1.Introduction

Extensive investigations have been conducted in recent years about the deformation of structural elements in civil engineering. Nevertheless, the measurement of structural deformation in the bulk of these studies was conducted using conventional equipment, such as a dial gauge. Several of these equipment items are characterized by high costs, whereas the remaining one lacks precision and is not specifically engineered for measuring or displaying dynamic deformation [1]. An excellent method for assessing the performance of a structure is to measure its displacement when subjected to operational loads. Nevertheless, measuring structural deformation with high precision is still challenging, especially in complicated structures [2]. The fatigue life of the structure can be reduced by fluctuating cyclic loading. Cracks are frequently observed as a result of fatigue failure in reinforced concrete structures [3]. Various imaging techniques, including laser scanners and digital photogrammetry, have demonstrated their effectiveness and accuracy in capturing deformations in both large and small areas subjected to static loading circumstances. Close-range photogrammetry (CRP) is widely recognised as a cost-effective, secure, and precise measuring method across various industries [4]. Videogrammetry is the technique used to acquire three-dimensional data of objects. It utilizes cameras to capture and analyse spatial data [5]. Videogrammetry, which involves determining the coordinates of object points using several video streams captured by camcorders, is an auspicious area of research that holds the capacity to surmount the constraints of current methodologies. A videogrammetric approach is automated and may produce high-quality results without the need for human intervention [6]. Recently, some studies have utilized a video camera and employed videogrammetry, a specialized branch of photogrammetry, to quantify the displacement of the oscillating bridge structure. Lidar has numerous advantages and a diverse range of applications in comparison to photogrammetry, particularly in accurately capturing the movements of objects in motion. The presence of objects makes it a desirable option as a 3D measurement tool [7, 8]. Multiple studies have suggested the potential of utilizing cameras and photogrammetric techniques to accurately quantify the movement of objects that can change shape in three dimensions [9–11]. For instance, the utilization of a high-resolution camcorder in digital photogrammetry on a shipyard enables the measurement of object points. This is done by using retro-reflective targets to provide accurate dimension checking and control [10]. To achieve precise calibration, a robust network geometry was established by capturing 8 images from 5 camera stations, some of which involved panning or rotating the camera axis [12]. Demonstrated that CRP may be employed in both static and dynamic modes. Furthermore, it emphasized the advantages of rapid measurements, comprehensive coverage, and non-contact, which were not possible with alternative methods. The researchers employed two Pulnix (TM-1020-15) digital cameras. Video cameras are used throughout the practical examinations. The cameras were fitted with a built-in ring lamp to provide uniform illumination for retroreflective targets. Moreover, numerous prior research has employed videogrammetric methods in industrial settings. A videogrammetric system with a large field of view, consisting of four cameras, was utilized to perform feature detection and matching, reconstruction of 3D coordinates and displacements, as well as computation of motion parameters. The experiments provided evidence that the suggested method achieved a high level of accuracy, with measurements of dynamic length accurate to within a margin of 0.5 mm [11].

The experiments tests showed that the four-camera video measurement system can accurately predict the position within a range of vision measuring 5000×5000 mm. Consequently, numerous researchers have successfully employed digital photogrammetric approaches to monitor deformations in structures and civil construction [13, 14]. In general, the digital photogrammetric method involves employing digital stereo images captured by a digital camera to monitor deflections in structures and civil elements. Digital photogrammetry offers numerous advantages compared to traditional tools when it comes to measuring deflection. Photogrammetry is a non-contact method that eliminates the need for manually reading dials and generates three-dimensional data. It takes measurements and generates visual recordings of the tests. It is particularly well-suited for conducting destructive testing since only a few inexpensive targets are lost or damaged, in contrast to the expensive Linear Variable Differential Transformers (LVDTs) or dial gauges [13]. For instance [15], photogrammetric techniques were used to evaluate various civil engineering materials. Two cameras with mirrors were used to analyse structures from a rear perspective. Additionally, photogrammetry was employed for on-site monitoring during load tests. Two distinct cameras were employed to capture images, and the results were compared toLVDTs displacement measures [16]. This study investigates the outcomes of utilizing photogrammetry to assess the distortions of bar and plate components in the steel structures of hoisting machines. It analyses the primary difficulties that arise during the processing of these components and suggests remedies to attain the necessary accuracy. The study suggested by [17] presents a novel videogrammetry technique to accurately measure the displacement of a vibration pre-stressed concrete bridge. The technique is applied in both daylight and day-night circumstances utilizing reflective targets. The investigation was carried out in two stages using four High-Definition (HD) video cameras. Additionally, [1] developed a unique transducer to measure the deformation of a high-speed shaking table. This was achieved by utilizing videogrammetric measurements with a high-speed CMOS camera. This study aimed to assess the precision of the shaking table's three-dimensional coordinates using the high-speed videogrammetric measurement method outlined. Based on the literature study, it is evident that digital photogrammetric and videogrammetric approaches are suitable for measuring and observing the changes in shape or structure in civil constructions. Previous studies have not examined the capability of utilizing the videogrammetric systems to identify deflections and the deformations in various types of steel beams subjected to the same load. Therefore, this study seeks to investigate the videogrammetric system's ability to detect deflections and deformations in different sections of steel beams under a dynamic uniform vertical load.

