Bayesian Identification of the Axial Forces, the Bending Stiffnesses, and the Connecting Point in Crossed Cables

In this paper, an asymptotic expression is derived for the natural frequencies of two interconnected cables with small but non-negligible bending stiffness. This simple analytical formulation serves as a starting point for solving the inverse problem. First, it ensures that it is possible to univocally identify five parameters: the axial force and the bending stiffness in each of the two cables, as well as the position of the crossing point. A Bayesian framework based on the Metropolis-Hasting sampling algorithm is then used to calculate the most probable values and posterior distributions of these five parameters. The methodology is finally verified on a lab experimental setup, and applied to vibration data collected on an actual bridge.