
i
z
a
z
iN
w
z
b
(10)
Expanding E
quation (10
)
, we can get N
sets of follo
wi
ng equ
ation
s
:
1
1
11
11
((
c
o
s
(
)
s
i
n
(
)
)
c
o
s
(
)
0
(
c
o
s
(
)
sin(
)
)
(
c
os(
)
sin(
)
(
sin
(
)
c
os(
)
)
0
(
(
c
o
s(
)
s
in
(
)
)
s
in(
N
N
tt
t
j
tt
t
j
j
i
i
j
jt
N
N
tt
t
j
tt
t
j
j
i
i
j
i
i
j
jt
i
i
j
i
j
i
ij
ij
tt
t
j
tt
t
j
j
i
aw
wx
b
w
wx
q
w
w
x
a
w
wx
b
w
wx
q
a
w
x
b
w
x
awx
w
x
b
wx
wx
a
w
wx
b
w
wx
q
w
w
1
11
)0
N
N
ij
jt
x
(11)
As we kno
w
, all mode
l function
s are o
r
thog
o
nal functio
n
s
. So we can al
so d
e
fine
12
((
)
,
(
)
,
,
(
)
)
N
f
xf
x
f
x
are o
r
thog
on
al function
s, and get N-1 sets of followin
g
equatio
ns:
0
0
(
s
in
(
)
c
o
s(
)
)
(
sin(
)
c
o
s
(
)
)
l
ii
i
i
t
t
t
t
i
it
a
w
xb
w
x
a
w
xb
w
x
d
x
ki
t
(12)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Applicatio
n of Inclinom
eter
in Arch Bri
d
g
e
Dynam
ic Deflection Me
a
s
urem
ent (Xianlon
g He
)
3335
If
1
3
NN
³
,
we can
so
lve
paramete
r
s
11
1
[,
,
,
,
,
,
]
N
NN
ab
w
a
b
w
L
from Equ
a
t
ion (1
1) an
d
(12
)
,
then we
ca
n solve pa
ram
e
ter
c
from eq
ua
tion (6). So
we solve a
ll p
a
r
amete
r
s
of static defle
ction
function
()
yx
.
If we define
all paramet
ers
have
ch
ange
d followi
ng time, we
can g
e
t the
dynamic
deflectio
n fun
c
tion:
1
(,
)
(
,
)
(
,
)
(
)(
s
i
n
(
)
(
)c
o
s
(
)
N
ti
i
ii
i
i
i
yx
t
c
f
x
t
f
x
t
a
t
wx
b
t
wx
(13)
4. Application in Arch Bri
dge
We
have
used QY i
n
cli
n
ometer an
d
other
se
nsors to te
st dy
namic defle
ction of
HUA
NG
HE River High
-Spe
ed Rail
way bridge
s. This b
r
idge ha
s 13
6
0
meters lon
g
and 23
spa
n
s.
We have
cho
s
en a 1
00 me
ter long a
r
ch bridg
e
to
test. Its shape i
s
shown as Fig
u
re 5.
Figure 5. The
Picture of Arch Brid
ge whi
c
h We Te
st
We
have
use
d
eleve
n
QY i
n
clin
omete
r
s
to test
thi
s
b
r
i
dge. Th
e p
o
si
tion of in
stalli
ng QY
inclin
omete
r
s are sh
own a
s
Figu
re 6.
Figure 6. Installing Positio
n
s of QY Incli
nomete
r
s
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02-4
046
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KA
Vol. 12, No. 5, May 2014: 3331 – 33
37
3336
At the sam
e
time, we
have
installe
d thre
e
Ca
ble-Di
spl
a
cem
ent sen
s
ors nea
r
25
and
5
0
and 7
5
mete
r long to te
st
the dynami
c
deflectio
n of
this bri
dge.
QY inclin
ome
t
ers h
a
ve be
en
installe
d in
th
e ri
ght
side
o
f
box b
eam.
We
used
the
sa
me t
r
ain
runnin
g
a
c
ross
with
differe
nt
spe
ed
as dyn
a
mic l
oad
s. T
he te
st re
sult
s a
r
e
sh
ow
n i
n
table
on
e t
o
table
thre
e, and
Figu
re
7
to
Figure 9.
