State observer-based data assimilation: a PID control-inspired observer in the pressure equation
Bibliographic record
Abstract
Abstract A novel state observer-based data-assimilation technique is described and then assessed with a numerical test case. This novel technique assimilates pressure data through a state observer that is constructed based on a proportional-integral-derivative control law and that acts on the pressure equation. The technique is assessed by comparing the performance to a standard simulation and a data-assimilated simulation using a previously-established technique, wherein a proportional observer is placed in the momentum equations. First, the mechanism through which measured pressure data is assimilated into simulations is described for both the previously-established and the novel technique. Next, the techniques are applied to a square cylinder in cross-flow at a Reynolds number of 100. A reference simulation is run on a dense mesh, and both standard and data-assimilated simulations are run on a much coarser mesh. The primary characteristic used to evaluate the techniques is their dynamic performance, in terms of how quickly vortex shedding is realized and how accurately the frequency of the vortex shedding is modeled on the coarser mesh. Both of the data assimilation techniques produce simulations with a much faster transition from initial conditions to vortex shedding than the standard simulation on the coarse mesh. The data-assimilated simulation using an observer in the pressure equations most accurately estimates the pressures and velocities at the probed locations and produces a frequency spectrum that most closely matches the reference simulation.
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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 | 0.001 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".