Covariance eigenpairs neighbour distance for fault detection in chemical processes
Bibliographic record
Abstract
Abstract This paper presents a new data‐driven fault detection method called covariance eigenpairs neighbour distance (CEND) for monitoring chemical processes. It processes measured data in one‐step sliding windows to estimate covariance, and the eigenpairs of each sample covariance matrix are recursively calculated using rank‐one modification. The eigenvalues and selected elements of eigenvectors are stacked into reference vectors. For each window data containing the latest measurement vector, the neighbour distance of eigenpairs from the reference matrix can be effectively calculated by virtue of k‐d tree. The neighbour distance serves as the detection index, whose control limit can be determined by validation dataset with assigning a significance level. A high neighbour distance exceeding the control limit implies the occurrence of fault. Simulations on the continuous stirred tank reactor (CSTR) and the Tennessee Eastman process (TEP) both indicate the superior fault detectability of the proposed method, compared with conventional multivariate statistical process monitoring (MSPM) methods such as principal component analysis (PCA) and independent component analysis (ICA).
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 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".