Cable tension force estimate using novel noncontact vision-based sensor
Introduction
Cables are generally designed to efficiently carry axial loads for cable-supported structures. Typical examples include stay cables in cable-stayed bridges, vertical hanger cables in suspension bridges and cables in tower mast and large-span roof structures. The accurate determination of cable tension force is of great importance for both construction control and overall structural condition assessment during its service life.
Currently, there are three primary techniques for estimating cable tension forces: direct measurement by devices such as hydraulic jacks and load cells, the magnetic method based on the magnetic permeability measurement, and the vibration method. Due to its easy operation, the vibration method is more widely employed in practical applications [1]. The vibration method is based on the relationship between cable natural frequencies and cable tension force. Conventionally, accelerometers are mounted on the cable surface to accurately obtain cable frequencies. Additionally, sensors need to be wired to external devices. This is generally expensive implement on structures with a large number of cables due to the cumbersome and time-consuming installation of contact-type sensors and the data acquisition system. To overcome these shortcomings, recent advances in sensor technology has enabled more efficient vibration measurement. For example, wireless sensors greatly improve monitoring efficiency, and the ubiquitous smartphone has provided a portable and low-cost sensor network for monitoring structural dynamic characteristics [2]. However, these contact-type sensors still require physical access to structures in order to be installed on the cable surface, which is often difficult or even impossible. Hence, noncontact sensor systems have been developed and applied for the measurement of cable vibrations, such as microwave remote sensing [3], digital image processing [4] and laser Doppler technology [5], [6].
As an emerging technique, noncontact vision-based sensors, which extract object vibrations from video images, have attracted significant research interest in that they offer a promising alternative to the conventional contact-type sensors [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30]. The real-time vision sensor system usually consists of a video camera, a zoom lens and a laptop computer installed with a developed image processing software package that can track either high-contrast artificial targets or low-contrast natural targets on a structural surface. Significant advantages of the vision sensor include its low cost, ease of operation and noncontact and multi-point vibration measurements from a single camera. On the other hand, the developed image processing software can also be used for post-processing the recorded video files. In this way, only a consumer-grade commercial video camera and tripod are needed to take videos during outdoor field tests. While most existing studies on vision sensors focus on the time-domain performance evaluation, recent efforts have been made to investigate the feasibility of utilizing displacement measurement by vision sensors for structural health monitoring (SHM), such as finite element model updating [17], structural modal analysis [31], [32], [33], [34], [35], [36] and damage detection [10], [37], [38]. For example, Yoon et al. carried out laboratory vibration experiments on a scaled frame structure. Modal parameters were identified and compared with those by the conventional accelerometer-based method, which show good agreements [36]. Only a few attempts have been made to apply vision-based sensors for cable force estimates [4], [9], [39]. For example, Ji and Chang [9] and Kim et al. [4] employed respectively the optical flow and normalized cross correlation temptation methods for cable vibration measurement and cable force estimates. In realistic field tests, various ill environmental conditions are often encountered, such as background disturbance, illumination fluctuation, long distance away from structure, etc. Therefore, there is a need to thoroughly investigate the capabilities and limitations of noncontact vision sensors for field applications, by employing different template matching as well as subpixel algorithms.
In this study, the adopted vision-based sensor system, enabled by the robust subpixel orientation code matching (OCM) algorithm, was previously developed by the authors [31]. One major contribution of this study is to demonstrate how the emerging vision-based sensor can be used as a more convenient and cost-effective alternative for monitoring structures, herein, for estimating cable tension forces. This paper is organized as follows. Section 2 presents the measurement procedure for cable tension forces based on the vibration method using a vision-based sensor. In order to validate the accuracy of the vision sensor for frequency measurement, laboratory tests on a simply supported beam model is conducted in Section 3. Section 4 introduces the cable force measurement for the cable-supported roof structure of the Hard Rock Stadium and the test setup. Section 5 presents and discusses the cable force measurement results, and Section 6 concludes this study.
Section snippets
Vibration method for cable tension estimate
The vibration method is based on the relationship between cable natural frequencies and cable tension forces. Among the equations for cable tension measurement, formulations from the taut string theory and beam theory are widely used. The string theory simplifies the analysis and can be expressed as:where T is the cable tension force, fn is the n-th measured natural frequency, m is the mass density per unit length, l is the cable length. Eq. (1) ignores the sag and bending stiffness
Laboratory validation of the frequency measurement accuracy
In order to validate the accuracy of the vision sensor for frequency measurement, a laboratory test on a simply supported beam model is firstly conducted, as shown in Fig. 2. The red dot area in Fig. 2 is selected as the template for motion tracking by the vision sensor. During the measurement, video images captured by the camera are digitized into 1280 × 240 pixel images in 8-bit grayscale and streamed into the computer through an USB 3.0 cable with a sampling rate of 50 frames per second. As a
Application description
During the construction of cable-supported structures, various measurements, such as elevation, deformation and structural stress, should be performed to ensure erection safety and quality. Among them, the cable tension force is one of the most important indices as it reflects the overall structural mechanical performance. Conventionally, design cable forces can be predicted by erection simulation analysis. Due to uncertainties in geometric and material properties as well as boundary conditions
Test results and discussions
The approximately mid-span cable segments framed by red squares in Fig. 7 are registered as templates for motion tracking. It is observed that the tie down cables can only be weakly vibrated by natural excitations, due to the fact that these relatively shorter cables are very stiff. Therefore, these cables are measured after they have been shaken for a few seconds.
Table 2, Table 3 tabulate the measured 1st natural frequencies for all the tie down cables at the four quads. The cable tension
Conclusions
This study proposed a novel and innovative procedure for measuring cable tension forces using noncontact vision-based sensor technologies. The accuracy of the vision sensor for frequency measurement is initially confirmed by comparison with the accelerometer through the laboratory test of a simply supported beam. Then the proposed method is applied to estimate the cable forces of the cable-supported roof structure of the Hard Rock Stadium. A series of field tests are carried out during
Acknowledgement
Special thanks go to Raymond Daddazio, Mark Tamaro and Michael DeLashmit at Thornton Tomasetti and Bill Senn at the Miami Dolphins organization for their assistance with planning field tests of the Hard Rock Stadium. The authors would also like to acknowledge the anonymous reviewers for their constructive comments which helped in improving the quality of this paper.
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Former Ph.D. student at Columbia University, USA.