Remote Bridge Deflection Measurement Using an Advanced ... - MDPI

sensors Article

Remote Bridge Deflection Measurement Using an Advanced Video Deflectometer and Actively Illuminated LED Targets Long Tian and Bing Pan * Institute of Solid Mechanics, Beihang University, Beijing 100191, China; [email protected] * Correspondence: [email protected]; Tel.: +86-135-8182-9441 Received: 12 June 2016; Accepted: 18 August 2016; Published: 23 August 2016

Abstract: An advanced video deflectometer using actively illuminated LED targets is proposed for remote, real-time measurement of bridge deflection. The system configuration, fundamental principles, and measuring procedures of the video deflectometer are first described. To address the challenge of remote and accurate deflection measurement of large engineering structures without being affected by ambient light, the novel idea of active imaging, which combines high-brightness monochromatic LED targets with coupled bandpass filter imaging, is introduced. Then, to examine the measurement accuracy of the proposed advanced video deflectometer in outdoor environments, vertical motions of an LED target with precisely-controlled translations were measured and compared with prescribed values. Finally, by tracking six LED targets mounted on the bridge, the developed video deflectometer was applied for field, remote, and multipoint deflection measurement of the Wuhan Yangtze River Bridge, one of the most prestigious and most publicized constructions in China, during its routine safety evaluation tests. Since the proposed video deflectometer using actively illuminated LED targets offers prominent merits of remote, contactless, real-time, and multipoint deflection measurement with strong robustness against ambient light changes, it has great potential in the routine safety evaluation of various bridges and other large-scale engineering structures. Keywords: Bridge deflection; video deflectometer; digital image correlation; Wuhan Yangtze river

1. Introduction Bridge deflection is an important parameter in safety examination of bridge structures, which reflects the overall stiffness of the bridge structure and is thus closely related to its bearing capacity and the ability to resist dynamic loadings such as traffic, gusts and earthquake. Currently, the most widely used bridge deflection measuring techniques are level gauges and displacement meters, which are relatively accurate, but in general can only be applied to measure static deflection, and thus are not suitable for continuous dynamic measurements. Moreover, these conventional techniques must be operated manually rather than automatically. In addition, these contacting measurement methods require the sensors be attached to a test bridge’s main beams, and some displacement sensors require fixed reference benchmarks as an installation platform. Considering that many bridges are built over highways, water, mountains and valleys, it is difficult to install and uninstall reference benchmarks and displacement sensors, which makes some important parts hard to be reached and tested and, thus, greatly limits the applications of these contact sensors. To overcome the limitations of traditional contract sensors, various non-contact displacement measurement systems using GPS technology [1,2], laser Doppler vibrometry [3], radar interferometry [4], robotic total station [5], and vision-based (or image-based) optical techniques [6–14], have been developed and advocated for bridge deflection measurement with their claimed advantages. It is also noted that some researchers combined several of these Sensors 2016, 16, 1344; doi:10.3390/s16091344

www.mdpi.com/journal/sensors

Sensors 2016, 16, 1344

2 of 13

technologies [2,15,16] to extend the application range and improve the sensitivity and accuracy of the measurement system. Despite the diversity of non-contact deflection measurement techniques, vision-based optical techniques have received increasing attention due to their outstanding advantages, such as low-cost and easy-to-use setup, multipoint real-time measurement and visualization, and wide range of resolution and applicability. Recently, a self-developed advanced video deflectometer based on the principle of off-axis digital image correlation (off-axis DIC) was developed by the present authors for remote, real-time, multipoint, and targetless bridge deflection measurement [14]. The video deflectometer relies on the natural texture on the bridge to track the vertical motion (i.e., deflection) of test bridges. With the aid of the state-of-the-art subpixel registration algorithm, the video deflectometer is able to provide real-time and high-accuracy deflection measurement provided that the texture on the test bridge has sufficient and constant intensity contrast during the whole measurement period. However, in certain cases, especially for deflection measurement of very large bridges at remote distance or at night, where sufficient and constant illumination is difficult or impossible, the texture of the bridge tends to be indiscernible, thus leading to a failure of targetless deflection measurement using the video deflectometer. In particular, to avoid the interference of daily traffic and to ensure the measurement accuracy, many safety examinations of bridges have to be carried out at night when these bridge are closed to traffic. During the night, one of the major challenge is that the visibility and resolution of the natural textures on the bridge are insufficient to be tracked by even the most robust image registration algorithms. To address the challenge of remote and accurate deflection measurement of large bridges at night, the novel idea of active imaging combining high-brightness monochromatic LED targets and bandpass filter imaging, which was originally proposed in [17,18] to realize deformation measurement in outdoor or high-temperature environments, is introduced. Thanks to the easy-to-implement but robust active imaging technique, the ambient light from the road lamps on the bridge can be effective suppressed to ensure high-accuracy motion tracking of LED targets. Compared with traditional contacting displacement measurement techniques, the video deflectometer has the advantages of compact configuration, ease-of-use, as well as remote, real-time, and multipoint deflection measurement. Additionally, in contrast to other vision-based optical techniques using various targets [6–14], the proposed technique offers outstanding advantage of being insensitive to ambient light variations just with a simple improvement made on LED targets and the optical imaging system. In the rest of this paper, system configuration, basic principles and measuring procedures of the video deflectometer are briefly described. Then, the accuracy of the video deflectometer in outdoor environments was characterized using in-plane vertical translation tests performed at night. Finally, field deflection measurement of the Wuhan Yangtze River Bridge with the aid of high-brightness red LED targets is demonstrated. 2. An Advanced Video Deflectometer for Real-Time, Remote Bridge Deflection Measurement 2.1. System Configuration Shown in Figure 1 is the self-developed video deflectometer for real-time, remote, and multipoint bridge deflection measurement, which consisted of a high-speed area scan monochrome camera (Genie HM1024, Teledyne DALSA, Waterloo, ON, Canada, resolution: 1024 × 768 pixels with 8-bit quantization, maximum frame rate: 117 fps), a fixed-focal optical lens (the focus length of the lens can be changed as per actual measurement requirements), a laser rangefinder (BOSCH GLM 250 VF Pro, Robert Bosch GmbH, Power Tools Division, Baden-Württemberg, Germany, measuring range: up to 250 m, accuracy: 1 mm), an optical theodolite, and a laptop computer (Thinkpad T440p, Lenovo, Beijing, China, Intel(R) Core(TM) i7-4700MQ CPU, 2.40 GHz main frequency and 8 GB RAM). The video camera is fixed onto a platform that is attached onto the horizontal axis of the optical theodolite. By use of the optical theodolite, the pitch angle and horizontal (or yaw) angle of the video camera can be adjusted readily and then fixed tightly. The camera equipped with an optical imaging

