Multivariate Gaussian process regression for nonlinear modelling with colored noise
Bibliographic record
Abstract
Nonlinearity of process systems along with colored noises is common in chemical processes. A multivariate (multiple inputs and multiple outputs) Gaussian process regression (MGPR) modelling approach, which can model multivariate nonlinear processes, is developed in this paper. The developed GPR model considers the Gaussian colored noise, rather than the traditional Gaussian white noise. The colored noise is described by the moving average (MA) model and the autoregressive (AR) model, respectively, with unknown parameters so that a MA-GPR model and an AR-GPR model are developed. These two colored noise based models are further extended to the MGPR model to generate the MA-MGPR model and the AR-MGPR model. The covariance functions of the MA-MGPR model or the AR-MGPR model are formulated with consideration of the autocorrelation of noises. Moreover, all parameters are estimated by using a unidimensional updated particle swarm optimization (PSO) algorithm, simultaneously. Numerical examples as well as a three-level drawing model of Carbon fiber production process are used to demonstrate the effectiveness of the proposed modelling approaches.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".