Identification of a linear model for nonlinear systems
Bibliographic record
Abstract
It is shown that the output of a certain class of nonlinear dynamic systems can match arbitrarily close the output of a linear dynamic system if the spectral content of the probing input is the same as that of the output of the nonlinear system. The class of nonlinear systems with cascade or feedback combination of static nonlinear elements and a linear dynamic system is considered. If the static nonlinearity is odd symmetric, and the input signal is periodic, persistently exciting with only odd harmonics then it is shown that an arbitrarily close match between the output of the linear system and the nonlinear system may be achieved. The proposed method differs from the traditional linear approximation model in that it captures the behavior of the nonlinear system over a larger region of the operating point. The proposed scheme is verified on simulated nonlinear systems, and tested on a physical system, and finds application in system identification for control design, fault diagnosis, and analysis of the behavior of the nonlinear system.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".