Frequency-Based Cable Tension Identification Using a Nonlinear Model with Complex Boundary Constraints

Abstract

Accurate estimation of the cable force affects the bridges’ long-term integrity and serviceability directly. The frequency method is often used for cable tension testing in bridge engineering. However, the generally used cable tension calculation formulae are based on “ideal hinge” or “ideal fixed” boundary conditions. The inclination, bending stiffness, and sag-extensibility of the cable are not properly considered, which results in non-negligible errors. A frequency-based method for precisely determining the tensile force of a cable with unknown rotational and support constraint stiffnesses at the boundary was proposed. A nonlinear mathematical model of the vibration of the cable was established. In addition to parameters such as inclination, sag, and bending stiffness, the effects of unknown rotational and support constraint stiffnesses at both ends of the cable were also considered. The finite difference method was employed to discretize and solve the mode equation of the cable vibration. A frequency-based sensitivity-updating algorithm was applied that can identify simultaneously several system parameters using multiorder measured natural frequencies. Calculation of the matrix eigenvalue derivatives was the key to obtaining the system sensitivity matrix. Numerical examples indicated that the algorithm can be used efficiently and precisely to identify multiple system parameters of the cable, including its tension, bending stiffness, and boundary constraint stiffnesses.