PSI - Issue 78

Ana Avramova et al. / Procedia Structural Integrity 78 (2026) 1633–1640

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T 7 6.941 0.849 0.9549 0.0245 0.9001 The statistics of the natural frequencies and mode shapes identified during the first year of monitoring are summarized in Table 1, in terms of average value ( f avg ), standard deviation ( σ f ), extreme values ( f min , f max ) of each frequency and the coefficient of determination frequency-temperature ( R 2 f-T ); furthermore, Table 1 also collects the average, the standard deviation and the minimum value of MAC. The values in Table 1 show that natural frequencies exhibit relatively low variability, with standard deviations generally below 0.06 Hz, and fluctuations limited to a few percentage points of the corresponding mean values. To better understand the dependence of frequencies on temperature, the correlation coefficient R 2 was computed: the results suggest that frequency variations are mainly driven by temperature variations. In addition, the bending and torsion modes turn out to exhibit different sensitivity to thermal effects, with the frequency of torsion modes being characterized by stronger correlation with temperature (0.849  R ²  0.906) compared to bending modes (0.663  R ²  0.878). It is further noticed that, among all the identified frequencies, only the R ² related to the first vertical bending frequency f B1 is characterized by a value that is lower than 0.70. Mode shape invariance was evaluated using the MAC, which should ideally remain close to unity and, most importantly, should not exhibit any abrupt or irreversible drop. As shown in Table 1, bending modes exhibit average MAC values very close to unity during the observation period, whereas the average MAC is slightly larger for torsion modes (that are also characterised by higher dispersion than the one observed for bending modes). 4. Novelty detection based on natural frequencies As previously stated, the minimization/removal of EOV effects on natural frequencies was first performed by applying the classic strategy based on PCA and specifically involving the following steps: (a) in the definition of the PCA-based regression, the first 9 months of monitoring were assumed as training period; (b) the lower 12 natural frequencies ( Error! Reference source not found. ), characterizing the vibration modes with higher identification rates, were selected for the application of PCA; (c) only 1 principal score has been retained to define the PCA-based regression. The effectiveness of the minimization/removal of EOV can be proven by comparing the time evolution of the natural frequencies in Error! Reference source not found. (a) and the cleansed natural frequencies in Figure 5. 6.779 0.043 6.694

Figure 5. Time evolution of the cleansed natural frequencies during the first year of monitoring.

As expected, the cleansed frequencies (Figure 5) still exhibit small dispersion, possibly hiding small structural changes: to investigate the possibility of occurrence of small changes, two different procedures have been used. The first one is the control chart based on Mahalanobis distance (Figure 6a), defined by using a 99th percentile Upper Control Limit (UCL). According to this approach, when the novelty index NI (Eq. 1) remains below the UCL, the system is normally operating; if the UCL is consistently exceeded, it may indicate the presence of a structural anomaly. As shown in Figure 6a, the control chart reveals no consistent exceedances in the present case: this