Identification of breathing cracks in a beam structure with entropy
Bibliographic record
Abstract
A cantilever beam with a breathing crack is studied to detect and evaluate the crack using entropy measures. Closed cracks in engineering structures lead to proportional complexities to their vibration responses due to weak bi-linearity imposed by the crack breathing phenomenon. Entropy is a measure of system complexity and has the potential in quantifying the complexity. The weak bi-linearity in vibration signals can be amplified using wavelet transformation to increase the sensitivity of the measurements. A mathematical model of harmonically excited unit length steel cantilever beam with a breathing crack located near the fixed end is established, and an iterative numerical method is applied to generate accurate time domain dynamic responses. The bi-linearity in time domain signals due to the crack breathing are amplified by wavelet transformation first, and then the complexities due to bi-linearity is quantified using sample entropy to detect the possible crack and estimate the crack depth. It is observed that the method is capable of identifying crack depths even at very early stages of 3% with the increase in the entropy values more than 10% compared with the healthy beam. The current study extends the entropy based damage detection of rotary machines to structural analysis and takes a step further in high-sensitivity structural health monitoring by combining wavelet transformation with entropy calculations. The proposed technique can also be applied to other types of structures, such as plates and shells.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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".