Real-Time Output-Only Identification of Time-Varying Cable Tension from Accelerations via Complexity Pursuit

In-service cables of structures, such as those in cable-supported buildings and cable bridges (e.g., stay cables and suspenders), suffer from cumulative fatigue damage caused by dynamic loads (e.g., the cyclic traffic loads on cable bridges) and wind excitation (on the cable-supported buildings and bridges). Monitoring the time history of time-varying cable tension for assessing their fatigue damage is thus essential to diagnose their health condition and predict their future performance. Currently, embedded measurement devices such as anchor load cells, elastomagnetic (EM) sensors, and optical fiber Bragg grating (OFBG) sensors are able to directly record the time-varying cable tension time history; however, poor durability, high costs, and intensive labor of installation significantly hinder their applicability in practice. On the other hand, a vibration-based technique manifests itself as a convenient, cost-effective, and reliable approach to determine the cable tension, and is widely used; it is based on an established formula (taut-string theory) between the cable tension and its frequency, which can be identified through the measured cable vibration responses. Existing research based on this approach, nevertheless, assume that the cable tension is time-invariant over a long time segment; real-time (online) identification of the time-varying cable tension has not yet been addressed. This paper develops a new computational framework to identify the time-varying cable tension time history through an unsupervised learning algorithm termed complexity pursuit (CP), which is capable of online tracking of the time-varying cable frequency, using as little information as the measured cable accelerations from only two accelerometers. The CP learning rule is especially exploited; it is found that CP can blindly separate the constituent modal responses of the cable even within a dramatically short duration such that the time-varying cable frequency can be identified, thereby computing the time-varying cable tension according to the taut-string theory. A hybrid example combining the simulated and real-measured data from an actual cable-stayed bridge and a laboratory experimental study of a scaled stay cable demonstrates that the proposed CP-based method performs accurate real-time identification of the time-varying cable tension. The proposed method is shown to be straightforward and efficient, with the potential to be an automated, economic, and convenient approach for health monitoring and assessing in situ or new cables of cable-supported structures.