Bridge Deflection Measurement Using Digital Image ... · Bridge Deflection Measurement Using Digital Image Correlation with Camera Movement Correction Satoru Yoneyama and Hiroki
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Bridge Deflection Measurement Using Digital Image Correlationwith Camera Movement Correction
Satoru Yoneyama and Hiroki Ueda
Department of Mechanical Engineering, Aoyama Gakuin University, Sagamihara 229-8558, Japan
When displacement measurement by digital image correlation is performed in outside for the inspection of real structures, the position andthe direction of a camera are often changed slightly because of wind, oscillations and the lack of stability of ground. In order to realize the bridgedeflection measurement by digital image correlation, a method for correcting the effect of camera movement is proposed in this study. Therelationship between images before and after the camera movement is described by an equation of perspective transformation. The unknowncoefficients of the equation are determined from undeformed regions of the images. Then, the effect of the camera movement is eliminated byusing the perspective transformation. The effectiveness is validated by applying the proposed method to the rigid body rotation and translationmeasurement of a planar specimen, the deflection measurement of a wide-flange beam, and the bridge deflection measurement. Results show thatthe effect of the camera movement can be corrected by the proposed method. It is emphasized that noncontact displacement measurement ispossible by simple and easy procedure with digital image correlation for the structural evaluation of infrastructures.[doi:10.2320/matertrans.I-M2011843]
(Received November 10, 2009; Accepted March 11, 2011; Published December 28, 2011)
Keywords: deflection, bridge, girder, digital image correlation, camera movement
1. Introduction
For the structural evaluation of bridges, various tests areusually performed to investigate the structural properties suchas natural frequencies, dynamic responses, and strains.13)
One of these properties is vertical deflection of bridge girders.Several different types of transducers and sensors can be usedto measure the deflection.46) However, most of these sensorsrequire the access to measurement location under bridges.Therefore, it would be required to interrupt traffic underbridges for the setup of these transducers. In addition, theinstallation of these transducers is time-consuming. There-fore, various techniques for the noncontact measurement ofbridge deflection have been studied.710) On the other hand,noncontact measurement of bridge deflection by a digitalimage correlation technique is possible as demonstrated byone author previously.11,12) Digital image correlation canobtain the surface deformation by comparing digital imagesof undeformed and deformed configurations.13) Since digitalimage correlation technique does not need a complicatedoptical system, the measurement can be performed simplyand easily. Thus, a lot of applications of this method tovarious problems can be found in the field of experimentalsolid mechanics.1416)
In digital image correlation, the camera position must notbe changed during the measurement because this techniqueextracts displacements from digital images directly. When themeasurement is performed in outside for the inspection ofreal structures, however, the position and the directionof a camera are often changed slightly because of wind,oscillations and the lack of stability of ground. In this case, thedisplacement cannot be measured because the effect of thecamera movement is included in the measured displacement.
In order to realize the bridge deflection measurement bydigital image correlation, a method for correcting the effect ofcamera movement is proposed in this study. The relationshipbetween images before and after the camera movement isdescribed by an equation of perspective transformation. The
unknown coefficients of the equation are determined fromundeformed regions of the images. Then, the effect of thecamera movement is eliminated by using the perspectivetransformation. The effectiveness is validated by applying theproposed method to the rigid body rotation and translationmeasurement of a planar specimen and the deflectionmeasurement of a wide-flange beam. In addition, theeffectiveness is also demonstrated by applying the proposedmethod to the deflection measurement of a real bridge girder.Results show that the effect of the camera movement can becorrected by the proposed method. It is emphasized thatnoncontact displacement measurement is possible by simpleand easy procedure with digital image correlation for thestructural evaluation of infrastructures.
2. Method for Correcting the Effect of CameraMovement
Figure 1 shows the outline of the proposed method. Anundeformed image (reference image) of an object such asbridge is recorded as shown in Fig. 1(a). The object isdeformed by a load as shown in Fig. 1(b). When the camerais moved before acquiring an image of the deformed object,the image includes information of not only the deformationbut also the camera movement, as shown in Fig. 1(d). In theproposed method, the camera movement shown in Fig. 1(c)is detected from the undeformed regions such as piers. Then,the deflection of the measured region such as a girder isobtained by eliminating the effect of the camera movement.
Figure 2 shows the geometric relationship between imageplanes of a camera before and after the camera movement. Inthis figure, a point P positioned at (x, y, z) on an object isprojected at P1 on an image plane. The point P1 is located at(u, v) on the image plane. The same point P on the object isimaged at the point P2 at (u¤, v¤) after the camera movement.In this case, the relationship between the coordinates (u, v) ofthe point P1, and (u¤, v¤) of the point P2 is expressed byperspective transformation as17)
where a1³a8 are the coefficients that express the cameramovement. Therefore, the coordinate (u¤, v¤) on the imageafter the camera movement can be corrected to the coordinate(u, v) before the camera movement provided that thecoefficients of the equation are known. The coefficients aredetermined from fixed reference points that can be consideredto be not deformed. Applying digital image correlationtechnique to the fixed region, the data sets of the coordinates(u, v) and (u¤, v¤) before and after the camera movement areobtained. Then, the coefficients in eq. (1) are determinedusing the method of linear least-squares. The coordinates ofthe deformed region such as a girder after the cameramovement are then corrected using eq. (1). After that, theactual displacements can be determined.
