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High-speed CMOS camera is a new kind of transducer to make the videogrammetric measurement for monitoring the displacement of high-speed shaking table structure. The purpose of this paper is to validate the three-dimensional coordinate accuracy of the shaking table structure acquired from the presented high-speed videogrammetric measuring system. In the paper, all of the key intermediate links are discussed, including the high-speed CMOS videogrammetric measurement system, the layout of the control network, the elliptical target detection, and the accuracy validation of final 3D spatial results. Through the accuracy analysis, the submillimeter accuracy can be made for the final the three-dimensional spatial coordinates which certify that the proposed high-speed videogrammetric technique is a better alternative technique which can replace the traditional transducer technique for monitoring the dynamic response for the shaking table structure.

In the field of civil engineer, under the simulation environment, the dynamic response of many structures needs to be tested to further verify the seismic performance to reduce disaster losses and maintain social stability before their application in practice, and one of the most frequently used experimental platforms is earthquake shaking table which is a device for shaking structural models or building components with a simulated seismic wave [

Another potential technique for making the target tracking is videogrammetry, which has been widely used in the medical, automotive, and astronautical fields dating from the 1970s [

The rest of the paper is organized as follows. Section

For the high-speed videogrammetric measurement, the high-speed videogrammetric measurement system plays the most important role which is the foundation of the videogrammetry. Generally, the high-speed videogrammetric measurement consists of high-speed CMOS cameras, host computers, a synchronous controller, and the capturing cards as shown in Figure

The configuration of high-speed videogrammetric measurement system.

To implement a completed videogrammetric measurement for the shaking table structure, five key links need to be done, including the camera calibration, the camera synchronization, the layout of the control points, the target detection and tracking, and the calculation of the 3D spatial coordinates of tracking points, containing many factors that will influence the accuracy of final results. In this section, we will make an analysis for the above key links of high-speed videogrammetric measurement, further, to validate the corresponding accuracy.

The purpose of camera calibration is to determine the interior orientation parameters and the distortion parameters for the accurate calculation of the 3D spatial coordinates of the tracking target coordinates. Because the interior orientation parameters and the distortion parameters of a camera change in different temperature and humidity, thus, the camera needs to be calibrated timely before or after the experiment. Two- dimensional camera self-calibration is a good selection which is a mathematically rigorous approach for calibrating high-precision stages and uses the stage to calibrate itself which offers many advantages including the possibility of standardizing measurements of accuracy. During the process of camera calibration, a system of equations is obtained which include the parameters of interior orientation of a camera and distortion parameters of a lens as unknowns [

Imaging model of videogrammetric measurement.

The parameters of the interior orientation of a camera define the spatial position of the perspective centre, the principal distance, and the location of the principal point, and the distortion parameters include radial and tangential distortion which is the deviation from the principle of central perspective, which can be described by the coplanarity condition equation:

Radial distortion is the major imaging error parameter for the most camera systems. The radial distortion is usually modeled with polynomial series with distortion parameters

Tangential distortion is mainly caused by decentering and misalignment of the lens, whose effect is smaller relative to the radial distortion. Tangential lens distortion is considered only for the high-precision measurement, such as the videogrammetric measurement for shaking table structure in the paper. Tangential distortion can be compensated by the following function:

In the paper, two kinds of high-speed CMOS cameras, named MC 1311 and CR1000, were calibrated with the method of two-dimensional self-calibration using PhotoModeler software. The results show that standard deviation of focal length ^{−5} mm, and the standard deviation of two coefficients ^{−5} mm.

