Estimating Poles of Motion Systems from Output-Only Measurements Using Generalized Transmissibility Operators
Bibliographic record
Abstract
Transmissibility operators are mathematical objects that relate two subsets of outputs of a dynamic system. Transmissibility operators are used in applications where the dynamics of the underlying system and the input excitation are not available. Therefore, output measurements collected using sensors, which represent the only available information about the dynamic system in this case, can be used to identify transmissibility operators. Generalized transmissibility operators, which have been recently introduced, provide a more general mathematical characterization of transmissibility operators by relaxing an assumption that requires knowledge of the dimension of the excitation signal to construct meaningful transmissibility operators. Although generalized transmissibility operators are constructed from the zeros of the underlying system and not the poles, we show in this paper that the determinant of the difference between two generalized transmissibility operators constructed between the same outputs but under different input locations can be used to determine the poles of the underlying system. We apply the proposed approach to determine the poles of a motion system from two transmissibility operators.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".