Copula-Based Time-Frequency Distribution Analysis for Planetary Gearbox Fault Detection
Bibliographic record
Abstract
Linear and bilinear time-frequency distributions (TFDs) have been employed in planetary gearbox fault diagnosis. For linear TFDs, there is a trade-off between the time localization and frequency resolution and the spectrogram may not have correct energy marginals. For bilinear TFDs, they cannot be interpreted as an energy distribution because of the existence of possible negative values even though they are designed for energy density representation. To overcome these shortcomings, TFDs based on copula theory have been reported in the literature. In this paper, we analyze two simulated data sets using linear TFD and copula-based TFD. The results show that the constructed copula-based TFD has desirable properties of being positive, free from cross-term interference, having high time-frequency resolution and matching well with true marginals. The copula-based TFD is also able to locate fault-induced impulses by vertical lines over a certain frequency range in the time-frequency domain. Consequently, this study confirms the advantages of the copula-based TFD as an energy distribution and its capability in fault detection for planetary gearboxes.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".