The purpose of camera synchronous controller is to guarantee the camera synchronization. Generally, the camera synchronous controller is controlled by a host computer, and once a synchronous signal is sent by the host computer, thousands of stereo images will be captured by the high-speed CMOS cameras. Ideally, each stereo image should be captured at the same time; thus, the better the camera synchronization is, the higher the accuracy of resulting 3D spatial coordinates of the tracking targets is. Therefore, the accuracy of camera synchronization will directly influence the accuracy of stereo videogrammetry. It is critical to validate the synchronization accuracy to control the influence of synchronization on the ultimate accuracy of the results. In the paper, an experiment of a frame rate of 100 fps was adopted to capture images for the two synchronous high-speed CMOS cameras, and the obtained stereo images from both cameras were selected as an example to validate the synchronization accuracy, and the results show that the accuracy of the camera synchronous controller between the two cameras reaches 3

Videogrammetry is a branch of photogrammetry, especially close range photogrammetry, and the layout of the control network will also influence the accuracy of final results. The purpose of the layout of control points is to calculate the elements of exterior orientation to further calculate the 3D spatial coordinates of tracking points. For the videogrammetry, the convergent photography was the best method to acquire images with higher accuracy [

For our videogrammetric measurement for shaking table structure, elliptical targets are adopted to monitor the dynamic response for the shaking table structure for its five degrees of freedom (DOF) comparing to the 2 DOFs for a line or point feature [

Circular target and the calculation of the elliptical target.

After obtaining the central pixel of all the tracking points, an integrated bundle algorithm is adopted to calculate the 3D spatial coordinate of all the tracking points [

Accuracy of the point coordinates obtained from the three-camera stereo videogrammetric system.

ID | Coordinates from the videogrammetric technique (m) | Coordinates from the electric total station (m) | Difference (mm) | ||||||
---|---|---|---|---|---|---|---|---|---|

| | | | | | | | | |

3 | 5.6082 | 6.9146 | 2.0294 | 5.6087 | 6.9140 | 2.029 | 0.5 | 0.6 | 0.5 |

7 | 4.8303 | 6.8226 | 1.1814 | 4.8301 | 6.8221 | 1.1821 | 0.4 | 0.5 | 0.6 |

8 | 5.1937 | 6.9139 | 0.7881 | 5.1932 | 6.9142 | 0.7884 | 0.5 | 0.3 | 0.3 |

11 | 4.5877 | 6.7308 | 0.3264 | 4.5871 | 6.7303 | 0.3261 | 0.3 | 0.5 | 0.4 |

RMS errors of coordinates | 0.43 | 0.49 | 0.49 |

Accuracy of the point coordinates obtained from the two-camera stereo videogrammetric system.

ID | Coordinates from the videogrammetric technique (m) | Coordinates from the electric total station (m) | Difference (mm) | ||||||
---|---|---|---|---|---|---|---|---|---|

| | | | | | | | | |

3 | 5.6080 | 6.9134 | 2.0295 | 5.6087 | 6.9140 | 2.029 | 0.7 | 0.6 | 0.5 |

7 | 4.8303 | 6.8224 | 1.1814 | 4.8301 | 6.8221 | 1.1821 | 0.4 | 0.5 | 0.7 |

8 | 5.1936 | 6.9140 | 0.7882 | 5.1932 | 6.9142 | 0.7884 | 0.4 | 0.2 | 0.5 |

11 | 4.5875 | 6.7310 | 0.3264 | 4.5871 | 6.7303 | 0.3261 | 0.4 | 0.7 | 0.3 |

RMS errors of coordinates | 0.49 | 0.53 | 0.52 |

High-speed videogrammetric measurement is a new noncontacted technique for monitoring the dynamic response. In the paper, we have made detailed analysis for the whole steps to validate the feasibility and accuracy. Through the accuracy analysis, a conclusion can be made that the submillimeter accuracy can be achieved, and all of the intermediate processes satisfy the requirement of videogrammetric measurement for the shaking table structure. Therefore, the proposed high-speed videogrammetric technique is a better alternative technique which can replace the traditional transducer technique for monitoring the dynamic response for the shaking table structure.

The authors declare that they have no conflicts of interest.

This work has been funded by the National Natural Science Foundation of China (Grant 41501494), the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions (Grant CIT&TCD201704053), and the Talent Program of Beijing University of Civil Engineering and Architecture.