Sensors 2016, 16, 1344

3 of 13

lens is connected to the laptop computer using a gigabit Ethernet standard LAN wire, through which Sensors 2016, 16, 1344 3 of 13 the live video images of a test bridge can be displayed in real-time. These live video images can be processed by the state-of-the-art DIC algorithm [14,19] described later to wire, extract image motions lens is connected to the laptop computer using a gigabit Ethernet standard LAN through which (in pixels) at specified measurement points, can bein subsequently converted into desired the live video images of a test bridge can which be displayed real-time. These live video images canphysical be processed by the state-of-the-art DIC algorithm described later to extract motions (in displacements (deflections) in millimeters based [14,19] on an easy-to-implement, butimage accurate, calibration at specified measurement points, which can be subsequently converted into desired physical modelpixels) introduced in the following section. displacements (deflections) in millimeters based on an easy-to-implement, but accurate, calibration It is quite necessary to note that, as an intensity-based image registration algorithm, DIC relies model introduced in the following section. on the random intensity distribution on the test object to realize accurate subpixel displacement It is quite necessary to note that, as an intensity-based image registration algorithm, DIC relies tracking. The developed video deflectometer can operate with two different kinds of measurement on the random intensity distribution on the test object to realize accurate subpixel displacement modes, namely targetless mode and target mode. The targetless measurement mode takes advantage tracking. The developed video deflectometer can operate with two different kinds of measurement of themodes, natural texture (e.g., mode trafficand sign, various varying structures) on a mode test bridge or structure, namely targetless target mode. The targetless measurement takes advantage as evidenced in our recent work [14]. The target measurement mode utilizes artificial targets (typically, of the natural texture (e.g., traffic sign, various varying structures) on a test bridge or structure, as specially-designed high-brightness LED lamps) attached onto the test bridge, which facilitates evidenced in our recent work [14]. The target measurement mode utilizes artificial targets (typically, the specially-designed high-brightness LED lamps) attached onto the test bridge, whichthe facilitates displacement tracking or deflection measurement of textureless surfaces or during night. the tracking or deflection texturelessambient surfaces or during the night. in outdoor Itdisplacement is important to note that, tomeasurement effectivelyofsuppress light variations It is and/or important to note that, and to effectively suppress ambient variations in outdoor environments during the night ensure high-accuracy target light tracking, the simple, but robust, environments and/or during the night and ensure high-accuracy target tracking, the simple, but active imaging technique, which was originally proposed by Pan et al. [17,18] to realize deformation robust, active imaging technique, which was originally proposed by Pan et al. [17,18] to realize measurement in outdoor or high-temperature environments, was incorporated into the established deformation measurement in outdoor or high-temperature environments, was incorporated into the videoestablished deflectometer. To be specific, high-brightness red LED lamps emitting at a wavelength of video deflectometer. To be specific, high-brightness red LED lamps emitting at a 620 ±wavelength 3 nm with of a power 3 Wwith wereaused as actively-illuminated Additionally,targets. a coupled 620 ± of 3 nm power of 3 W were used astargets. actively-illuminated bandpass optical filter with bandpass a center wavelength of 620 nm and a full-width at nm a half-maximum Additionally, a coupled optical filter with a center wavelength of 620 and a full-widthvalue of 30 at nm, which merelyvalue allows thenm, redwhich light to passallows through, before the lens of the video a half-maximum of 30 merely the is redmounted light to pass through, is mounted before thetolens of the the video deflectometer to of minimize adverse influence of the ambient lightnoise deflectometer minimize adverse influence ambientthe light variations. Since random variations. Since the random noise in the video images due to ambient light can be greatly in the video images due to ambient light can be greatly suppressed, the accuracy and precision in suppressed, the accuracy and precision in displacement tracking are expected toLED be improved byshort, displacement tracking are expected to be improved by using actively-illuminated targets. In using actively-illuminated LED targets. In short, compared with existing video-based systems [6–14] compared with existing video-based systems [6–14] for bridge deflection monitoring, which mainly for bridge deflection monitoring, which mainly relies on precise targets with evident geometric relies on precise targets with evident geometric characteristics and customized image processing characteristics and customized image processing algorithms, the present video deflectometer is more algorithms, the present video deflectometer is more practical, robust and versatile. practical, robust and versatile.

Computer

Figure 1. The established video deflectometer for bridge deflection measurement.

Figure 1. The established video deflectometer for bridge deflection measurement.

Sensors 2016, 16, 1344

4 of 13

2.2. Measurement Procedures and Principles The bridge deflection measurement using the established system involves the following three steps: (1) Measurement Preparation Place the video deflectometer on the ground that permits imaging the test bridge far away. Note that the measuring system should be kept stationary during the whole measurement period, because small vibrations of the camera can lead to considerable displacement errors [12,20]. Then, tune the imaging distance and aperture of the lens to get a clear image of the bridge with sufficient contrast and without overexposure. Afterwards, specify discrete measurement points in the live image of the test bridge. For each measurement point a subset with proper size should be chosen, which should contain sufficient local natural texture or a pre-installed LED target to allow an accurate subset-based pattern matching. In general, the optical axis of the video camera is oblique to the test bridge surface, which implies the magnification factor for each measurement point is different. To calibrate the corresponding magnification factor for each point, the distance D from the camera sensor to each measurement point is measured using the laser rangefinder. Thus, the objective distance of the point (i.e., the distance from optical center to the measurement point) L can be estimated as L = D − f with f being the focus length of the camera lens. Additionally, the pitch angle β of the camera can either be measured by the laser rangefinder or by the optical theodolite. These two parameters will be subsequently used to convert image displacements to real displacements using the calibration model described below. (2) Displacement Tracking Using DIC After defining the measurement points and corresponding subsets, the image displacements of these interrogated points can be tracked by an efficient but accurate inverse-compositional Gauss-Newton (IC-GN) algorithm. More details of the subset tracking using the IC-GN algorithm can be found in our previous publications [14,19], and is briefly reviewed hereafter. To be specific, the displacements at each measurement point can be computed with subpixel accuracy by optimizing the by optimizing the following robust zero-mean normalized sum of squared difference (ZNSSD) criterion.

