Sage Journals: Discover world-class research

Abstract

To monitor three-dimensional structural displacements in civil engineering, a stereovision displacement measurement method based on structure coordinate system is proposed in the present paper, and the absolute displacements of structure can be obtained through establishing the structure coordinate system and coordinate transformation. The center identification algorithm for circular target is studied to acquire the subpixel coordinates of center by combining Canny algorithm and Zernike algorithm. The epipolar constraint is introduced to conduct stereo matching of initial image pairs, and Kalman filtering and neighborhood searching algorithm are both employed to track circular targets on the left and right sequence images. To validate the effectiveness of the proposed method, a destructive test of concrete beams strengthened with ultraviolet-cured glass fiber reinforced polymer is performed in lab. Results show that the load–displacement curves obtained by the proposed stereovision method and linear variable differential transformer agree with each other; this verifies that the proposed stereovision method is feasible and effective for monitoring structural displacement in a destructive test.

Keywords

Structural health monitoring stereovision displacement measurement computer vision

Introduction

Under various factors such as wind, wave, flow, earthquake, and corrosion,¹ some damages such as fracture, crack, instability, and stripping^1–3 may occur in components of in-service structure. This affects the overall bearing capacity of structure and causes the potential safety hazard. To ensure the safety of structure, the damaged components must be reinforced. In recent years, the prefabricated fiber reinforced sheet or laminate pasted on surface of concrete beam has become increasingly popular in civil engineering. Engineering studies have found that fiber reinforced plastic (FRP) is effective in the flexural and shear strengthening. However, the bonded layer between FRP and concrete may be destroyed in a harsh environment; this means the reinforcement failure and results in the adverse consequence, even the significant economic loss and casualty. Therefore, it is very necessary to research the performance of concrete beam strengthened with FRP.⁴

The destructive test is often used to analyze the elastic properties, plastic properties, ductile properties, and ultimate bearing capacity of structure. Displacement and the strain are the performance indicators of structural component under static load. The traditional methods used to measure displacement and strain mainly include the displacement meter, dial gauge, and resistance strain gauge. In recent years, the fiber grating method has also become a common method for strain measurement.⁵ Above methods mostly require more time to install sensors and surface treatment, and the prepared work is rarely complicated.

Different from the above methods, the visual testing is a noncontact optical measurement method.⁶ In the last two decades, the visual testing method has been gradually applied in civil engineering. Ye et al.⁷ proposed three kinds of image processing algorithms for structural displacement measurement, i.e., the grayscale pattern matching algorithm, the color pattern matching algorithm, and the mean shift tracking algorithm. A vision-based system programmed with the three image processing algorithms was developed for structural displacement measurement. Based on the inverse compositional matching strategy and the auxiliary displacement functions, Bai et al.⁸ proposed an inverse compositional Gauss–Newton algorithm with a new second-order shape operator for the nonuniform and large deformation measurements; a rubber tension experiment with a large deformation of 27% was performed by a camera to validate the feasibility of the proposed algorithm. Kong and Li⁹ proposed a vision-based noncontact bolt loosening detection method based on a consumer-grade digital camera. The performance and robustness of this approach had been validated through a series of experiments using three laboratory setups. Park proposed a 3D displacement measurement model using a motion capture system (MCS) which included three cameras,¹⁰ a wand was adopted to calibrate MCS and performed the coordinate transformation from the wand coordinate system to the structure coordinate system. The proposed method can measure 3D displacements of markers on two adjacent sides of structure. Yoon et al.¹¹ proposed a target-free method to measure the vibration response of a six-story building model using the different consumer-grade cameras, and the temporal aliasing problem was discussed. Based on target-free method, Yoon et al.¹² employed an unmanned aerial system with a camera to conduct structural displacement measurement, resolving the influence of nonstationary motion of camera.

Except for above visual measurement methods which employ one camera or three cameras, the stereovision method using two cameras is another 3D displacements measurement method. In recent years, more and more people pay attention to the stereovision measurement method based on DIC. The related 3D DIC system developed quickly and the price is very expensive.^13–15 However, the 3D DIC method usually needs to spray speckles or plot grids on the structural surface, and the prepared work is complicated. In terms of image matching algorithm, essentially the DIC method is a kind of area matching algorithm,¹⁶ it is difficult to ensure the uniqueness of any grid or speckle. Therefore, there exists the image mismatch of grids or speckles when the DIC method is used to conduct 3D matching in stereovision measurement.^17,18

To deal with the problem of image mismatch, the epipolar constraint is introduced to conduct stereo matching of the initial image pairs in the present paper. The epipolar constraint is a very important constraint relationship in stereo matching, which can give the corresponding relation between point and line and guide the matching of corresponding points. In addition, Kalman filtering and neighborhood searching algorithm are both adopted to complete sequence matching of circular targets. The center identification algorithm of circular target is proposed to achieve the subpixel coordinates of center through Canny–Zernike combination algorithm. Based on above image processing algorithms, a stereovision displacement measurement method based on structure coordinate system is proposed in the present paper, and the absolute displacement of structure can be gained through coordinate transformation. To testify the effectiveness of the proposed method, a destructive test of concrete beams strengthened with ultraviolet (UV)-cured glass fiber reinforced polymer (GFRP) is performed in lab.

