PSI - Issue 84

Andy Duarte-Taño et al. / Procedia Structural Integrity 84 (2026) 280–287

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identification of translational and torsional motions (Fig. 6a). The monitoring system continuously acquires ambient vibration responses over 25-minute intervals at a sampling frequency of 100 Hz. To establish a detailed modal baseline, a multi-setup ambient vibration test was conducted on 12 September 2025. Two accelerometers were fixed at the belfry level and used as reference sensors, while the remaining two were roved across six different elevations. The recorded signals were pre-processed by removing linear trends, applying a fourth order Butterworth band-pass filter between 0.5 and 24 Hz, and decimating the data to 50 Hz. Modal identification was performed using the CoV-SSI algorithm, considering model orders from 2 to 160 and a time lag of 2.56 s. The results were subsequently combined using the MOVA-MOSS software. Fig. 6b presents the identified vibration mode shapes of the bell tower, including two first-order bending modes along the tower diagonal (a, b), one local bending mode of the upper tower section (c), one global torsional mode (d), and two second-order bending modes (e, f).

Fig. 6. San Jerónimo Monastery bell tower a) Setup layout. b) Identified vibration mode shapes from the multi-setup ambient vibration campaign. Panels correspond to the first six modes (left to right), with identified natural frequencies and damping ratios: 1 = 1.87Hz , 1 = 0.61% ; 2 = 2.31Hz , 2 = 0.75% ; 3 = 3.45Hz , 3 = 1.76% ; 4 = 4.23Hz , 4 = 1.35% ; 5 = 6.20Hz , 5 = 1.50% ; 6 = 7.22Hz , 6 = 3.93% . For training the network, acceleration data recorded on 13–14 September 2025 were considered (65 records) to account for environmental variability. The signals were decimated to 20 Hz, segmented into overlapping windows of length =4096 and standardized using zero-mean, unit-variance scaling. For this field dataset, the frequency domain term in the loss was formulated using magnitude-based spectral representations, including FFT magnitude and power spectral density (PSD), which are more robust to environmental variability than phase-sensitive formulations. Due to environmental variability and measurement noise, a conservative compression ratio of = 2 was adopted, as higher compression levels did not provide reliable modal identification. Fig. 7 shows a representative reconstruction result for the -direction of the triaxial reference accelerometer located at the belfry level. Although minor amplitude differences are observed, the dominant temporal features are preserved, providing a suitable basis for subsequent operational modal analysis. OMA was performed on both original and reconstructed signals using the CoV-SSI algorithm, implemented in the MOVA-MOSS software, considering model orders from 2 to 120 and a time lag of 4.25s. Fig. 8a compares the vibration modes identified from the original and reconstructed acceleration records, showing close agreement in terms of both natural frequencies and modal displacements. Fig. 8b reports the MAC matrix between the selected modes identified from the original and reconstructed signals (top), together with the Auto-MAC matrix of the original signals (bottom). The MAC matrix exhibits clear diagonal dominance, with all matched modes showing MAC values above 0.90 and several exceeding 0.99 , indicating strong correspondence between original and reconstructed modes. The Auto-MAC matrix reveals non-negligible off-diagonal values for certain mode pairs, attributed to the low spatial coverage of the continuous monitoring system, with accelerometers located only at two tower levels. The similarity observed between the two matrices confirms that these correlations are intrinsic to the structural dynamics and are not introduced by the compression–reconstruction process. Overall, even under real operating conditions, the proposed autoencoder preserves the dominant modal characteristics of the structure, supporting its applicability to practical SHM deployments.