Time Frequency Representation Enhancement via Frequency Matching Linear Transform for Bearing Condition Monitoring under Variable Speeds
Bibliographic record
Abstract
Instantaneous frequency (IF) of shaft rotation is pivotal for bearing fault diagnosis under variable speed operations. However, shaft IF cannot always be measured as tachometers are not allowed to be installed in every case due to design reasons and cost concerns. Extracting the shaft IF ridge from time frequency representation (TFR) of vibration signals, therefore, becomes an alternative. Linear transform (LT), such as short time Fourier transform (STFT), has been widely adopted for such a purpose. Nevertheless, the accuracy of extracted IF ridges relies on the readability of TFR. Unfortunately, readability of TFR from STFT is often impaired by the smearing effect caused by non-synchronous frequencies between bases and signal components and limited time frequency resolution capability, which in turn adversely influences the accuracy of IF ridge extraction. To accurately extract IF ridges from vibration signals, this paper focuses on the first factor, which causes the smearing problem, and proposes a method named frequency matching linear transform (FMLT) to enhance the TFR, where transforming bases with frequencies varying with the shaft IF are constructed to alleviate the smearing effects. To construct the transforming bases with frequencies synchronous with shaft IF, a fast path optimization (FPO) algorithm, which generates all possible optimization paths among amplitude peaks and thereby ensures the continuity of extracted IF ridges, is adopted for IF pre-estimation. The TFR with improved readability can be subsequently obtained via FMLT, paving the way for accurate IF ridge extraction. Then, multiple IF ridges can be iteratively extracted using the FPO algorithm. The accuracy of extracted IF ridges before and after TFR enhancement is compared, indicating that the proposed FMLT can enhance the readability of TFR and lead to more accurate IF ridge extraction for bearing condition monitoring.
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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 | 0.001 |
| 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 | 0.001 |
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".