Inverse-free second moment method for electrical systems with uncertain parameters: Research Articles
Bibliographic record
Abstract
Engineering systems are usually designed deterministically, but if there are uncertainties in parameters, an appropriate approach is to use probabilistic methods. For reliability estimation it is necessary to have at least the first two moments including means and covariances of the output variables. Most of the existing methods applied to problems involving linear systems need inverses of matrices. There are two problems with these approaches. First, for large sparse linear systems (for example, a tri-diagonal system) the inverse is fully dense. Second, the mean of the random matrix has to be non-singular. In this paper, we present a new method to automatically formulate the moment equations that aims to overcome the drawbacks of these methods and apply it on electrical networks. This method does not require an inverse and able to solve problems when the mean matrix of a system is singular. In addition, it takes advantage of both sparsity (zero elements) and deterministic coefficients. This method can be used to solve both uncorrelated and correlated cases. To demonstrate the feasibility of this method, a quantitative comparison with another existing method requiring the inverse and with Monte Carlo results is done. Copyright © 2005 John Wiley & Sons, Ltd.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.004 | 0.001 |
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".