A Bridge Deflection Monitoring System Based on CCD

A Bridge Deflection Monitoring System Based on CCD
Hindawi Publishing Corporation
Advances in Materials Science and Engineering
Volume 2016, Article ID 4857373, 11 pages
http://dx.doi.org/10.1155/2016/4857373
Research Article
A Bridge Deflection Monitoring System Based on CCD
Baohua Shan,1,2 Lei Wang,3 Xiaoyang Huo,2 Wenting Yuan,2 and Zhilin Xue2
1
Key Lab of Structures Dynamic Behavior and Control (Harbin Institute of Technology), Ministry of Education, Harbin 150090, China
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
3
School of Civil Engineering and Architecture, University of Jinan, Jinan 250022, China
2
Correspondence should be addressed to Baohua Shan; [email protected]
Received 9 June 2016; Revised 6 September 2016; Accepted 21 September 2016
Academic Editor: Ying Wang
Copyright © 2016 Baohua Shan et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
For long-term monitoring of the midspan deflection of Songjiazhuang cloverleaf junction on 309 national roads in Zibo city,
this paper proposes Zhang’s calibration-based DIC deflection monitoring method. CCD cameras are used to track the change
of targets’ position, Zhang’s calibration algorithm is introduced to acquire the intrinsic and extrinsic parameters of CCD cameras,
and the DIC method is combined with Zhang’s calibration algorithm to measure bridge deflection. The comparative test between
Zhang’s calibration and scale calibration is conducted in lab, and experimental results indicate that the proposed method has higher
precision. According to the deflection monitoring scheme, the deflection monitoring software for Songjiazhuang cloverleaf junction
is developed by MATLAB, and a 4-channel CCD deflection monitoring system for Songjiazhuang cloverleaf junction is integrated in
this paper. This deflection monitoring system includes functions such as image preview, simultaneous collection, camera calibration,
deflection display, and data storage. In situ deflection curves show a consistent trend; this suggests that the proposed method is
reliable and is suitable for the long-term monitoring of bridge deflection.
1. Introduction
It is very significant that monitoring bridge deflection can
evaluate the health status of bridge and can provide the
important reference base for the structural performance
and operational status of bridge. Currently, there are two
kinds of deflection measurement methods which are the
traditional measurement method and the automatic measurement method. The traditional measurement methods
include dial indicator, level, and total station. The principle
of dial indicator measuring bridge deflection is very simple
[1]. However, due to the great height of bridge, it is very
inconvenient to install the dial indicator on main girder of
bridge. The level is usually used to measure bridge deflection
along with a scale [2], and this increases the complexity of
measurement work. Furthermore, the total station is easily
influenced by temperature and humidity and is not suitable
for long-term monitoring in the wild [3]. In a word, the
traditional measurement methods are rarely used to execute
the long-term monitoring of bridge deflection, except for the
temporary measurement.
The automatic measurement methods comprise accelerometer, microwave interferometer, GPS, connected pipe
optoelectronic liquid level sensor, and so forth. The highfrequency component occupies a large proportion in the data
collected by accelerometer, so the low-frequency component
is drowned out when the displacement is obtained by computing the integral for acceleration data. However, the bridge
deflection is exactly the low-frequency component. In the
meantime, the double integral brings about errors. As a result,
the accelerometer has lower precision [4]. The microwave
interferometer can detect the bridge deflection according
to the phase difference of reflected wave before and after
deformation. Although the microwave interferometer has
higher precision, this method is not suitable for the case that
the transverse deformation and longitudinal deformation
simultaneously occur on bridge [5]. GPS has very good
practicability. Nevertheless, the cost of GPS is higher and the
2
Advances in Materials Science and Engineering
P
u
z
v
Id
(u0 , 0 )
Iu
Zw
R, T
o
O
Yw
Xw
x
y
Camera center
Image plane
Figure 1: Sketch map of distortion model.
accuracy of GPS can only achieve centimeter level [6]. When
the connected pipe optoelectronic liquid level sensors are
used to detect the deflection of bridge, many pipes and pressure transmitters need to be mounted inside the main girder
of bridge in advance, and the laying work is very complicated
[7].
Based on the above comparative analysis, the CCD
camera is chosen to monitor bridge deflection in this paper.
The CCD image technology has some advantages such as
fast speed, noncontact, high precision, and simple operation.
With the development of image processing technology, the
CCD inspection imaging technology is gradually applied to
engineering practice. In 1999, Olaszek adopted the computer
vision technology to detect the dynamic performance of
bridge structure [8]. In 2002, Yu et al. utilized CCD cameras
to measure the bridge deflection. However, the camera
calibration was very complicated, and the five cross mark
symbols installed on the bridge pier were used to calibrate the
camera and measure the deformation. The three horizontal
crosses were used to calibrate the horizontal ratio value,
and the three vertical crosses were used to calibrate the
vertical ratio value [9]. In 2007, Yoneyama et al. employed
the DIC method to inspect the longitudinal deformation
of a single-span simply supported bridge. The DIC method
required spraying speckles along the longitudinal direction
of bridge, and it was only suitable for detecting the smallspan bridge [10]. In 2007, Chen et al. adopted the DIC
method to measure the hookup that connects the two parts
of a movable steel bridge. An artificial speckle pattern was
formed on the hookup surface and an on-site camera system
with a removable camera set was used to measure stress
concentration at the hookup [11]. In 2015, Shan et al. presented
a stereovision method to conduct the vibration test of a
stayed-cable model, and the proposed stereovision method
acquired 3D displacement curves and had a higher precision
[12].
