Dynamic nonlinear batch process fault detection and identification based on two‐directional dynamic kernel slow feature analysis
Bibliographic record
Abstract
Abstract The batch process generally covers high nonlinearity and two‐directional dynamics: time‐wise dynamics, which correspond to inherently time‐varying dynamics resulting from the slowly varying underlying driving forces within each batch duration; and batch‐wise dynamics, which are associated with different operating modes among different batches. However, most existing dynamic nonlinear monitoring methods cannot extract the slowly varying underlying driving forces of the nonlinear batch process and rarely tackle the batch‐wise dynamic characteristics among batch runs. In order to address these issues, a new monitoring scheme based on two‐directional dynamic kernel slow feature analysis (TDKSFA) is developed by combining kernel SFA with a global modelling strategy. In the TDKSFA method, kernel SFA is integrated with the ARMAX time series model to mine the nonlinear and time‐wise dynamic properties within a batch run due to its capability of extracting the slowly varying underlying driving forces. Furthermore, the global modelling strategy is presented to handle the batch‐wise dynamics among batches by calculating the total average kernel matrix of all training batches. After the slow features are extracted, Hotelling's T2 and SPE statistics are built to detect faults. To solve the issue of fault variable nonlinear identification, a novel nonlinear contribution plot inspired by the pseudo‐sample variable projection trajectories in the TDKSFA model is further proposed to identify fault variables. Finally, the feasibility and effectiveness of the TDKSFA‐based fault diagnosis strategy is demonstrated through a numerical system and the penicillin fermentation process.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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".