Metamodels in Computational Mechanics for Bayesian FEM Updating of Ancient High-Rise Masonry Structures

In order to estimate their behaviour as realistic as possible, masonry structures and historical complex buildings are frequently assessed with demanding non-linear procedures, whether for static or dynamic purposes. However, uncertainties related to the epistemic and aleatory field, especially for historical masonry, can widely influence the output reliability and diminish the value of the deterministic approach (one input – one output) in a decision making workflow: for instance, the necessity for urgent structural interventions or even the possibility to close the building or civil object for safety reasons. This paper aims to show how these uncertainties could be quantified, based on a multi-parameter input approach, and consequently handled. In sequence, i) the knowledge, based on the state-of-the-art survey of the object (geometry, quality and characteristics of the materials, etc.) and scientific or engineering contents (constitutive laws, possible sources of excitation, solution methods, etc.) can be put inside a numerical model in order to find a solution for the desired output, ii) input parameters could be treated as variables, so that the model space could be explored for different sets of values and iii) a probabilistic model or distribution could be adopted for each parameter, based on previous known observations. The outputs of such a model will be of statistic nature and will have a probabilistic distribution as well: based on this data, produced by the numerical model (f.i. a finite element model), a relationship between inputs and outputs could be established in an approximated mathematical formulation, the so-called metamodel. In this context, the newly generated (meta)model has the following characteristics: i) it has been validated as the correct representation of the original model, ii) it is much less computationally demanding than the original model, iii) it establishes a direct relationship between the input parameters and the output, iv) it can be used both for input parameters calibration, based on new observations, and, possibly, for the risk assessment. Based on these considerations, the metamodel could be assumed as a fast and validated decision-making tool. An elucidating example is herein discussed with reference to a historic masonry tower.