Prognosis of Bearing Degeneration Using Adaptive Quaternion Least Mean Biquadrate Under Framework of Hypercomplex Data
Bibliographic record
Abstract
Prognostics of bearing degeneration play a crucial role in implementation of systems maintenance strategies. Although numerous classical prognostic models have been developed, these models are carried out based on channel-wise processing and therefore fail to capture the inherent nonlinear and coupling nature of multi-dimensional or multi-channel data. To address this issue, a novel prognostics method based on adaptive quaternion-valued least-mean biquadrate (AQ-LMB) algorithm is proposed for a unified processing of hypercomplex data by the virtue of quaternion algebra. The cost function of the proposed AQ-LMB algorithm is designed via the biquadrate form of system output error to adapt to the more common nonlinear and non-Gaussian data, and the update weight vector is derived through Hamilton calculus instead of traditional complex gradient calculation. First, the time series of health indicators (e.g., root-mean-square, RMS) derived from historical data are decomposed by a nonconvex sparse regularization (SR) algorithm associated with a nonconvex penalty, that is, the low frequency trend component (LFC) and high frequency noise component (HFC) are obtained. Then both LFC and HFC are respectively predicted by the AQ-LMB algorithm. The final predicted health indicators can be obtained by integrating the correspondingly predicted LFC and HFC. The separate analysis of both sub-components makes it possible to distinguish their respective contributions to the entire degeneration process, thus avoiding false deviation and improving the prediction accuracy. Finally, the effectiveness of the proposed nonconvex SR and AQ-LMB approach in improving prognostic accuracy is illustrated via three-and four-dimensional run-to-failure datasets of the rolling bearings.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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) | 0.000 | 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 teacher head, 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".