Equivalent boundary stiffness identification based on CMA-ES for refined cable tension inversion

Construction control of cable-supported bridges requires reliable vibration-based refined cable-tension identification, yet its accuracy is often limited by uncertain elastic end restraints that are difficult to quantify in practice. This study presents a modal-data-driven framework for refined cable-tension evaluation under uncertain boundary conditions. The framework combines a finite-element forward model with two coupled inverse modules: equivalent boundary-stiffness identification and cable-tension inversion. A Monotone–Bracketing Newton scheme is developed for tension inversion, integrating bracketing, MAC-based modal-branch locking, and sensitivity-driven Newton updates. Boundary stiffness is identified by optimizing non-dimensionalized variables through a tailored covariance matrix adaptation evolution strategy using a joint objective based on frequency residuals. Numerical studies on 50 cables show that, when cable tension is estimated using the 100 identified sets of equivalent boundary stiffnesses, the 95th-percentile error is 5.59 × 10 −4 . Laboratory strand tests under three unknown boundary conditions yield tension errors mostly within 0.5%, with a maximum of 0.92%. An in-construction cable-stayed bridge case further demonstrates practical applicability, with tension errors within 1% for instrumented cables, stage-wise tension differences mostly within 2%, and a maximum main-girder vertical alignment deviation of about 5 cm. The results demonstrate that the proposed framework provides an effective and practical approach for vibration-based refined evaluation of cable tension in the presence of boundary uncertainty.