Using Decoupling Methods to Reduce Polynomial NARX Models
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Bibliographic record
Abstract
The polynomial NARX model, where the output is a polynomial function of past inputs and outputs, is a commonly used equation error model for nonlinear systems. While it is linear in the variables, which simplifies its identification, it suffers from two major drawbacks: the number of parameters grows combinatorially with the degree of the nonlinearity, and it is a black box model, which makes it difficult to draw any insights from the identified model. Polynomial decoupling techniques are used to replace the multiple-input single-output polynomial with a decoupled polynomial structure comprising a transformation matrix followed by bank of SISO polynomials, whose outputs are then summed. This approach is demonstrated on two benchmark systems: The Bouc-Wen friction model and the data from the Silverbox model. In both cases, the decoupling results in a substantial reduction in the number of parameters, and allows some insight into the nature of the nonlinearities in the system.
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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) | 0.001 | 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 it