Maximum Likelihood Estimation to Localize Leaks in Water Distribution Networks
Bibliographic record
Abstract
Leaks cause significant water loss in underground water distribution networks, which makes it critical that utilities quickly detect, localize, and repair them. Acoustic leak detection and localization methods using hydrophones and accelerometers are the most studied technology; however, most studies for localizing leaks have focused on simple straight pipe segments using the cross-correlation technique. Leak localization in a network of pipes is significantly more challenging, and this problem remains largely unexplored in the literature. The difficulty arises because the cross-correlation between two acoustic sensor measurements yields multiple time delays corresponding to multiple paths between the acoustic source and the sensors in a network. Hence, the problem of localizing the leak correctly requires taking such multiple paths into account. In this paper, we propose a new method for localizing leaks in a network of pipes. Our method operates on multiple time difference of arrival (TDOA) by calculating the cross-correlation of the signals from different pairs of hydrophone sensors. A conditional probability distribution function is calculated corresponding to each TDOA, and the leak location is found based on the principle of maximum likelihood estimation. We also formally propose a new term called interior points where we define the conditions in which leaks can be pinpointed or only localized to the closest pipe joint. Using simulation studies, the proposed method is shown to accurately pinpoint leaks for the cases when the simulated leak satisfies appropriate conditions. The method is also validated by conducting experiments on a laboratory test bed where a simulated leak is pinpointed to within 10 cm of the actual 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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| 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 | 0.001 |
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".