Stereovision displacement measurement method based on the structure coordinate system

Stereovision principle

Considering the general case, that is no requirement of two cameras’ position.¹⁹ As shown in Figure 1, assume that the left camera coordinate system $o_{l} - x_{l} y_{l} z_{l}$ coincides with the world coordinate system $o_{w} - x_{w} y_{w} z_{w}$ , $O_{l} - X_{l} Y_{l}$ is the corresponding left image coordinate system, $o_{r} - x_{r} y_{r} z_{r}$ is the right camera coordinate system, and $O_{r} - X_{r} Y_{r}$ is the right image coordinate system accordingly. The origins of $O_{l} - X_{l} Y_{l}$ and $O_{r} - X_{r} Y_{r}$ superpose the principal points of cameras. $P_{l} (x, y, z)$ and $P_{r} (x_{r}, y_{r}, z_{r})$ are the 3D coordinates of a spatial point $P (x_{w}, y_{w}, z_{w})$ in $o_{l} - x_{l} y_{l} z_{l}$ and $o_{r} - x_{r} y_{r} z_{r}$ with the projected imaged points $p_{l} (X_{l}, Y_{l})$ and $p_{r} (X_{r}, Y_{r})$ , respectively. According to the pinhole camera model, the projective transformation is expressed as follows

{\begin{array}{l} s_{l} p_{l} = M_{l} X_{w} \\ s_{r} p_{r} = M_{r} X_{w} \end{array}

(1)

where

s_{l}

and

s_{r}

are scale factors and

p_{l}

and

p_{r}

are homogenous image coordinates in the left and right camera coordinate systems.

M_{l}

and

M_{r}

are projection matrix of left and right cameras, respectively, and

X_{w}

is 3D coordinates of a spatial point

P (x_{w}, y_{w}, z_{w})

in the world coordinate system.

Figure 1.

Binocular stereovision model.

The relationship between $o_{l} - x_{l} y_{l} z_{l}$ coordinate system and $o_{r} - x_{r} y_{r} z_{r}$ coordinate system is expressed by the following transformation matrix

[\begin{array}{l} x_{r} \\ y_{r} \\ z_{r} \end{array}] = M_{l r} [\begin{array}{l} x_{l} \\ y_{l} \\ z_{l} \\ 1 \end{array}] = [\begin{array}{l} r_{1} r_{2} r_{3} t_{x} \\ r_{4} r_{5} r_{6} t_{y} \\ r_{7} r_{8} r_{9} t_{z} \end{array}] [\begin{array}{l} x_{l} \\ y_{l} \\ z_{l} \\ 1 \end{array}]

(2)

where

R_{l r} = [\begin{array}{l} r_{1} r_{2} r_{3} \\ r_{4} r_{5} r_{6} \\ r_{7} r_{8} r_{9} \end{array}]

and

T_{l r} = [\begin{matrix} t_{x} \\ t_{y} \\ t_{z} \end{matrix}]

are the rotation matrix and translation vector from

o_{l} - x_{l} y_{l} z_{l}

coordinate system to

o_{r} - x_{r} y_{r} z_{r}

coordinate system, respectively.

The 3D coordinates of a spatial point $P$ in the left camera coordinate system $o_{l} - x_{l} y_{l} z_{l}$ can be obtained by equations (1) and (2) ²⁰

{\begin{array}{l} x_{l} = z_{l} X_{l} / f_{l} \\ y_{l} = z_{l} Y_{l} / f_{l} \\ z_{l} = \frac{f_{l} (f_{r} t_{x} - X_{r} t_{z})}{X_{r} (r_{7} X_{l} + r_{8} Y_{l} + f_{l} r_{9}) - f_{r} (r_{1} X_{l} + r_{2} Y_{l} + f_{l} r_{3})} \end{array}

(3)

where

f_{l}

and

f_{r}

are the scale factors of left and right cameras, respectively.

From equation (3), if the scale factors $f_{l}$ , $f_{r}$ and the image coordinates $(X_{l}, Y_{l}), (X_{r}, Y_{r})$ of point $P$ in left and right image coordinate systems are all known, the 3D coordinates of the spatial point $P$ in left camera coordinate system can be calculated provided that rotation matrix $R_{l r} = [\begin{array}{l} r_{1} r_{2} r_{3} \\ r_{4} r_{5} r_{6} \\ r_{7} r_{8} r_{9} \end{array}]$ and translation matrix $T_{l r} = [\begin{matrix} t_{x} \\ t_{y} \\ t_{z} \end{matrix}]$ can be solved. Among them, the extrinsic parameters $[\begin{matrix} R_{l r} & T_{l r} \end{matrix}]$ and intrinsic parameters of stereovision system can be acquired by Zhang’s calibration algorithm based on 2D planar pattern.²¹