1.1.Mathematical Algorithm

The mathematical algorithm employed in videogrammetry encompasses the utilization of photogrammetric procedures, such as bundle correction, which relies on collinearity Equations (1) and (2). Bundle adjustment is a prevalent optimization technique that finds extensive application in the field of image processing.

Scene reconstruction is a fundamental aspect of computer vision and computer graphics [18]. The methodology involves the utilization of recorded picture coordinates as well as the consideration of external and internal factors. The intrinsic camera parameters, along with the object space coordinates of the seen points, are essential components in computer vision and image processing. The latter entities exert control over the resultant nonlinear system. The equations of collinearity serve as the fundamental basis for the proposed mathematical model and integrate the observed picture coordinates with the outside and internal camera parameters. The characteristics, as well as the object space coordinates, of the observed points were determined:

                                     (1)

                                     (2)

where    are image coordinates of an object and a principal point respectively;  rotation matrix according to angles   : focal length of a camera;    are ground coordinates of the object and principal point respectively.

1.2.Structural Concrete Beam Design

Three identical concrete beams were prepared and monitored for testing under emotional load. The length of the beams is 3200 mm and has a rectangular cross-section of 130×100 mm (Fig. 1a). Each type of concrete consists of a different ratio of mixtures, as the first specimen contains a mixture (1:2:4), which means one part of resistant cement two parts of fine sand and four parts of coarse gravel. The second specimen is the mixing ratio (1:3:6) one part of resistant cement, half a part of fine sand, and three parts of crushed gravel (crushed kashi). The third specimen is the mixing ratio (1:1:2), which is one part of resistant cement, one part of fine sand, and two parts of coarse gravel. The concrete used in the beams contains compressive design strength at 28 days and has a fair face. Note that the reason behind testing three concrete beams made from three different ratios of mixture is to make sure that the developed videogrammetric system can capture dynamic deformations of various types of concrete beams. Each girder is reinforced with two lower bars with a diameter of 12 mm and two top bars with a diameter of 12 (Fig. 1). Models have been tested on a testing machine.

c)

b)

a)

 Figure 1. The tested concrete beam: a) longitudinal view; b) perspective view; c) cross-section.

2.Methods

Two non-metric Canon IXUS 185 cameras were used in the study. Additionally, engineering testing equipment manufacture was studied. The equipment is a 10-ton hydraulic jack. Three different concrete formulations have been used to make 10×13×300 cm concrete beams. Custom-made Light Emitting Diode (LED) gadget for video-frame synchronisation was used. The Topcon Total Station (GM 50 series) is used in surveying and construction. Our research relies on this equipment's exact three-dimensional ground coordinate and distance readings. The target was encoded in 10 pixels. Project management software creates targets. Print and attach captured objects. During processing, the project management software may recognise and detect targets in object photos. These targets' proportions depend on the camera's distance from captured items. This study attaches targets to industrial videogrammetric systems. These targets are likewise mounted on the systems' front of concrete beams' surfaces. Internet-accessible Virtual Dub software is free. This tool software breaks a movie into image sequences for many uses. Extract photos from the video. Software like PhotoModeler Scanner (PMS) creates precise 3D models from photos. This programme was integrated by Canadian business Eos Systems Inc. PMS has many uses. Many photogrammetric and videogrammetric applications include quantifying 3D points and creating 3D models. Using images or videos to analyse surfaces as shown in Fig. 2.

Figure 2. The chart showing the Research Methodology processing.

