Optimization of Batch Operating Policies. Part I. Handling Multiple Solutions#
Bibliographic record
Abstract
Jaeckle and MacGregor ( AIChE J. 1998, 44, 1105−1118) introduced a data-driven technique to estimate conditions at which a process should operate (i.e., temperature, pressure, and reactant amounts recipe) in order to yield a final product with a desired set of quality characteristics. Their proposed technique utilizes empirical latent variable models that are fitted to historical process data from existing process grades. This paper extends the methodology to include estimation of the entire set of time-varying profiles for the manipulated variables for batch processes. The problem is formulated in an optimization framework to include both equality and inequality constraints in the objective function. Since often the solution is not unique, the locus of the multiple solutions (defined as the null space) is studied and approaches to selecting the best solution for the final variable settings and trajectories are discussed. Finally, a parallel approach based on a derivative-augmented model is suggested that avoids considering null spaces to select the final design. An industrial batch digester from the pulp and paper industry is considered throughout the paper to explain and illustrate the key concepts.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".