PSI - Issue 64

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

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Fig. 2. Plan of the Milan Cathedral and general layout of the dynamic monitoring system.

It should be noticed that the dynamic monitoring setup is complemented by a static monitoring system including vibrating wire extensometers, installed on selected tie-rods, as well as temperature and humidity sensors for monitoring both internal and external environmental conditions. The vibration based SHM strategy applied in the Milan Cathedral involves the following steps: (a) Preliminary pre-processing of the raw data; (b) Automated modal parameter estimation (MPE) and modal tracking (MT); (c) Removal of environmental effects from the natural frequencies; (d) Novelty detection. The Modal Parameters Estimation (MPE) employs the covariance-based Stochastic Subspace Identification algorithm (SSI-Cov, Peeters and De Roeck, 1999) and an automatic procedure  using damping ratios and modal complexity (Pappa et al., 1993)  to detect and remove the spurious poles from the stabilization diagrams; subsequently, poles exhibiting comparable characteristics in terms of frequencies and mode shapes are clustered within each dataset. After each MPE, the identified modes are tracked in time and the properties monitored for SHM purposes are natural frequencies, damping ratios, the modal deflection of each instrumented node, the Modal Assurance Criterion (MAC, Allemang and Brown, 1982), and the Mean Phase Collinearity (MPC, Pappa et al., 1993) quantifying the complexity of mode shapes. As agreed in scientific literature, the natural frequencies of structures are influenced by environmental and operational variability (EOV). In this study, Principal Component Analysis (PCA, Jollife, 2002) has been adopted to mitigate the effects of EOV on natural frequencies. The PCA is calibrated using data from the initial year of monitoring and, once established, it can effectively remove EOV-related variance from subsequently identified natural frequencies. The resulting cleansed natural frequencies, or the residuals, only reflect structural conditions for SHM. Anomalies in prediction errors are promptly detected using Hotelling’s T 2 distance (Montgomery, 2013) where any structural irregularities cause T 2 values to consistently exceed a predefined threshold. The grid of seismometers permanently installed in the Cathedral allowed the identification and good spatial description of 8 vibration modes. The lower 6 modes, as identified on the first day of continuous monitoring, are shown in Fig. 3 (where blue lines mark the modes with dominant N-S bending of the columns, whereas red lines refer to modes with main E-W motion). Notably, while all 8 modes are tracked, only the lower 6 (illustrated in Fig. 3 and characterized by a higher identification rate) are used for SHM purposes.