Quantification of uncertainties in back-analysis of radar-tracked rockfall trajectories
Bibliographic record
Abstract
Accurate estimation of rockfall trajectories is essential for mitigation of rockfall hazards. Nowadays, Doppler radar technologies can measure rockfall trajectories with centimeter resolution. Calibrating a numerical model to fit these measured trajectories, i.e. back analysis, often involves manual trial-and-error processes and subjective goodness-of-fit criteria. Here, we propose a framework that uses the chi-square statistic to quantify the misfit between modeled and measured rockfall trajectories. The framework can also quantify the uncertainty bounds on the best-fit model parameters. The approach is validated using field data from an Australian copper mine under two scenarios. (1) We perform an unconstrained back-analysis where the initial position and velocity of the rock, in addition to the coefficients of restitution (COR), are free variables. This scenario yields a normal COR R n = 0.866 ± 0.109 and tangential COR R t = 0.29 ± 0.151 with 68% confidence. (2) We perform a constrained back-analysis using predetermined initial position and velocity of the rock, which further constrains R n to 0.8 ± 0.014 and R t to 0.39 ± 0.065. Both scenarios show a higher uncertainty in R t than in R n . We also demonstrate the adaptability of the back-analysis framework to two-dimensional (2D) rockfall modeling using the same data. To the best of our knowledge, this is the first quantitative goodness-of-fit metric for trajectory-based rockfall back analysis that supports the estimation of inherent uncertainty. The simplicity of the metric lends itself to robust model optimization of rockfall back-analysis and can be adapted to other model assumptions (e.g. rigid-body mechanics) and metrics (e.g. velocity or energy).
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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 | 0.001 |
| 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".