Modeling and prediction of nonlinear cable slab dynamics using Koopman operators
Bibliographic record
Abstract
A novel approach for modeling the nonlinear dynamics of cable slabs using Koopman operator theory is presented. Cable slab dynamics are a critical challenge in precision motion systems, as the cables can induce undesired vibrations and disturbances on motion stages. To address this, a higher-dimensional state-space model with nonlinear observable functions is developed to approximate the cable slab dynamics. The proposed model achieves a prediction error within ∼ 1 % over the specified motion range and demonstrates robustness in predicting untrained, randomized, acyclic cable slab motions. A systematic evaluation of various observable functions was conducted to minimize the modeling errors, leading to an optimized model with fractional-order exponents. When compared with a neural network-based state-space model (NN-SS), the Koopman approach demonstrated faster training and better performance. For force prediction, the Koopman approach achieved a reduction of three-quarters in maximum error when compared with the NN-SS method. This work offers a concise and experimentally validated analytical framework specifically for developing accurate predictive models of nonlinear cable slab dynamics.
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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) | 0.001 | 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 | 0.001 | 0.000 |
| 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".