Experimental data based cable tension identification via nonlinear static inverse problem

This work proposes a new cable tension identification technique based on a static inverse method that, by coupling a universal cable model with displacement and strain sensors data, exploits the differences between the original cable equilibrium problem and that of the cable loaded by a suitable added mass. The formulated inverse problem thus defines a data misfit functional based on the differences in terms of transverse displacements and elongations between the two equilibrium configurations. The inverse problem is implemented in a two-step identification procedure. First, the axial stiffness and mass per unit length are kept constant and the length of the cable is approximately found via a simple line search algorithm using finite differences to estimate the functional derivatives. Second, the other physical parameters are assessed using an adjoint method for which the direct problem, the adjoint problem and the parameters sensitivities are found as derivatives of a Lagrangian functional with respect to dual variables, primary variables, and parameters, respectively. Due to the ill-conditioning nature of the problem, the proposed method does not allow an exact parameter identification but it does lead to an acceptable tension assessment. An experimental test campaign conducted on a multilayered stranded cable 21 m long and 22 mm in diameter subject to several tension levels confirms the relevance and operational feasibility of the proposed inverse method.