Open AccessProceeding Paper

Sensor Placement for Rupture Detection Using a Continuous Monitoring Strategy^†

Elena Batzella

^*,

Giacomo Ferrarese

and

Stefano Malavasi

Civil and Environmental Engineering Department, Politecnico di Milano, 20133 Milan, Italy

Author to whom correspondence should be addressed.

^†

Presented at the 3rd International Joint Conference on Water Distribution Systems Analysis & Computing and Control for the Water Industry (WDSA/CCWI 2024), Ferrara, Italy, 1–4 July 2024.

Eng. Proc. 2024, 69(1), 91; https://doi.org/10.3390/engproc2024069091

Published: 9 September 2024

(This article belongs to the Proceedings of The 3rd International Joint Conference on Water Distribution Systems Analysis & Computing and Control for the Water Industry (WDSA/CCWI 2024))

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Abstract

This work proposes an analysis of the active monitoring method for rupture detection. The analysis regards the effect of sensor sensibility on the effectiveness of the localization method. This paper approaches the problem in two steps: the first step regards the detection of ruptures according to a method based on a sensitivity matrix and correlation analysis. The second step regards the selection of an effective sensor placement strategy. The aim is to determine the most effective position in terms of rupture localization ability of a predetermined number of sensors using sensor sensibility within the input variables.

Keywords:

sensor placement; rupture localization; sensitivity analysis

1. Introduction

Water leakages have considerable consequences for distribution system sustainability, causing the wastage of water resources and energy and the provision of an inefficient service. Many studies [1] provides methods and technologies for detecting and locating existent water leakages. However, detecting and, in the best-case scenario, repairing existing leaks does not represent a definitive management solution, as new ruptures may occur. Within this scope, continuous and real-time monitoring can play a crucial role in detecting new ruptures in the network [2]. The aim of this work is to study the rupture detection ability of a pressure monitoring system when varying the number, position, and sensibility of pressure sensors. The benchmark network used in this study is the well-known network introduced by [3]. To predict potential leaks, pressure distribution residuals generated by introducing synthetic ruptures of predefined entities (referred to as the “signature” residual matrix) are compared with the pressure distribution residuals generated by randomly placed ruptures with random entities (referred to as the “real” residual matrix) [4]. The comparison is performed through the correlation analysis of residual matrixes. The predictive capacity is evaluated based on a predefined number of sensors, optimizing their placement to achieve the maximum number of detectable leaks. Finally, the sensitivity of pressure sensor is introduced as an input parameter to verify its effect on the methodology’s capabilities and consequently on its actual applicability.

2. Methods

This work was developed on the “Araujo” network [3], represented in Figure 1 and firstly introduced by [5]. Fictitious nodes (in red) were added at mid-lengths of the pipes, in which, one by one, the ruptures were simulated to create the “signature” residual matrixes. The software used for the implementation was EPANET 2.2.5 and its toolkit for Matlab R2021b.

2.1. Localization Method

Water leakages were modeled according to the following equation:

q = {k p}^{γ}

(1)

where

q

is the leakage flow,

k

is the emitter coefficient,

p

is the node pressure where the leakage occurs, and

γ

is a theoretical coefficient equal to 0.5 [6]. The rupture localization method is based on the pressure residuals analysis between the scenario with and without a leak. The residuals were saved in reference “signature” matrices and compared with those generated by leakages with random entities and positions through a correlation analysis. The localization was obtained by identifying the matrix with the highest correlation coefficient. The matrix structure is as follows:

S_{f_{j}} = (\begin{matrix} {\hat{p}}_{1 f_{1}} - {\hat{p}}_{10} & \dots \begin{matrix} {\hat{p}}_{1 f_{j}} - {\hat{p}}_{10} & \dots \end{matrix} & {\hat{p}}_{1 f_{n_{p}}} - {\hat{p}}_{10} \\ ⋮ & \dots \begin{matrix} {\hat{p}}_{i f_{j}} - {\hat{p}}_{i 0} & \dots \end{matrix} & ⋮ \\ {\hat{p}}_{n_{s} f_{1}} - {\hat{p}}_{n_{s} 0} & \dots \begin{matrix} {\hat{p}}_{n_{s} f_{j}} - {\hat{p}}_{n_{s} 0} & \dots \end{matrix} & {\hat{p}}_{n_{s} f_{n_{p}}} - {\hat{p}}_{n_{s} 0} \end{matrix})

(2)

where

{\hat{p}}_{i 0}

is the pressure at node i for the base scenario,

{\hat{p}}_{i f_{j}}

is the pressure at node i due to the leakage of entity

f

at node j,

n_{p}

is the number of potential positions where a leakage can occur (equal to the number of links), and

n_{s}

is the number of installed sensors. Reference signature matrices were built using emitter values equal to [10⁻⁴ 10⁻³ 10⁻² 10⁻¹]. For the estimation of the “real” residual matrix, emitter values were chosen randomly in the range [10⁻⁴–1].

2.2. Sensor Placement Method

To find the sensor configuration able to identify the greatest number of leaks, all possible combinations were tested. Assuming a network with

n_{p}

nodes and

n_{s}

sensors to be installed, the

(\begin{matrix} n_{s} \\ n_{p} \end{matrix}) = \frac{n_{p}!}{(n_{p} - n_{s})! n_{s}!}

(3)

combination was tested by varying

n_{s}

from 1 to

n_{p}

. Starting from the minimum number of sensors, an exhaustive approach was used, increasing

n_{s}

until an acceptable computational cost and localized loss rate was reached. The procedure described in Section 2.1 was applied for each sensor combination to evaluate its leakage localization capability. The result for

n_{s} = 4

is the configuration shown in Figure 1b, which is able to identify 78% of the simulated ruptures.

