Identification of tie-rod properties in monumental buildings under uncertainty

Abstract

Abstract. Tie-rods are simple structural elements that have been commonly used throughout the centuries to improve the stability of old masonry buildings. Measuring the dynamic vibrations of such elements can give important information on the structural performance variation with time if proper system models can be calibrated taking into account all the relevant sources of uncertainties. This paper poses and solves the inverse problem of quantifying the uncertainty in the mechanical properties, tensile axial force and boundary conditions of tie-rods from measurements of their experimental frequencies of vibrations. It is assumed that the probabilistic models of the random entries of the problem, i.e., the mass per unit length, the bending stiffness, the tensile force and the boundary conditions, are known up to some parameters which need to be estimated. Both the physical and probability spaces are discretized using finite dimensional (FD) models, i.e., deterministic functions of time and/or space and finite numbers of random variables. Monte Carlo simulation is finally used to completely characterize the uncertain features obtaining the best estimation of all the unknown features such as mass per unit length, stiffness, boundary conditions and tensile force that give the target free vibration modal parameters, i.e. natural frequencies.