PROBABILISTIC DAMAGE IDENTIFICATION THROUGH BAYESIAN INFERENCE

Damage identification in historic buildings often involves the solution of an inverse problem, with the goal to assess the extent of possible damage based on observed responses. However, existing methods typically overlook sources of uncertainty that could significantly impact the results. Typically, numerical models are frequently used to assess the structural performance of existing constructions. These models rely on a set of unknown input parameters including geometry, mechanical characteristics, physical properties, boundary conditions, etc. Deter-ministic 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, uncertainties associated with both the numerical model input pa-rameters and measurements are usually neglected. In this sense, the Bayesian approach can be used to estimate the unknown numerical model parameters and their associated uncertainties (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 functions). Despite its benefits, it’s worth noting that these models often encounter intractable likelihood functions. In this study, it is proposed to quantify 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. To discuss the approach a Cultural Heritage case study, the Torre Grossa of San Gimignano in Italy, is reported. strengths and weaknesses in terms of protection and conservation strategies against natural risks are discussed.