CZNSSD (∆p) =

i h  f (x + W (ξ; ∆p)) − f

∑ ξ

∆f

−

2 [ g (x + W (ξ; p)) − g]  ∆g

(1)



where f (x) and g(x) denote the grayscale levels at x = (x, y)T of reference image and the deformed image, f = N1 ∑ f (x + W (ξ; ∆p)), g = N1 ∑ g (x + W (ξ; p)) are the mean intensity value of the two ξ ξ s r h i2 subsets, ∆ f = ∑ f (x + W (ξ; ∆p)) − f and ∆g = ∑ [ g (x + W (ξ; p)) − g]2 . ξ = (∆x, ∆y) T is ξ

ξ

the local coordinates of the pixel point in each subset. W (ξ; p) is the warp function, also known as the displacement mapping function (or shape function) in DIC, depicting the position and shape of the target subset relative to the reference subset; W (ξ; ∆p) is the incremental warp function exerted on the reference subset. Despite that various (e.g., zero-, first-, and second-order) shape functions can be used in the IC-GN algorithm to approximate the possible local deformation of the target subsets, the use of overmatched higher-order shape functions with heavier computational complexity has not shown an improvement in displacement measurement accuracy for remote bridge deflection measurement [21]. Due to this reason, only the simplest, but practical, zero-order displacement mapping function, which only allows rigid body translation of the target subset, is used. Thus, the ZNSSD criterion becomes a non-linear objective function with respect to two displacement components, which can be solved iteratively

Sensors 2016, 16, 1344

5 of 13

only allows rigid body translation of the target subset, is used. Thus, the ZNSSD criterion becomes a non-linear objective function with respect to two displacement components, which can be solved iteratively using Sensors 2016, 16, 1344 the IC-GN algorithm and bicubic spline interpolation. Benefiting from the high5 of 13 efficiency and high-accuracy IC-GN algorithm, the video deflectometer can realize real-time displacement tracking at 30 discrete measurement points at a frame rate of 117 fps [14]. using the IC-GN algorithm and bicubic spline interpolation. Benefiting from the high-efficiency and (3) Converting Image Displacement to Physical Displacement high-accuracy IC-GN algorithm, the video deflectometer can realize real-time displacement tracking at 30 discrete points at a frame rate of 117 fps In fieldmeasurement measurement of bridge deflection using the[14]. proposed video deflectometer, the optical axis of the video camera is no longer perpendicular to the test (3) Converting Image Displacement to Physical Displacementsurface of the test bridge. Consequently, the pitch angle and yaw angle of the camera are no longer zero values. However, since the established field measurement of bridgeto deflection the proposed videodisplacement), deflectometer, the axis videoIndeflectometer was designed measureusing deflection (i.e., vertical the optical yaw angle of the no longer vertical perpendicular to the test surface bridge. Consequently, the has novideo effectcamera on theismeasured displacement and, thus,ofisthe nottest indicated in the calibration pitch angle and yaw angle of the camera are no longer zero values. However, since the established model (Figure 2). In this case, the magnification factor at each measurement point is not a constant, video deflectometer wasparameters designed to measurethe deflection (i.e., vertical thepoint yaw (x, angle but depends on various including image coordinates ofdisplacement), the measurement y), has no effect on the measured vertical displacement and, thus, is not indicated in the calibration the pitch angle β of the camera, the focus length f of the camera lens, as well as the object distance L model 2). In this case, magnification factor at each measurement point is not afor constant, of the (Figure measurement point. Tothe determine the position-dependent magnification factor video but depends onthe various parameters including the image coordinates the measurement point (x, y), deflectometer, pinhole camera model is used to relate an objectofpoint with its corresponding the pitch angle β of the camera, the focus length f of the camera lens, as well distance image point, as schematically shown in Figure 2. Assume a measurement pointasP1the on object the test bridge L of the measurement point. To determine the position-dependent magnification factor for video undergoes a vertical motion V and moves to P2. Thus the corresponding image point moves from p1 deflectometer, the pinhole camera model is used to relate an object point with its corresponding to p2 on the CCD sensor target. To facilitate understanding, an auxiliary line P1O1//p1Oc is plotted in image point, as schematically Figure 2.PAssume a measurement point bridge 1 on the testtriangle Figure 2. Thus, the extension shown of OP2 in intersects 1O1 at point P2′. According to Phomothetic undergoes a vertical V and2 moves theory, it can be seenmotion from Figure that: to P2 . Thus the corresponding image point moves from p1 to p2 on the CCD sensor target. To facilitate understanding, an auxiliary line P1 O1 //p1 Oc is plotted in Figure 2. Thus, the extension of OP2 intersects P1 O1 at point P2 0 . According to homothetic triangle  OP1 L 1 2 theory, it can be seen fromPP Figure  2 that: (2) 2 p p Op1  x  xc  yL yc 2  l ps2  f 2 OP1 P11P220 h i = = r (2) p1 p2 Op1 2 2 2 2 ( x − xc ) + (y − yc ) l ps + f where (x, y) and (xc, yc) are the image coordinate of the measurement point and the optical center, where (x, y) and (xcthat , yc ) are image coordinate measurement point and thefor optical center, respectively. Note the the latter is assumed to of bethe located in the image centre simplicity; respectively. Note that the latter is assumed to be located in the image centre for simplicity; l = 7.4 µm ps l ps = 7.4 μm is the physical size of each pixel unit; f is the focal length of the camera lens used in the is the physical size of each pixel unit; f is the focal length of the camera lens used in the following following tests. L is from the distance from to optical center to the measurement point, whichusing can the be tests. L is the distance optical center the measurement point, which can be measured measured using the laser rangefinder. laser rangefinder.



 



Figure 2. Schematic Schematic representation representation of the calibration model.

In general, the focal length of the camera lens is much larger than the half height of the sensor target (=2.84 mm), thus the angle ∠OP2 0 P1 approximates to 90◦ , and the desired vertical displacement of the interrogated point can be computed as:

In general, the focal length of the camera lens is much larger than the half height of the sensor target (=2.84 mm), thus the angle ∠OP2′ P1 approximates to 90°, and the desired vertical displacement of the interrogated point can be computed as: Sensors 2016, 16, 1344

V 

L

vl ps

6 of 13

2   x  xc  2   y  yc  2  l ps  f 2 cos    vl ps L V∼ = rh i

(3)

(3) cosβ 2 where the pitch angle β of the camera can xc )also + (be y −measured yc )2 l 2ps +either f 2 by the laser rangefinder or the (x − optical theodolite. where the pitch angle β of the camera can also be measured either by the laser rangefinder or the 3. Accuracy Validation of the Video Deflectometer for Tracking LED Targets optical theodolite.

