An approximate expectation maximisation algorithm for estimating parameters in nonlinear dynamic models with process disturbances
Bibliographic record
Abstract
Stochastic terms are included in fundamental dynamic models of chemical processes to account for disturbances, input uncertainties and model mismatch. The resulting equations are called stochastic differential equations (SDEs). An approximate expectation maximisation (AEM) algorithm using B‐splines is developed for estimating parameters in SDE models when the magnitude of the disturbances and model mismatch is unknown. The AEM method is evaluated using a two‐state nonlinear continuous stirred tank reactor (CSTR) model. The proposed algorithm is compared with two other maximum‐likelihood‐based methods (continuous time stochastic modelling (CTSM) [Kristensen and Madsen, Continuous Time Stochastic Modelling: CTSM 2.3 User's Guide, 2003; Kristensen et al., Automatica 2004; 40: 225] and extended approximate maximum likelihood estimation (AMLE) [Varziri et al., Can. J. Chem. Eng . 2008; 86: 828]). For the CSTR examples studied, the AEM algorithm provides more accurate estimates of model parameters, unknown initial conditions and disturbance intensities. SDE models and associated parameter estimates obtained using AEM will be helpful to engineers who subsequently implement on‐line state estimation and process monitoring schemes because the two types of uncertainties that are considered (i.e. measurement noise and stochastic process disturbances) are consistent with the error structure used in extended Kalman filters.
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How this classification was reachedexpand
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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".