# Analysis of Optimal Sensor Placement in Looped Water Distribution Networks Using Different Water Quality Models

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup and Conditions

^{3}of water (Figure 2). The pumping system, which consists of four vertical multistage centrifugal electric pumps and an air vessel that allows pressure stabilisation, behaves like a constant load tank, keeping the pressure constant and equal to a pre-set value between 1 and 6 bar with a tolerance of 0.05 bar; the pumping system varies the speed of the pumps.

#### 2.2. Optimisation of Sensor Placement

- F_1, the detection likelihood, i.e., the probability that a sensor configuration will detect the contamination;
- F_2, the detection time, i.e., the average time between contamination and detection in 200 simulations;
- F_3, the detection redundancy, i.e., the probability that two sensors detect the contamination within 20 min.

## 3. Results and Discussions

## 4. Conclusions

- When the advective approach was used to solve the optimisation problem, the sensors were positioned in areas with high Reynolds numbers, where the flow regimes are predominantly turbulent and transition;
- The sensors were positioned in a linear pattern and covered most of the network using the dispersive AZRED approach;
- The EPANET-DD model provided the best performance, with a contamination event detection likelihood of 95%, a redundancy of 70%, and a detection time of approximately 9 min;
- Different configurations for sensor positions are obtained depending on the model used to solve the optimisation problem, as are different detection efficiencies for the objective functions. For example, the parameter values determined by the advective model are much lower than those determined by the dynamic dispersive model (EPANET-DD).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Overview of the experimental water distribution network (

**a**), pumping system (

**b**), and recirculation system (

**c**).

**Figure 5.**The Pareto front, including only advection (row (

**a**)), dispersion (AZRED by Romero-Gomez and Choi 2011, row (

**b**)), and dispersion (EPANET-DD) (row (

**c**)): F_1–F_3 (left), F_1–F_2 (centre), and F_2–F_3 (right).

Advective Model | Romero-Gomez and Choi (2011) Model | EPANET-DD Model | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Objective Functions | Optim. Values | Sensor Node Index | Optim. Values | Sensor Node Index | Optim. Values | Sensor Node Index | ||||||

Detection Likelihood (F_1) | 0.66 | 5 | 6 | 10 | 0.65 | 6 | 8 | 9 | 0.95 | 6 | 7 | 10 |

Detection Time [s] (F_2) | 517.13 | 5 | 6 | 10 | 858.54 | 6 | 8 | 9 | 538.96 | 6 | 7 | 10 |

Redundancy (F_3) | 0.52 | 5 | 6 | 11 | 0.54 | 5 | 6 | 7 | 0.70 | 6 | 7 | 10 |

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**MDPI and ACS Style**

Piazza, S.; Sambito, M.; Freni, G. Analysis of Optimal Sensor Placement in Looped Water Distribution Networks Using Different Water Quality Models. *Water* **2023**, *15*, 559.
https://doi.org/10.3390/w15030559

**AMA Style**

Piazza S, Sambito M, Freni G. Analysis of Optimal Sensor Placement in Looped Water Distribution Networks Using Different Water Quality Models. *Water*. 2023; 15(3):559.
https://doi.org/10.3390/w15030559

**Chicago/Turabian Style**

Piazza, Stefania, Mariacrocetta Sambito, and Gabriele Freni. 2023. "Analysis of Optimal Sensor Placement in Looped Water Distribution Networks Using Different Water Quality Models" *Water* 15, no. 3: 559.
https://doi.org/10.3390/w15030559