Issue 75

A. Aabid et alii, Fracture and Structural Integrity, 75 (2025) 55-75; DOI: 10.3221/IGF-ESIS.75.06

Crack Length (mm)

SIF (MPa √ mm)

Mode – I 4.8471 8.4248 13.5572 22.4255

Mode – II

Mode - III

5

4.3604 6.4045 8.8951 13.7334

4.0529 6.4127 9.0606 12.2541

10 15 20

Table 1: Theoretical results of SIF.

Theoretical and noise-augmented SIF data To enhance the robustness and generalization ability of ML models, synthetic noise was added to the original theoretical SIF values, as illustrated in Tab. 2. Although this study does not utilize sensor-acquired experimental data, the idea of introducing noise originates from the need to simulate real-world uncertainty. In practice, SHM systems often experience various sources of noise such as sensor measurement errors, signal transmission distortions, environmental, and operational disturbances. These disturbances can significantly affect the accuracy of measured fracture parameters like the SIF. To emulate such effects computationally, we applied additive Gaussian noise across seven SNR levels: 0 dB (original), 5 dB, 10 dB, 15 dB, 20 dB, 25 dB, and 30 dB. This range corresponds with noise magnitudes typically reported in experimental systems and allows for the evaluation of ML model performance under varied uncertainty levels for better training and accuracy in findings [29]. To optimize the damage stage, the SIF values for each noise are given for various Modes. These SIF values will be utilized to anticipate the crack length in a damaged thin plate.

SIF (MPa √ mm)

Crack Length (mm)

Noise Level (dB)

Mode – I 4.8471 4.8138 4.7696 4.8017 4.9693 4.6817 4.9155 8.4248 8.4267 8.3717 8.3842 8.382 8.7291 8.8989 13.5572 13.6757 13.4147 13.196 13.2507 13.7187 13.6358 22.4255 22.3746 22.2954 22.2502 22.0268 22.4153 22.975

Mode – II

Mode - III

5

0dB 5dB

4.3604 4.3476 4.4108 4.4744 4.4378 4.1452 4.1656 6.4045 6.3917 6.4276 6.2568 6.4004 6.159 6.5148 8.8951 8.8599 8.9832 8.8461 8.7473 8.925 8.5279 13.7334 13.787 13.4989 14.1011 13.423 13.5316 13.2383

4.0529 4.0423 4.1141 4.1233 3.9604 3.9036 4.2788 6.4127 6.3817 6.3468 6.485 6.419 6.6492 6.6365 9.0606 9.0888 9.1113 9.2942 9.1701 8.7067 9.338 12.2541 12.239 12.482 12.5374 11.9683 12.2946

10dB 15dB 20dB 25dB 30dB 0dB 5dB 10dB 15dB 20dB 25dB 30dB 0dB 5dB 10dB 15dB 20dB 25dB 30dB 0dB 5dB 10dB 15dB 20dB 25dB 30dB

10

15

20

11.9458 Table 2: Theoretical and noise-augmented SIF values for Modes I, II, and III across different crack lengths and noise levels (0–30 dB).

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