Estimating continuous highway vertical alignment using the least-squares method
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Bibliographic record
Abstract
Highway profile information may not be available or may not be up to date, especially for old highways. In these cases, profile data are collected using global positioning systems (GPS) or by extracting them from digital images. This paper presents an optimization model for estimating the parameters of continuous vertical alignments, involving multiple parabolic vertical curves that best fit existing highway profile data using the least-squares method. The optimization involves two levels: single-curve optimization and multiple-curve optimization. The former is used to obtain the approximate length of each vertical curve based on the approximate tangent parameters determined from the outline controlling points. The latter is used to obtain the global optimal parameters for tangents and vertical curves. The model is validated and applied using actual data of a vertical alignment. The proposed model presents a useful extension to existing methods for estimating simple vertical alignments and therefore should be of interest to highway engineering professionals.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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