Bayesian Updating for Random Tensile Force Identification of Ancient Tie Rods Using Modal Data

Abstract

Tie rods play a crucial role in civil engineering, particularly in controlling lateral thrusts in arches and vaults, and enhancing the structural integrity of masonry buildings, both historic and contemporary. Accurately assessing the tensile axial forces in tie rods is challenging due to the limitations of existing methodologies. These methodologies often rely on indirect measurements, computational models, and optimization procedures, resulting in single-point solutions and neglecting both modeling and measurement uncertainties. This study introduces a novel Bayesian updating framework to effectively address these limitations. The framework aims to accurately identify the structural parameters influencing tie rod behavior and estimate uncertainties using natural frequencies as references. A key innovation lies in the mathematical formulation of Bayesian updating, which is founded upon the definition of computational models integrating uncertain updating parameters and latent random variables derived from a rigorous sensitivity analysis aimed at quantifying the impact of the updating parameters on the natural frequencies. Notably, the application of Bayesian updating to the structural identification problem of ancient tie rods represents a significant advancement. The framework provides a comprehensive description of the uncertainties associated with computational models, offering valuable insights for practitioners and researchers alike. Moreover, the results of the sensitivity analysis serve as a valuable tool for setting up inverse problems geared towards accurately identifying tensile axial forces.