Chaos in nonlinear dynamic systems: Helicopter vibration mechanisms
Bibliographic record
Abstract
The nonlinear dynamic behavior of a helicopter is considered in this paper, using only real-time flight data analysis. The main objective of this study is to characterize the vibration mechanism(s). based on the analysis of the time-series data of the dynamical system, specifically acceleration for two different airspeeds with a sampling rate of 1024 Hz. We explore the possibility of the presence of chaotic behavior in the time-series data, using a systematic, detailed approach. Some background in the theory of chaos in nonlinear dynamical systems is discussed, and techniques for the identification of chaos in time-series data are presented. Several topics including delay-coordinate embedding theory, delay time and dimension calculation, and Lyapunov exponent computation for chaotic systems are described. In each section, time-series data sets from the helicopter are analyzed and examined: in some sections classical examples such as the Henon Map and Lorenz System are also considered to provide illustrative results. Finally, implications regarding the possibility of chaotic behavior in the dynamical system is discussed, and the next steps in this study are presented.
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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".