Multi‐layer features ensemble soft sensor regression model based on stacked autoencoder and vine copula
Bibliographic record
Abstract
Abstract It is crucial in industrial processes to consider key variables to ensure safe operation and high product quality. Moreover, these variables are difficult to obtain using traditional measurement methods; hence, it makes sense to develop soft sensor regression models to process the variable prediction. However, there are numerous variables integrating noisy and redundant information in complex industrial processes. Using such variables in traditional regression models may result in reducing the model's efficiency and performance. Thus, this paper proposes a multi‐layer feature ensemble soft sensor regression method using a stacked auto‐encoder (SAE) and vine copula (ESAE–VCR) to address these problems. To do so, the number of neurons in the hidden layer of the SAE is determined by the principal component analysis (PCA). The multi‐layer features of the process variables are extracted using a stacked AE, and the regression models are established for each feature layer. A linear regression ensemble method is used to combine the regression models with the multi‐layer features to obtain the final predictive model that will estimate the values of the key variables. The effectiveness and practicality of the ESAE–VCR are validated by comparing them with several common soft measurement methods in two examples. In the numerical example, the ESAE–VCR yields an accuracy of prediction ( R 2 ) of 0.9898 and a root mean square error (RMSE) of 0.1804. In the industrial example, the ESAE–VCR yields an R 2 of 0.9908 and an RMSE of 0.1205.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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".