Approximate Maximum Likelihood Parameter Estimation for Nonlinear Dynamic Models: Application to a Laboratory-Scale Nylon Reactor Model
Bibliographic record
Abstract
In this article, parameters and states of a laboratory-scale nylon 612 reactor model (Schaffer et al. Ind. Eng. Chem. Res. 2003, 42, 2946−2959; Zheng et al. Ind. Eng. Chem. Res. 2005, 44, 2675−2686; and Campbell, D. A. Ph.D. Thesis, Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada, 2007) are estimated using a novel approximate maximum likelihood estimation (AMLE) algorithm (Poyton et al. Comput. Chem. Eng. 2006, 30, 698−708; Varziri et al. Comput. Chem. Eng., published online, http://dx.doi.org/10.1016/j.compchemeng.2008.04.005; Varziri et al. Ind. Eng. Chem. Res. 2008, 47, 380−393; and Varziri et al. Can. J. Chem. Eng., accepted for publication). AMLE is a method for estimating the states and parameters in differential equation models with possible modeling imperfections. The nylon reactor model equations are represented by stochastic differential equations (SDEs) to account for any modeling errors or unknown process disturbances that enter the reactor system during experimental runs. In this article, we demonstrate that AMLE can address difficulties that frequently arise when estimating parameters in nonlinear continuous-time dynamic models of industrial processes. Among these difficulties are different types of measured responses with different levels of measurement noise, measurements taken at irregularly spaced sampling times, unknown initial conditions for some state variables, unmeasured state variables, and unknown disturbances that enter the process and influence its future behavior.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".