The above methods in [8–11] need to paste the scale
on structural surface for converting the measurement unit
from pixel into millimeter, and the prepared work is very
complicated. The method in [12] employed Kalman filtering
algorithm to track the circular target on the sequential
images. Compared with the DIC method, Kalman filtering
algorithm needs more time to search image for tracking
of target and uses a lot of memory of computer. This has
little effect on the short-term inspection. However, this
influences the image capture in the long-term monitoring
of bridge. Aimed at the monitoring requirement of bridge
deflection, Zhang’s calibration-based DIC deflection monitoring method is proposed in this paper, and the corresponding bridge deflection monitoring system is integrated and
adopted by Songjiazhuang cloverleaf junction.
2. Principle of Zhang’s Calibration Algorithm
According to the pinhole imaging model [13], the projection
of a spatial point 𝑃 on the imaging plane of camera can be
expressed as
𝑋𝑤
𝑓𝑥 𝛾 𝑢0
𝑟11 𝑟12 𝑟13 𝑡𝑥 [ ]
𝑢
] [ 𝑌𝑤 ]
][
[ ] [
]
𝑠 [ V ] = [ 0 𝑓𝑦 V0 ] [𝑟21 𝑟22 𝑟23 𝑡𝑦 ] [
[𝑍 ]
[ 𝑤]
[1] [ 0 0 1 ] [𝑟31 𝑟32 𝑟33 𝑡𝑧 ]
[ 1 ]
𝑋𝑤
(1)
[ ]
[ 𝑌𝑤 ]
]
= 𝐴 [𝑅 𝑇] [
[𝑍 ] ,
[ 𝑤]
[ 1 ]
where 𝑠 is an arbitrary scale factor and 𝐴 is the intrinsic
parameter matrix of camera without distortion. [𝑅, 𝑇] is the
extrinsic parameter matrix of camera. 𝑅 and 𝑇 are the rotation matrix and translation vector from the world coordinate
system to the camera coordinate system, respectively. [𝑢, V]𝑇
is the 2D coordinate of point 𝑃 in the image coordinate
system. [𝑋𝑤 , 𝑌𝑤 , 𝑍𝑤 ]𝑇 is the 3D coordinate of point 𝑃 in the
world coordinate system.
As shown in Figure 1, owing to the distortion of lens,
there exists a certain deviation between the actual image point
and the ideal image point. To eliminate the distortion of
lens, a camera calibration algorithm based on a 2D planar
pattern was proposed by Zhang [14]. Considering the radial
distortion, a distortion model including two parameters was
adopted in Zhang’s calibration algorithm. This distortion
model can be expressed as follows [15]:
Advances in Materials Science and Engineering
3
𝑋𝑑 = 𝑋𝑢 + 𝑘1 𝑋𝑢 𝑟2 + 𝑘2 𝑋𝑢 𝑟4 ,
𝑌𝑑 = 𝑌𝑢 + 𝑘1 𝑌𝑢 𝑟2 + 𝑘2 𝑌𝑢 𝑟4 ,
(2)
where 𝑟 = √𝑋𝑢2 + 𝑌𝑢2 and (𝑋𝑑 , 𝑌𝑑 ) is the normalized
coordinate of image point under distorted condition. (𝑋𝑢 , 𝑌𝑢 )
is the normalized coordinate of image point under undistorted condition. Both 𝑘1 and 𝑘2 are the radial distortions
coefficients. The matrix 𝐴 in (1) and 𝑘1 , 𝑘2 are collectively
called the intrinsic parameters of camera.
Zhang’s calibration algorithm only requires the camera to
observe a planar pattern shown at a few (at least two) different
orientations. Either the camera or the planar pattern can be
freely moved. The motion need not be known. The detailed
calibration procedure of Zhang’s algorithm is given as
below.
2.1. Solving the Intrinsic and Extrinsic Parameters of Camera. As seen from (1), there exists the projective transformation relation between the world coordinate system
and the image coordinate system. Suppose that the 2D
planar pattern is selected as the model plane of the world
coordinate system; namely, 𝑍𝑤 = 0. Let us denote the
𝑖th column of the rotation matrix 𝑅 by 𝑟𝑖 . From (1), we
have
−𝑇
−1
𝐵=𝐴 𝐴
𝐵11 𝐵12
[𝐵 𝐵
= [ 21 22
[𝐵31 𝐵32
(7)
with V𝑖𝑗 = [ℎ𝑖1 ℎ𝑗1 , ℎ𝑖2 ℎ𝑗1 +ℎ𝑖1 ℎ𝑗2 , ℎ𝑖2 ℎ𝑗2 , ℎ𝑖3 ℎ𝑗1 +ℎ𝑖1 ℎ𝑗3 , ℎ𝑖3 ℎ𝑗2 +
ℎ𝑖2 ℎ𝑗3 , ℎ𝑖3 ℎ𝑗3 ]𝑇 .