Establishment of structure coordinate system

To visually express structural displacement, $x o y$ plane of the structure coordinate system $o - x y z$ is usually established on structural surface, where the measured points are located on structural surface at initial state. Therefore, the structure coordinate system does not coincide with the left camera coordinate system. It is necessary to conduct coordinate transformation for obtaining actual coordinates of the measured point on structural surface. The transformation matrix $[\begin{matrix} R & T \end{matrix}]$ must be first obtained. Thereto $R$ and $T$ are the rotation matrix and translation matrix from the left camera coordinate system to the structure coordinate system, respectively. In the present paper, a checkerboard pattern is used to solve the transformation matrix $[\begin{matrix} R & T \end{matrix}]$ . The solving process of $[\begin{matrix} R & T \end{matrix}]$ using a checkerboard pattern is described as follows.

(i) Calibration of stereovision measurement system

The stereovision measurement system is first calibrated by Zhang’s algorithm, and the intrinsic and extrinsic parameters of stereovision system are obtained. The extrinsic parameters include the rotation matrix $R_{l r}$ and the translation matrix $T_{l r}$ from the left camera coordinate system to the right camera coordinate system. The intrinsic parameters include the effective focal length, scale factor, distortion coefficient, etc.

(ii) Establishing the structure coordinate system

As shown in Figure 2(a), a checkerboard pattern is closely put on the measured structure and is parallel to structural surface. This checkerboard pattern is used to establish a structural reference plane in the present paper, which is $x o y$ plane of the structure coordinate system $o - x y z$ .

Figure 2.

Establishing the structure coordinate system on structural surface. (a) Establishment of structure coordinate system and (b) identification of corner points.

As shown in Figure 2(a), two sides of checkerboard pattern are placed horizontally and vertically, respectively. The origin of the established structure coordinate system $o - x y z$ is located at the first corner point on upper corner of checkerboard pattern. The positive direction of x-axis is vertical downward, the positive direction of y-axis is horizontal to right, and the positive direction of z-axis is perpendicular to the checkerboard pattern and points to camera.

(iii) Extracting the image coordinates of each corner point on checkerboard pattern

As shown in Figure 2(b), a checkerboard pattern includes $9 \times 9$ girds whose size is $60 mm \times 60 mm$ . The image coordinate $(X, Y)$ of each corner on checkerboard pattern in left image coordinate system is extracted by Harris corner detector.²² The first corner point on upper right corner is numbered as 1 and goes from top to bottom in the order of 1–8. Then, the first corner point on the second column from right to left is numbered as 9. In the same way, the bottom left corner point is numbered as 64. All the image coordinates of the identified corner points are listed in Table 1.

(iv) Defining 3D coordinates of each corner points on checkerboard pattern

Table 1.

Pixel coordinates of corner points in the left image coordinate system.

Corner point1–8	Corner point9–16	Corner point 17–24	Corner point25–32	Corner point 33–40	Corner point41–48	Corner point 49–56	Corner point 57–64
(673,524)	(700,524)	(727,523)	(754,523)	(782,522)	(809,522)	(837,521)	(864,521)
(674,550)	(701,550)	(728,550)	(755,549)	(782,548)	(810,548)	(837,548)	(864,548)
(675,576)	(702,576)	(729,575)	(756,575)	(783,574)	(810,574)	(837,574)	(864,574)
(676,601)	(702,601)	(729,601)	(756,601)	(783,600)	(810,600)	(837,600)	(865,600)
(677,627)	(703,627)	(730,626)	(757,626)	(784,626)	(811,626)	(838,626)	(865,626)
(678,652)	(704,652)	(730,652)	(757,652)	(784,652)	(811,651)	(838,651)	(865,651)
(678,677)	(705,677)	(731,677)	(758,677)	(784,677)	(811,676)	(838,676)	(865,676)
(679,702)	(706,702)	(732,702)	(758,702)	(785,702)	(811,702)	(838,702)	(865,702)

The physical dimensions of checkerboard pattern are known; this means that actual 3D coordinates $(x, y, z)$ of each corner point in the structure coordinate system are also known. The grid size of checkerboard pattern is $60 mm \times 60 mm$ . Because z-axis of the established structure coordinate system is perpendicular to checkerboard pattern, the z-coordinate of each corner point is set to be 0. The x-coordinate and y-coordinate of each corner point on checkerboard pattern are defined according to the actual physical size and are listed in Table 2.

(v) Solving the transformation matrix $[\begin{matrix} R & T \end{matrix}]$

Table 2.

X-coordinates and y-coordinates of corner points in the structure coordinate system (mm).

