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

Abstract

A dynamic principal component analysis is proposed to monitor the stability, and detect any atypical behavior, of the Brunelleschi’s Dome of Santa Maria del Fiore, in Florence. First cracks in the Dome appeared at the end of the 15th century and nowadays they are present in all the Dome’s webs, although with an heterogenous distribution. A monitoring system has been installed in the Dome since 1955 to monitor the behavior of the cracks; today, it counts more than 160 instruments, such as mechanical and electronic deformometers, thermometers, piezometers. The analyses carried out to date show slight increases in the size of the main cracks and, at the same time, a clear relationship with some environmental variables. However, due to the extension of the monitoring system and the complexity of collected data, to our knowledge an analysis involving all the detected variables has not yet conducted. In this contribution, we aim at finding simplified structures (i.e., latent common factors or principal components) that summarize the measurements coming from the different instruments and explain the overall behavior of the Dome across the time. We found that the overall behavior of the Dome tracked by multiple sensors may be satisfactorily summarized with a single principal component, which shows a sinusoidal time trend characterized, in a one-year period, by an expansive phase followed by a contractive phase. We also found that some webs contribute more than others to the Dome’s movements.

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

“…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).…”

“…Both of these studies aimed to assess the possibility of developing software tools for predicting the structural evolution of the monument. Unfortunately, the vast amount of data and the numerous model parameters led the authors to limit their proposals, both in space (a single web; Bertaccini 2015) and time (measurements gathered in a specific year; Bertaccini et al 2020).…”