Table 1. The
Max Measure
m
ent Defle
c
tion of Two System
s at 25 meter Lo
ng
Train-speed
（
km/h
）
inclinometer
D1
Cable-Displacement D2
(D1-
D2)/D
2
5
3.78mm
3.69mm
2.5%
60
3.67mm
3.73mm
-1.7%
120
3.86mm
3.75mm
2.9%
Table 2. The
Max Measure
m
ent Defle
c
tion of Two System
s at 50 meter Lo
ng
Train-speed
（
km/h
）
inclinometer
D1
Cable-Displacement D2
(D1-
D2)/D
2
5
3.28mm
3.49mm
-6.1%
60
3.39mm
3.56mm
-4.7%
120
3.69mm
3.55mm
3.9%
Table 3. The
Max Measure
m
ent Defle
c
tion of Two System
s at 75 meter Lo
ng
Train-speed
（
km/h
）
inclinometer
D1
Cable-Displacement D2
(D1-
D2)/D
2
5
3.52mm
3.67mm
-4.1%
60
3.57mm
3.78mm
-5.6%
120
3.65mm
3.82mm
-4.5%
Figure 7. The
Dynamic
Def
l
ection
Curve
of 25
meter Point when Train Ru
ns Acro
ss
with
5Km/h spe
e
d
Figure 8. The
Dynamic
Def
l
ection
Curve
of 50
meter Point when Train Ru
ns Acro
ss
with
5Km/h Speed
Figure 9. The
Dynamic
Def
l
ection
Curve
of 75 me
ter P
o
int when Train Runs
Acros
s
with 5Km/h
Speed
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TELKOM
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ISSN:
2302-4
046
Applicatio
n of Inclinom
eter
in Arch Bri
d
g
e
Dynam
ic Deflection Me
a
s
urem
ent (Xianlon
g He
)
3337
Comp
ari
ng wi
th cable
-
di
spl
a
cem
ent sen
s
or, te
st re
sul
t
s of using
Q
Y
inclinom
ete
r
to test
dynamic d
e
flection have
smaller than 7
percent er
ro
rs, and also h
a
ve similar d
y
namic defle
ction
curv
e
s
.
5. Conclusio
n
Acco
rdi
ng in
clination to
cal
c
ulate
dynam
ic d
e
flection
of Hig
h
-Spe
e
d
Railway B
r
i
dge i
s
a
good m
easurement metho
d
. We have
develop
ed a
new
kind of
pre
c
isi
on in
cl
inomete
r
and
a
new th
eo
ry to fast
cal
c
ula
t
e dynami
c
d
e
flection f
r
om
dynami
c
in
cl
ination d
a
ta,
and h
a
ve u
s
ed
eleven i
n
clin
ometers to
test the
dyna
mic d
e
flecti
o
n
of o
ne
arch bri
dge
whi
c
h i
s
a p
a
rt
of
HUA
NG
HE River Hi
gh-S
peed Railwa
y
Bridge with
a same trai
n runni
ng a
c
ross with different
spe
ed
as the
dynamic loa
d
s
. Comp
arin
g
with te
st
re
sults
of ca
ble
-
displ
a
cement
se
nsors, we can
get so
me
con
c
lu
sion: u
s
in
g
eleven in
clin
ometers to
te
st dynami
c
d
e
flection
of arch b
r
id
ge
s h
a
s
smalle
r tha
n
7% error; a
nd can g
e
t simila
r dy
na
mic d
e
flectio
n
cu
rve
s
, an
d ca
n a
c
hiev
e a
pre
c
isi
on of 0
.
1mm.
Usi
ng i
n
cli
n
o
m
eters to
me
asu
r
e
or mon
i
tor
dyna
mic
deflectio
n of
bridg
e
s is a
g
ood
and
easy op
eratio
n method, be
cau
s
e in
clin
o
m
eters ca
n
b
e
installe
d into box beam o
r
on the de
ck of
bridg
e
, and d
o
not need a
static refere
n
c
e poi
nt.
Ackn
o
w
l
e
dg
ements
Suppo
rted b
y
Key Labo
ratory of Ea
rthqua
ke
E
ngi
neeri
ng and Enginee
ring
Vibration,
Institute of Enginee
ring Me
cha
n
ics, CEA
Based Fu
nd:
2013B08
Referen
ces
[1]
Z
hou Z
h
e
n
ji
an
g. Compar
in
g w
i
t
h
sever
a
l
w
a
y
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ge d
e
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n
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a
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199
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[2] Yang
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ans
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e
vic
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T
he re
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rt of impr
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g
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o
a
d
def
l
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c
t
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a
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d
g
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Univers
i
t
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a
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002.
[4]
Xi
an lo
ng H
e
,
T
i
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zhen Z
h
a
o
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w
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y
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on Me
asurem
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H
i
g
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ay
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r
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d
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ed Mec
han
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angxi
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y
n
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ng He. T
he
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e
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slo
p
e
a
ngl
e
mo
nito
red
w
i
t
h
S
e
rvo
-
slop
e
se
nsor.
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n
: chin
a e
a
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ake pr
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[7]
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Xu
ans
ha
n. A ne
w
w
a
y for brid
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e
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c
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ng
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urna
l
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[8]
Yang
Xua
n
sh
an. T
he rese
arch o
n
inc
lin
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ie
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a
rthqu
ake E
n
gin
eeri
ng
an
d
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neer
in
g Vi
bratio
n
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[9]
Harik IE, Sha
aba
n AM. Uni
t
ed States Bri
dge F
a
i
l
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Journ
a
l of Pe
rformance of
Constructe
d
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990
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[10]
Kumal
a
sari W
a
rdh
ana, F
a
hi
an C. Ha
di
pri
ono. An
al
ysis
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nt Bri
dges
F
a
ilur
e
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n
ite
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l
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nc
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d Faciliti
e
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0
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[11]
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ountai
n R
S
,
T
hunman CE.
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on
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e
l
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ay
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g
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e
d
i
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nal En
gi
n
eeri
ng Co
nfere
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e
w
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01: 21
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[12]
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o
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LT
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bratio
n an
d D
e
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o
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an
d
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y
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id
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an State
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h
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a
y
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e
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rtment. 199
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[13]
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g
e
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rl
y
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