Time reversal method for damage detection of cracked plates in the medium frequency range: the case of wavelength-size cracks
Bibliographic record
Abstract
The use of time reversal methods for localization and characterization of damages in plates is usually combined with high frequency guided waves in a local elastic wave propagation formulation. In such a situation, pulses and echos may be clearly separated in time. As a consequence, the diffracted field on a damage with large geometrical dimensions compared to the wavelength used for wave propagation allows to consider the structure itself as "near infinite" because the modal behavior is not apparent. However, those high requencies may not be required and in the presented approach, medium frequencies are used and boundary conditions need to be considered. The interest of this frequency range is in using lightweight signal processing devices limited to low data transfer rates as expected for in flight fuselage skin inspections. It also allows to filter artifacts like very small damages in the structure. This study focuses on the case of wavelengths which are in the order of the largest geometrical dimension of the cracks. In the paper, a modelling tool is first extended to describe the vibration behavior of pristine and damaged finite thin plates in the low and medium frequency range below 50 kHz. The proposed analytical model employs a Hierarchical Trigonometric Functions Set (HTFS) to characterize homogeneous plates with through cracks. To approximate the effect of a small crack in a plate for all combinations of classical boundary conditions, high order approximation functions are required. The proposed approach takes the advantage of the stability of the HTFS for these high orders. A notable advantage of this model is that it does not require a dense uniform meshing of the plate, with a minimum of 10 nodes per wavelength, as most finite element models require. The time reversal concept introduced before is thus validated with this model for a finite plate with known boundary conditions. Experimental validation of the model is conducted in the time domain for pristine and cracked plate structures and shows great potential for crack detection.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".