Therefore, (5) can be expressed by the following equation:
𝑇
V12
] 𝑏 = 0.
[
V11 − V22
(8)
(3)
𝑋𝑤
[
]
= 𝐴 [𝑟1 𝑟2 𝑡] [ 𝑌𝑤 ] .
[ 1 ]
𝑇
̃ = [𝑋𝑤 𝑌𝑤 1]; we have
̃ = [𝑢 V 1] and 𝑀
Let 𝑚
̃
𝑠̃
𝑚 = 𝐻𝑀,
(4)
where 𝐻 = 𝜆𝐴 [𝑟1 𝑟2 𝑡] = [ℎ1 ℎ2 ℎ3 ], where 𝜆 is an
arbitrary scalar.
Computing 𝐻 is a process that solves the minimum
residual error between the actual image coordinate 𝑚𝑖 and the
̃ 𝑖 which is calculated by (4); the objective
image coordinate 𝑚
̃ 𝑖 (𝐻)‖2 .
function is min ∑𝑖 ‖𝑚𝑖 − 𝑚
After solving 𝐻, two basic constraints on the intrinsic
parameters 𝐴 are obtained according to the orthogonality and
given as follows:
ℎ1𝑇 𝐴−𝑇 𝐴−1 ℎ2 = 0,
ℎ1𝑇 𝐴−𝑇 𝐴−1 ℎ1 = ℎ2𝑇 𝐴−𝑇 𝐴−1 ℎ2 .
(5)
Let
V0 𝛾 − 𝑢0 𝑓𝑦
𝑟
1
− 2
]
[
𝑓𝑥
𝑓𝑥 𝑓𝑦
𝑓𝑥2 𝑓𝑦
]
[
]
[
𝐵13
2
[
𝛾
(V
𝛾
−
𝑢
𝑓
)
𝛾
V0 ]
𝑟
1
0
0 𝑦
]
]
[
−
+
−
−
𝐵23 ] = [
.
𝑓𝑥2 𝑓𝑦
𝑓𝑥2 𝑓𝑦2 𝑓𝑦2
𝑓𝑥2 𝑓𝑦2
𝑓𝑦2 ]
]
[
]
[
2
𝐵33 ] [
]
V02
]
[ V0 𝛾 − 𝑢0 𝑓𝑦 𝛾 (V0 𝛾 − 𝑢0 𝑓𝑦 ) V0 (V0 𝛾 − 𝑢0 𝑓𝑦 )
−
−
+
+
1
2𝑓
2 𝑓2
2
2 𝑓2
2
𝑓
𝑓
𝑓
𝑓
𝑓
𝑥 𝑦
𝑥 𝑦
𝑦
𝑥 𝑦
𝑦
]
[
Note that 𝐵 is symmetric, defined by a 6D vector 𝑏 =
[𝐵11 , 𝐵12 , 𝐵22 , 𝐵13 , 𝐵23 , 𝐵33 ]𝑇 .
Let the 𝑖th column vector of 𝐻 be ℎ𝑖 = [ℎ𝑖1 , ℎ𝑖2 , ℎ𝑖3 ]𝑇 ; then
we have
ℎ𝑖𝑇 𝐵ℎ𝑗 = V𝑖𝑗𝑇 𝑏
𝑋𝑤
𝑢
[ ]
[ 𝑌𝑤 ]
[ ]
]
𝑠 [ V ] = 𝐴 [𝑟1 𝑟2 𝑟3 𝑡] [
[ 0 ]
[ ]
[1]
[ 1 ]
(6)
If 𝑛 images of the model plane are observed, by stacking
𝑛 such equations as (8), we have
𝑉𝑏 = 0,
(9)
where 𝑉 is a 2𝑛 × 6 matrix. If 𝑛 > 3, we will have in general a
unique solution 𝑏 defined up to a scale factor.
Once 𝑏 is estimated, we can compute all camera intrinsic
parameters. The matrix 𝐵 is estimated up to a scale factor, that
is, 𝐵 = 𝜆𝐴−𝑇 𝐴−1 , with 𝜆 being an arbitrary scale. Without
difficulty, we can uniquely extract the intrinsic parameters
from matrix 𝐵. Once 𝐴 is known, the extrinsic parameters
for each image are readily computed. From (4), we have
𝑟1 = 𝜆𝐴−1 ℎ1 ,
𝑟2 = 𝜆𝐴−1 ℎ2 ,
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Advances in Materials Science and Engineering
𝑟3 = 𝑟1 × 𝑟2 ,
Through the above two steps, the intrinsic and extrinsic
parameters including nonlinear distortion coefficients of
camera are all achieved.
𝑡 = 𝜆𝐴−1 ℎ3 ,
(10)
−1
−1
where 𝜆 = 1/‖𝐴 ℎ1 ‖ = 1/‖𝐴 ℎ2 ‖.
2.2. Maximum-Likelihood Estimation. In general case, the
distortion of lens cannot be ignored. Therefore, in the second
step, the intrinsic and extrinsic parameters derived in the first
step are regarded as the initial values to execute optimization.
