Leak Localization in Looped Pipe Networks Based on a Factorized Transient Wave Model: Theoretical Framework

Chuan, Tong; Wang, Xun; Ghidaoui, Mohamed Salah

doi:10.1029/2021wr031364

Cited by 12 publications

(36 citation statements)

References 54 publications

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“…If there is no measurement noise, the

{h}_{j}^{NL}

at Sensor M4 can be computed based on

{q}_{j}\left({x}_{1}^{U}\right),{h}_{j}\left({x}_{1}^{U}\right)

{q}_{j}\left({x}_{2}^{U}\right)

, and

{h}_{j}\left({x}_{2}^{U}\right)

by the following wave propagation model (Che et al., 2022)

\begin{matrix} right (\begin{matrix} center q_{j}^{N L} \\ center h_{j}^{N L} \end{matrix}) & center = & left {boldF}^{N L} (x_{4}^{U} \to x_{4}^{M}) {boldF}^{N L} (x_{3}^{U} \to x_{3}^{D}) {boldF}^{N L} (x_{1}^{U} \to x_{1}^{D}) (\begin{matrix} center q_{j} (x_{1}^{U}) \\ center h_{j} (x_{1}^{U}) \end{matrix}) \\ right & center - & left {boldF}^{N L} (x_{4}^{U} \to x_{4}^{M}) {boldF}^{N L} (x_{3}^{U} \to x_{3}^{D}) {boldP}_{11} (\begin{matrix} center q_{j} (x_{2}^{U}) \\ center h_{j} (x_{2}^{U}) \end{matrix}) \end{matrix}

…”

Section: Alternative Methods To Tikhonov Regularizationmentioning

confidence: 99%

“…As proved by Che et al (2022), to formulate a tree-shaped control volume for the one-loop network with a unknown leak, 4P = 16 unknown pipe end hydraulic properties needs to be computed by boundary measurements at Sensors M1 and M4. At the jth frequency ω j , the measured pressure heads by Sensors M1 and M4 can be expressed as = coordinates of Sensors M1 and M4; h = pressure head without noise; h n = measured pressure head with noise; n = measurement noise; and the subscript "j" means that the physical quantity is at the frequency ω j .…”

Section: Overall Shape Distortion Of Desired Signalsmentioning

confidence: 99%

“…At the frequency ω j , all 4P = 16 linear equations of the one-loop network, including Equations 3 and 4, can be written in the following matrix equation form (Che et al, 2022) The optimal pipe end hydraulic property vector 𝐴𝐴 x𝐱𝑝𝑝 𝐴𝐴𝐴𝐴 of the one-loop network can be estimated by a least squares solution of Equation 5as…”

Section: Overall Shape Distortion Of Desired Signalsmentioning

confidence: 99%

“…Once all pipe end hydraulic properties are determined by Equation 6, a tree-shaped control volume of the one-loop network can be formulated in Figure 1b, where the original loop structure is broken by two infinitely close Nodes (5′) and (6′). The detailed principles and criteria for the control volume formulation were given by Che et al (2022). If there is no measurement noise, the pressure head at Sensor M4 can be expressed by the factorized model as (Che et al, 2022)…”

Section: Overall Shape Distortion Of Desired Signalsmentioning

confidence: 99%

See 3 more Smart Citations

Leak Localization in Looped Pipe Networks Based on a Factorized Transient Wave Model: 2. Regularization of Ill‐Conditioned Problems

Chuan

Wang

Louati

et al. 2022

Water Resources Research

Self Cite

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show abstract

“…If there is no measurement noise, the

{h}_{j}^{NL}

at Sensor M4 can be computed based on

{q}_{j}\left({x}_{1}^{U}\right),{h}_{j}\left({x}_{1}^{U}\right)

{q}_{j}\left({x}_{2}^{U}\right)

, and

{h}_{j}\left({x}_{2}^{U}\right)

by the following wave propagation model (Che et al., 2022)

\begin{matrix} right (\begin{matrix} center q_{j}^{N L} \\ center h_{j}^{N L} \end{matrix}) & center = & left {boldF}^{N L} (x_{4}^{U} \to x_{4}^{M}) {boldF}^{N L} (x_{3}^{U} \to x_{3}^{D}) {boldF}^{N L} (x_{1}^{U} \to x_{1}^{D}) (\begin{matrix} center q_{j} (x_{1}^{U}) \\ center h_{j} (x_{1}^{U}) \end{matrix}) \\ right & center - & left {boldF}^{N L} (x_{4}^{U} \to x_{4}^{M}) {boldF}^{N L} (x_{3}^{U} \to x_{3}^{D}) {boldP}_{11} (\begin{matrix} center q_{j} (x_{2}^{U}) \\ center h_{j} (x_{2}^{U}) \end{matrix}) \end{matrix}

