###### Abstract  
Cables have been increasingly utilized in modern long-span or tied-arch bridges as the main bearing structures. Real-time identification of time-varying cable tension is essential for assessing the service performance of bridges. Vibration-based methods have been an increasing research focus in recent decades. However, a long time interval is needed to estimate structural frequency using vibration-based methods, increasing the calculating time of cable tension. The time-varying cable tension is thus difficult to extract. This study proposes a time-frequency reassignment-based algorithm to reduce the detection time to address this issue. Combined with a time-frequency analysis tool and vibration theory of cables, the algorithm can identify the time-varying frequency and further quickly calculate the time-varying cable tension within 12.8 s. The features of the proposed algorithm are mainly threefold: identifying the time-varying frequencies with high precision; without some prior knowledge of vibration; having no other requirements for sensor modes. Moreover, the experimental validation is conducted using a quasi-static loading in a workshop and a dynamic field test on Sutong Bridge, respectively. The results show that the proposed algorithm can be used to identify time-varying tension and assess the service performance of cables, providing a new path for real-time condition monitoring of bridges in service. cable tension; dynamic responses; time-frequency reassignment; field experiment; structural health monitoring +
Footnote †: journal: Medical Imaging and Biomedicine  
to identify the cable tension, including the load cell method [15], fiber Bragg grating method [16; 17], elasto-magnetic method [18], elasto-magneto-electric method [19], and vibration-based method. The load cell and fiber Bragg grating method need to be pre-installed and calibrated during the construction stage and can online measure the tension with high precision. However, the reliability will gradually decrease over time due to sensor debonding or biological bite damage. The elasto-magnetic method can be used to measure the tension and detect the broken wire damage of cables. However, the test equipment is relatively expensive, and the method is time-consuming during the excitation process. The elasto-magneto-electric method is an emerging method with significant advantages in identifying cable tension, but it has high requirements for measurement conditions (e.g., stationary temperature and humidity). Among the above evaluation methods, vibration-based methods have been proven as cost-effective in tension identification due to the advantages of explicit mechanical formulation, facilitation in acquiring dynamic response, and abundant application cases [20; 21; 22]. The foundation of this method is according to vibration theory which represents the physical relationship between tension and vibration frequency [23; 24; 25; 26; 27]. Many studies clarify this relationship in various models by considering the effect of sag, inclination, or bending stiffness [27; 28; 29]. In particular, structural frequencies can be identified by the measured dynamic responses such as acceleration. Afterward, the cable tension can be indirectly calculated using structural frequencies based on the mechanical models. Generally, the vibration-based method requires a sampling interval for frequency identification via some time-frequency analysis tools such as the Fourier transform (FT). The cable tension is supposed to be a constant during this time interval. However, in practical engineering, cable tension is associated with the variation of loads and thus is a time-varying parameter under different operating conditions. The time-varying cable tension is an important indication and thus is the main concern of bridge management departments. Therefore, to reflect the time-varying tension, the measurement interval for frequency identification should be made as soon as possible, i.e., the time-varying instantaneous frequency of structures is necessary.