To validate the measurement of the video deflectometer in outdoor 3. Accuracy Validation of the Video accuracy Deflectometer forestablished Tracking LED Targets environments during the night time, a group of in-plane translation tests along the vertical direction validate measurement the established video deflectometer in outdoor wereTo carried out the using a motorized accuracy precision of translation stage equipped with a red LED lamp as environments during the night time, a group of in-plane translation tests along the vertical direction shown in Figure 3. The red LED lamp emitting at a wavelength of 620 ± 3 nm with a power of 3 W were carried out a motorized translation equipped with a red lamp as was attached ontousing the sliding block ofprecision the translation stage,stage which is subsequently usedLED as the target shown in Figureby 3. the The proposed red LED lamp emitting at a wavelength of 620 ± 3 nmwith withaacoupled power ofbandpass 3 W was point tracked advanced video deflectometer outfitted attached onto the sliding block of the translation stage, which is subsequently used as the target point optical filter. tracked by the proposed advanced video deflectometer outfitted with a coupled bandpass optical filter. In the following translation tests, the video deflectometer using an optical lens with a fixed focus In of the50 following tests,m,the videom, deflectometer using an lens with fixed focus length mm wastranslation placed 10.605 49.963 101.428 m, 201.485 m,optical and 300.152 m, arespectively, length of 50 mm was placed 10.605 m, 49.963 m, 101.428 m, 201.485 m, and 300.152 m, respectively, away from the motorized precision translation stage. Then, based on these distances measured by away fromrangefinder the motorized stage. on Then, ontheodolite, these distances bybe the0 the laser andprecision the pitchtranslation angle indicated thebased optical whichmeasured was set to laser rangefinder and the pitch angle indicated on the optical theodolite, which was set to be 0 degrees degrees in these tests, the magnification factors at different distances can be precisely calculated in these tests, the magnification factors at different can be preciselytests, calculated according according to Equation (3). It should be noted that, indistances the first two translation the sliding block to Equation (3). It should be noted that, in the first two translation tests, the sliding block moved moved upwards by 60 mm at a speed of 50 mm/s, and the sliding block paused for two seconds every upwards by 60 mm at a speed of 50 mm/s, and the sliding two seconds every mm, 2 mm, whereas the sliding block was reset to pause for 10 sblock everypaused 10 mmfor translation in the later2three whereas the sliding block was reset to pause for 10 s every 10 mm translation in the later three tests. tests.

Figure 3. Tracking the movements of an LED lamp using the video deflectometer: the left insert shows Figure 3. Tracking the movements of an LED lamp using the video deflectometer: the left insert shows the motorized precision translation stage and the right insert indicates an enlarged video image of the the motorized precision translation stage and the right insert indicates an enlarged video image of the LED target. target. LED

The vertical translations of the LED lamp were tracked by the video deflectometer in real time. The vertical translations of the LED lamp were tracked by the video deflectometer in real time. The left part of Figure 3 shows a real image of the LED lamp recorded by the video deflectometer The left part of Figure 3 shows a real image of the LED lamp recorded by the video deflectometer placed placed 49.963 m away. It is evident that ambient light has been successfully suppressed thanks to the 49.963 m away. It is evident that ambient light has been successfully suppressed thanks to the attached bandpass optical filter. To accurately track the position of the LED lamp, a subset of 41 × 41 pixels centered at the LED lamp was chosen. The detected vertical displacements for all the five translation

Sensors 2016, 16, 1344

7 of 13

Sensors 2016, 16, 1344

7 of 13

attached bandpass optical filter. To accurately track the position of the LED lamp, a subset of 41 × 41 pixels centered at the LED lamp was chosen. The detected vertical displacements for all the five tests are plotted functionasofatime in Figure 4a, in in Figure which the ladder-like curves are in translation tests as area plotted function of time 4a, in which thedisplacement ladder-like displacement perfect agreement with preset motions. curves are in perfect agreement with preset motions.

Figure Figure 4. 4. (a) (a) Measured Measured vertical vertical motions motions of of the the LED LED target target at at different different distances; distances; (b) (b) comparison comparison of of the the measured measured results results to to the the actual actual values values at at the the distance distance of of 49.963 49.963 m; m; and and (c) (c) the the differences differences between between the the measured measured results results and and the the actual actual value value at at the thedistance distanceof of49.963 49.963m. m.

