###### Abstract
To approach this purpose, many existing studies have been focused on identifying the time-varying instantaneous frequency of cables, including the extended Kalman filter [30], complexity pursuit [31], adaptive sparse time-frequency analysis [32], an extended analytical mode decomposition-Hilbert transform-zoom synchrosqueezing wavelet transform combined method [33], conjugate-pair decomposition [34], and variational mode decomposition [35]. In particular, the extended Kalman filter-based method is firstly proposed to address the key problem of time-varying tension identification in the research field. The effectiveness of the method is verified by both numerical examples and experimental verification in the laboratory. Then, the complexity pursuit algorithm can also identify the time-varying tension with high accuracy but requires at least two acceleration sensors to implement the process of independent component analysis. Next, the adaptive sparse time-frequency analysis is used to identify the time-varying tension, yet the initial phase of vibration should be determined before time-frequency analysis. Moreover, the mentioned combined method can identify the time-varying first order frequency and further calculate the tension with excellent results, although the algorithm has a complex identification process in dealing with a narrowband signal. In addition, the effectiveness of the conjugate-pair decomposition is proved by the numerical examples, but still needs further experimental verification in the future. Finally, the variational mode decomposition can extract the instantaneous change of cable tension with acceptable results. However, the number of decomposition layers is an artificial setting parameter that impacts the identification results. The time-varying instantaneous tension is well identified using the above methods with both numerical and experimental verification. However, these methods are only applied in the laboratory and lack a field experiment verification in practical engineering. Meanwhile, the identified time-varying tension is not used to evaluate the operating conditions of cables in bridge engineering. Therefore, it is essential to develop a method to real-time identify the cable tension and assess the service performance of cables in practical bridge engineering. This study proposes a time-frequency reassignment (TFR)-based algorithm for identifying time-varying cable tension. The proposed algorithm, combined with a time-frequency analysis tool and the vibration theory of cables, can identify the time-varying instantaneous frequency and further calculate the time-varying cable tension with satisfactory results. Compared with existing methods, this work is a different attempt, especially focusing on the applicability of the algorithms to practical engineering. The main innovation of the proposed algorithm lies in three parts: (a) the reassignment operator can give the algorithm the ability to identify the time-varying frequencies with high precision; (b) the algorithm is developed without some prior knowledge of vibration; (c) the application of the algorithm is verified using concrete engineering tests and have no other requirements on sensor modes. One accelerometer is enough for the implementation of the proposed algorithm. The rest of the paper is organized as follows: Section 2 briefly introduces the basic theory and features of TFR. Section 3 formulates an identification algorithm with a concrete implementation process. Section 4 experimentally demonstrates the algorithm through a large-scale cable with loading and unloading tests in a workshop. Section 5 further investigates the proposed algorithm for practical bridge engineering using an in situ field experiment. The service performance of the measured cable is also evaluated using the identified time-varying tension. Section 6 presents the conclusions of this study.