Corner point1–8	Corner point9–16	Corner point17–24	Corner point25–32	Corner point33–40	Corner point41–48	Corner point49–56	Corner point 57–64
(420,420)	(360,420)	(300,420)	(240,420)	(180,420)	(120,420)	(60,420)	(0,420)
(420,360)	(360,360)	(300,360)	(240,360)	(180,360)	(120,360)	(60,360)	(0,360)
(420,300)	(360,300)	(300,300)	(240,300)	(180,300)	(120,300)	(60,300)	(0,300)
(420,240)	(360,240)	(300,240)	(240,240)	(180,240)	(120,240)	(60,240)	(0,240)
(420,180)	(360,180)	(300,180)	(240,180)	(180,180)	(120,180)	(60,180)	(0,180)
(420,120)	(360,120)	(300,120)	(240,120)	(180,120)	(120,120)	(60,120)	(0,120)
(420,60)	(360,60)	(300,60)	(240,60)	(180,60)	(120,60)	(60,60)	(0,60)
(420,0)	(360,0)	(300,0)	(240,0)	(180,0)	(120,0)	(60,0)	(0,0)

When the 3D coordinate $(x, y, z)$ of each corner point in the structure coordinate system and the image coordinate $(X, Y)$ of each corner point in the left image coordinate system are all known, the extrinsic parameters from the left camera coordinate system $o_{l} - x_{l} y_{l} z_{l}$ to the structure coordinate system $o - x y z$ can be obtained through the direct linear transformation method.²³ The transform matrix between these two coordinate systems can be expressed by²⁴

s {[\begin{matrix} f_{x} & 0 & u_{o} \\ 0 & f_{y} & v_{o} \\ 0 & 0 & 1 \end{matrix}]}^{- 1} [\begin{matrix} X \\ Y \\ 1 \end{matrix}] [\begin{matrix} r_{11} & r_{12} & r_{13} & t_{x} \\ r_{21} & r_{22} & r_{23} & t_{y} \\ r_{31} & r_{32} & r_{33} & t_{z} \end{matrix}] [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}] = [\begin{matrix} R & T \end{matrix}] [\begin{matrix} x \\ y \\ z \\ 1 \end{matrix}]

(4)

where

[\begin{matrix} f_{x} & 0 & u_{0} \\ 0 & f_{y} & v_{0} \\ 0 & 0 & 1 \end{matrix}]

is the known intrinsic parameters of left camera, which is acquired by Zhang’s calibration algorithm.

s

is a nonzero scale factor.

{[\begin{matrix} X & Y & 1 \end{matrix}]}^{T}

is the homogenous image coordinate in pixel unit,

{[\begin{matrix} x & y & z & 1 \end{matrix}]}^{T}

is the actual 3D coordinates of each corner point on checkerboard pattern. Thus, the transformation matrix

[\begin{matrix} R & T \end{matrix}]

from left camera coordinate system to the structure coordinate system can be obtained by equation (4).

Figure 3 shows the flowchart of establishment of structure coordinate system using a checkerboard pattern. It is noted that only the left image sequences are used to establish the structure coordinate system on structural surface. Only the intrinsic parameters of left camera obtained by Zhang’s calibration algorithm are used to solve the transformation matrix $[\begin{matrix} R & T \end{matrix}]$ , and the extrinsic parameter $[\begin{matrix} R_{l r} & T_{l r} \end{matrix}]$ of stereovision system obtained by Zhang’s calibration algorithm is not employed during the solving process.

Figure 3.

Flowchart of establishment of structure coordinate system using checkerboard pattern.

Calculation of 3D displacements

The 3D coordinates of the measured point in the left camera coordinate system $o_{l} - x_{l} y_{l} z_{l}$ can be obtained according to equation (3). Through the transformation matrix [R T] obtained by equation (4), the 3D coordinates of the measured point in the structure coordinate system $o - x y z$ can be given in equation (5), which is established on structural surface

[\begin{matrix} x \\ y \\ z \end{matrix}] = R^{- 1} ([\begin{matrix} x_{l} \\ y_{l} \\ z_{l} \end{matrix}] - T)

(5)

Therefore, the out-of-plane displacement and in-plane displacement of structure at each moment can be acquired by equation (5). Assume that the 3D coordinate of the measured point $P_{0}$ at initial time $t_{0}$ is $(x_{0}, y_{0}, z_{0})$ . Due to structural deformation, the 3D coordinate of the measured point $P_{i}$ at time $t_{i}$ is $(x_{i}, y_{i}, z_{i})$ , and the in-plane displacement and out-of-plane displacement of the measured point $P_{i}$ at time $t_{i}$ are expressed by

{\begin{array}{l} d_{i n - p l a n e} = \sqrt{{(x_{i} - x_{0})}^{2} + {(y_{i} - y_{0})}^{2}} \times s i g n (\frac{x_{i} - x_{0}}{\sqrt{{(x_{i} - x_{0})}^{2} + {(y_{i} - y_{0})}^{2}}}) \\ d_{o u t - o f - p l a n e} = z_{i} - z_{0} \end{array}

(6)

From the above analysis, the key problem of 3D structural displacements measurement is how to identify the same measured point in different fields of view. One of solutions is selecting appropriate image feature to match the measured point in different fields of view. Therefore, identification and matching of image feature is the key in stereovision measurement.