2.1.Video Camera Calibration

Through camera calibration, the focal length  main point coordinates  and radial and decentering lens distortions are determined to determine the camera's internal orientation parameters (IOPs). As [13] stated, camera characteristics largely affect relative photogrammetric measurements.  The (IOPs) are calculated by linearizing collinearity equations for unknown parameters such as camera lens centre coordinates  orientation , and lens distortion    provides intermediate precision. Wide-angle cameras and accurate photogrammetric applications require  and  Also, least-squares methods are used to determine the decentering parameters  and their affinity and shear properties  Iterative computation estimates small constant corrections like the sensor chip's principle distance  and principal point  The collinearity models determine the target's 3D coordinates after obtaining parameter values. The calibration sheet has four coded targets and 96 grid dots (Fig. 2a). Each camera captured 12 videos. Each camera was photographed on Fig. 3a's calibration sheet. For calibration, each photo was taken from a different location and angle (Fig. 3b). The calibrating process for sheets frequently requires three movies from each corner. Capture video frames with Virtual Dub. The PMS programme then generates a report with the selected cameras' calibrated inner orientation parameters and camera calibration residuals Root Mean Square Error (RMSE). Information is in Table 1. Camera 1 had 0.102 pixels residuals and camera 2 0.112 pixels. Every calibration residual was below half a pixel. The lens distortion PMS calibration process has been employed to enhance the accuracy of picture coordinates. The study's camera parameters are Type (1) and type (2) cameras including the Canon IXUS 185.

(b)

(a)

Figure 3. (a) Single-sheet for camera calibration PhotoModeler User Manual, 2020; (b) Twelve photos by every chosen camera were captured on the calibration sheet, PhotoModeler User Manual, 2020.

Table 1. Camera calibration parameters of the two selected cameras.

Items

Camera Canon IXUS 185

Left camera

Right Camera

Focal length

7.51563 mm

7.493389 mm

(X0, Y0)

4.596474 mm × 2.596654 mm

4.503162 mm ×2.585972 mm

K1

4.735e-04

5.540e-04

K2

–2.907e-06

–6.138e-06

K3

0.000e+00

0.000e+00

P1

–3.9843e-04

–1.971e-04

P2

3.984e-04

1.372e-04

No. of photos

12

12

Overall RMSE

o.106

0.111

Maximum RMSE

0.322

0.266

2.2.Load Cell Calibration

A load cell is a measuring instrument utilized for the direct or indirect measurement of loads. There are different types of load cells available, namely hydraulic load cells, pneumatic load cells, and strain gauge load cells [19, 20]. Only pneumatic load cells were utilized in this paper. The steel beams were attached to an electrical indication device to measure the imposed load. The calibration was performed between the load cell and the indication. By utilizing varying weights of 5 kg, 10 kg, and 15 kg, as depicted in Fig. 4.

Figure 4. Load Cell Calibration steps.

2.3.Capturing and Processing Videos

After calibration, cameras are set at the right distance from objects. To generate perfect stereo films, the base-to-height ratio was about 1. As shown in Fig. 6, "base" is the horizontal distance between the two cameras' exposure stations, while "height" is the vertical distance between the cameras, the ground, and the subject taken by the camera. As mentioned, stereo recordings use two cameras along the same line to film objects simultaneously. The video parts were then analysed and manipulated on a computer. Uploading videos to Virtual Dub turned them into frames. The two contemporaneous stereo images from the left and right cameras were visually selected for processing. The PMS determines the tridimensional (   , and ) coordinates of test apparatus points. Fig. 6 shows the camera's position relative to the test apparatus's targets.

Figure 6. Study area and the equipment for this investigation.

2.4.Accuracy Assessment

This article employed an accuracy assessment to validate the outcomes of video measuring methodologies. The evaluation was conducted by examining the coordinates and extracting the horizontal distances between the points; where these points were fixed on the steel frame (yellow frame), as shown in Fig. 6. The technique involves recording the coordinates of 24 targets, with 12 points serving as a control and 12 points as a chick point. A total station (GM50) with an accuracy of 1 mm was utilized to find the precise 3D ground coordinates of the 24 target points. PMS software was used also to determine the 3D ground coordinates of the 12 checkpoints using the selected stereo images from the video frames. The accuracy assessment process was done by comparing the coordinates of the 12 checkpoints that were measured using the total station with the coordinates of the same points computed using PMS. Subsequently, the variance for each point was computed, followed by the calculation of the cumulative residual of all the points.