2.3. Sensor Sensitivity Effect

To account for real sensor capabilities, two approaches were applied, namely an ex post analysis, that considered the placement obtained considering ideal sensors and recalculating the localization capability, and an ex ante analysis, where the sensitivity of the sensor was used as the input data for the placement method. The sensitivity was set to 0.001, 0.01 and 0.1 bar, respectively.

3. Results

3.1. Ex Post Analysis

To consider the sensitivity variations, the pressure values obtained from the simulation were truncated to the reference significant digit. A random error within the range corresponding to the considered sensitivity was added and the value was rounded to the reference significant digit. To properly consider the random aspect, the error addition was repeated several times, resulting in a sample of 20 values for each sensitivity.

The results in Figure 2a were obtained considering ruptures varying in size and in position. It is shown how reducing instrument sensitivity also causes a decrease in localization capability. For the sensor combination obtained in Section 2.2, the detection capability ranges from 78% for ideal sensitivity to 30% for 0.001 bar, 11% for 0.01 bar, and 4% for 0.1 bar.

The analysis was repeated considering the leakage magnitude and thus a specific emitter value (k = 0.0004 and k = 0.2660). As expected, the detection capability grows with increasing leakage size. The results are shown in Figure 2b.

3.2. Ex Ante Analysis

In this section, the analysis is developed by first considering the sensitivity as an input parameter for the sensor placement method. Different optimal placements were obtained (Figure 3b) for each sensitivity, and their detection capability increases compared to that obtained considering realistic sensitivity in post-processing (Figure 3a). The detection capability increases from 30% to 67% for 0.001 bar, from 11% to 52% for 0.01 bar, and from 4% to 28% for 0.1 bar.

4. Conclusions

The analysis undertaken addresses the issue of sensor placement in water distribution networks for the localization of occurring ruptures. In addition to the complexity of determining the number and positioning of sensors, the analysis considers the influence of measurement sensitivity and shows its significant impacts on the rupture localization effectiveness. This study not only demonstrates how reducing sensitivity diminishes leak localization capability but also highlights the importance of considering sensibility in the sensor placement procedure.

Author Contributions

Conceptualization, G.F. and S.M.; methodology, all authors; software, E.B.; validation, all authors; formal analysis, E.B.; investigation, E.B. and G.F.; data curation, E.B.; writing—original draft preparation, all authors; writing—review and editing, all authors. All authors have read and agreed to the published version of the manuscript.

Funding

Investigation performed within the MUSA—Multilayered Urban Sustainability Action—project, funded by the European Union—NextGenerationEU, under the National Recovery and Resilience Plan (NRRP) Mission 4 Component 2 Investment Line 1.5: Strengthening of research structures and creation of R&D “innovation ecosystems”, set up of “territorial leaders in R&D”.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

References

Zaman, D.; Tiwari, M.K.; Gupta, A.K.; Sen, D. A review of leakage detection strategies for pressurised pipeline in steady-state. In Engineering Failure Analysis; Elsevier Ltd.: Amsterdam, The Netherlands, 2020; Volume 109. [Google Scholar]
Kim, R.; Choi, Y.H. The Development of a Data-Based Leakage Pinpoint Detection Technique for Water Distribution Systems. Mathematics 2023, 11, 2136. [Google Scholar] [CrossRef]
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Figure 1. (a) Araujo network with fictitious nodes; (b) optimal node combination (in green) obtained in Section 2.2.

Figure 2. (a) Detection capability function of instrument sensitivity used to localize ruptures with a variable emitter in the range [

10^{- 4} 1

]. (b) Comparison of detection capability considering a variable emitter in the range [

10^{- 4} 1

] and specific emitter values (k = 0.0004 and k = 0.2660).

Figure 2. (a) Detection capability function of instrument sensitivity used to localize ruptures with a variable emitter in the range [

10^{- 4} 1

]. (b) Comparison of detection capability considering a variable emitter in the range [

10^{- 4} 1

] and specific emitter values (k = 0.0004 and k = 0.2660).

Figure 3. Comparison of detection capability considering an ex ante and ex post approach.

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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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MDPI and ACS Style

Batzella, E.; Ferrarese, G.; Malavasi, S. Sensor Placement for Rupture Detection Using a Continuous Monitoring Strategy. Eng. Proc. 2024, 69, 91. https://doi.org/10.3390/engproc2024069091

AMA Style

Batzella E, Ferrarese G, Malavasi S. Sensor Placement for Rupture Detection Using a Continuous Monitoring Strategy. Engineering Proceedings. 2024; 69(1):91. https://doi.org/10.3390/engproc2024069091

Chicago/Turabian Style

Batzella, Elena, Giacomo Ferrarese, and Stefano Malavasi. 2024. "Sensor Placement for Rupture Detection Using a Continuous Monitoring Strategy" Engineering Proceedings 69, no. 1: 91. https://doi.org/10.3390/engproc2024069091

APA Style

Batzella, E., Ferrarese, G., & Malavasi, S. (2024). Sensor Placement for Rupture Detection Using a Continuous Monitoring Strategy. Engineering Proceedings, 69(1), 91. https://doi.org/10.3390/engproc2024069091

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Sensor Placement for Rupture Detection Using a Continuous Monitoring Strategy^†

Abstract

1. Introduction