We are given 𝑛 images of a 2D planar plane and there are
𝑚 points on the planar plane. Assume that the image points
are corrupted by independent and identically distributed
noise. For different point on a planar plane, the initial values
of distortion coefficients 𝑘1 , 𝑘2 can be solved from (2) by the
least square method. The detailed process can refer to the
technical report [16].
These initial values including the intrinsic and extrinsic
parameters and the distortion coefficients are substituted into
the objective function to optimize camera. The maximumlikelihood estimate can be obtained by minimizing the
following function:
𝑛 𝑚
󵄩
󵄩2
̃ (𝐴, 𝑘1 , 𝑘2 , 𝑅𝑖 , 𝑇𝑖 , 𝑀𝑗 )󵄩󵄩󵄩󵄩 ,
∑ ∑ 󵄩󵄩󵄩󵄩𝑚𝑖𝑗 − 𝑚
𝑖=1 𝑗=1
(11)
̃ (𝐴, 𝑘1 , 𝑘2 , 𝑅𝑖 , 𝑇𝑖 , 𝑀𝑗 ) is the projection of point 𝑀𝑗 in
where 𝑚
image 𝑖 according to (4).
Minimizing (11) is a nonlinear minimization problem,
which is solved with the Levenberg-Marquardt algorithm
[17]. It requires an initial guess of 𝐴, [𝑅𝑖 , 𝑡𝑖 ] (𝑖 = 1, . . . , 𝑛),
which can be obtained using the technique described in the
previous section.
𝐶ZNCC =
3. Zhang’s Calibration-Based DIC Deflection
Monitoring Method
The DIC method is widely used to measure the surface
displacement or strain according to the correlation of light
intensity of speckles before and after deformation, which are
distributed on specimen surface randomly [18]. When the
DIC method is employed to detect deformation, a single
CCD camera is usually required to be perpendicular to the
measured surface and the angle between the optical axis of
CCD camera and the vertical line of measured surface cannot
be larger than 5∘ [18]. In engineering, the angle between the
optical axis of CCD camera and the vertical line of measured
surface is often larger than 5∘ . As a result, the DIC method
cannot be directly used to measure deformation when the
skew angle is larger than 5∘ . To deal with this problem,
Zhang’s calibration algorithm is introduced to figure out
strict limit of the skew angle of CCD camera. Furthermore,
Zhang’s calibration algorithm can eliminate lens distortion
and convert measurement unit.
3.1. Principle of DIC. The correlation criterion needs to be
firstly confirmed when the DIC method is used to calculate
deformation. The zero-mean normalized cross-correlation
(ZNCC) criterion has the most robust noise-proof performance and is insensitive to the linear scale and offset in
lighting on images. Considering the requirement of actual
application, the ZNCC criterion is chosen to conduct area
matching in this paper. The ZNCC criterion is given as follows
[19]:
𝑀
∗ ∗
∑𝑀
𝑥=−𝑀 ∑𝑦=−𝑀 [𝑓 (𝑥, 𝑦) − 𝑓] ⋅ [𝑔 (𝑥 , 𝑦 ) − 𝑔]
𝑀
√ ∑𝑀
𝑥=−𝑀 ∑𝑦=−𝑀 [𝑓 (𝑥, 𝑦)
− 𝑓] ⋅
where 𝑓(𝑥, 𝑦) is the gray value of reference image subset,
𝑔(𝑥∗ , 𝑦∗ ) is the gray value of target image subset, and 𝑓, 𝑔 are
the mean gray of reference image subset and target image.
The conics fitting method is used to conduct subpixel
search in this paper. Assume that the pixel position of a point
whose absolute value is the largest in the matrix of correlation
criterion 𝐶ZNCC is 𝑄(𝑥0 , 𝑦0 ). Total nine points composed of
point 𝑄 and its eight nearest-neighbor points can locally
constitute the quadratic surface, and the surface equation is
given as below:
Φ (𝑥, 𝑦) = 𝑎𝑥2 + 𝑏𝑦2 + 𝑐𝑥𝑦 + 𝑑𝑥 + 𝑒𝑦 + 𝑓.
2
(13)
Utilizing the pixel positions of nine points and the correlation coefficients of corresponding positions, the values of
𝑎 ∼ 𝑓 in (13) can be solved, and the extreme point coordinates
𝑀
∗ ∗
√∑𝑀
𝑥=−𝑀 ∑𝑦=−𝑀 [𝑔 (𝑥 , 𝑦 )
2
− 𝑔]
,
(12)
of surface can be obtained, that is, ((𝑐𝑒−2𝑏𝑑)/(4𝑎𝑏−𝑐2 ), (𝑐𝑑−
2𝑎𝑒)/(4𝑎𝑏 − 𝑐2 )). This extreme point is exactly the center
of subset on the deformed image; the center coordinate’s
difference between the reference image and the deformed
image is just the displacement of point 𝑄, whose unit is pixel.
Before test, the traditional DIC method needs to paste
the scale whose length is known on the measured surface
for converting measurement unit from pixel into millimeter.
In most cases, the scale may be the coordinate paper with a
certain length or the geometry size of specimen. According
to the ratio of the actual length of scale to the pixel length
on image, the traditional DIC method can convert the
measurement unit of displacement from pixel into millimeter.