Image processing of circular target

Center identification of circular target

In the present paper, circular target is selected as feature point for image matching. To identify circular target, the center coordinate of circular target needs to be extracted first. To position the center of circular target, a Canny–Zernike combination algorithm is proposed to conduct edge detection of circular target. The flowchart of center identification of circular target is shown in Figure 4, and the detailed process is described as follows.

(i) Image preprocessing

Figure 4.

Flowchart of center identification algorithm for circular target.

Due to the influence of some factors such as light, noise, and lens distortion, the image filtering must be conducted first. SUSAN filtering is used to filter image noise in the present paper,^25,26 which can preserve the original characteristics of image, sharpen border and corner of image, and improve image quality.

(ii) Extraction of circular target

As shown in Figure 5(b), a rectangular zone which surrounds a circular target is selected to extract the measured circular target and obtain the binarized image; the binarized image of circular target is shown in Figure 5(c).

(iii) Obtaining the geometric parameters of circular target

Figure 5.

Process of center identification of circular target: (a) original image, (b) extraction of circular target, (c) image binarization, (d) edge detection, (e) subpixel edge detection, and (f) center positioning.

To locate the center of circular target, the geometric parameters of circular target in the binary image need to be acquired, which are the form factor, eccentricity, spherical, circularity and edge length, etc. By calculating the geometric parameters of each zone, the shape threshold is set to remove the noncircular target area.

(iv) Edge detection of circular target using Canny–Zernike combination algorithm

As shown in Figure 5(d), Canny algorithm²⁷ is used to roughly extract the edge of circular target. The extracted edge is linked together, meanwhile some noncircular target edges are eliminated. Then Zernike moment operator²⁸ is used to obtain the subpixel edge of circular target, as illustrated in Figure 5(e). The detailed Canny–Zernike algorithm is described in Shan et al.²⁹

(v) Positioning the center coordinate of circular target

The ellipse fitting method is adopted to position the center of circular target. The least-squares algorithm is utilized to fit the ellipse equation. The threshold of the distance between each edge point and the fitted ellipse center is set adequately, and the position precision of the fitted ellipse is improved through iteration. To improve the fitting precision, every time 5% edge points are removed until the standard deviation of the distance is less than the presupposed threshold. As shown in Figure 5(f), the accuracy of 0.02 subpixel can be achieved finally.

Matching pursuit of circular target

According to equations (3) and (5), the 3D coordinates of center of circular target can be calculated based on stereovision principle. Therefore, the same circular target on the synchronized left and right image pairs needs to match each other. In addition, the same circular target on the left or right sequence images also needs to be tracked. To address this issue, the circular target matching pursuit algorithm is proposed in the present paper and the detailed flowchart of matching pursuit of circular target is given in Figure 6.

Figure 6.

Flowchart of matching pursuit of circular target.

Due to noise disturbance, ray and perspective distortion, etc., there may exist several corresponding candidate points on right image toward an object point on left image. Therefore, some constraint conditions are adopted in image matching. Some constraint conditions, e.g. epipolar constraint, unique constraint, and ordering coherence constraint, are commonly employed in image matching. According to geometric feature of circular target, the epipolar constraint³⁰ is selected to perform stereo matching of the initial image pairs.

As shown in Figure 7, the projected points of a spatial point $P$ in the left and right images are $p_{l}$ and $p_{r}$ , respectively. To avoid confusion, the homogenous image coordinates of projection points are represented by $p_{l}$ and $p_{r}$ . Equation (7) is given by

p_{r}^{T} F p_{l} = 0

(7)

where

F

is a

3 \times 3

matrix, which is called as the base matrix,

r a n k (F) = 2

. The base matrix is expressed by

F = A_{r}^{- T} S R A_{l}^{- 1}

(8)

where

A_{l}

and

A_{r}

are the intrinsic parameter matrix of the left and right cameras, respectively.

R_{l r}

is the rotation matrix from the left camera coordinate system to the right camera coordinate system,

S

is an antisymmetric matrix which is determined by

T_{l r}

. Thereto

T_{l r}

is the translation matrix from the left camera coordinate system to the right camera coordinate system.

A_{l}, A_{r}, R_{l r}, T_{l r}

can be obtained through camera calibration.

Figure 7.

Sketch map of epipolar geometry.

In stereovision field, this mutual corresponding constraint relation expressed by equation (7) is called as the epipolar constraint.³⁰ The epipolar constraint not only provides the correspondence between point and line, but also guides matching of the corresponding points. Based on this characteristic, as shown in Figure 6, the epipolar constraint is employed to conduct stereo matching of the initial image pairs.

Toward the tracking problem of circular targets on sequence images, the neighborhood searching algorithm is generally used to pursuit feature point. This algorithm is simple and highly efficient. However, the precondition of neighborhood searching algorithm is that the distance between feature points attached on structural surface is larger than the maximum displacement of measured point motion. This precondition limits the number of circular targets and also leads to inconvenience of matching sequence images when the motion of measured structure is unknown.

