# Estimation of Water Demand in Water Distribution Systems Using Particle Swarm Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Objective Function

#### 3.2. Modeling of Water Demand Multipliers

#### 3.3. Process Simulation Model

#### 3.4. Selection of Sensor Placement Locations

## 4. Simulation Results and Discussion

#### 4.1. Case Study I: Estimation of Nodal Demands with Measurements from Pressure Head Sensors

#### 4.2. Case Study II: Estimation of Nodal Demands with Measurements from Flow Sensors and Pressure Sensors

#### 4.3. Case Study III: Estimation of Water Demand in a Larger Water Network

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**Case I: Estimation of water demands with demand multiplier resolutions of $\Delta $ = 0.05 and $\Delta $ = 0.01 at nodes (

**a**) 2, (

**b**) 4, (

**c**) 6, and (

**d**) 9.

**Figure 10.**Case II: Estimation of pipe flow rates in pipes (

**a**) 2, (

**b**) 5, (

**c**) 6, and (

**d**) 7 using uncertain measurements.

**Figure 11.**Case II: Estimation of pipe flow rates in pipes (

**a**) 3, (

**b**) 8, (

**c**) 10, and (

**d**) 11 using uncertain measurements.

Parameter | Value |
---|---|

Population (P) | 50 |

Number of iterations (N) | 100 |

Inertia factor (${w}_{max},{w}_{min}$) | 0.5, 0.05 |

Social rate (${C}_{1}$) | 0.9 |

Cognitive rate (${C}_{2}$) | 2.5 |

Node | Actual | Estimated | % Error |
---|---|---|---|

2 | 9.46 | 9.44 | 0.2 |

3 | 9.46 | 8.24 | 12.9 |

4 | 6.31 | 6.49 | 2.7 |

5 | 9.46 | 9.55 | 0.1 |

6 | 12.62 | 13.40 | 6.2 |

7 | 9.46 | 8.58 | 9.3 |

8 | 6.31 | 6.35 | 0.6 |

9 | 6.31 | 6.17 | 2.2 |

**Table 3.**Case I: Comparison of estimated nodal demands (gallons per minute—GPM) using particle swarm optimization (PSO) and the genetic algorithm (GA).

Node | Actual | Estimated (PSO) | Estimated (GA) | % Error (PSO) | % Error (GA) |
---|---|---|---|---|---|

2 | 150 | 149.60 | 118.67 | 0.2 | 20.9 |

3 | 150 | 130.59 | 131.45 | 12.9 | 12.4 |

4 | 100 | 102.85 | 93.15 | 2.7 | 6.9 |

5 | 150 | 151.35 | 164.15 | 0.1 | 9.43 |

6 | 200/(150) | 212.36 | 140.58 | 6.2 | 6.3 |

7 | 150/(300) | 135.97 | (327.15) | 9.3 | 9.1 |

8 | 100/(50) | 100.63 | (50.34) | 0.6 | 0.7 |

9 | 100/(50) | 97.78 | (35.90) | 2.2 | 28.2 |

Node | Actual | Estimated ($\Delta $ = 0.05) | % Error | Estimated ($\Delta $ = 0.01) | % Error |
---|---|---|---|---|---|

2 | 9.39 | 9.33 | 0.3 | 9.37 | 0.2 |

3 | 9.39 | 8.58 | 8.6 | 8.75 | 6.8 |

4 | 6.26 | 6.39 | 2.1 | 6.43 | 2.7 |

5 | 9.39 | 9.75 | 3.8 | 9.57 | 1.9 |

6 | 12.53 | 12.87 | 2.7 | 13.10 | 4.5 |

7 | 9.39 | 8.65 | 7.9 | 8.57 | 8.7 |

8 | 6.26 | 6.22 | 0.6 | 6.30 | 0.6 |

9 | 6.26 | 6.17 | 1.4 | 6.15 | 1.7 |

Node | Actual | Estimated | % Error |
---|---|---|---|

2 | 9.39 | 9.59 | 2.1 |

3 | 9.39 | 9.42 | 0.3 |

4 | 6.26 | 5.77 | 7.9 |

5 | 9.39 | 8.78 | 6.5 |

6 | 12.53 | 13.08 | 4.4 |

7 | 9.39 | 9.75 | 3.8 |

8 | 6.26 | 6.50 | 3.7 |

9 | 6.26 | 5.99 | 4.4 |

Pipe | Actual | Estimated | % Error |
---|---|---|---|

1 | 117.75 | 117.73 | 0.0 |

2 | 77.62 | 77.74 | 0.2 |

3 | 8.22 | 7.95 | 3.2 |

4 | 12.11 | 12.55 | 3.6 |

5 | 7.54 | 7.57 | 0.5 |

6 | 2.81 | 2.58 | 8.3 |

7 | −48.44 | −48.85 | 0.9 |

8 | 30.68 | 30.40 | 0.9 |

9 | 11.52 | 11.52 | 0.0 |

10 | 1.91 | 2.18 | 13.9 |

11 | 9.12 | 9.07 | 0.5 |

12 | 3.49 | 3.41 | 2.2 |

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**MDPI and ACS Style**

Letting, L.K.; Hamam, Y.; Abu-Mahfouz, A.M.
Estimation of Water Demand in Water Distribution Systems Using Particle Swarm Optimization. *Water* **2017**, *9*, 593.
https://doi.org/10.3390/w9080593

**AMA Style**

Letting LK, Hamam Y, Abu-Mahfouz AM.
Estimation of Water Demand in Water Distribution Systems Using Particle Swarm Optimization. *Water*. 2017; 9(8):593.
https://doi.org/10.3390/w9080593

**Chicago/Turabian Style**

Letting, Lawrence K., Yskandar Hamam, and Adnan M. Abu-Mahfouz.
2017. "Estimation of Water Demand in Water Distribution Systems Using Particle Swarm Optimization" *Water* 9, no. 8: 593.
https://doi.org/10.3390/w9080593