Model-based water distribution network leak localization

QC 20260511

Abstract

Water is an essential resource, and providing reliable water supply to all citizens is a critical societal responsibility. In urban areas, this is typically achieved through water distribution pipe networks. Unfortunately, such networks are universally plagued by leakages, which account for substantial water losses, wasting both energy and financial resources while reducing supply capacity. Beyond these economic consequences, leaks pose serious hazards: they can undermine and damage infrastructure, and create risks of contamination and disease spread. The prompt localization and repair of leakages is therefore of paramount importance.

Hydraulic model-based leak localization is an approach that estimates leak positions by combining equations describing network hydraulics with sensor measurements of water production, consumption, pressure, and potentially flow. The field has a long history of academic research, with many sophisticated and effective methods having been proposed. This thesis aims to complement the existing literature, which largely relies on simulation-based performance evaluation, by establishing theoretical conditions under which leak localization can be guaranteed to succeed. The results are derived under idealized assumptions, yet they illuminate behavior that is observed in more general circumstances.

The thesis is based on five articles presented across four technical chapters, preceded by a modeling chapter that introduces the abstractions and assumptions adopted throughout. The modeling chapter also serves to unify notation and, notably, introduces a formulation for leakages that can occur anywhere along any pipe in the network, going beyond the common practice of restricting attention to node leakages only.

In the first technical chapter, a single-pipe scenario is considered. The leaking pipe has unknown hydraulic resistance parameters, and the problem of simultaneously estimating the uncertain model and localizing the leak is analyzed. Under a particular parameterization, the problem takes a bilinear form, for which dedicated solution methods are examined and convergence rates derived. Practical performance is further assessed through a simulation study.

In the second technical chapter, hydraulic resistance parameter estimation is considered; a problem that, much like leak localization, is often ill-posed. For a small-scale network representing a well-field for water production, sufficient conditions for unique parameter estimation are derived. These conditions highlight the necessity of adequate data variation, and a simulation example illustrates how estimation performs in practice.

In the third technical chapter, leak localization is investigated in a network with pipes connected in parallel. This configuration serves as a condensed representation that isolates the positional ambiguity introduced by loops. Necessary sensor conditions for leak localization are derived, and it is shown that even under maximal sensorization, unique determination of the leak position is often impossible or at least severely limited. The findings are validated through both simulation examples and physical laboratory experiments.

In the fourth and final technical chapter, leak localization in general networks is examined. The distinguishability and localizability problems---fundamental prerequisites for reliable leak localization---are studied, and structural sufficient conditions on network topology and pressure sensor placement are derived to guarantee both properties. Illustrative examples in small-scale networks are provided to elucidate the theoretical findings.

Taken together, the presented results offer rigorous insight into the requirements for reliable leak localization, while also pointing to open questions that remain to be addressed in future work.

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