3.2. Displacement Calculation of Measured Point. As shown
in Figure 1, suppose that the coordinate of point 𝑃 in the
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world coordinate system 𝑂 − 𝑋𝑤 𝑌𝑤 𝑍𝑤 is (𝑋𝑤 , 𝑌𝑤 , 𝑍𝑤 )𝑇 , and
its coordinate in the camera system 𝑜 − 𝑥𝑦𝑧 is (𝑥, 𝑦, 𝑧)𝑇 .
In the image coordinate system, the homogeneous image
coordinate in millimeters is (𝑋, 𝑌, 1)𝑇 , and the homogeneous
image coordinate in pixels is (𝑢, V, 1)𝑇 . After subpixel search
of DIC, (𝑢, V, 1)𝑇 has been given. As a result, the relation
between (𝑋, 𝑌, 1)𝑇 and (𝑢, V, 1)𝑇 can be described as follows
[20]:
𝑑𝑋 0 −𝑢0 × 𝑑𝑋
𝑋
[
(𝑌) = [ 0
1
[ 0
1
]
𝑠
[𝑓
[
(𝑦) = [ 0
[
𝑧
[0
1
0 0
𝑋
]
𝑠 ]
0] ( 𝑌 ) ,
𝑓 ]
0 𝑠] 1
(15)
where 𝑓 is the focal length and 𝑠 is the scale factor.
The coordinate (𝑋𝑤 , 𝑌𝑤 , 𝑍𝑤 )𝑇 in the world coordinate
system and the coordinate (𝑥, 𝑦, 𝑧)𝑇 in the camera system
meet the following equation:
𝑥
𝑋𝑤
−1
( 𝑌𝑤 ) = 𝑅 ((𝑦) − 𝑇) ,
𝑍𝑤
(16)
𝑧
where 𝑅 is the rotation matrix from the camera system into
the world coordinate system and 𝑇 is the translation matrix
from the camera system into the world coordinate system.
𝑅, 𝑇 can be acquired by Zhang’s calibration algorithm.
Equation (14) is substituted into (15), and (17) is given as
below:
𝑑𝑋 0 −𝑢0 × 𝑑𝑋
𝑢
𝑠 [
]
(𝑦) = [ 0 𝑑𝑌 −V0 × 𝑑𝑌 ] ( V ) .
𝑓
𝑓
𝑧
] 1
[ 0 0
𝑥
(17)
Combining (16) and (17), the coordinate (𝑋𝑤 , 𝑌𝑤 , 𝑍𝑤 )𝑇 in
the world coordinate can be solved from the homogeneous
image coordinate in pixels (𝑢, V, 1)𝑇 .
In (17), the scale factor 𝑠 must be obtained firstly. The
value of 𝑠 is related with the selection of world coordinate
system. In this paper, the world coordinate system is established on the measured surface. The plane 𝑋𝑤 𝑌𝑤 of the world
coordinate system coincides with the measured surface, and
𝑍𝑤 axis conforms to the right-handed coordinate system. Any
three points in the word coordinate system are selected to
(18)
where 𝐴, 𝐵, 𝐶, 𝐷 are the coefficients of plane equation.
Equation (17) can also be expressed by the equation set as
follows:
(14)
where 𝑑𝑋 and 𝑑𝑌 are the physical size of a pixel on 𝑥-axis and
𝑦-axis, respectively, in mm/pixel, and these two parameters
are the intrinsic parameters. (𝑢0 , V0 )𝑇 is the coordinate of
principal point, in pixels.
The relation between the coordinate (𝑥, 𝑦, 𝑧)𝑇 in the
camera coordinate system and the homogeneous image
coordinate in millimeters (𝑋, 𝑌, 1)𝑇 is expressed as below:
𝑥
𝐴𝑥 + 𝐵𝑦 + 𝐶𝑧 + 𝐷 = 0,
𝑢
𝑑𝑌 −V0 × 𝑑𝑌 ]
] (V) ,
0
establish the plane equation, and the equation is described as
follows:
𝑥=
𝑠 (𝑢 − 𝑢0 ) 𝑑𝑋
,
𝑓
𝑦=
𝑠 (V − V0 ) 𝑑𝑌
,
𝑓
(19)
𝑧 = 𝑠.
Equation (19) is substituted into (18); 𝑠 can be given by the
following equation:
𝑠=
−𝐷
.
𝐴 (𝑢 − 𝑢0 ) (𝑑𝑋/𝑓) + 𝐵 (V − V0 ) (𝑑𝑌/𝑓) + 𝐶
(20)
Through the above calculation, the homogeneous image
coordinate (𝑢, V, 1)𝑇 in pixels can be converted to the coordinate (𝑋𝑤 , 𝑌𝑤 , 𝑍𝑤 )𝑇 in millimeters in the world coordinate
system. Therefore, this paper implements the conversion of
measurement unit from millimeters into pixels by Zhang’s
calibration algorithm.
The sketch map of target image acquired by each CCD
camera is shown in Figure 2. The solid circle surrounded
by a rectangle is exactly white spot in Figure 2, which is
the target tracked by each CCD camera. The rectangle in
Figure 2 is the matching subset extracted by DIC method,
which is used for calculating deformation. Assume that the
image coordinate of matching subset’s center at 𝑡0 is (𝑥0 , 𝑦0 ).
