Time-Frequency Representation Based on Robust Local Mean Decomposition
Bibliographic record
Abstract
Fourier transform based frequency representation makes an underlying assumption of stationarity and linearity for the target signal whose spectrum is to be computed, and thus it is unable to track time varying characteristics of non-stationary signals that also widely exist in the physical world. Time-frequency representation (TFR) is a technique to reveal useful information included in the signals, and thus the TFR methods are very attractive to the scientific and engineering world. Local mean decomposition (LMD) is a TFR technique used in many fields, e.g. machinery fault diagnosis. Similar to Hilbert-Huang transform, it is an alternative approach to demodulate amplitude-modulation (AM) and frequency-modulation (FM) signals into a set of components, each of which is the product of an instantaneous envelope signal and a pure FM signal. TFR can then be derived by the instantaneous envelope signal and the pure FM signal. However, LMD based TFR technique still has two limitations, i.e. the end effect and the mode mixing problems. Solutions for the two limitations greatly depend on three critical parameters of LMD that are boundary condition, envelope estimation, and sifting stopping criterion. Most reported studies aiming to improve performance of LMD have focused on only one parameter a time, and thus they ignore the fact that the three parameters are not independent to each other, and all of them are needed to address the end effect and the mode mixing problems in LMD. In this paper, a robust optimization approach is proposed to improve performance of LMD through an integrated framework of parameter selection in terms of boundary condition, envelope estimation, and sifting stopping criterion. The proposed optimization approach includes three components. First, the mirror extending method is employed to deal with the boundary condition problem. Second, moving average is used as the smooth algorithm for envelope estimation of local mean and local magnitude in LMD. The fixed subset size is the only parameter that usually needs to be predefined with a prior knowledge. In this step, a self-adaptive method based on the statistics theory is proposed to automatically determine a fixed subset size of moving average for accurate envelope estimation. Third, based on the first and the second steps, a soft sifting stopping criterion is proposed to enable LMD to achieve a self-adaptive stop for each sifting process. In this last step, we define an objective function that considers both global and local characteristics of a target signal. Based on the objective function, a heuristic mechanism is proposed to automatically determine the optimal number of sifting iterations in the sifting process. Finally, numerical simulation results show the effectiveness of the robust LMD in terms of mining time-frequency representation information.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".