A Target-Less Vision-Based Displacement Sensor Based on Image Convex Hull Optimization for Measuring the Dynamic Response of Building Structures

Abstract

Existing vision-based displacement sensors (VDSs) extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called "TVDS") is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS). The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image.

Keywords: dynamic characteristics; image convex hull; non-marker; scaling factor map; vision-based displacement sensor.

Figure 1

Displacement data acquisition diagram using the target-less vision-based displacement sensor.

Figure 2

(a) Examples of the image convex hull; (b) Displacement extraction algorithm of the proposed TVDS.

Figure 3

Relationship between the image plane and the physical plane. (a) 3D view; (b) Plane view.

Figure 4

Scaling factor map according to the distance, angle, and focal length. (a) Distance = 930 mm, angle = 0, focal length = 45 mm; (b) Distance = 930 mm, angle = 60°, focal length = 45 mm.

Figure 5

Scaling factor map validation test using a 50-mm-diameter marker plate and a commercial camera.

Figure 6

Comparison of the scaling factors calculated by the marker and the scaling factor map, respectively.

Figure 7

Maximum scaling factor error between SF₁ and SF₂ in accordance with the distance and the angle.

Figure 8

Dimensions of the scaled model and experimental set-up of scaled model white noise excitation test using shake table (unit: mm).

Figure 9

50 Hz-bandwidth white noise. (a) Time domain acceleration data; (b) Frequency domain representation data.

Figure 10

Comparison of dynamic displacement data between VDS and LDS according to the floor level. (a) 1st floor; (b) detail comparison of the 1st floor; (c) 2nd floor; (d) 3rd floor; (e) peak displacement error.

Figure 11

Comparison of natural frequencies obtained from the TVDS and LDS according to the floor level. (a) 1st floor; (b) 2nd floor; (c) 3rd floor.

Figure 12

Comparison of the analytical and experimental mode shapes of the scaled model.