Fault detection and isolation of dissipative parabolic PDEs: Finite-dimensional geometric approach
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Bibliographic record
Abstract
In this paper, a nonlinear geometric fault detection and isolation (FDI) method is developed for a system that is governed by a dissipative parabolic partial differential equation (PDE) and that can be approximated by a finite-dimensional ordinary differential equations (ODE). The Galerkin method is employed to derive an approximate ODE which is utilized to design a geometric FDI system. Using singular perturbation theory, it is shown that under certain conditions the designed FDI system can detect and isolate faults corresponding to the original PDE. In addition, the Approximate Inertial Manifold (AIM) concept is used to improve the performance of the designed FDI filter. It is shown that by using the AIM-based approach, one can accomplish fault detection to an arbitrary degree of accuracy, although this technique cannot improve the fault isolation problem.
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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 | 0.001 |
| 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