A two-step methodology for cable force identification

Vibration-based force identification of cables has been studied for several decades. Most of this work relies on the natural frequencies of the cable for an estimation of the cable force. However, these natural frequencies are also affected by bending stiffness, sag effect and boundary conditions. In the present work, a two-step methodology is developed that allows taking into consideration these effects in the force identification. First, a segment of the cable is considered which is sufficiently short for the sag effect to be negligible. The axial force in this segment is estimated by fitting the measured response to the analytical solution for the transverse motion of the cable in the frequency domain. In this procedure, the bending stiffness is updated exploiting the fact that the estimated axial force should not depend on the frequency, while the boundary conditions do not need to be known. Next, an analytical solution of the static state of the entire cable is derived, taking into account the sag effect, bending stiffness and boundary conditions. The parameters of the entire cable model can then be updated, using the estimated value of the axis force at the location of the segment. Finally, the updated analytical model of the entire cable allows evaluating internal forces such as the cable force and bending moment, as required for estimating the stresses in the cable considering bending deformation. The feasibility of the proposed methodology is verified by means of numerical simulations considering measurement noise and an inaccurate initial guess of the bending stiffness, proving its potential for the health monitoring of cable structures.