Uncertainty-informed identification of tie-rod mechanical properties in monumental buildings

Tie-rods are classic structural elements that have been used for centuries to enhance stability in historic masonry buildings and offer valuable insights into structural performance over time through dynamic vibration measurements. This paper tackles the inverse problem, aiming to quantify uncertainties in mechanical properties, tensile axial force and boundary conditions of tie-rods based on experimental vibration frequencies. The approach assumes known probabilistic models for random parameters, such as mass per unit length, bending stiffness, tensile force and boundary conditions, with certain parameters requiring estimation. Finite dimensional models, i.e., deterministic functions in time and/or space, and a finite number of random variables are employed to discretize both physical and probability spaces. The paper concludes with a Monte Carlo simulation, that provides a comprehensive characterization of uncertainties and the best estimates for unknown features, including mass per unit length, stiffness, boundary conditions and tensile force necessary for achieving target free vibration modal parameters, i.e. natural frequencies.