Bayesian Inference for Probabilistic Damage Identification

Damage identification in civil structures often involves solving inverse problems, where the goal is to determine the extent of damage based on observed responses. However, existing methods typically overlook sources of uncertainty that could significantly impact the results. The structural performance of existing constructions is typically assessed using accurate numerical models. These models rely on a set of unknown input parameters, including geometry, mechanical characteristics, physical properties, and boundary conditions. Deterministic optimization functions aim to minimize the discrepancy between the numerical model’s output and the measured dynamic and static structural responses. However, in this deterministic framework, uncer-tainties associated with both the numerical model input parameters and measure-ments are usually neglected. In this sense, the Bayesian approach can be used to estimate the unknown numerical model parameters and their associated uncer-tainties (posterior distributions) updating the model parameters prior knowledge (prior distributions) using current measurements and accounting explicitly for all the source of uncertainties that affect observed quantities (via likelihood func-tions). Despite its benefits, it’s worth noting that these models often encounter intractable likelihood functions. In this study, we propose quantifying uncertainty through a fully Bayesian approach based on Approximate Bayesian Computation (ABC). This class of methods overcomes the evaluation of the likelihood function directly and only require the ability on simulating responses from the model. We test the method at work on a case study of the Cultural Heritage, the Torre Grossa of San Gimignano, to discuss its strengths and weaknesses in terms of protection and conservation strategies against natural risks.