PARAMETER ESTIMATION TECHNIQUES FOR NONLINEAR DYNAMIC MODELS WITH LIMITED DATA, PROCESS DISTURBANCES AND MODELING ERRORS
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Bibliographic record
Abstract
In this thesis appropriate statistical methods to overcome two types of problems that occur during parameter estimation in chemical engineering systems are studied.The first problem is having too many parameters to estimate from limited available data, assuming that the model structure is correct, while the second problem involves estimating unmeasured disturbances, assuming that enough data are available for parameter estimation.In the first part of this thesis, a model is developed to predict rates of undesirable reactions during the finishing stage of nylon 66 production.This model has too many parameters to estimate (56 unknown parameters) and not having enough data to reliably estimating all of the parameters.Statistical techniques are used to determine that 43 of 56 parameters should be estimated.The proposed model matches the data well.In the second part of this thesis, techniques are proposed for estimating parameters in Stochastic Differential Equations (SDEs).SDEs are fundamental dynamic models that take into account process disturbances and model mismatch.Three new approximate maximum likelihood methods are developed for estimating parameters in SDE models.First, an Approximate Expectation Maximization (AEM) algorithm is developed for estimating model parameters and process disturbance intensities when measurement noise variance is known.Then, a Fully-Laplace Approximation Expectation Maximization (FLAEM) algorithm is proposed for simultaneous estimation of model parameters, process disturbance intensities and measurement noise variances in nonlinear SDEs.Finally, a Laplace Approximation Maximum Likelihood Estimation (LAMLE) algorithm is developed for estimating measurement noise variances along with model parameters and disturbance intensities in nonlinear SDEs.The effectiveness of the proposed algorithms is compared with a maximum-likelihood based method.For the CSTR examples studied, the proposed algorithms provide more accurate estimates for the parameters.Additionally, it is shown that the performance of LAMLE is superior to the performance of FLAEM.SDE models and associated parameter estimates obtained using the proposed
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.004 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it