To examine the the accuracy accuracyof ofthe thevideo videodeflectometer, deflectometer,the theaverage average displacement To quantitatively quantitatively examine displacement at at each dwell time estimated. A comparison between the averaged measured displacements each dwell time waswas estimated. A comparison between the averaged measured displacements of the of redlamp LED(indicated lamp (indicated blue circle dots) theones applied ones line) fortranslation the third redthe LED by blue by circle dots) with the with applied (solid line)(solid for the third translation test withofa49.963 distance 49.963inmFigure is shown in Figure 4b. between The differences between the test with a distance m isofshown 4b. The differences the measured results measured results and are theplotted actual values are4c, plotted in Figure in which label shows It the and the actual values in Figure in which the left4c, label shows the the left errors in pixels. is errors in pixels. It is observed that these data points distribute averagely on both sides of the zero observed that these data points distribute averagely on both sides of the zero line, with an estimated line, with an estimated error of to 0.42 mm (corresponds to 0.0508 pixels). The approximately maximum error of 0.42maximum mm (corresponds 0.0508 pixels). The approximately sinusoidal distributed sinusoidal error curve be interpreted as the systematic errors associated with image error curvedistributed can be interpreted as can the systematic errors associated with image noise and imperfect noise and imperfect subpixel interpolation algorithm [22–24]. It should be emphasized here that subpixel interpolation algorithm [22–24]. It should be emphasized here that the interferencethe of interference of ambient vibrations orinpossible in outdoor environment notwork considered ambient vibrations or possible winds outdoorwinds environment was not consideredwas in this which, in this workgreatly which,lessened generally,the greatly lessened the measurement of the established video generally, measurement accuracy of the accuracy established video deflectometer deflectometer according to our experiences. according to our experiences. Table Table 11 summarizes summarizes the the mean mean errors errors and and standard standard deviation deviation errors errors of of vertical vertical displacements displacements measured by the video deflectometer at different measuring distances. It is observed the video deflectometer at different measuring distances. observed that that the the mean mean error and and standard standard deviation deviation error error increase increase almost almost exponentially exponentially with with the the increases increases of of measuring measuring distance. The The mean mean error error was was estimated estimated as 0.5674 mm for the maximum maximum measuring measuring distance distance of of 300.152 m, which is comparable to that evaluated from the deflection curve of the real bridge test comparable real bridge test before after loading. The The rapidrapid non-linear increase of measurement errors canerrors be explained beforeloading loadingand and after loading. non-linear increase of measurement can be by the following twofollowing aspects: (1) with the increase of measuring distances, the corresponding image explained by the two aspects: (1) with the increase of measuring distances, the size of the LEDimage targetsize will as a function of theassquare of the measuring As a corresponding of decrease the LED target will decrease a function of the square ofdistance. the measuring result, valid information used for target tracking, whichtracking, can be characterized a parameter distance. Asgrayscale a result, valid grayscale information used for target which can bebycharacterized called the sum of square of subset intensity gradient (SSSIG) [25], (SSSIG) is decreased andgreatly; (2) the by a parameter called the sum of square of subset intensity gradient [25], isgreatly; decreased influences winds,from lights, and ambient vibrations an outdoor are more pronounced and (2) thefrom influences winds, lights, and ambientinvibrations inenvironment an outdoor environment are more at longer measuring distances. It should be noted that webe have conducted same translation in pronounced at longer measuring distances. It should noted that wethe have conducted thetests same the daytime. Although the ambient light mainly due to sunlight can also be effectively suppressed, translation tests in the daytime. Although the ambient light mainly due to sunlight can also be we observedsuppressed, that the errors measured displacement almost two times largerare than those two measured effectively we in observed that the errors inare measured displacement almost times during the night. The enhanced accuracy of the deflectometer using actively-illuminated LED larger than those measured during the night. Thevideo enhanced accuracy of the video deflectometer using targets at night is dueLED to the fact that the ambient timelight is much weaker than actively-illuminated targets at night is due tolight the during fact thatthe thenight ambient during the night sunlight and, weaker thus, hasthan lesssunlight contribution thehas image time is much and, to thus, lessnoise. contribution to the image noise.

Sensors 2016, 16, 1344

8 of 13

Table 1. Measurement errors of the video deflectometer at different measuring distances. Measuring Distance (m)

Mean Error (mm)

Standard Deviation (mm)

10.605 49.963 101.428 201.485 300.152

0.0091 0.0150 0.0970 −0.1542 0.5674

0.0074 0.0695 0.2021 0.2795 0.5897

4. Deflection Measurements of the Wuhan Yangtze River Bridge under Static Loading The Wuhan Yangtze River Bridge [26], with a length of more than 1670 m, was opened to traffic in 1957. The upper layer of the bridge is highway, and the nether layer is double-track railway. There are eight piers and nine apertures, and the distance between each two piers is 128 m, under which ships as heavy as tens of thousands tons could pass through. For every three apertures, there is a continuous beam, and the whole bridge is constituted of three continuous beams. As one of the most prestigious and most publicized constructions in China, the Wuhan Yangtze River Bridge is not only the first double-track railway and highway bridge built across the Yangtze River since the founding of the People’s Republic of China, but also the first Yangtze river bridge, and is generally referred to as the First Bridge of the Thousands of Miles Yangtze River. The bridge links the three towns in Wuhan city, promoting traffic convenience and economic development tremendously. Meanwhile, the bridge connects South China and North China, and the Beijing–Hankou railway and the Canton-Hankou railway are also linked by the bridge as the complete Beijing-Guangzhou railway, playing an important role in promoting the north-south economy and constructing the national economy. Due to the fast economic development of China, the 58-year-old Wuhan Yangtze River Bridge is facing increasingly heavier missions than when it was designed. At present, 296 trains pass through the bridge in a day, approximately a train every five minutes, on average. Meanwhile, passing motor vehicles have escalated from thousands at the beginning to more than a hundred thousand. To examine the real technical status of the bridge structure, and ensuring its safety and reliability, the Wuhan Railway Bureau conducted a fully safety examination from 3 to 9 June 2015. The examination includes static loading and dynamic loading tests, expecting to fully evaluate the working performance of the bridge structure in different conditions, so as to provide a scientific basis for the bridge maintenance. In the examination, the bridge’s second aperture was loaded by vehicles, while deflections of the second and third apertures were measured by the video deflectometer. Figure 5a shows a real picture of the bridge and a schematic figure of the loading cases. Vehicles on the highway and trains on the railway were loaded simultaneously and stopped at the same place as schematically shown in Figure 5b. Two motorcades and two trains were used in the examination. Each motorcade had six trucks whose full load is 180 KN (18.37 tons) and a truck whose full load is 300 KN (30.61 tons). The trains were pulled by two HXD1B locomotives at the head and the end, with six fully-loaded C70 railway cars in between, weighing 861.6 tons. Details of the three loading cases are given as follows: (1) (2) (3)

Partly loading on the upward way: the vehicles and the trains were loaded on the upward way simultaneously; Full loading: the vehicles and trains were loaded on both the upward and downward ways; Partly loading on the downward way: unload the vehicles and cars on the upward way and remain the loads on the downward way.

Finally, the loads exerted on the downward way were removed, and the examination was ended. To avoid the interference of daily traffic and ensure the measurement accuracy of static deflection, the examination was executed with the bridge was closed to traffic at night. Since the visibility and the resolution of the bridge are insufficient to be discerned, six high-brightness red LED targets were installed equally on the second and third apertures. The horizontal distance between adjacent two LED targets is 32 m, as shows on Figure 6b. The video deflectometer was placed at the riverside (Figure 6a).

