PSI - Issue 64

Carmelo Gentile et al. / Procedia Structural Integrity 64 (2024) 677–684 Author name / Structural Integrity Procedia 00 (2019) 000–000

682 6

Fig. 6. Cleansed natural frequencies of the Milan Cathedral versus time (from 16/10/2018 to 31/10/2023).

Fig. 7. Hotelling’s T 2 control chart.

Since the cleansed frequencies (Fig. 6) still exhibit some scattering, according to T 2 control chart (Montgomery, 2013), the statistical properties of each newly acquired subgroup of residuals are compared to the values identified during the training period: as long as the time evolution of T 2 remains below an upper control limit (UCL), the process is in control; conversely, if the UCL is systematically exceeded, the occurrence of structural anomaly is detected. The control chart shown in Fig. 7 has been evaluated by using sub-groups of 12 hours and the UCL corresponds to the 95% percentile of T 2 values during the training period: the inspection of the chart confirms that no abnormal UCL exceedances occur, suggesting that no significant and permanent anomaly has occurred to the Milan Cathedral during the 5-year monitoring period. 5. Response to seismic events As previously stated, two seismic events occurred on December 17th, 2020, and December 18th, 2021, respectively. The first earthquake corresponded to a seismic event of 3.8 Richter magnitude with an epicentre very close to Milan, whereas the second event was characterized by a 4.4 Richter magnitude and epicentre close to Bergamo. Thanks to the wide sensor network installed inside the Cathedral, it was possible to record the response of the structure to the two earthquakes and to assess the effects exerted by the two events on the historic monument. Firstly, the earthquake response spectra were compared to the (elastic) design spectra prescribed by the Italian Building Code, incorporating site hazard considerations. Figure 8 shows the elastic response spectra of the real earthquakes along with the spectra of the Italian Building Code, referred to both the Limit State of Operability (SLO) and the Limit State of Damage (SLD). Figure 8 indicates that the 2020 earthquake (represented by the green lines) is expected to induce minor effects. Conversely, the response spectrum of the 2021 earthquake (represented by