Maximum likelihood estimation for leak localization in water distribution networks using in-pipe acoustic sensing
Bibliographic record
Abstract
With drinking water resources rapidly depleting with time, water conservation efforts have received special emphasis, especially in arid regions like California. One of the major sources of unused water expenditure is inconspicuous leaks in underground water distribution networks (WDN), making it highly essential to quickly detect and localize them. The leak detection and localization problem has been widely studied for a straight pipeline system, however, estimating the leak location in a pipe network remains largely unexplored. In this study, we measure the acoustic pressure signals inside a pipe network at multiple locations using state-of-the-art hydrophone-enabled devices. To localize the leaks in pipe networks, we propose maximum likelihood estimation, which has previously shown high efficacy in localizing mobile devices in a cellular network. In this approach, the cross-correlation of the filtered signals from different sensor pairs yields multiple time delays corresponding to multiple acoustic paths traversed by the leak noise in the pipe network, which is more difficult to solve compared to a straight pipe system. The leak location is then identified by maximizing a conditional probability distribution function of the distance between the sensor and the leak location.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".