Sensors 2016, 16, 1344

Sensors 2016, 16, 1344

9 of 13

9 of 13

By using an optical lens with a fixed focus length of 8 mm, and adjusting the orientation of the video Sensors 2016, 16, 1344 9 of 13 deflectometer, all video six LED targets can be in images overlap. Then, the distances orientation of the deflectometer, all discerned six LED targets can bewithout discerned in images without overlap. from the sensor to the the camera targets, sensor as well to as the the targets, pitch angle of the measured using Then, thecamera distances from as well as camera, the pitchwere angle of the camera, orientation of the video deflectometer, all six LED targets can be discerned in images without overlap. the rangefinder. In thisthe examination, the distances from thethe camera sensor to the thecamera six LEDsensor targets were measured using rangefinder. In this examination, distances from Then, the distances from the camera sensor to the targets, as well as the pitch angle of the camera, to are measured as 107.3 134.2 m, 164.2 226.1 m, m, 257.4 m,distances and226.1 288.9 m,257.4 respectively, andtothe the six measured LED targets arem, measured as 107.3 134.2 164.2 m, m, m, and 288.9 m, were using the rangefinder. In m, thism, examination, the from the camera sensor pitch angle is determined as 7 degrees. Note that the distances from the latter three LED targets to respectively, and the pitch angle is determined as 7 degrees. Note that the distances from the latter the six LED targets are measured as 107.3 m, 134.2 m, 164.2 m, 226.1 m, 257.4 m, and 288.9 m, the video are larger the maximum measuring distance of the laser rangefinder. three LEDdeflectometer targets the video deflectometer areas larger than the maximum measuring distance of the respectively, andto the pitch angle isthan determined 7 degrees. Note that the distances from the latter In reality, these distances were measured but from between these laser In the reality, these distances were measured but relationships estimated distance from geometric threerangefinder. LED targets to videonot deflectometer areestimated largernot than the geometric maximum measuring of the regularly-spaced targets. Allregularly-spaced of these these distances parameters are not subsequently input to the relationships between targets. All measured of these parameters arevideo subsequently input laser rangefinder. In these reality, were but estimated fromdeflectometer geometric software to calculate the magnification factor for each measurement point. torelationships the video deflectometer software to calculate the magnification factor for each measurement point. between these regularly-spaced targets. All of these parameters are subsequently input to the video deflectometer software to calculate the magnification factor for each measurement point.

Figure 5.5.(a) (a) Wuhan Yangtze River Bridge;and and(b) (b)the theschematic schematicofof of the static loading test. Figure (a)Wuhan WuhanYangtze YangtzeRiver RiverBridge; Bridge; and the static loading test. Figure 5. the schematic the static loading test.

Figure The video deflectmeter placed the riverside;and and(b) (b)the thedistances distancesand andorentation orentationofofthe Figure 6. 6. (a)(a) The video deflectmeter placed atat the riverside; Figure 6. (a) The video deflectmeter placed at the riverside; and (b) the distances and orentation of the video deflectometer relative themeasuring six measuring points. video deflectometer relative to thetosix points. the video deflectometer relative to the six measuring points.

Figure 7a,bshow showreal realimages imagesof ofthe the Wuhan Wuhan Yangtze Yangtze River using thethe Figure 7a,b River bridge bridgewithout withoutand andwith with using Figure optical 7a,b show Wuhan River without and with using bandpass filter.real In images contrast of to the Figure 7a, itYangtze is seen that thebridge ambient light mainly from roadthe bandpass optical filter. In contrast to Figure 7a, it is seen that the ambient light mainly from road lamps bandpass optical filter. In contrast to Figure 7a, it is light mainly from road lamps was almost completely suppressed in Figure 7bseen due that to thethe useambient of the bandpass optical filter. was almost completely suppressed in Figure 7b due to the use of the bandpass optical filter. Then, lamps was almost completely suppressed in Figure 7b due to the use of the bandpass optical filter. Then, to determine the image motions of the six LED target, six rectangular subsets centered at these to determine the image motions of the six LED target, six rectangular subsets centered at these targets Then, to determine the image motions thethree six LED target, rectangular centered these targets were selected. Note that for theofleft targets, twosix square subsetssubsets with a size of 41 at × 41 were selected. Note that for the left three targets, two square subsets with a size of 41 × 41 pixels were targets Note thattofor the left targets,oftwo square subsets with asubsets size of were 41 × 41 pixelswere were selected. chosen. However, exclude thethree interference other targets, rectangular chosen. However, to exclude the interference of other targets, rectangular subsets were chosen for the chosen for chosen. the otherHowever, four targets. pixels were to exclude the interference of other targets, rectangular subsets were other four targets.

chosen for the other four targets.

Sensors 2016, 16, 1344 Sensors 2016, 16, 1344

10 of 13 10 of 13

Figure 7. 7. The digital bridge(a) (a)without; without;and and(b) (b)with with using Figure The digitalimages imagesofofthe theWuhan Wuhan Yangtze Yangtze River River bridge using thethe bandpass optical filter. The red rectangles are the subsets centered at the six LED targets. bandpass optical filter. The red rectangles are the subsets centered at the six LED targets.

Figure 8 showsthe thedeflection-time deflection-time curve curve of of the the six located onon thethe Figure 8 shows six measurement measurementpoints pointsevenly evenly located second and third apertures. It can be observed that: (1) before loading and after loading, the second and third apertures. It can be observed that: (1) before loading and after loading, the deflections deflections of all the six measurement points fluctuate around zero with an estimated standard of all the six measurement points fluctuate around zero with an estimated standard deviation deviation from 0.19 mm, mm demonstrating to 0.57 mm, demonstrating the good repeatability the video ranging fromranging 0.19 mm to 0.57 the good repeatability of the video of deflectometer; the deflection directions of the three points on the second aperture and the three (2)deflectometer; the deflection (2) directions of the three points on the second aperture and the three points on the third points on the third aperture are opposite, which is consistent with actual deformation case of the aperture are opposite, which is consistent with actual deformation case of the bridge. The second bridge. The second aperture sank due to the applied loading, which the cocked third aperture can be aperture sank due to the applied loading, which the cocked third aperture can be well explained by the well explained by the continuity of the beam; (3) on the second aperture, the deflection of the point continuity of the beam; (3) on the second aperture, the deflection of the point in the middle is always in the middle is always larger than the other two, which are approximately the same because of larger than the other two, which are approximately the same because of symmetry; and (4) on the third symmetry; and (4) on the third aperture which is cocking, the point at the 1/4 position is larger than aperture which cocking, positionThis is larger than point atbythe and the the point at theismiddle andthe thepoint pointat atthe the 1/4 3/4 position. can be alsothe explained themiddle deformation point at the 3/4 position. This can be also explained by the deformation continuity of the continuous

Sensors 2016, 16, 1344 Sensors 2016, 16, 1344

11 of 13 11 of 13

continuity themaximum continuous beam. Also, themiddle maximum of theaperture middle point theloading second beam. Also,ofthe deflection of the pointdeflection on the second underonfull aperture undertofull was measured be loading 47.4 mm.was measured to be 47.4 mm.

