# Research on Non-Contact and Non-Fixed Cable Force Measurement Based on Smartphone
## 3 Experiment and Validation
### Shuidongwan Bridge in Guangdong, China
#### 3.1.2 Validation of the Proposed Method  
The vibration video data of the chosen cables under seven different working conditions was obtained. The seven working conditions are specified in Table 4, regarding various lighting conditions, video resolutions, frame rates and durations. By following the image processing procedures in Section 2.2, cable displacements were first identified and tracked. Spectrum analyses were then conducted on top of the displacement-time history, and the results are presented in Figure 14. Cable forces were estimated based on the dynamic responses, i.e., peak frequencies and the corresponding orders of frequency. Errors of frequencies, i.e., \(E_{F}\), were calculated by comparing the estimations and on-site measurement, based on which the cable force errors, i.e., \(E_{T}\), were generated. The following equations, i.e., Equations (9) and (10), can be used.  
\[E_{F}=\frac{\left|F_{img}-F_{sensor}\right|}{F_{sensor}}\times 100\% \tag{9}\]  
\[E_{T}=\frac{\left|T_{img}-T_{sensor}\right|}{T_{sensor}}\times 100\% \tag{10}\]  
Figure 13: Results of the sensor-based dynamic measuring: (**a**) Cable 18#, (**b**) Cable 20# and (**c**) Cable 21#.  
It is noted that \(F_{img}\) and \(T_{img}\) represent the frequency and cable force obtained by using the proposed smartphone-based method, while \(F_{sensor}\) and \(T_{sensor}\) represent the the frequency and cable force measured by sensors, respectively.  
Figure 14: Spectrum analysis under seven on-site working conditions. (**a**) Working condition 1. (**b**) Working condition 2. (**c**) Working condition 3. (**d**) Working condition 4. (**e**) Working condition 5. (**f**) Working condition 6. (**g**) Working condition 7.  
The measurements and accuracy comparison under seven working conditions are summarized in Table 4. It can be inferred from Figure 14 that due to the influence of hardware equipment, shaking noise, lighting conditions, etc., the recognized dynamic responses of stay cables based on the smart terminal was of a third-order vibration frequency. Low-order and high-order vibration frequencies were not obvious, but this does not mean that the low-order or high-order vibration frequency cannot be identified under other working conditions. The successful identification of frequencies in other orders is related to factors such as the cable status, the vibration reduction measures and the external environment while sampling. As for the accuracy of the proposed smartphone-based method, it was observed that the light-weight method achieved a maximum error of 0.99% for frequency identification and a maximum error of 1.99% for cable force estimation, which can meet the requirements in practical applications and have improved the methods proposed in previous studies (as summarized in Table 1).  
Based on the experiment results, discussion will be illustrated in the following three aspects. Firstly, the reliability and accuracy of the proposed smartphone-based method has been verified given the fact that the maximum error of cable force estimation and the traditional dynamic measurement is 1.99% and the average error is 0.85%. Secondly, since the third-order vibration frequency is in the range of 2.332 Hz\(\sim\)2.625 Hz, a frame rate of 24 FPS can meet the requirements for video data collection. However, if the vibration frequency is higher or higher-order vibration frequencies need to be identified, the sampling frame rate needs to be increased accordingly. Thirdly, increasing sampling duration can improve sampling accuracy. However, an increase in the video resolution, sampling frame rate and sampling time can result in an increase in the time for data processing.