PSI - Issue 54

J.V. Araújo dos Santos et al. / Procedia Structural Integrity 54 (2024) 575–584 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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A more quantitative assessment of the effects of noise in the damage identifications, obtained with the norm of modal strains, can be achieved by evaluating a correlation coefficient. In the present work, the correlation coefficient is defined as (‖ ( ) ‖ 2 ,‖ ( (n ) ) ‖ 2 )= ∑ ∑ (‖ ( ) ‖ 2 ( , )−‖ ( ) ‖ 2̅̅̅̅̅̅̅̅̅ )(‖ ( (n ) ) ‖ 2 ( , )−‖ ( (n ) ) ‖̅̅̅̅̅̅̅̅̅) =1 =1 [∑ ∑ (‖ ( ) ‖ 2 ( , )−‖ ( ) ‖ 2̅̅̅̅̅̅̅̅̅ ) =1 =1 ] 1/2 [∑ ∑ (‖ ( (n ) ) ‖ 2 ( , )−‖ ( (n ) ) ‖̅̅̅̅̅̅̅̅̅) =1 =1 ] 1/2 (4.3) where ‖ ( (n ) ) ‖ 2 ( , ) is the norm of modal strains computed with noisy displacements and ‖ε (i) ‖ 2 ( , ) is the norm of modal strains computed with clean displacements, respectively. The bar denotes the norm of modal strains mean value, and are the coordinates of a point where the displacement is measured, being and the total number of points on the and direction, respectively. This correlation coefficient evaluates the differences between the two norms, taking the value zero if the norms are completely different and approximately one when these differences are negligible. As can be seen in Figure 4.9, the correlation coefficient depends considerable on the damage scenario. Indeed, the correlation coefficient for scenarios 1 and 2 (single damage scenarios) with 30 dB are larger than the ones for scenario 3 (multiple damage), reaching, in cases of medium and high damage intensity (cases 4 and 5), values higher than 0.95. This implies, as expected, that multiple damage scenarios are more difficult to identify than single ones. This difficulty seems to have its origin in coupling effects due to the existence of more than one slot, which give rise to more complex strain shapes.

(a) (c) Figure 4.9: Correlation coefficients of the norm of modal strains computed without and with noise levels in the range [20, 60] dB for (a) scenario 1, (b) scenario 2, and (c) scenario 3 To get a better visualization of the results with different noise levels, Figure 4.10 depicts profiles taken at constant and coordinates. It can be seen that satisfactory or good identifications can only be accomplished for all range of noise levels if the damage, in particular single damage, is severe, i.e. if the slots have large thickness reductions (damage case 5 in Figure 4.10). For the case where the slots have the lowest thickness reduction, we only obtain good identifications with medium and low levels of noise (damage case 1 in Figure 4.10). In view of Figures 4.9 and 4.10 it is possible to conclude that a threshold of 0.95 for the correlation coefficient can be defined to describe a good damage identification from a less satisfactory one. (b)

(a) (c) Figure 4.10: Profiles of the norm of modal strains with 20, 30, 40, 50, and 60 dB noise levels for lowest and highest slots thickness reduction and: (a) scenario 1, (b) scenario 2, and (c) scenario 3 (b)