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.

中文翻译：

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基于非线性静力反问题的索张力识别

提出了一种新的识别技术来使用静态逆方法来评估电缆的张力，该方法将通用电缆模型与位移传感器、应变计和应保持操作可负担性的附加质量相结合。逆问题被公式化为数据失配函数的最小化，该函数基于缆索的两个平衡配置（即一个负载和另一个自由）之间在垂直位移和轴向应变方面的差异。逆问题公式与非常规泛函的参数研究相呼应，提出了一种识别电缆参数的方法，即其长度、轴向刚度和每单位长度的质量。逆问题的计算解决是作为一个两步识别程序来实现的。第一的，轴向刚度和每单位长度的质量保持恒定，电缆的长度通过简单的线搜索算法使用有限差分来估计函数导数来近似找到。其次，使用伴随方法评估其他物理参数，其中直接问题、伴随问题和参数敏感性分别定义为拉格朗日函数关于对偶变量、原始变量和参数的导数。由于问题的病态，所提出的方法不能实现精确的参数识别，但会产生良好的张力评估。在承受多个张力水平的多层 21 米长绞合电缆上进行的实验测试活动证实了所提出的逆方法的相关性。还介绍了该方法在 Bonny-sur-Loire（法国）悬索桥的三个 120 米长电缆上的现场测试活动。它证明了整个张力识别过程的可靠性和可承受性。