# A Digital Twin of a Water Distribution System by Using Graph Convolutional Networks for Pump Speed-Based State Estimation

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Temporal-Graph Convolutional Neural Networks

#### 2.2. Evaluation Parameters

#### 2.3. Pressure and Flow Calculation from the Estimated Relative Speed

## 3. Case Studies

#### 3.1. Network 1: Patios Network-Villa del Rosario

#### 3.2. Network 2: C-Town Network

#### 3.3. Data Set Generation for T-GCN Application

## 4. Results

#### 4.1. T-GCN Evaluation for Pump Speed Estimation

#### 4.2. Estimation of Pressure and Flowrate Using Estimated Pump Speeds

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Methodology for pressure and flow rate estimation based on estimated relative pump speeds.

**Figure 3.**Topology and spatial distribution of sensors in (

**a**) Patios-Villa del Rosario (Network 1), (

**b**) C-Town (Network 2).

**Figure 4.**Comparison between estimated and real relative pump speed for Patios-Villa del Rosario WDS.

**Figure 6.**Comparison curve of model predicted values and real values of the relative pump speeds for Network 2. (

**a**) PU2, (

**b**) PU4, (

**c**) PU6, (

**d**) PU8, (

**e**) PU10.

**Figure 7.**Scatter plots of predicted and real values of relative pump speeds for Network2. (

**a**) PU2 (

**b**) PU4 (

**c**) PU6 (

**d**) PU8 (

**e**) PU10.

Parameter | Network 1 | Network 2 |
---|---|---|

Total length | 43.54 km | 56.73 km |

Roughness Coefficient | 0.0015 mm (Darcy-Weisbach) | 60–140 (Hazen-Williams) |

Pipe diameter | 75–762 mm | 51–610 mm |

Number of pipes | 67 | 429 |

Number of nodes | 62 | 388 |

Number of reservoirs | 5 | 1 |

Number of pumps | 2 | 11 |

Number of tanks | 0 | 7 |

Number of valves | 0 | 5 |

Parameter | PU2 | PU4 | PU6 | PU8 | PU10 |
---|---|---|---|---|---|

$RMSE$ | 0.028 | 0.026 | 0.026 | 0.027 | 0.027 |

$MAE$ | 0.021 | 0.020 | 0.020 | 0.021 | 0.021 |

${r}^{2}$ | 0.801 | 0.815 | 0.799 | 0.802 | 0.802 |

Network 1 | Network 2 | ||||
---|---|---|---|---|---|

Parameter | Node 14 | Node J269 | Node J256 | Pipe p397 | Pipe J379 |

$RMSE$ | 1.8 | 2.9 | 1.7 | 1.8 | 9.7 |

$MAE$ | 1.1 | 2.0 | 1.3 | 1.2 | 2.6 |

${r}^{2}$ | 0.923 | 0.448 | 0.592 | 0.949 | 0.632 |

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**MDPI and ACS Style**

Bonilla, C.A.; Zanfei, A.; Brentan, B.; Montalvo, I.; Izquierdo, J.
A Digital Twin of a Water Distribution System by Using Graph Convolutional Networks for Pump Speed-Based State Estimation. *Water* **2022**, *14*, 514.
https://doi.org/10.3390/w14040514

**AMA Style**

Bonilla CA, Zanfei A, Brentan B, Montalvo I, Izquierdo J.
A Digital Twin of a Water Distribution System by Using Graph Convolutional Networks for Pump Speed-Based State Estimation. *Water*. 2022; 14(4):514.
https://doi.org/10.3390/w14040514

**Chicago/Turabian Style**

Bonilla, Carlos A., Ariele Zanfei, Bruno Brentan, Idel Montalvo, and Joaquín Izquierdo.
2022. "A Digital Twin of a Water Distribution System by Using Graph Convolutional Networks for Pump Speed-Based State Estimation" *Water* 14, no. 4: 514.
https://doi.org/10.3390/w14040514