# Research on Non-Contact and Non-Fixed Cable Force Measurement Based on Smartphone
###### Abstract  
Stay cable is the major load-carrying element in cable-stayed bridges. The process of monitoring cable forces would be beneficial to ensure the safety of bridges. The conventional sensor-based approaches to measure stay cable forces is complicated in operation, time-consuming and relatively expensive. In order to confront these disadvantages, a lightweight measurement method using smartphone imagery was proposed in this paper. The video data acquisition process was first standardized by using a pre-designed target. Then, a novel algorithm to extract the vibration displacement of stay cables under complex condition was developed. An automatic correction algorithm was provided to further improve the displacement results. On top of that, a smartphone-based software for determining cable forces was developed and tested on a real-life bridge. The results showed a maximum error of 1.99% compared with the cable force obtained by using a dynamic tester. The developed software is proven to be feasible in real-life projects and can achieve high accuracy in cable force determination. At the same time, the proposed method does not require a fixed camera for measurement and is not limited by personnel experience and measurement time, facilitating real-time monitoring of multiple projects, multiple cable surfaces and multiple personnel in a visual vibration environment. cable force measurement; image processing; target recognition; smartphone images +
Footnote †: journal: Medical  
responses (i.e., natural frequencies and mode shapes) by retrieving the spatio-temporal displacements out of the two image sequences. Using a single camcorder, [PERSON] et al. [13] developed a videogrammetric approach to measure dynamic parameters of stay cables using no artificial targets and verified its advantages on a real bridge. Similarly, [PERSON] and [PERSON] [14] adopted optical flow methods to eliminate the need for target installation in the proposed image-based technique for cable vibration measurement. Based on the identified dynamic properties, stay cable forces can be further determined. [PERSON] et al. [15] used two methods, i.e., digital image processing (DIP) and digital image correlation (DIC), to first identify modal frequencies and then to determine the cable force at a single point and multiple points. The identified frequencies and cable tensile forces were compared with sensor-based frequency measurement and numerical analysis results separately. Acceptable deviations on cable tensions, i.e., 1.09% for single-point and 3.05% for multi-point measurement, proved the reliability of the proposed methods. The DIC technique was also used to extract temporal displacements of cables in [16], where the cable force estimation was achieved based on cable mode shapes. In order to extend the applicability of image-based measurement systems for long-term monitoring of cable forces, a set of consecutive studies [17; 18] focused on the development of a vision-based monitoring system, which was installed on a real-life cable-stayed bridge and tested under various weather conditions in order to validate its applicability. The vision-based monitoring system achieved satisfactory accuracy, with an error rate of \(\pm\)1% for modal frequency identification and a maximum error of \(\pm\)5% for cable force determination. [PERSON] et al. [19] used a fixed industrial camera to estimate the cable force and tested on a cable-supported roof structure of a stadium under renovations. After close monitoring of the ever-changing cable forces, it was found the maximum deviation between estimations and the \"ground truth\" was 5.6%. Other than fixed cameras, the use of mobile reality capture devices would be beneficial in practice. [PERSON] et al. [20] used an unmanned aerial vehicle (UAV)-based camera to obtain vibration images of cables for frequency retrieval.