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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4.4. Influence of Noise In actual experimental measurements there is always noise and thus it is important to analyze how it affects the results of any damage identification method. To assess the noise influence on the quality of damage identifications with the present approach, noise is simulated by adding normally distributed numbers to the modal displacements, according to (Lopes et al. (2019)) ( (n ) ) ( , ) = ( ) ( , ) + ( ) ( , ) (4.1) where ( (n ) ) ( , ) , and ( ) ( , ) are the displacements of mode with and without noise, respectively, being ( ) ( , ) random numbers generated from the standard normal distribution. The noise levels are determined by the signal-to-noise ratio (SNR) [ ( (n ) ) ( , )] = 20 log 10 [ ( (n ) ) ( , )] [ ( ) ( , )] (4.2) where [ ( (n ) ) ( , )] and [ ( ) ( , )] are the root-mean-squares of the noisy displacements of mode and the added noise, respectively. According to Rosso et al. (2023), one may consider three levels of noise to simulate realistic performances of data acquisition systems: (a) 20 dB, (b) 40 dB, and (c) 60 dB, corresponding to low, medium and good quality systems, respectively. Figure 4.6 shows the results for the single damage scenario with a square slot, having the lowest decrease in thickness, located at the center of the plate (damage scenario 1, case 1) obtained by computing the strains of the 3rd mode shape, which has been contaminated by the three levels of noise defined by Rosso et al. (2023). It is clear that with the highest level of noise (20 dB) (Figure 4.6(a)) it is not possible to identify the slot, because the damage signature is completely masked by the noise. We see, however, that one gets a fair identification for the medium noise level (40 dB) (Figure 4.6(b)) and good results for the lowest noise level (60 dB) (Figure 4.6(c)). The conclusions drawn from the results of damage identifications of scenario 1 and case 1 are also verified for scenario 2 and case 1, as we see in Figure 4.7. The identification of multiple damage (scenario 3), when the thickness reduction of the slots is very small (e.g. case 1), is very difficult to accomplish. However, it is possible to get satisfactory results for medium and low levels of noise, as those reported in Figure 4.8, where for noise levels of 40 and 60 dB we clearly see the location of the three slots for the damage case with the largest reduction in thickness (case 5). The results in Figures 4.6, 4.7, and 4.8 were obtained with filters having 11 points and polynomials of degree one for smoothing and degree three for differentiation.

(a) (c) Figure 4.6: Identification of damage scenario 1, case 1 with 3rd mode shape with noise levels of: (a) 20 dB, (b) 40 dB, and (c) 60 dB (b)

(a) (c) Figure 4.7: Identification of damage scenario 2, case 1 with 3rd mode shape with noise levels of: (a) 20 dB, (b) 40 dB, and (c) 60 dB (b)

(a) (c) Figure 4.8: Identification of damage scenario 3, case 5 with 3rd mode shape with noise levels of: (a) 20 dB, (b) 40 dB, and (c) 60 dB (b)