A Robust Probabilistic Quality-Relevant Monitoring Model With Laplace Distribution
Bibliographic record
Abstract
The historical data collected from industrial processes are generally disturbed by ambient noise and outliers. Hence, accurate estimation of process uncertainty is essential in order to correctly determine the status of the process systems. In this study, a robust probabilistic quality-relevant monitoring model with a Laplace distribution is proposed for industrial process monitoring under noisy environment. Because of the heavy tailed characteristic of Laplace distribution, the proposed model is more robust than models with Gaussian distribution. The solution of the proposed probabilistic model is provided through variational Bayesian inference and maximum likelihood estimation after recasting Laplace distribution as Gaussian scale mixtures. Based on the obtained model parameters and estimated latent variables, a quality-relevant monitoring model can be established and four statistics are designed. According to the calculated statistics, the proposed method can effectively detect and differentiate quality-relevant from quality-independent faults. The performance of the proposed method is illustrated using a numerical simulation and a condenser application, which are disturbed by ambient noise and outliers. Experimental results demonstrate that Laplace distribution can better reveal the process uncertainty to effectively alleviate their negative effect. As a result, the proposed method performs better than some commonly used quality-relevant monitoring strategies.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".