PSI - Issue 84

F. Foria et al. / Procedia Structural Integrity 84 (2026) 645–652

651

Figure 4 represents the Gaussian Regression Process curve interpolating filtered pairs of model order - time lag that satisfy the acceptance threshold for distance according to Cosine Similarity and Mahalanobis metric (Step 8, and 9).

Figure 4 GRP interpolating curve of the admissible model order-time lag pairs

Table 3 shows the frequencies with the highest multiplicity obtained through the analysis of 38 recordings (step 10). These are the ones that are most likely to be the natural frequencies of the bridge, that is 5.84 Hz (m=2112), 8.26 Hz (m=5082), 11.55 Hz (m=1441), 13.87 Hz (m=2172), 18.16 Hz (m=4396).

Table 3. Identified natural frequencies – 38 recordings data Average Minimum Maximum Multiplicity

Damping

5.84 8.26

5.45 7.64

6.27 9.96

2112 5082 1441 2172 1812 4396 20

0.058 0.028 0.043 0.013 0.024 0.026 0.016 0.021 0.026 0.011 0.018

11.55 12.87 13.87 15.54 18.16 20.98 22.96 23.91 24.96

79.53 12.86 13.38 14.97 17.29 20.47 21.55 23.89 24.23

12.43 12.89 14.37 16.19 19.20 21.24 22.49 23.93 25.47

349 342

5

686

The following conclusions can be drawn from a comparison with the numerical frequencies provided by the modal analysis: • Realistically, the numerical frequency of 2.36 Hz obtained from the modal analysis, does not exist and therefore the FEM model was revised in terms of degradation of the structural elements, constraints, geometries, and materials. The updated FEM model confirmed the non-existence of the above frequency. • The algorithm is able to capture the first main frequency of 5.84 Hz close to the first frequency identified by updated FEM model, corresponding to a vertical vibration mode. • The frequency of 8.26 Hz obtained from the analysis of 38 recordings includes as a matter of fact two distinct real modes, at 8.00 and 8.54 Hz, which are clearly visible through the analysis of individual recordings and which have high stable pole multiplicity. This problem can be solved adding a MAC criterion to the selection of most probable modes, in addition to a multiplicity criterion.