To deal with this problem, Kalman filtering algorithm³¹ is adopted to track circular targets on left and right sequence images in the present paper. As shown in Figure 6, the position of circular target at the next moment is preliminarily located by Kalman filtering algorithm, and then neighborhood searching algorithm is performed. The combination of two algorithms can decrease searching radium and save computation time.

Destructive test of concrete beams strengthened with UV-cured GFRP

Experimental setup

In the destructive test, the section size of concrete beam was $70 mm \times 90 mm$ , and the length of concrete beam was 900 mm. A basalt fiber reinforced polymer tendon with 8 mm diameter was put in the center of concrete beam. The concrete strength was C30, and the thickness of concrete cover was 31 mm. As shown in Figure 8(a), the UV-cured GFRP sheet was pasted on the middle part of bottom side of concrete beam. The size of UV-cured GFRP sheet was $200 mm×20 mm×1 .3 mm$ . Then, one concrete beam strengthened with UV-cured GFRP sheet was placed in indoor environment for six months, and the other two concrete beams strengthened with UV-cured GFRP sheet were immersed in alkaline solution for six months.

Figure 8.

Experimental setup: (a) loading schematic, (b) local photo, and (c) experimental photo. LVDT: linear variable differential transformer; UV-GFRP: ultraviolet-cured glass fiber reinforced polymer.

As shown in Figure 8(c), the destructive test of three concrete beams was sequentially conducted on the universal testing machine whose type was WDW-100D. The universal testing machine can be controlled by two ways which were force loading and displacement. In the present paper, the universal testing machine was controlled by force loading; the step loading of 1 KN was gradually applied to each concrete beam until each concrete beam was destroyed. As shown in Figure 8(b), the loading end of the universal testing machine was imposed on the middle part of concrete beam. A linear variable differential transformer (LVDT) was put on the mid-span of concrete beam and was used to measure the mid-span deflections of concrete beam, which can be compared with the corresponding results of the proposed stereovision method. The measurement range and precision of LVDT were 50.0 and 0.2 mm, respectively.

As shown in Figure 8, a circular target with 15 mm diameter was pasted on one side of concrete beam, which was right under the position where the universal testing machine applied the load. Under each loading, the deformation images of concrete beam at each moment were captured by the stereovision measurement system with the sampling frequency of 1 Hz. Because the destructive test of concrete beam is a static test, and is not a dynamic test. There exist no temporal aliasing during samping, and the sampling frequency of 1 Hz can make sure to synchronously capture left and right images of ecah moment.

As shown in Figure 8(c), the stereovision measurement system was faced to concrete beam with some angle during test. The stereovision measurement system was composed of a computer, two CCD cameras, a tripod, a synchronizer trigger, and the stereovision measurement software. Two Pike F-100c cameras can synchronously capture left and right images with the resolution of 1000 × 1000 at the highest sampling frequency of 60 Hz. Two cameras were equipped with an optical zoom lens of the focal length ranging between 12 and 30 mm. As shown in Figure 9, the stereovision measurement software was comprised of image collection module and image processing module, and had the functions of image capturing, displaying, saving, analyzing, and results output. In the test, a checkerboard pattern was used to calibrate the stereovision measurement system and the intrinsic and extrinsic parameters of stereovision measurement system can be obtained accordingly. In addition, a 1300 W halogen tungsten lamp was selected as a supplemental light source.

Figure 9.

Software interface of stereovision measurement system.

To study the influence of field of view and the inclined angle between stereovision system and specimen on accuracy, for the first UV-GFRP strengthened concrete beam at room temperature, the stereovision system was placed 1.5 m away from concrete beam, the fields of view of two cameras were about $0.5 m×0 .5 m$ , and the inclined angle between first concrete beam and stereovision system was relatively large. For the other two concrete beams soaked in alkaline solution, the system was placed 0.75 m away from the beam, the fields of views were about $0.25 m×0 .25 m$ , and the inclined angles between other concrete beams and stereovision system were smaller than the inclined angle of first concrete beam. The detailed experimental setting of stereovision system for three concrete beams in the destructive test is listed in Table 3.

Table 3.

Experimental setting of stereovision system in destructive test.

Number of experimental setting	View of field (m²)	Object distance (m)	Inclined angle (°)	Number of concrete beam
1	0.50 × 0.50	1.50	large	1
2	0.25 × 0.25	0.75	small	2
2	0.25 × 0.25	0.75	small	3

Note: The inclined angle of the second concrete beam is equal to that of the third concrete beam.

Analysis of experimental results

For each concrete beam strengthened with UV-GFRP, before loading, the pictures of three concrete beams which were in static condition were continuously collected for analyzing the sensitivity of stereovision system and the measurement results are given in Figure 10.

Figure 10.

Sensitivity of stereovision measurement system: (a) first beam, (b) second beam, and (c) third beam.

As can be seen from Figure 10(a), when the fields of view of two cameras were approximately $0.5 m×0 .5 m$ , the object distance between the first concrete beam and stereovision system was 1.5 m, 95% of zero drifts of stereovision system are less than 0.15 mm, indicating that the sensitivity of stereovision system can meet the measurement requirements. The reason why the zero drift of stereovision system is larger is that the inclined angle between stereovision system and the first concrete beam was relatively large, which affected the precision of stereovision system.

