Accurate and fast identification of time-varying tension in bridge cables via variational nonlinear chirp mode extraction

In cable-stayed bridges, cables are susceptible to fatigue damage due to cyclic traffic loads. The accurate monitoring of cable tension is critical in assessing fatigue damage and ensuring the service performance of cables. The vibration method establishes a formula between the cable tension and its vibration frequency. Therefore, the main challenge in identifying the time-varying cable tension is to determine the instantaneous frequencies (IFs) of the cable. Variational nonlinear chirp mode decomposition (VNCMD) exhibits promising advantages in identifying IFs from measured vibration signals, owing to its robustness against noise interference. However, hyperparameter selection significantly affects the IF identification accuracy of VNCMD, limiting its applicability. In this study, an improved VNCMD, termed variational nonlinear chirp mode extraction (VNCME), is proposed to address this limitation and is used to identify the time-varying cable tension. First, VNCME constructs a novel algorithm framework by modifying the optimisation function of VNCMD, eliminating the need for hyperparameter presetting and enabling the identification of a specific-order IF for the cable. The identified IF is then incorporated into the formula of the vibration method to calculate the time-varying cable tension. Examples of nonstationary signals of a sinusoidal function, finite element model of a cable, and laboratory experiments of scaled cables are used to illustrate the advantages of the proposed method, which proves to be successful in time-varying cable tension identification. In addition, the proposed method is implemented on an actual highway cable-stayed bridge to identify the time-varying cable tension over a 24-h duration. The results demonstrate that the proposed method is practical and reliable, providing a new path for the real-time monitoring of cable tension.