Santa Maria del Fiore Dome Behavior: Statistical Models for Monitoring Stability

Abstract

The article describes the work in progress for analysis of the behavior of the web cracks on Brunelleschi's Dome of Santa Maria del Fiore. The web cracks in the Dome have always given rise to concern about the stability of the monument. The analyses performed show a slight increase in the size of the main cracks and, at the same time, a relationship with the environmental variables. None of the studies conducted in the past simultaneously involved all the variables detected by the monitoring system. Understanding the relationships among all the endogenous and exogenous variables characterizing the phenomenon under study can help to predict the static evolution of the monument and to automatically detect any atypical behavior, the identification of which would, of course, be of paramount importance for the preservation of the monument, and, more in general, for the preservation of the cultural heritage.

A Dynamic Latent Variable Model for Monitoring the Santa Maria del Fiore Dome Behavior

“…This model showed an excellent goodness of fit, clearly revealing the underlying breathing mechanism of the Dome. Compared to the dynamic factor analysis performed in [ 2 ], where the algorithm did not converged but stopped after reaching the maximum number of iterations, the GDPC provided much better convergence properties (results not shown here). The proposed analysis represents a useful instrument for the professionals (architects and structural engineers) to globally evaluate the behavior of the Brunelleschi’s Dome.…”

“…To our knowledge, such an analysis has never been presented in any of the studies conducted in the past. A first tentative in this direction was made by Bertaccini [ 2 ] who estimated a structural equation model to explain the behavior of the fourth web (in which 13 deformometers and 3 thermometers are installed) in response to the external events (of exceptional and non-exceptional nature).…”

Revealing the structural behaviour of Brunelleschi’s Dome with machine learning techniques

“…This is particularly true in the present case, because over time the monitoring system has produced a huge amount of data highlighting a sort of "breathing mechanism" of the vault: namely, the cracks tend to expand and contract cyclically according to Revealing the structural behaviour of Brunelleschi's... seasons and their relative temperatures, some in a harmonious relationship, others in the opposite way (Ottoni and Blasi 2014;Bertaccini 2015). Therefore, the Dome may be assimilated to what in physics is defined as a "closed system": the structural constraints define the relationship of forces among the various cracks, which in turn are affected by the action of the "surrounding" environment (Bertaccini 2015). Nevertheless, the statistical analyses carried out to date have generally been conducted on a single or on a limited set of devices, showing a progressive increase in the size of the main cracks and, at the same time, a clear relationship with meteorological and seismic variables (Bartoli et al 1996;Ottoni et al 2010).…”

“…Managing and analysing sensor data is often challenging (Nieto et al 2021). This is particularly true in the present case, because over time the monitoring system has produced a huge amount of data highlighting a sort of "breathing mechanism" of the vault: namely, the cracks tend to expand and contract cyclically according to Revealing the structural behaviour of Brunelleschi's... seasons and their relative temperatures, some in a harmonious relationship, others in the opposite way (Ottoni and Blasi 2014;Bertaccini 2015). Therefore, the Dome may be assimilated to what in physics is defined as a "closed system": the structural constraints define the relationship of forces among the various cracks, which in turn are affected by the action of the "surrounding" environment (Bertaccini 2015).…”

“…Since the behaviour of the Dome as a whole (or of its wide masonry surfaces) cannot be fully understood from single sensor measurements alone, a more comprehensive analysis than what has been carried out so far is necessary. Recently, Bertaccini (2015) and Bertaccini et al (2020) -fully aware that the structural behaviour of the Dome and its response to the surrounding environment are "hidden" within the data collected by the sensors -tried to model the complex relationships between endogenous and exogenous variables involved in the monitoring process in order to describe the underlying structural (latent) behaviour of the Dome. In the light of the nature of the variables involved (mainly, multivariate time series data with exogenous and endogenous variables), both Bertaccini (2015) and Bertaccini et al (2020) relied on the estimation of latent variables models (Bartholomew et al 2011), as structural equation models (Hox and Bechger 1998;Bollen et al 2008) and dynamic factor models (Pena and Yohai 2016;Asparouhov and Muthén 2018).…”