Inverse algorithm for extraction of multiple parameters using analytical model of eddy current response
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Bibliographic record
Abstract
Eddy current (EC) technology is commonly used for detecting flaws, measuring geometric parameters, or determining properties of conducting materials. However, the measurement of a particular parameter can become more challenging if multiple influential parameters vary simultaneously. In particular, eddy current-based measurement of separation (gap) between a pressure tube (PT) and a calandria tube (CT) in the fuel channels of CANDU® reactors is made more difficult by variations in PT wall thickness, resistivity, and probe lift-off. An analytical model of the EC response to changes in PT–CT gap has been developed by approximating the geometry of the PT within the larger diameter CT as a pair of concentric tubes, where gap is varied by changing the CT radius. In this article, this model is used in combination with an error minimization algorithm to construct an inverse algorithm for the extraction of PT–CT gap, PT resistivity (ρ), and PT wall thickness (WT) from measured multi-frequency eddy current signals. Application of a linear regression tool in MATLAB, with fourth-order polynomial fitting of modeled data with varying ρ and WT as a function of PT–CT gap, is used to obtain coefficients that depend on ρ and WT. Output of multidimensional fitting of these coefficients is scaled and rotated to calibration data. Finally, implementation of an error minimization algorithm in MATLAB is used to produce estimates of multiple target parameters from experimental data. Simultaneous extraction of either one, two, or three parameters is examined, using experimental data obtained at frequencies used for in-reactor inspection of 4.2, 8, and 16 kHz, or just two frequencies of 4.2 and 8 kHz. Under full gap variation conditions, the inverse algorithm predicts gap to within 0.1 mm at gaps between 0 and 9 mm and to within 0.4 mm at gaps between 9 and 18 mm. PT resistivity is predicted to within 1 μΩ cm (2% relative error) and PT wall thickness within 0.03 mm (1% relative error) when each is the only extracted parameter. An excellent agreement between actual and predicted values of gap demonstrates the potential of the inverse algorithm for application to in-reactor gap measurement and simultaneous extraction of either PT wall thickness or resistivity when the other parameter is known. The extraction of PT resistivity may be particularly useful, as this parameter cannot otherwise currently be measured in-reactor.
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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 | 0.001 | 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 it