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

摘要

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.