Deformations are found on bridge under load, and the
image coordinate of matching subset’s center at 𝑡𝑖 is (𝑥𝑖 , 𝑦𝑖 ).
Thereby, the displacement of measured point on bridge at
𝑡𝑖 can be obtained by subtracting two coordinates, and the
displacement equation is given by
Δ𝑥 = 𝑥𝑖 − 𝑥0 ,
Δ𝑦 = 𝑦𝑖 − 𝑦0 ,
(21)
where Δ𝑥 is the transverse displacement of measured point
on bridge at 𝑡𝑖 and Δ𝑦 is the vertical displacement of
measured point on bridge at 𝑡𝑖 , which is exactly the bridge
deflection in pixels.
Through the above conversion of measurement unit, the
bridge deflection in millimeters can be acquired accordingly.
4. Comparative Test of Calibration Algorithms
To testify effectiveness and feasibility of Zhang’s calibrationbased DIC deflection monitoring method proposed in this
paper, the comparative test of two calibration methods is
conducted in lab. One is Zhang’s calibration algorithm and
the other is the scale calibration adopted by traditional DIC
method.
Advances in Materials Science and Engineering
Matching
subset
x
o
x
Matching
subset
yi
o
y0
6
x0
xi
y
y
(a)
(b)
Figure 2: Schematic of change of target’s position: (a) initial stage; (b) deformation stage.
9 × 30 mm
Specimen
O
Mobile platform
Y
Dial gauge
9 × 30 mm
X
Translation knob
Figure 3: Experimental photo.
4.1. Experimental Setup. As illustrated in Figure 3, the specimen is 300 mm in length and 50 mm in width. The specimen
surface is coated with white paint, and some silicon carbides
sprayed randomly on white paint are regarded as speckles.
The specimen is fixed on the mobile platform, the translation
knob in Figure 3 can control the horizontal movement of
specimen, and the moving range from left to right is 20 mm.
To compare with the detection results of the proposed
method in this paper, the dial gauge is pressed against
the measured specimen. The measurement range of dial
gauge is 25 mm, and the precision is 0.001 mm. The measured specimen moved horizontally along with the mobile
platform; each movement distance is about 1 mm. In test,
the dial gauge read is recorded and the specimen image is
simultaneously captured by CCD camera along with each
rotation of translation knob. The CCD camera is placed 1 m
away from the specimen. The cameras can record the highdefinition images with a pixel resolution of 1280 × 960 at 1 fps.
The CCD camera is equipped with an optical zoom lens of
F1.8–16 and focal length ranging between 12 and 36 mm.
During test, both Zhang’s calibration algorithm and scale
calibration are adopted to convert the measurement unit of
horizontal displacement in this paper. The scale selected by
the traditional DIC method is the actual length of specimen,
which is 300 mm, and the corresponding length in image is
647.93 pixels. Therefore, the scale factor between actual size
and pixel size is 0.4630 mm/pixel, and this value is exactly
the conversion coefficient of measurement unit used by the
traditional DIC method.
Figure 4: Planar pattern.
As shown in Figure 4, a planar pattern consisting of
eighty-one 30 mm × 30 mm black and white squares is used to
calibrate CCD camera. The open software “Camera Calibration Toolbox for MATLAB” [21], which is compiled according
to Zhang’s algorithm based on a planar pattern, is employed
to execute the camera calibration in this paper. Before test, 9
images of the planar pattern in different postures are firstly
captured by the CCD camera for camera calibration. Then,
8 × 8 corner points on each image, which are expressed by
the red rectangle in Figure 4, are selected to execute camera
calibration by the calibration software. Finally, the intrinsic
and extrinsic parameters including nonlinear distortion coefficients of CCD camera are all obtained by the calibration
software.
4.2. Experimental Result Analysis. The displacement curves
acquired by two different calibration algorithms are shown in
Figure 5. It can be seen that two displacement curves have
the same trend and agree very well. The displacement data
obtained by dial gauge are regarded as the truth-value of
displacement in this paper, and the displacement errors of the
other two calibration algorithms are analyzed accordingly.
Figure 6 gives the absolute error and relative error curves
of two calibration algorithms. As can be seen from Figure 6,
the displacement precision of the proposed method is higher
Advances in Materials Science and Engineering
7
20
Displacement (mm)
16
12
8
4
0
0
5
10
Time (s)
15
20
Scale calibration
Zhang’s calibration
Figure 5: Displacement measurement results of two calibration methods.
1.0
0.8
0.09
Relative error (mm)
Absolute error (mm)
0.12
0.06
0.03
0.6
0.4
0.2
0.0
0.00
0
5
10
15
20
0
5
Time (s)
Zhang’s calibration
Scale calibration
(a)
10
Time (s)
15
20
Zhang’s calibration
Scale calibration
(b)
Figure 6: Error analysis of two calibration algorithms: (a) absolute error curve and (b) relative error curve.
that of traditional DIC method. The mean absolute error of
displacement measured by the DIC method based on Zhang’s
calibration is 0.033 mm, and the relative error is floated at
0.5%. The mean absolute error of displacement detected by
the DIC method based on scale calibration is 0.050 mm, and
the relative error is larger than that of the former.
