Adaptive Exponential Fault Estimation for 1-D Linear Parabolic PDEs With Process Uncertainties
Bibliographic record
Abstract
The problem of fault estimation is addressed for one-dimensional (1-D) linear boundary control and boundary observation (BCBO) parabolic partial differential equations (PDEs) with a faulty boundary measurement. The considered plant is subjected to simultaneous unknown multiplicative faults entering the boundary input and boundary measurement. Difficulties arise due to the coupling between the sensor fault parameter and unknown boundary state appearing in the measurement. With the only boundary input and faulty boundary measurement, it is rather challenging to estimate the accurate values of faults and state simultaneously. Therefore, most existing results only consider correct and healthy measurement for PDE systems. To this end, novel adaptation laws and an adaptive observer are designed in this work to provide exponential convergent joint fault-state estimation, where we design and leverage a set of novel filters. It is first time that unknown multiplicative fault parameter in the measurement can be estimated accurately in the PDE systems.
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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".