For the last two UV-GFRP strengthened concrete beams immersed in alkaline solution, when the fields of view of two cameras were reduced to 0.25 m×0.25 m and the object distances between specimens and stereovision system were decreased to 0.75 m, it can be found from Figure 10(b) and (c) that more than 95% of zero drifts are less than 0.03 mm. In addition, the inclined angles between stereovision system and other two concrete beams soaked in alkaline solution became smaller. This shows that the reduced field of views and the small inclined angle can effectively improve the sensitivity of stereovision system.

The measurement results of three concrete beams strengthened with UV-cured GFRP are shown in Figure 11. It can be seen from Figure 11 that indoor environment has little effect on the maximum load of concrete beam strengthened with UV-cured GFRP. Compared with the first concrete beam, the maximum loads of the last two concrete beams strengthened with UV-cured GFRP show a downward trend, which were immersed in alkaline solution. Because alkaline solution has the corrosive effect on UV curing resin, the degradation of UV-GFRP sheet was exacerbated, resulting in the decrease of mechanical properties. Therefore, the bonding strength between UV curing resin and concrete beam is reduced through six months’ immersion in alkaline solution.

Figure 11.

Load–displacement curves of concrete beams strengthened with UV-cured GFRP: (a) first beam (indoor environment), (b) second beam (alkaline solution), and (c) third beam (alkaline solution). LVDT: linear variable differential transformer.

From Figure 11, the load–displacement curves obtained by the proposed stereovision method and LVDT have the same trend and agree well with each other. It can be seen from Figure 11 that the measurement results obtained by the stereovision method are slightly different from that of LVDT. The reason is the difference in the measurement positions of two methods and the local compression damage of concrete beam. As shown in Figure 8, the distance between the load position applied by the universal testing machine and the position of circular target measured by the stereovision method is about 20 mm. As shown in Figure 12, the local compression damage can be found on the loading positions of concrete beam.

Figure 12.

Typical failure modes of concrete beams: (a) indoor environment and (b) alkaline solution.

From Figure 11(a), the load–displacement curves obtained by the stereovision method and LVDT have the same trend. The first concrete beam strengthened with UV-cured GFRP has the characteristic of small plastic deformation and brittle failure. From Figure 11(b) and (c), it can be seen that the displacement curves obtained by two methods can accurately describe the static performance of concrete beams strengthened with UV-cured GFRP. The curves have the obvious elasticity and plastic stages, and the last two concrete beams strengthened with UV-GFRP bring forth the ductility damage.

As shown in Figure 12, the failure mode of concrete beam changed from the shear failure to the bending-shear failure, indicating that the UV-cured GFRP sheet has lost its reinforcing effect. This shows that bond failure between UV curing resin and concrete beam occurs in alkaline solution.

Conclusions

Based on the binocular stereovision model, a 3D displacements measurement method based on structure coordinate system is proposed in the present paper, and the absolute displacements of structure can be acquired by establishing the structure coordinate system and coordinate transformation. The center identification algorithm for circular targets can access the subpixel coordinates of centers, and the matching pursuit algorithm accomplishes 3D matching of circular targets. The mid-span deflections of concrete beams strengthened with UV-cured GFRP in a destructive test are monitored by the proposed stereovision method. Stereovision measurement results are compared with the corresponding results obtained by LVDT, and the following conclusions are drawn:

The load–displacement curves obtained by the proposed stereovision method and LVDT have the same trends, and the load–displacement curves of two methods agree well with each other, this verifies the effectiveness of the proposed stereovision measurement method.

Experimental results show that the inclined angle between specimen and cameras and the view of field have a significant influence on the sensitivity of stereovision measurement system. Results indicate that the sensitivity of stereovision measurement system is significantly improved by reducing the field of view and the inclined angle between cameras and concrete beam.

Results show that the proposed stereovision method can be used for monitoring the entire destructive test. One thing needs to be noted that the measurement precision of the proposed stereovision method decreases with the increase of object distance. Therefore, when the proposed method is used to measure actual structure in outdoor field, the object distance should be controlled within the appropriate range between several hundreds of centimeters and several meters.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This paper is supported by the National Natural Science Foundation of China under Grant No. 51478148, the Natural Science Foundation of Heilongjiang Province under Grant No. E201434, and the Technological Innovation Talent Foundation of Harbin City under Grant No. 2015RAQXJ028.

References

Duan

Xiao

YQ.

Safety evaluation for offshore platform structures – theory, method and application. Beijing: Science Press, 2003.

Yun

YF.

Durability of CFRP-concrete joints under freeze-thaw cycling. Cold Regions Sci Technol 2011; 65: 401–412.

Pan

Xian

Silva

MAG.

Effects of water immersion on the bond behavior between CFRP plates and concrete substrate. Constr Build Mater 2015; 101: 326–337.

