Selecting an initial condition for normal form analysis
Bibliographic record
Abstract
In normal form (NF) analysis, the nonlinear dynamical system being analyzed is modeled with nonlinearities. If the second order NF is used in the analysis, the nonlinearities only up to second order are modeled. Due to the presence of nonlinearities in the model, the results of second order NF analysis is dependent in the initial conditions [C.-M. Lin et al., May 1996] [S. Zhu et al., November 2001]. If the state of the power system with respect to the stable equilibrium point (SEP), /spl Delta/X/spl Delta//sub 0/, at the instant of removal of the fault is used as an initial condition, then NF analysis may fail to give correct results. It is shown in this paper that the initial condition must be chosen such that the two main assumptions made in NF analysis are met. If the system being studied is stable, the post fault system will eventually reach the SEP. We propose to select an initial condition at an instant subsequent to clearing a fault, to achieve more reliable results from the NF analysis. The time domain simulations are presented to support the analysis.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".