PSI - Issue 71

Rakesh Kumar Sahu et al. / Procedia Structural Integrity 71 (2025) 203–209

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3.1. Validation For the validation of the numerical method, the present tone burst response of the pristine state is compared with the literature (Yu and Giurgiutiu, 2005) represented in Fig. 3. There is some variation in validation because the piezoelectric actuator and sensor were not designed separately but follow the trend of symmetric and anti-symmetric mode. Once the validation of data is completed, we can normalize the response of pristine and damaged states by the maximum amplitude of a particular response in the range of -1 to 1. Normalization of response follows by the mode purification step to suppress certain modes to quantify the damage.

Fig. 3. Response at sensor under 100 kHz modulated five-cycle tone burst excitation: Comparison with the results of Giurgiutiu et al. (2005)

4. Results Fig. 4(a-b) represents the RMSD values for varying width and location of damage at various frequencies. From Fig. 4(a), it can be observed that as the damage width increases from 1mm to 20mm (with an increment of 1), the RMSD value increases monotonically. (Here, the damage location is kept at 750mm from the reference point, and the depth of damage is constant at 0.75 mm.) Fig. 4(b) it can be observed for 50 kHz as the number of damage changes from one to two the RMSD value decreases then for two to four damages the RMSD value increases. For 150, 175 and 200 kHz the RMSD value increases from one to four damages but for three to four damage RMSD value plateaus. For frequencies from 225 to 300 kHz, the RMSD value increases sharply. (Single damage (10 mm) at 750mm from reference, two damage (5 mm) at 675 mm and 825 mm, three damage (3.33 mm) at 675 mm, 750 mm and 825 mm, four damage (2.5 mm) at 660 mm,720 mm,780 mm and 840 mm and depth of damage as 0.75 mm). Fig. (5-6) represents the performance plot which evaluates the performance of the trained neural network. In the performance plot, if the difference between training, testing and validation is less, this exhibits a good fit. There is a moderate learning curve of a good fit model at the beginning due to a high training loss which decreases gradually as more training examples are added and flattens out. A good fit indicates that errors between training and testing are minimal. It can be observed from the plot training, testing, and validation data is converging.

(b)

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Fig. 4. Damage index variation with width of damage and number of damages