Identification of Hammerstein Models With Cubic Spline Nonlinearities
Bibliographic record
Abstract
This paper considers the use of cubic splines, instead of polynomials, to represent the static nonlinearities in block structured models. It introduces a system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, where cubic splines represent the static nonlinearity and the linear dynamics are modeled using a finite impulse response filter. The algorithm uses a separable least squares Levenberg-Marquardt optimization to identify Hammerstein cascades whose nonlinearities are modeled by either cubic splines or polynomials. These algorithms are compared in simulation, where the effects of variations in the input spectrum and distribution, and those of the measurement noise are examined. The two algorithms are used to fit Hammerstein models to stretch reflex electromyogram (EMG) data recorded from a spinal cord injured patient. The model with the cubic spline nonlinearity provides more accurate predictions of the reflex EMG than the polynomial based model, even in novel data.
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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 | 0.003 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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".