2.5.Determining the Target Points' Three-D Coordinates for Deflection Detection

To detect deflection, the team will put 11 10-pixel targets on reinforced concrete beams. To synchronise the camera, an LED light was attached to the steel frame (Fig. 10) before videotaping. TOPCON Total Station (GM50) accuracy (1 mm) The target points' 3D ground coordinates were measured before and after loading. Video measurement determined the target points' 3D positions. Thus, the two cameras recorded six videos of the thing. The video camera's detection is tested. Load-induced deflection of three similar reinforced concrete beams with varied mixture percentages The photos' stereo recordings were uploaded from both cameras before and after the application was installed to the PC for processing. Virtual Dub converted stereo. Videos for every situation in stereo frames. Optical synchronisation of stereo frames from left and right cameras allows PMS software to calculate target point 3D coordinates. Installed encrypted targets (fixed objects) were control points. 12 checkpoints (CPs) were established to provide data tracking and calculating coordinates for targets on steel frames and concrete beams under stresses.. Ensure the 3D coordinates are precise and free of artefacts.

Figure 8. Shows the distribution targets on the test device.

3.Results and Discussion

Accuracy Assessment Result

Important (error-free) 3D coordinates of target sites as measured using a total station were considered in section 6. The device used PMS to determine the 3D spatial placement of target points attached to the steel frame using stereo video images. The 3D spatial location of target points (PMS) findings were measured by the total station, as shown in Table 2.

Table 2. 3D GCP coordinates of fixed-on-a-steel-frame targets, measured, computed, and residuals.

No.

Observed (m) (Total Station)

Computed coordinates (with photo modeller) (m)

Differences between coordinates (m)

x

y

z

x

y

z

vx

vy

vz

1

104.6454

101.9679

30.9364

104.6414

101.9628

30.936

0.004

0.005

0.004

2

104.4009

102.2072

30.9474

104.4059

102.2134

30.9486

–0.005

–0.006

–0.001

3

104.1327

102.4848

30.9436

104.1355

102.4876

30.9416

–0.002

–0.002

0.002

4

103.8176

102.8082

30.9429

103.8189

102.8052

30.9427

–0.001

0.003

0.002

5

103.6078

103.0228

30.9389

103.6028

103.0178

30.9387

0.005

–0.005

–0.004

6

102.9734

103.6647

30.9374

102.9722

103.6632

30.9376

0.001

0.001

–0.002

7

102.7611

103.8751

30.9279

102.7639

103.8765

30.9268

–0.002

–0.001

0.001

8

102.4655

104.1763

30.9354

102.4645

104.175

30.9366

0.001

0.001

–0.001

9

102.2094

104.4314

30.9481

102.2078

104.4298

30.9473

0.002

0.002

–0.002

10

101.9559

104.689

30.9273

101.9492

104.6855

30.9275

–0.006

0.003

–0.002

11

101.7376

104.9028

31.0787

101.7361

104.9031

31.0747

0.001

–0.003

0.004

12

103.3112

103.3678

32.0807

103.3117

103.3648

32.0787

–0.005

0.003

0.003

RMSE

0.00313

0.00321

0.00258

Concrete Beam Deflection Results According to Applying Load

Three experiments were performed for each type of reinforced concrete beam of 3.2 m length utilizing a video imaging technology system to record two clips. 11 points for each type of concrete beam were determined using the four loading case weights. Tables following exhibit the length law in Equation (3) used to compute the lengths between every two coordinates of the same object point of no-load situation. According to load, these distances are concrete beam deviation values. At beam number one, the deviation value was high, notably in the bearing zone, as illustrated in Tables 3 and 4 and in Fig. 8. The concrete beam's natural high deflection, especially in the loading area, makes the video measurement system reliable for precise applications. Fig. 9 shows that the gradient in the deflection value of the second and third beams, which have significant resistance, decreases with concrete beam stiffness, verifying these readings. According to Table 5, the video imaging technology system's accuracy lies in sensing deflection values detected for small values (millimetres) and not in loading areas. Figs. 10–12 depict Tables 6 to 12.

                                             (3)

Table 3. The three-dimensional coordinates of the targets that were installed on the first concrete beam were measured before and after loading 300 kg.