Durability of concrete strengthened with FRP under environmental and loading conditions. PhD Thesis, Dalian University of Technology, China, 2009.

Xie

Kang

, et al. A brief review and prospect of experimental solid mechanics in China. Acta Mech Solida Sin 2010; 23: 498–548.

Zhang

ZY.

Computer vision. Beijing: Science Press, 1998.

Dong

Liu

Image-based structural dynamic displacement measurement using different multi-object tracking algorithms. Smart Struct Syst 2016; 17: 935–956.

Bai

Jiang

Lei

, et al. A novel 2nd-order shape function based digital image correlation method for large deformation measurements. Optics Lasers Eng 2017; 90: 48–58.

Kong

Image registration-based bolt loosening detection of steel joints. Sensors 2018; 18: 1000.

10.

Park

Kim

, et al. 3D displacement measurement model for health monitoring of structures using a motion capture system. Measurement 2015; 59: 352–362.

11.

Yoon

Elanwar

Choi

, et al. Target-free approach for vision-based structural system identification using consumer-grade cameras. Struct Control Health Monit 2016; 23: 1405–1416.

12.

Yoon

Shin

Specner

Jr.

Structural displacement measurement using an unmanned aerial system. Computer-Aided Civil Infrastruct Eng 2018; 33: 183–192.

13.

Linda

Mikael

Fredrik

Microscopic 3-D displacement field measurements using digital speckle photography. Optics Lasers Eng 2004; 41: 767–777.

14.

Kurtz

Balaguru

Helm

Experimental study of interfacial shear stresses in FRP-strengthened RC beams. J Compos Constr 2008; 12: 312–322.

15.

Lander

Stijn

Measuring of crack bridging of CFRP strengthened concrete by digital image correlation. In: Non-destructive testing in civil engineering, Nantes, France, 2009.

16.

Key techniques and systems of sheet metal formability analysis based on machine vision. PhD Thesis, Nanjing University of Aeronautics and Astronautics, China, 2010.

17.

Michael JM, Brain S, Michelle H, et al. 3-D digital image correlation-an underused asset for structura test, In: Structures Congress of ASCE, Chicago, U.S., Edited by John Carrato, P.E., S.E., and Joseph G. Burns, P.E., S.E (eds) March 29-31, 2012. pp. 1958–1969. American Society of Civil Engineers, Reston, VA.

18.

Kashfuddoja

Ramji

Whole-field strain analysis and damage assessment of adhesively bonded patch repair of CFRP laminates using 3D-DIC and FEA. Compos Part B Eng 2013; 53: 46–61.

19.

Longuet-Higgins

A computer algorithm for reconstructing a scene from two projections. Nature 1981; 239: 133–135.

20.

Sun

Zhang

Wei

Large 3D free surface measurement using a mobile coded light-based strereo vision system. Sens Actuators A Phys 2006; 132: 460–471.

21.

Zhang

ZY.

A flexible new technique for camera calibration. IEEE Trans Pattern Anal Mach Intell 2000; 22: 1330–1334.

22.

Zhang

GJ.

Vision measurement. Beijing: Science Press, 2008, pp.134–136.

23.

Abdel-Aziz

Karara

Hauck

Direct linear transformation from comparator coordinates into object space coordinates in close-range photogrammetry. Photogramm Eng Remote Sensing 2015; 81: 103–107.

24.

FC.

Mathematical method in computer vision. Beijing: Science Press, 2008.

25.

Zhang

Wang

Improved SUSAN filter with edge information reserved. Foreign Electron Meas Technol 2007; 26: 33–35.

26.

Smith

Brady

JM.

SUSAN – a new approach to low level image processing. J Comput Vis 1997; 23: 45–78.

27.

Canny

A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 1986; 8: 679–698.

28.

Cui

Chen

, et al. A fast subpixel edge detection method using Sobel-Zernike moments operator. Image Vis Comput 2005; 23: 11–17.

29.

Shan

Zheng

JP.

A stereovision-based crack width detection approach for concrete surface assessment. KSCE J Civ Eng 2016; 20: 803–812.

30.

Åström

Cipolla

Giblin

PJ.

Generalised epipolar constraints. Technical report, Dept. of Mathematics, Lund University, 1996. In: 4th European Conference on Computer Vision, Cambridge, UK, April 15-18, 1996, 2: 95–108, Springer, Switzerland.

31.

Faragher

Understanding the basis of the Kalman filter via a simple and intuitive derivation. IEEE Signal Process Mag 2012; 29: 128–132.

Stereovision monitoring of deflection of concrete beam strengthened with ultraviolet-cured glass-fiber reinforced polymer in a destructive test

Abstract

Keywords

Introduction

Stereovision displacement measurement method based on the structure coordinate system

Stereovision principle

Establishment of structure coordinate system

Calculation of 3D displacements

Image processing of circular target

Center identification of circular target

Matching pursuit of circular target

Destructive test of concrete beams strengthened with UV-cured GFRP

Experimental setup

Analysis of experimental results

Conclusions

Footnotes

Declaration of conflicting interests

Funding

References