Results of comparative test of two calibration algorithms indicate that Zhang’s calibration-based DIC deflection
monitoring method has higher precision, and this testifies
effectiveness and feasibility of the proposed method in this
paper.
5. Deflection Monitoring for Songjiazhuang
Cloverleaf Junction
Songjiazhuang cloverleaf junction is located on G309 National Highway, Zibo city, Shandong province. The total length of
bridge is 670.06 m. The superstructures of bridge are 22 m ×
30 m prestressed concrete simply supported box beams and
have 12 box girders in the transverse direction. The substructures of bridge are column piers and bored pile foundation.
The deck width is 32 m, and the layout of deck is 0.5 m +
15 m + 1 m + 15 m + 0.5 m; it is a six-lane two-way bridge. The
bridge was opened to traffic in 2005. The monitored bridge in
this paper is crossing through Jiaozhou-Jinan railway, which
is located under Songjiazhuang cloverleaf junction.
5.1. Monitoring Scheme. According to the deflection monitoring requirement of Songjiazhuang cloverleaf junction, the
midspan deflections of the 3rd, 4th, 9th, and 10th box girders
need to be detected (see Figure 7). Four targets are installed
on the midspan position of the 3rd, 4th, 9th, and 10th box
girders. As shown in Figure 7(b), every two CCD cameras
are mounted on the middle pier of corresponding deck for
8
Advances in Materials Science and Engineering
150 mm
3
4
9
Side with spot
150 mm
150 mm
Φ100 mm
Side with
expansion bolts
Bolt holes
10
Figure 9: Schematic diagram of circular target.
Piers
Waterproof
power box
(a)
3202
3
1550
4
9
Duty
room
10
7
8
9
10
11
12
4# target
15 m
Figure 10: Schematic diagram of deflection monitoring system for
Songjiazhuang cloverleaf junction.
0.16 m
2m
7.334 m
Waterproof
power box
2 CCD cameras
(two 50 W spotlights)
15 m
15 m
Spotlight
2# target
3# target
PC
Figure 7: Box girder of Songjiazhuang cloverleaf junction. (a)
Photo; (b) profile.
Waterproof
power box
2 CCD cameras
(two 50 W spotlights)
50
(b)
CCD
2
3
4
5
6
1# target
Cable
(wire)
11
1550
50
1
15 m
Middle
pier
15 m
Middle
pier
Target
Figure 8: Installation location of CCD along longitudinal direction.
monitoring respective target and recording target image at
each time.
As illustrated in Figure 8, a CCD camera is put 2 m
away from the lower surface of the cap beam. The horizontal
distance between each CCD camera and the corresponding
target is about 15 m. In addition, the distance between the
middle pier and the nearest box girder is 1.35 m under each
deck. Thereby, the distance between each CCD camera and
the corresponding target is about 15.19 m. For making CCD
camera capture clear images, a spotlight is installed below
each CCD camera and is used to provide illumination for the
corresponding CCD camera at night.
Four targets are separately installed on the midspan
position of 3rd, 4th, 9th, and 10th box girders, and the vertical
surface of each target is perpendicular to the corresponding
box girder (see Figure 8). Each target is made of stainless
steel with 10 mm depth and is bent up to 90∘ . As shown in
Figure 9, both the length and width of target’s vertical surface
are 150 mm, and the size of target’s horizontal surface is same
as that of vertical surface. The horizontal surface of target is
fixed on the midspan position of corresponding box girder
with expansion bolts. The background color of target is black,
and there exists a white solid circle on the center of vertical
surface, which is 100 mm in diameter. This white circle is
exactly the target tracked by CCD camera at different time.
5.2. Deflection Monitoring System Based on CCD Cameras.
Based on the deflection monitoring scheme for Songjiazhuang cloverleaf junction, the corresponding deflection
monitoring system for Songjiazhuang cloverleaf junction is
integrated in this paper. As shown in Figure 10, the deflection
monitoring system for Songjiazhuang cloverleaf junction
includes a computer, CCD cameras, lenses, spotlights, and
targets. The computer is the core of deflection monitoring
system, which is placed in the duty room and controls
the operation of deflection monitoring system. Considering
the long-term requirement of deflection monitoring for
Songjiazhuang cloverleaf junction, the computer chooses
8 GB memory, 1862 GB hard disk capacities. The computer’s
motherboard contains 5 cable interfaces, and four interfaces
are connected to four CCD cameras through network cable.
