State Identification of Duffing Oscillator Based on Extreme Learning Machine
Bibliographic record
Abstract
As an important weak target detection method, Duffing oscillator is very effective in detecting signals with very low signal-to-noise ratio. However, the accurate discrimination between chaotic and periodic states is a crucial problem and that is the prerequisite for using the Duffing oscillator. Conventionally, the Lyapunov exponent is used as an index to identify different states, but as this indicator has the problem of heavy computation cost, slow convergence rate, and requires a mass of data, its application becomes seriously limits. To solve this problem, a novel method for state identification of the Duffing oscillator based on extreme learning machine (ELM) is proposed. The feature data, as the input of ELM, are extracted from the phase diagram and the time series of the Duffing oscillator. Three effective features are extracted in this letter, i.e., ratio of points in and out of the closed region, average distance, and power spectrum. Computer simulations are presented to validate the proposed method and demonstrate that the state classification performance is superior to other related methods with higher computation efficiency, faster convergence rate, and better accuracy.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".