Minimum-Zone Form Tolerance Evaluation Using Rigid-Body Coordinate Transformation
Bibliographic record
Abstract
This paper presents an optimization approach for the accurate evaluation of minimum-zone form tolerances from discrete coordinate measurement data. The approach minimizes the minimum-deviation objective function defined as the difference between the maximum and minimum distances of the measured coordinate data from the reference feature. The objective function is formulated as a function of rigid-body coordinate transformation parameters and involves fewer independent parameters than the existing tolerance evaluation algorithms. As a result, improved convergence efficiency and numerical stability are achieved. A standard direct search algorithm, the downhill simplex search algorithm, is employed to minimize the objective function. The least-squares estimates are employed as good initial conditions to facilitate convergence to the global solutions. A new method, named as the Median Technique, is implemented to well center the circularity measured data and well align the cylindricity measured data in order to provide valid least-squares estimates based on the Limacon approximation. Results from simulation and comparative studies have shown that the proposed method evaluates minimum-zone form tolerances with reliable accuracy.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".