Improved 2-D Multiscale Fractional Dispersion Entropy: A Novel Health Condition Indicator for Fault Diagnosis of Rolling Bearings
Bibliographic record
Abstract
The multiscale dispersion entropy (MDE), which measures the irregularity or chaos of 1-D univariate time series through a dispersion pattern, is a useful tool to extract features from bearing signals. However, the stable dynamical characteristics of bearing signals are commonly hidden in high-dimensional state spaces, which cannot be easily captured by MDE. A large number of fractional chaotic information is filtered due to the application of integer-order pattern probability, negatively impacting the characterization performance of MDE on nonlinear signals. Therefore, an improved 2-D multiscale fractional dispersion entropy (IMFDE2-D) is proposed to overcome the shortcomings of MDE. In IMFDE2-D, the proper state space is constructed to reveal the high-dimensional dynamic characteristics of bearing signals. Meanwhile, the 2-D fractional dispersion pattern is developed to scan the space structure and supplement the fractional chaotic information. Furthermore, the first point of 2-D coarse-graining process is diagonally moved to alleviate the space compression, which further improves the stabilities of entropy metrics. The Logistic and Hénon maps demonstrate that IMFDE2-D has a better capability to describe the states of complex systems compared with MDE. To establish the intelligent health condition identification scheme, a novel feature selection algorithm called iterative Davies–Bouldin index (iDBI) is further designed to refine entropy features. The experimental results demonstrate that under the condition of supervised learning, IMFDE2-D–iDBI achieves the average accuracies of 100% and 99.91%, respectively, in various bearing experiments. Furthermore, even with an unsupervised classifier, the average accuracies can still reach 95.57% and 100%, which are much higher than those of traditional indicators.
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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".