…”

Section: Alternative Methods To Tikhonov Regularizationmentioning

confidence: 99%

Section: Overall Shape Distortion Of Desired Signalsmentioning

confidence: 99%

Section: Overall Shape Distortion Of Desired Signalsmentioning

confidence: 99%

Section: Overall Shape Distortion Of Desired Signalsmentioning

confidence: 99%

See 2 more Smart Citations

Leak Localization in Looped Pipe Networks Based on a Factorized Transient Wave Model: 2. Regularization of Ill‐Conditioned Problems

Chuan

Wang

Louati

et al. 2022

Water Resources Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…In further studies, the method has been extended for multiple defects detection and leak detection in multiple pipeline systems, demonstrating that the method is robust and noise-tolerant (X. Che et al, 2022;X. Wang & Ghidaoui, 2018a.…”

mentioning

confidence: 99%

Efficient Pipe Burst Detection in Tree‐Shape Water Distribution Networks Using Forward‐Backward Transient Analysis

Pan

Duan

Keramat

et al. 2022

Water Resources Research

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Transient‐based leak/burst detection has received more and more attentions in the operation and management of water distribution networks. However, with the increase in pipe network complexity, it is hard to detect and locate the potential pipe defects and water losses efficiently. Recently, we proposed an efficient leak/burst localization strategy in single pipelines based on the forward and backward transient analysis, and in this work, this effective approach is customized for the more realistic branched (tree‐shaped) pipe networks. Unlike traditional transient‐based methods which rely on tedious optimization procedures, the proposed method uses a mismatch property between forward and backward analyses of transient signals for the pipe burst detection during the water supply process. Compared with other developed methods, this method can directly calculate the defect location, so it is expected to have high efficiency and wide applicability. To fulfill this goal, a framework for burst detection in a tree‐shaped pipe network is developed in this paper. Using the mass conservation and energy relations at the branched junctions, the forward and backward transient analysis is extended from one pipe to another until the burst is found and then located in the network. Both experimental and numerical tests show the effectiveness of the proposed method, and further analysis has shown that the method is also valid for leak detection in both transient and steady conditions, confirming the robustness and practicality of this proposed method. At last, this paper discusses the influence of transient sources and the potential combination of the method with other methods.

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State‐of‐the‐art review of leak diagnostic experiments: Toward a smart water network

Bakhtawar

Zayed

2023

WIREs Water

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Effective water pipeline leak detection and localization can help water practitioners save water losses and reduce pipe rehabilitation budgets. Different sensing technologies can provide essential data aiding model development for predicting future leaks in the water distribution networks. Solutions for applying different sensing technologies to real water distribution networks are being developed for real‐time data collection, precise leak localization, reducing false alarms, and continuous pipeline monitoring. Experiments of different scales and specifications have been conducted to test the application and effectiveness of sensing technologies for leak diagnosis in water pipelines. Quality data collection is especially crucial for the successful implementation of these experiments. However, practitioners need help designing effective leak detection and localization experiments, wasting time, and resources. There needs to be a greater understanding of the design parameters for more accurate testing, such as sensor selection, sensor placement, ambient noise sources, and system operations. The current study, therefore, delineates design parameters for design leak diagnosis experiments for lab, testbed, and real networks. For application in real water networks, expert opinion is used to help identify the benefits and limitations and the implementation issues of available sensing technologies. An example experiment design using multi‐sensing technologies for smart leak diagnostics in Hong Kong is also presented. The study can guide water practitioners and researchers to design a multi‐sensing leak diagnostic experiments enabling a smart and sustainable utility management.This article is categorized under: Engineering Water > Methods Engineering Water > Sustainable Engineering of Water Science of Water > Water Extremes

show abstract

Leak Localization in Looped Pipe Networks Based on a Factorized Transient Wave Model: Theoretical Framework

Cited by 12 publications

References 54 publications

Leak Localization in Looped Pipe Networks Based on a Factorized Transient Wave Model: 2. Regularization of Ill‐Conditioned Problems

Leak Localization in Looped Pipe Networks Based on a Factorized Transient Wave Model: 2. Regularization of Ill‐Conditioned Problems

Efficient Pipe Burst Detection in Tree‐Shape Water Distribution Networks Using Forward‐Backward Transient Analysis

State‐of‐the‐art review of leak diagnostic experiments: Toward a smart water network

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