Figure 8. 8. Measured Measured deflection-time deflection-time curves curves for for the the six six targets. targets. Figure

To To quantitatively quantitatively evaluate evaluate the the accuracy accuracy and and precision precision of of the the video video deflectometer deflectometer for for field field measurements, the measured deflection curves of the six LED targets, lasting 80 s before loading, measurements, measured deflection curves of the six LED targets, lasting 80 s before loading, are are further analyzed extract their mean errorand andstandard standarddeviation deviationerror. error. In In this this period, the actual further analyzed to to extract their mean error actual deflections sixsix LEDLED targets should be zeros. Thus, the estimated errors in the detected deflections deflectionsofofthethe targets should be zeros. Thus, the estimated errors in the detected also reflect the and precision the videoofdeflectometer for different distances. deflections alsoaccuracy reflect the accuracy andofprecision the video deflectometer formeasuring different measuring As shown in 2, in although mean errors randomly fluctuate around zero values, thevalues, standard distances. AsTable shown Table 2,the although the mean errors randomly fluctuate around zero the deviation errors increase the increase the measuring distances. distances. Further, these observed standard deviation errorswith increase with theofincrease of the measuring Further, these standard are almost at the sameatmagnitude as those measured the validation observeddeviation standard errors deviation errors are almost the same magnitude as those from measured from the tests. The small in standardindeviation between field measurements and validation validation tests.differences The small differences standarderrors deviation errors between field measurements and tests are acceptable, considering the optical lens used and the measuring environment of these two validation tests are acceptable, considering the optical lens used and the measuring environment of tests distinctly theseare two tests aredifferent. distinctly different. Table Table2.2.Mean Meanerrors errorsand and standard standarddeviation deviationerrors errorsof ofthe the deflections deflectionsmeasured measuredfor forthe thesix six LED LED targets targets in the stationary condition. in the stationary condition.

Target (m) Mean MeanError Error(mm) (mm) TargetNo. No. Measuring Measuring Distance Distance (m) 1 107.3 −0.1566 1 107.3 −0.1566 22 134.2 0.1898 134.2 0.1898 33 164.2 0.1190 164.2 0.1190 226.1 −−0.1157 0.1157 44 226.1 5 257.4 0.2107 5 257.4 0.2107 6 288.9 0.0204 6 288.9 0.0204

StandardDeviation Deviation (mm) Standard (mm) 0.1960

0.1960 0.2337 0.2337 0.2978 0.2978 0.4783 0.4783 0.4519 0.4519 0.5712

0.5712

To Tointuitively intuitivelyshow showthe theoverall overalldeformation deformationof ofthe thebridge, bridge, the the deflection deflection curves curves of of the the six six points points on the second and third apertures in this static loading examination are shown in Figure It can on the second and third apertures in this static loading examination are shown in Figure 9. 9. It can be be seen more clearly that thesecond secondaperture aperturesank sankand andthe thethird thirdaperture aperturecocked cocked in in all all of seen more clearly that the of the the three three loading the downward way, thethe load is applied to loadingcases. cases.Moreover, Moreover,asasfor forthe thecase caseofofpartial partialloading loadingonon the downward way, load is applied the placeplace relatively far away six measurement points. Consequently, the resulting to the relatively far from awaythe from the six measurement points. Consequently, thedeflections resulting are larger than partial loading onloading the upward way, in which same load was deflections are those largermeasured than thosefor measured for partial on the upward way,the in which the same

load was exerted on the position closer to these target points. These different deformations are also reasonably shown in Figure 9.

Sensors 2016, 16, 1344

12 of 13

exerted on the position closer to these target points. These different deformations are also reasonably Sensors 2016, 16, 13449. 12 of 13 shown in Figure

Figure 9. 9. Measured deflection curves curves for for the the two two spans spans under under three three different different loading loading conditions. conditions. Figure Measured deflection

5. Conclusions 5. Conclusions Real-time, remote,and andfield fielddeflection deflection measurement of the Wuhan Yangtze Bridge at Real-time, remote, measurement of the Wuhan Yangtze RiverRiver Bridge at night night an advanced deflectometer and actively illuminated targets is described in using using an advanced videovideo deflectometer and actively illuminated LED LED targets is described in this this work. The principles basic principles and measuring procedures of the video deflectometer briefly work. The basic and measuring procedures of the video deflectometer are brieflyare reviewed. reviewed. Theofaccuracy ofdeflectometer the video deflectometer in the similar conditions (outdoor environments The accuracy the video in the similar conditions (outdoor environments during the during the night time) was carefully characterized detecting vertical of an LED target night time) was carefully characterized by detecting by vertical motions of anmotions LED target with precisely with precisely controlled translations. The curves deflection-time of the six measurement points controlled translations. The deflection-time of the six curves measurement points evenly located on evenly on of thethe two apertures the bridge were and thecurves overall curves the twolocated apertures bridge were of measured, and the measured, overall deflection atdeflection different loading at different loading cases of the measured deflections agree loading well with practical cases were presented. Allwere of thepresented. measuredAll deflections agree well with practical conditions. loading Since the proposed video offers prominent advantages of remote, Since theconditions. proposed video deflectometer offersdeflectometer prominent advantages of remote, contactless, robust, contactless, robust, real-time,deflection and multipoint deflectionatmeasurement at both targetless target real-time, and multipoint measurement both targetless and target and modes, it modes, it demonstrates great in potential in the routine safety evaluation various bridges and other demonstrates great potential the routine safety evaluation of various of bridges and other large-scale large-scale engineeringengineering structures. structures. Acknowledgments: This work work isissupported supportedbybythe theNational National Natural Science Foundation of China (Grant Acknowledgments: This Natural Science Foundation of China (Grant No. No. 11272032, 11322220 and 11427802), the Beijing Nova Program (xx2014B034), the Science Fund of State 11272032, 11322220 and 11427802), the Beijing Nova Program (xx2014B034), the Science Fund of State Key Key Laboratory of Automotive Safety and Energy (Grant No. KF16162), the opening fund of State Key Laboratory Laboratory Automotive Safety and Energy (Grant No. KF16162), the opening of StateJiaotong Key Laboratory of of Explosionof Science and Technology and State Key Laboratory of Traction Power offund Southwest University Explosion and Technology and State Key Laboratory of Traction Power of Southwest Jiaotong University (Grant No.Science TPL1607). (Grant No. TPL1607). Author Contributions: Bing Pan conceived the video deflectometer using actively illuminated LED targets. Long Tian performed the experiments and analyzed data. Bing Pan wrote the paper. Author Contributions: Bing Pan conceived the videothe deflectometer using actively illuminated LED targets. Long and analyzed the data. Bing Pan wrote the paper. Tian performed the experiment Conflicts of Interest: The authorss declare no conflict of interest.

