PSI - Issue 84

Mario Costantini et al. / Procedia Structural Integrity 84 (2026) 859–866

863

Table 1. Results on the vibrating corner reflectors near Trento, Italy, and Glasgow, Scotland. SAR image & Azimuth resolution Ground Truth (Amp. & Freq.) DPC measurement (Amp. & Freq.) Relative Error % (Amp. & Freq.)

TSX - 16.0 cm 30 mm - 2Hz Umbra -19.6 cm 90 mm -2Hz Umbra - 22.0 cm 90 mm - 1Hz Umbra - 18.3 cm 10 mm - 2Hz Umbra - 16.9 cm 2 mm - 2Hz Umbra - 16.9 cm 2.8 mm - 2Hz 1.9 mm - 4Hz

29.7 mm - 2.02 Hz 74.1 mm - 1.98 Hz

3.9 -1.4 14.1 - 1.0

100.5 mm - 1.02 Hz 8.3 - 2.0

8.9 mm - 2.04 Hz 2.1 mm - 2.12 Hz 3.0 mm - 2.09 Hz 2.4 mm - 4.46 Hz

17.1 - 2.2 0.5 -5.8 7.3 -4.7 25.8 - 11.4

(a)

(b)

Fig. 1. (a) Vibrating corner reflector (Trento, TerraSAR-X): the original image displays azimuth replicas (top), which disappear after motion compensation (middle). The azimuth amplitude profile (bottom) confirms this suppression (red) relative to the original artifacts (green). (b) Azimuth Fourier transform phase comparing original unwrapped data (green) and the estimated model (red).

3.2. Bridge monitoring We analyzed the South Portland Street Suspension Bridge (Glasgow, UK) using UMBRA-5 scenes from May 16 (DPC) and May 20, 2024 (SPOT), comparing results against five in-situ accelerometers (Fig. 2a). SPOT results (Fig. 3a–c) successfully captured velocity magnitudes decreasing from ~2 to 0.5 mm/s, confirming the capability to measure real structural vibrations (Lotti et al., 2026). Fig. 3d–g report the outcomes obtained with the DPC analysis. The coherence map (Fig. 3d) highlights more reliable points near the bridge ends, whereas the mid-span yields fewer stable scatterers. The estimated dominant vibration frequency (Fig. 3e) is largely uniform along the deck, with most values clustering between 1.6 and 1.8 Hz. The vibration-amplitude map (Fig. 3f) suggests reduced motion near the extremities and around the middle of the span, while other portions exhibit larger oscillations. This spatial pattern is compatible with a standing-wave behaviour, with a mode shape whose characteristic half-wavelength is on the order of half the bridge span. Taken together, the observations indicate a higher-order mode in which the ends and the mid-span remain close to stationary while the intermediate sections undergo approximately sinusoidal motion (see Fig. 3g). This interpretation is consistent with the accelerometer spectra in Fig. 2c, which show a main component at 1.59 Hz. The dominant frequency estimated from DPC agrees well with the in-situ data, differing by roughly 0.15 Hz. While this accuracy is already adequate for the intended use, additional refinements are being investigated. Regarding amplitude, the SAR-derived results also follow the same qualitative trend as the ground measurements: notably, the weaker response associated with the sensor located near the centre of the bridge supports the reduced-amplitude region detected by DPC, in line with the nodal behaviour inferred from the spatial maps.