Cable tension identification via nonlinear static inverse problem

A new identification technique is proposed to evaluate the tension of a cable using a static inverse approach that couples a universal cable model with displacement sensors, strain gauges and added masses that should preserve operational affordability. An inverse problem is formulated as the minimization of a data misfit functional based on the differences in terms of vertical displacements and axial strains between two equilibrium configurations of the cable, namely, one loaded and the other free. The inverse problem formulation echoes the parametric study of a non-conventional functional suggesting a way to identify the cable parameters, namely, its length, its axial stiffness, and its mass per unit length. The computational resolution of the inverse problem is implemented as 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 parameter sensitivities are defined as derivatives of a Lagrangian functional with respect to dual variables, primal variables, and parameters, respectively. Due to the ill-conditioning of the problem, the proposed method does not enable an exact parameter identification but yields a good tension assessment. An experimental test campaign conducted on a multilayered 21-m long stranded cable subject to several tension levels confirms the relevance of the proposed inverse method. A field test campaign of the method on three 120-m long cables of Bonny-sur-Loire (France) suspension bridge is also presented. It proves the reliability and affordability of the overall tension identification process.