Reliability analysis of the uncertain fractional‐order dynamic system with state constraint
Bibliographic record
Abstract
Uncertain fractional-order differential equations driven by Liu process are of significance to depict the heredity and memory features of uncertain dynamical systems. This paper primarily investigates the reliability analysis of the uncertain fractional-order dynamic system with a state constraint. On the basis of the first-hitting time (FHT), a novel uncertain fractional-order dynamic system considering a state constraint is proposed. Secondly, in view of the relation between the initial state and the required standard, such uncertain fractional-order dynamic systems are subdivided into four types. The concept of reliability of proposed uncertain system with a state constraint is presented innovatively. Corresponding reliability indexes are ulteriorly formulated via FHT theorems. Lastly, the uncertain fractional-order dynamic system with a state constraint is applied to different physical and financial dynamical models. The analytic expression of the reliability index is derived to demonstrate the reasonableness of our model. Meanwhile, expected time response and American barrier option prices are calculated by using the predictor-corrector scheme. A sensitivity analysis is also illustrated with respect to various conditions.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 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 | 0.001 |
| 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".