Coupled Gaussian Mixtures For Modal Analysis: EM Inference and CramÉr-Rao Bounds
Bibliographic record
Abstract
Order-Based Modal Analysis estimates resonances at frequencies that are integer multiples of a rotating machine’s speed. These resonances are represented as a cloud of frequency-versus-speed intersections revealing the natural modes of the mechanical structure. This paper shows that grouping these intersections can be cast as inference in a coupled affine Gaussian mixture model where each mode is represented by a straight line shared across all harmonic orders, while a uniform component captures outliers. A dedicated expectation maximisation (EM) algorithm is investigated for this model, estimating mixture weights in closed form and the other model parameters through a one-dimensional search. Cramér-Rao lower bounds are derived for the joint estimation of slopes, intercepts and mixing proportions in the proposed statistical model allowing performance of the estimators of the unknown parameters to be studied. Monte-Carlo simulations illustrate how the variances of EM estimates approach those bounds. Applied to data from an industrial turbomachine, the method extracts modal lines whose characteristics agree with historical benchmarks, despite strong deterministic harmonics and regime-dependent drifts.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".