The type of CCD camera used for monitoring deflection
is AVT Company’s GT1290, which utilizes network cable to
transmit image. The CCD camera has the image resolution
Advances in Materials Science and Engineering
9
Deflection curve
Image collection
Measured points image of bridge
Deflection curves of measured points
Point 1
Deflection (mm)
4
Point 2
Point 1
Point 2
Point 3
Point 4
2
0
−2
−4
16:20
16:30
Parameter input
Sampling
10
s
periods
17:00
17:10
17:20
Deflection monitoring
Preview
Collecting
File
save
1
d
Stop
preview
Stop
Target
size
100
mm
Calibration
Exit
Parameter input
16:50
Time
Layout of measured points
Point 4
Point 3
16:40
1
2
3
4
Sampling
time
Point 1
Point 2
Point 3
Point 4
17:15
0.60624
−0.16265
1.1319
1.7993
Operation button
Deflection value
Figure 11: Deflection monitoring software interface for Songjiazhuang cloverleaf junction.
of 1280 × 960 and the sample frequency of 1 Hz. The
CCD camera is set to shoot black and white images when
monitoring deflection, and its range of operating temperature
is −20∘ C–60∘ C. The lens with 50 mm focal length is employed
to capture clear target images when the object distance is
farther, which is made in Computar Company. Moreover, it is
noted that the white circle on target should always appear in
the field of view (FOV) of camera within the allowable range
of bridge deflection.
Based on the deflection monitoring scheme for Songjiazhuang cloverleaf junction, the deflection monitoring software for Songjiazhuang cloverleaf junction is compiled by
MATLAB. This deflection monitoring software is a standalone executable program. Running the deflection monitoring software for Songjiazhuang cloverleaf junction only
needs installing MCRInstaller, which is the dynamic linking
library (DLL) of MATLAB; no MATLAB complier needs to
be installed. The deflection monitoring software for Songjiazhuang cloverleaf junction has functions such as image
preview, image collection, camera calibration, deflection
display, and data storage.
As illustrated in Figure 11, the software interface includes
five functional zones, namely, image collection, parameter
input, operation button, deflection curve, and value display.
For the convenience of adjusting the FOV size of CCD
Parameters
input
Camera
calibration
Image
preview
Stop
preview
Exit
Data
storage
Deflection
display
Image
collection
Figure 12: Operation flowchart of deflection monitoring software
for Songjiazhuang cloverleaf junction.
cameras, the area of image collection in software interface
can display the FOV of four CCD cameras in real time.
The areas of parameter input and operation button are the
core part of deflection monitoring software, which are used
for controlling image acquisition and processing. The area
of deflection curve and value display can show deflection
curves and calculate deflection values in real time. The
operation flowchart of deflection monitoring software for
Songjiazhuang cloverleaf junction is given in Figure 12.
5.3. In Situ Deflection Monitoring Results. The in situ deflection data of Songjiazhuang cloverleaf junction are shown in
Figure 13. Three deflection curves measured on Sep. 10–17,
2014; Oct. 9–17, 2014; and Oct. 20–28, 2014, are given in this
paper, and the time period of each curve is one week.
Point 1
Point 2
17 20:55
17 15:55
16 14:55
15 13:55
14 12:55
13 11:55
12 10:55
10 08:55
−6
11 09:55
−4
16 19:55
−2
15 18:55
0
14 17:55
2
13 16:55
4
12 15:55
Deflection (mm)
Deflection (mm)
6
7
6
5
4
3
2
1
0
−1
−2
11 14:55
8
1013:55
Advances in Materials Science and Engineering
9 12:55
10
Time
Time
Point 3
Point 4
Point 1
Point 2
Point 3
Point 4
(a) Sep. 10–17, 2014
(b) Oct. 9–17, 2014
8
Deflection (mm)
6
4
2
28 14:05
27 13:05
26 12:05
25 11:05
24 10:05
23 09:05
22 08:05
20 06:05
−2
21 07:05
0
Time
Point 1
Point 2
Point 3
Point 4
(c) Oct. 20–28, 2014
Figure 13: In situ deflection curves of Songjiazhuang cloverleaf junction.
As can be seen from Figure 13, the deflection curves of 4
measured points in each subgraph have jitters. The reason of
jitters is vehicles passing across the bridge deck. However, the
deflection curves’ trends of four measured points are basically
consistent. The trend consistency of four deflection curves
indicates that four CCD cameras can work stably on site and
the proposed method can accurately measure the deflection
deformations of bridge, and the bridge works in the good
condition. Experimental results verify the reliability of the
proposed method, indicating that the proposed deflection
monitoring method in this paper can meet the long-term
requirements of bridge deflection.
6. Conclusions
Aiming at meeting the requirement of deflection monitoring
for Songjiazhuang cloverleaf junction, Zhang’s calibrationbased DIC deflection monitoring method is proposed in
this paper. According to the proposed method, the deflection monitoring software is developed by MATLAB, and
4-channel CCD deflection monitoring system for Songjiazhuang cloverleaf junction is integrated accordingly. The in
situ deflection data show that deflection curves of four measured points have the consistent trends, and this suggests that
Songjiazhuang cloverleaf junction works in good condition,
and the proposed deflection monitoring method in this paper
is reliable and accurate. Compared with other deflection
measurement methods, the proposed method is simple to
operate and costs less and is convenient to conduct automatic
measurement and long-term monitoring. This proves that
this method will have the broad application foreground in
engineering.
Competing Interests
The authors declare that they have no competing interests.
Acknowledgments
This study is supported by the National Natural Science Foundation of China under Grants nos. 51478148 and 51408261, the
Advances in Materials Science and Engineering
Natural Science Foundation of Heilongjiang under Grant no.
E201434, and the foundation of Harbin City under Grant no.
2015RAQXJ028.
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