PSI - Issue 78

Antonio Sánchez López-Cuervo et al. / Procedia Structural Integrity 78 (2026) 1791–1798

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Table 1: Percentage variation of natural frequencies under di ff erent Damage Scenarios (D.S.).

Sensor Mode D.S. 1 D.S. 2 D.S. 3 D.S. 4 D.S. 5 D.S. 6 D.S. 7 D.S. 8 D.S. 9 D.S. 10 D.S. 11

Acc. Acc. Acc. Acc. Acc.

1 2 3 4 5

0.31

0.27

0.23

0.12

-0.65

-

-

-

-2.34

-2.30 -2.27 -4.77 -5.40 -4.18 -2.41 -2.35 -5.40 -5.47 -4.30

-3.03 -2.25 -5.09 -6.06 -4.33 -3.18 -2.29 -5.35 -6.47 -4.48

-0.47 -0.68 -0.80 -1.21 -1.68 -2.22 -2.67 -2.49 -2.34 -1.03 -1.27 -1.97 -2.80 -3.23 -4.30 -5.01 -5.05 -5.07 -0.76 -1.17 -1.53 -2.24 -2.52 -2.83 -3.01 -3.84 -4.36

-0.59 -0.73 -0.89 -1.28 -1.96 -3.12

-

-

-4.22

Strain 1 Strain 2 Strain 3 Strain 4 Strain 5

0.08

0.04

0.04

-0.04 -0.80 -1.61 -2.22 -2.49 -2.57

-0.47 -0.87 -0.73 -1.31 -1.68 -2.33 -2.19 -2.39 -2.47 -1.01 -1.32 -1.65 -2.93 -3.13 -4.29 -4.47 -5.56 -5.09 -0.88 -1.27 -1.54 -2.58 -2.60 -2.94 -2.47 -4.28 -4.55 -0.74 -0.77 -0.91 -1.45 -2.08 -3.25 -3.50 -4.54 -4.24

(a)

(b)

Damage Scenarios

Damage Scenarios

Damage Scenarios

Fig. 5: E ff ect of damage on 4th mode shape; (a) displacement mode shapes; (b) strain mode shapes.

it is 0.946 for strain-based identification (Fig. 5(b)). Similarly, the average o ff -diagonal MAC values are higher for displacement modes (0.984) than for strain modes (0.978). This suggests that strain mode shapes exhibit greater sensitivity to damage, in agreement with observations reported in the literature (Anastasopoulos, 2020). This trend holds across all modes except for the first one, whose identification was more challenging for the accelerometers system, and thus being expected to be subjected to more noise. Finally, it is worth noting that more severe damage does not always result in greater MAC variations. For example, the MAC for the fourth mode between D.S.0 and D.S.11 is 0.985 and 0.980 for displacement and strain modes, respectively. However, the MAC between D.S.0 and D.S.6 drops to 0.950 and 0.945. Consequently, future work on damage localization using mode shapes will explore alternative sensor-based metrics such as the Coordinate modal assurance criterion (COMAC) (Lieven and Ewins, 1988).

3.2. FEM calibration

This section presents the results of the FEM updating procedure based on the modal parameters identified in the undamaged configuration (D.S.0) using both sensing systems. A multi-objective optimization problem was formulated and solved using the NSGA-II genetic algorithm, implemented through the Python library developed by (Blank and Deb, 2020). The following parameters were selected for calibration: