PSI - Issue 78

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

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Figure 2. Measurement points adopted during the continuous dynamic monitoring.

The bridge deck (Figure 1b) includes: (a) two main longitudinal steel girders, with each girder consisting of a welded I cross-section of constant depth (2.80 m) and exhibiting varying girder spacing (between 8.75 m and 11.17 m) and (b) a reinforced concrete slab, 31 cm thick, which is composite with the girders through Nelson-type shear connectors. The roadway platform, whose width ranges from 14.70 m to 17.125 m, is characterized by the presence of a pedestrian curb of 2.70 m. The steel-concrete composite deck is supported by two concrete abutments (S1 on the Solbiate side and S2 on the Mozzate side) and three piers (P1-P3). All the bearing devices are elastomeric seismic isolators, characterised by: (a) appropriate dissipative capacity, (b) low horizontal stiffness to guarantee the decoupling between the horizontal motion of deck and piers/abutments and (c) high vertical rigidity to support vertical loads. Ambient vibration tests (AVTs) were performed before the installation of the dynamic monitoring system. During those tests, carried out in early March 2023 (Garcia-Fernandez et al.,2024), the sensor layout subsequently adopted for the permanent monitoring (Figure 2) was defined: the monitoring system includes 28 MEMS accelerometers (Figure 2), that were installed on the top of the I girder bottom flanges, as well as 2 temperature sensors to monitor the air temperature evolution in time. Every hour, the acceleration time series, sampled at 200 Hz, are sent to a dedicated computer on site for data storage and analysis. Each raw dataset is pre-processed (signal detrending, computation of peak and RMS values, application of a low-pass filter and subsequent down-sampling) and subsequently organized into a database suitable for automated OMA. In more details, modal parameter estimation (MPE) and subsequent modal tracking (MT) were automatically performed by using the MATLAB-based software package DYMOND (Gentile et al., 2024). The covariance-driven Stochastic Subspace Identification algorithm (SSI-Cov, (Peeters and De Roeck, 1999)) is applied to automatically perform the MPE. The implemented SSI-Cov procedure exploits a stabilization diagram to identify stable physical modes of the structure, in terms of natural frequency, mode shape and damping ratio. In each stabilization diagram (where the poles obtained with increasing model order are represented together), only the poles characterized by realistic values of modal damping ratios (e.g., 0% < ζ < 10 %) and Mean Phase Collinearity (MPC, (Pappa et al., 1993)) (e.g., MPC > 0.9) are retained; subsequently, a hierarchical clustering is used to group the physical poles representing the same structural mode (based on the sensitivity of frequencies and mode shapes to the increase of the model order). To detect potential structural anomalies, the time invariance of mode shapes − through the values of Modal Assurance Criterion (MAC, (Allemang and Brown, 1982)) − is checked since the beginning of the monitoring (just after the reference mode shapes have been established). Concurrently, the time evolution of natural frequencies is investigated, with the objective of identifying and the influence of environmental and operational variability (EOV). To this purpose, the PCA algorithm (Sharma, 1995) is used to identify the common trends in the time series of natural frequencies. In more detail, given a matrix Y  N  M collecting M natural frequencies identified for N observations, a PCA regression model is built with a sub-matrix Y tr  T  M (with T < N ) of features collected during a training period in which the structure is supposed to be in normal condition and under typical EOVs. Once trained, the PCA model is used to predict the monitored features Y PCA  N  M and the residuals E obtained as E = Y – Y PCA should contain only the effects of possible structural variations. Hence, reference is made to the following Novelty Index (NI, (Worden et al., 2000)) based on the Mahalanobis distance: NI = √ E T R – 1 E (1) where R – 1 = (1/N) YY T is the covariance matrix of the identified natural frequencies. The control region of the NI is delimited by an upper control limit (UCL), equal to the m -th percentile of the NI in the training period: when a persistent number of data points are outside the control zone because they exceed the UCL,