3. Rigid Body Rotation and Translation Measurement
Figure 4 shows the images obtained in this experiment.The random pattern created by spray painting for obtainingthe correlation between two images is observed on both themeasured and the fixed regions. The x-directional componentux of the displacement obtained by digital image correlationis plotted in Fig. 5. In this figure, the displacement withoutthe camera movement, that is, the actual displacement is alsoshown. The displacement distribution obtained when thecamera is moved is different from the actual displacement bythe effect of the camera movement. Figure 6 shows thedifference ux ¹ uxact between the displacements with andwithout camera movement. The difference, that is, the error
Reference imageBridge girder(measured region)
Pier (fixed region)
Deformation
Camera movement
Actual image(Deformation &camera movement)
+
=Detection ofcamera movementExtract deformation
DIC
(a)
(b)
(c)
(d)
Ideal image
Fig. 1 Outline of the proposed method of camera movement correction.
P(x,y,z )
P1(u,v ) P2(u’ ,v’ )
O1O2
Camera movement
Image plane
Object
x
y
z
o
O1, O2:Lens center
Fig. 2 Geometrical relationship between image planes before and after thecamera movement.
xz
y
Translation 1 mm
Rotation 2 deg
Specimen
Fixed object
Fixed object
CCD camera
u
v
w
u’
v’w’
8 mm
0.6 deg
Fig. 3 Experimental setup for rigid body rotation and translation test.
S. Yoneyama and H. Ueda286
introduced by the camera movement is about 0.6mm.Applying the proposed method, the displacement obtainedwith the camera movement is corrected. The differenceuxcorr ¹ uxact between the corrected displacement and theactual displacement is also shown in this figure. As shown inthis figure, the difference about 0.6mm is corrected to zero.
The camera is moved again and the measurement isrepeated as shown in Fig. 7. The average value of thedifference of the actual and the corrected displacements withrespect to the angle ª of the camera are shown in Fig. 8. Asshown in this figure, the difference is less than 0.1mm even ifthe angle of the camera is large as 30 degrees. The difference
of 0.1mm corresponds to the small value of about 0.6 pixels.The results of the rigid body rotation and translation testshow that the effect of the camera movement is corrected bythe proposed method.
4. Measurement of the Deflection of a Wide-FlangeBeam
Experimental tests have been performed to evaluate theapplicability of the proposed method to the deflection
(a) (b)
Fig. 4 Images obtained for rigid body rotation and translation test: (a) reference image; (b) image after rotation and translation.
Fig. 5 x-directional displacement distributions obtained with and withoutcamera movement.
Fig. 6 Differences between the displacements with and without cameramovement correction and the actual displacement.
θ
CCD camera
Measured region Fixed regionFixed region
7000 mm
Fig. 7 Setup for additional rigid body rotation and translation test.
Fig. 8 Difference between the corrected displacement and the actualdisplacement, and its standard deviation.
Bridge Deflection Measurement Using Digital Image Correlation with Camera Movement Correction 287
Fig. 9 Schematic diagram of the experimental setup for deflection measurement of wide-flange beam.
Fig. 10 Photograph of the experimental setup for deflection measurement of wide-flange beam.
S. Yoneyama and H. Ueda288
Applying digital image correlation to these images, thedeflection distributions are determined. Figure 11 shows thedeflection curve obtained by digital image correlation.Different values of the deflection at the both supports areobtained. The deflection curves in Fig. 11 are corrected bythe proposed method. Figure 12 shows the deflection curvesafter the camera movement correction. In this figure, thedeflections corrected by the proposed method agree well withthose obtained by the displacement transducers. The resultsof the beam deflection measurement also show that the effectof the camera movement is corrected by the proposedmethod.
The photographs of the bridge before and after load areshown in Fig. 13. The fixed reference regions are both sides
of the bridge as shown in this figure. The measured andcorrected deflection distributions of the bridge girder areshown in Fig. 14. The abscissa shows the position that ismeasured from the left edge of the bridge. Because there is abarrier, the deflection at the left side is not obtained. In thisfigure, the deflection without the camera movement is alsoshown for comparison. The reasonable deflection distributionis obtained by correcting the camera movement. In addition,the values of the corrected deflection agree well with thevalues obtained without the camera movement. The resultsof the field study show that the bridge deflection can bemeasured by digital image correlation even if the position ofthe camera is moved.
Fig. 11 Deflection distributions without the camera movement correction.
Fig. 12 Deflection distributions with the camera movement correction.
(a) (b)
Fig. 13 Images of bridge: (a) before load; (b) after load with camera movement.
Fig. 14 Bridge deflection distribution before and after the camera move-ment correction.
Bridge Deflection Measurement Using Digital Image Correlation with Camera Movement Correction 289
The results shown in this paper indicate that digital imagecorrelation can be used in place of displacement transducers.That is, easy and simple but effective measurement ofstructures can be realized using digital image correlation.
6. Conclusions
A method for correcting the effect of the camera move-ment is proposed for field application of two-dimensionaldigital image correlation. The validity of the proposedmethod is demonstrated by measuring the rigid bodydisplacements, the deflection of the beam, and the deflectionof the bridge. Results show that the effect of the cameramovement can be corrected by the proposed method. It isemphasized that noncontact displacement measurement ispossible by simple and easy procedure with digital imagecorrelation for the structural evaluation of infrastructures.
Acknowledgment
The part of this work was supported by Hitachi ZosenCorporation and Nichizo Tech Incorporated. Their assistanceand cooperation are greatly appreciated.
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