Conflicts of Interest: The authors declare no conflict of interest.

References

References 1. Brown, C.J.; Karuma, R.; Ashkenazi, V.; Roberts, G.W.; Evans, R.A. Monitoring of structures using the global positioning system. Struct. Build. 1999, 134, 97–105. [CrossRef] 1. Brown, C.J.; Karuma, R.; Ashkenazi, V.; Roberts, G.W.; Evans, R.A. Monitoring of structures using the 2. Meng, X.; Dodson, A.H.; Roberts, G.W. Detecting bridge dynamics with GPS and triaxial accelerometers. global positioning system. Struct. Build. 1999, 134, 97–105. Eng. Struct. 2007, 29, 3178–3184. [CrossRef] 2. Meng, X.; Dodson, A.H.; Roberts, G.W. Detecting bridge dynamics with GPS and triaxial accelerometers. 3. Xia, H.; Roeck, G.D.; Zhang, N.; Maeck, J. Experimental analysis of a high-speed railway bridge under Eng. Struct. 2007, 29, 3178–3184. Thalys trains. J. Sound Vib. 2003, 268, 103–113. [CrossRef] 3. Xia, H.; Roeck, G.D.; Zhang, N.; Maeck, J. Experimental analysis of a high-speed railway bridge under Thalys trains. J. Sound Vib. 2003, 268, 103–113. 4. Pieraccini, M.; Parrini, F.; Fratini, M.; Atzeni, C.; Spinelli, P.; Micheloni, M. Static and dynamic testing of bridges through microwave interferometry. NDT E Int. 2007, 40, 208–214.

Sensors 2016, 16, 1344

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

13 of 13

Pieraccini, M.; Parrini, F.; Fratini, M.; Atzeni, C.; Spinelli, P.; Micheloni, M. Static and dynamic testing of bridges through microwave interferometry. NDT E Int. 2007, 40, 208–214. [CrossRef] Psimoulis, P.A.; Stiros, S.C. Measuring deflections of a short-span railway bridge using a robotic total station. J. Bridge Eng. 2013, 18, 182–185. [CrossRef] Stephen, G.A.; Brownjohn, J.M.W.; Taylor, C.A. Measurements of static and dynamic displacement from visual monitoring of the Humber Bridge. Eng. Struct. 1993, 154, 197–208. [CrossRef] Oleszak, P. Investigation of the dynamic characteristic of bridge structures using a computer vision method. Measurement 1999, 25, 227–236. [CrossRef] Wahbeh, A.M.; Caffrey, J.P.; Masri, S.F. A vision-based approach for the direct measurement of displacements in vibrating systems. Smart Mater. Struct. 2003, 12, 785–794. [CrossRef] Lee, J.J.; Shinozuka, M. Real-time displacement measurement of a flexible bridge using digital image processing techniques. Exp. Mech. 2006, 46, 105–114. [CrossRef] Yoneyama, S.; Kitagawa, A.; Iwata, S.; Tani, K.; Kikuta, H. Bridge deflection measurement using digital image correlation. Exp. Tech. 2007, 31, 34–40. [CrossRef] Busca, G.; Cigada, A.; Mazzoleni, P.; Zappa, E. Vibration monitoring of multiple bridge points by means of a unique vision-based measuring system. Exp. Tech. 2014, 54, 255–271. [CrossRef] Ribeiro, D.; Calcada, R.; Ferreira, J.; Martins, T. Non-contact measurement of the dynamic displacement of railway bridges using an advanced video-based system. Eng. Struct. 2014, 75, 164–180. [CrossRef] Feng, D.; Feng, M.Q.; Ozer, E.; Fakuda, Y. A vision-based sensor for noncontact structural displacement measurement. Sensors 2015, 15, 16557–16575. [CrossRef] [PubMed] Pan, B.; Tian, L.; Song, X.L. Real-time, non-contact and targetless measurement of vertical deflection of bridges using off-axis digital image correlation. NDT E Int. 2016, 79, 73–80. [CrossRef] Moschas, F.; Stiros, S.C. Three-dimensional dynamic deflections and natural frequencies of a stiff footbridge based on measurements of collocated sensors. Struct. Control Health Monitor. 2014, 21, 23–42. [CrossRef] Jung, W.; Shin, D.; Woo, S.; Park, W.; Kim, S. Hibrid approach of cameras and GPS for displacement measurements of super long-span bridges. In Proceedings of the 28th Congress of the International Association for Automation and Robotics in Construction, Seoul, Korea, 29 June–2 July 2011. Pan, B.; Wu, D.F.; Wang, Z.Y.; Xia, Y. High-temperature digital image correlation for full-field deformation measurement at 1200 ◦ C. Meas. Sci. Technol. 2011, 22, 015701. [CrossRef] Pan, B.; Wu, D.F.; Xia, Y. An active imaging digital image correlation method for deformation measurement insensitive to ambient light. Opt. Laser Technol. 2012, 44, 204–209. [CrossRef] Pan, B.; Li, K.; Tong, W. Fast, robust and accurate digital image correlation calculation without redundant computations. Exp. Mech. 2013, 53, 1277–1289. [CrossRef] Yoneyama, S.; Ueda, H. Bridge deflection measurement using digital image correlation with camera movement correction. Mater. Trans. 2012, 53, 285–290. [CrossRef] Yu, L.P.; Pan, B. The errors in digital image correlation due to overmatched shape functions. Meas. Sci. Technol. 2015, 26, 045202. [CrossRef] Schreier, H.W.; Braasch, J.R.; Sutton, M.A. Systematic errors in digital image correlation caused by intensity interpolation. Opt. Eng. 2000, 39, 2915–2921. [CrossRef] Pan, B. Bias error reduction of digital image correlation using Gaussian pre-filtering. Opt. Lasers Eng. 2013, 51, 1161–1167. [CrossRef] Baldi, A.; Bertolino, F. Experimental analysis of the errors due to polynomial interpolation in digital image correlation. Strain 2015, 51, 248–263. [CrossRef] Pan, B.; Xie, H.; Wang, Z.; Qian, K.; Wang, Z. Study on subset size selection in digital image correlation for speckle patterns. Opt. Express 2008, 16, 7037–7048. [CrossRef] [PubMed] Wuhan Yangtze River Bridge. Available online: https://en.wikipedia.org/wiki/Wuhan_Yangtze_River_ Bridge (accessed on 20 August 2016). © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).