Point

Before loading (Zero Load)

After loading (300 Kg)

Deflection (m)

X₀ (m)

Y₀ (m)

Z₀ (m)

Xᴀ (m)

Yᴀ (m)

Zᴀ (m)

1

104.3971

102.3046

31.52695

104.3951

102.2966

31.51895

0.008

2

104.19

102.5238

31.52496

104.185

102.5168

31.51596

0.009

3

103.9855

102.7428

31.52421

103.9765

102.7358

31.51321

0.011

4

103.7807

102.9602

31.52325

103.7717

102.9522

31.51125

0.012

5

103.5734

103.1759

31.52564

103.5634

103.1669

31.51264

0.013

6

103.3636

103.3947

31.5255

103.3506

103.3867

31.5105

0.015

7

103.1502

103.6098

31.52291

103.1402

103.6008

31.50991

0.013

8

102.9399

103.82

31.52311

102.9309

103.812

31.51111

0.012

9

102.7266

104.0337

31.52465

102.7186

104.0277

31.51465

0.01

10

102.5201

104.2485

31.52768

102.5151

104.2415

31.51868

0.009

11

102.3093

104.4604

31.51998

102.3073

104.4524

31.51198

0.008

Table 4. The three-dimensional coordinates of the targets that were installed on the first concrete beam were measured before and after loading 600 kg.

Point

Before loading (Zero Load)

After loading (600 Kg)

Deflection (m)

X₀ (m)

Y₀ (m)

Z₀ (m)

Xᴀ (m)

Yᴀ (m)

Zᴀ (m)

1

104.3971

102.3046

31.52695

104.3831

102.2956

31.50995

0.017

2

104.19

102.5238

31.52496

104.173

102.5148

31.50596

0.019

3

103.9855

102.7428

31.52421

103.9655

102.7358

31.50321

0.021

4

103.7807

102.9602

31.52325

103.7587

102.9532

31.50025

0.023

5

103.5734

103.1759

31.52564

103.5504

103.1689

31.50164

0.024

6

103.3636

103.3947

31.5255

103.3396

103.3867

31.5005

0.025

7

103.1502

103.6098

31.52291

103.1282

103.6018

31.49991

0.023

8

102.9399

103.82

31.52311

102.9189

103.813

31.50111

0.022

9

102.7266

104.0337

31.52465

102.7066

104.0297

31.50465

0.02

10

102.5201

104.2485

31.52768

102.5031

104.2395

31.50868

0.019

11

102.3093

104.4604

31.51998

102.2953

104.4514

31.50298

0.017

Table 5. The three-dimensional coordinates of the targets that were installed on the first concrete beam were measured before and after loading 900 kg.

Point

Before loading (Zero Load)

After loading (900 Kg)

Deflection (m)

X₀ (m)

Y₀ (m)

Z₀ (m)

Xᴀ (m)

Yᴀ (m)

Zᴀ (m)

1

104.3971

102.3046

31.52695

104.3761

102.2876

31.49995

0.027

2

104.19

102.5238

31.52496

104.174

102.5008

31.49696

0.028

3

103.9855

102.7428

31.52421

103.9635

102.7218

31.49421

0.03

4

103.7807

102.9602

31.52325

103.7567

102.9392

31.49125

0.032

5

103.5734

103.1759

31.52564

103.5454

103.1559

31.49164

0.034

6

103.3636

103.3947

31.5255

103.3346

103.3727

31.4895

0.036

7

103.1502

103.6098

31.52291

103.1292

103.5838

31.48991

0.033

8

102.9399

103.82

31.52311

102.9169

103.799

31.49211

0.031

9

102.7266

104.0337

31.52465

102.7036

104.0127

31.49365

0.031

10

102.5201

104.2485

31.52768

102.5001

104.2275

31.49868

0.029

11

102.3093

104.4604

31.51998

102.2883

104.4434

31.49298

0.027

Figure 9. Beam1 deflection under 300, 600, and 900 kg vertical load.

Table 6. The three-dimensional coordinates of the targets that were installed on the second concrete beam were measured before and after loading 300 kg.

Point

Before loading (Zero Load)

After loading (300 kg)

Deflection (m)

X₀ (m)

Y₀ (m)

Z₀ (m)

Xᴀ (m)

Yᴀ (m)

Zᴀ (m)

1

104.3973

102.3037

31.527

104.3953

102.2977

31.521

0.006

2

104.191

102.5241

31.5238

104.189

102.5161

31.5158

0.008

3

103.9853

102.7429

31.5232

103.9802

102.7359

31.5142

0.009

4

103.7827

102.9622

31.5228

103.7747

102.9562

31.5128

0.01

5

103.5721

103.1734

31.5263

103.5630

103.1664

31.5153

0.011

6

103.363

103.3924

31.5237

103.3520

103.3834

31.5107

0.013

7

103.153

103.6116