PSI - Issue 84

Ana Avramova et al. / Procedia Structural Integrity 84 (2026) 560–568

563

resulting cleansed frequencies—or the associated prediction errors (residuals)—are features that reflect only the structural condition and are therefore well-suited for SHM. To enable early detection and amplification of anomalous patterns within the residuals, the use of control charts, such as Hotelling’s T² statistic (Hotelling, 1947), is recommended: in presence of structural anomalies, the statistical characteristics of the residuals are expected to shift abruptly, causing the T² values to consistently exceed a predefined threshold. It is further noticed that the anomaly detection based on natural frequencies is fully active only after the training period (i.e., after having understood the normal variation of natural frequencies that is associated to EOV). On the other hand, a quite well-distributed grid of accelerometers is available on the investigated bridges: hence, the mode shape variations have been also examined to provide global and local information on possible structural changes. To achieve this aim, the MAC and the MPC values are examined as well as the time evolution of each modal deflection. Unlike the frequency-based novelty analysis, the inspection of mode shapes variations can be conveniently performed from the beginning of monitoring activities. 4. Selected results from dynamic monitoring During the dynamic tests performed before the installation of the monitoring systems, 10 and 9 vibration modes were identified for the VI03 and VI04 viaducts, respectively. For both bridges, the beginning of dynamic monitoring activities revealed the possibility to identifying with confidence a larger number of normal modes. In more details: (a) 12 normal modes were identified for the VI03 bridge (6 vertical bending modes and 6 torsional modes, as shown in Fig. 4) and (b) 14 modes were identified (7 vertical bending modes and 7 torsional modes) for the VI04 bridge. The identified modes exhibit high similarity between the two bridges: in particular, mode shapes for both structures are nearly identical, except the last two modes of VI04, which were not identified from the acceleration data collected on the bridge. Notably, for both bridges, the first 4 vertical bending modes (B 1 –B 4 ) and the first 4 torsional modes (T 1 –T 4 ), as shown in Fig. 4, align closely with the theoretical modal characteristics expected for a continuous 4-span beam. The evolution of natural frequencies in the investigated period for the two infrastructures (i.e., from 05 June 2024 until 01 October 2025) is illustrated in Fig. 5(a) and 5(b), whereas the corresponding changes of air temperature— ranging between -3°C and +37°C—are shown in Fig. 6. By inspecting Fig. 5 and Fig. 6, it is evident that since the early stages of the monitoring campaign, the automatically identified natural frequencies have exhibited daily and seasonal trends, both of which can reasonably be attributed to variations in air temperature.

(a) Mode B 1 : f B1 = 1.535 Hz

(b) Mode T 1 : f T1 = 1.807 Hz

(c) Mode B 2 : f B2 = 1.934 Hz

(d) Mode T 2 : f T2 = 2.170 Hz

(e) Mode B 3 : f B3 = 2.468 Hz

(f) Mode T 3 : f T3 = 2.664 Hz

(g) Mode B 4 : f B4 = 2.854 Hz

(h) Mode T 4 : f T4 = 3.008 Hz

(i) Mode B 5 : f B5 = 5.266 Hz

(j) Mode T 5 : f T5 = 5.532 Hz

(k) Mode B 6 : f B6 = 5.926 Hz

(l) Mode T 6 : f T6 = 6.115 Hz

Fig. 4 VI03 viaduct: reference dynamic characteristics identified at the beginning of the continuous monitoring (05/06/2024, h 16:00).