For cable bridges, the cable tension force plays a crucial role in their construction, assessment and long-term
structural health monitoring. Cable tension forces vary in real time with the change of the moving vehicle
loads and environmental effects, and this continual variation in tension force may cause fatigue damage of a
cable. Traditional vibration-based cable tension force estimation methods can only obtain the time-averaged
cable tension force and not the instantaneous force. This paper proposes a new approach to identify the
time-varying cable tension forces of bridges based on an adaptive sparse time-frequency analysis method. This
is a recently developed method to estimate the instantaneous frequency by looking for the sparsest
time-frequency representation of the signal within the largest possible time-frequency dictionary (i.e. set of
expansion functions). In the proposed approach, first, the time-varying modal frequencies are identified from
acceleration measurements on the cable, then, the time-varying cable tension is obtained from the relation
between this force and the identified frequencies. By considering the integer ratios of the different modal
frequencies to the fundamental frequency of the cable, the proposed algorithm is further improved to increase
its robustness to measurement noise. A cable experiment is implemented to illustrate the validity of the
proposed method. For comparison, the Hilbert–Huang transform is also employed to identify the time-varying
frequencies, which are then used to calculate the time-varying cable-tension force. The results show that the
adaptive sparse time-frequency analysis method produces more accurate estimates of the time-varying cable
tension forces than the Hilbert–Huang transform method.