# Estimation of Non-Revenue Water Ratio Using MRA and ANN in Water Distribution Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. General Research on the NRW Ratio and Theoretical Background

#### 2.1. Non-Revenue Water of a Water Distribution Network

_{b}is the volume of billed water per time unit [2].

- (a)
- Physical losses comprise leaks from all parts of a water distribution system and overflow at water storage tanks. They can be caused by poor operations and maintenance, lack of active leakage control, and poor quality of underground assets.
- (b)
- Commercial losses are caused by under-registration of customer meters, data handling errors, and theft of water in various forms.
- (c)
- Unbilled authorized consumption includes water used by a utility for operational purposes, that used in firefighting, and that provided free to certain consumer groups.

#### 2.2. Multiple Regression Analysis

#### 2.3. Artificial Neural Network

## 3. Methodology for Estimating the NRW Ratio Using MRA and ANN

^{2}) can be commonly used to compare measured and simulated values. Finally, the parameters that represent the simulated value most similar to the measured value is selected for application of ANN.

## 4. Application to Study Area

#### 4.1. Description of Data Collection and Parameters

#### 4.2. Result of MRA for Estimating NRW Ratio

^{2}of 0.15 shows a low correlation with the real measured NRW ratio.

^{−0.0240}+ 0.038 number of leaks

^{1.511}+ 5.945 deteriorated pipe ratio

^{0.274}+ 0.038 demand energy ratio

^{4.368}– 6.065 mean pipe diameter

^{0.345}– 32.523 pipe length per junction

^{−0.059}

#### 4.3. Result of ANN for Estimating NRW Ratio

^{2}value than other the number of neurons applied case.

#### 4.4. Accuracy Assessment for Analyzing Application Method

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic Diagram of Multilayer Feed-Forward Neural Network [21].

**Figure 3.**Water Distribution System of DMAs in Incheon [28].

Water Produced | Effective water | Revenue water | Billed and metered |

Exported | |||

Others | |||

Effective NRW | Supplier’s use | ||

Public use | |||

Illegal use | |||

Metering under-registration | |||

Ineffective water | Ineffective NRW | Discounted | |

Leaks |

Classification | Total |
---|---|

DMA (District metered area) | 278 (76%) |

From DMA to unblocked DMA | 52 (14%) |

Unblocked DMA | 37 (10%) |

* Total | 367 (100%) |

Classification | Parameter | Data Collection |
---|---|---|

Operational parameter | Demand energy ratio | Simulated data |

No. of leaks | Measured data | |

Physical parameter | Mean pipe diameter | Designed data |

Pipe length/demand junction | Designed data | |

Water supply quantity/demand junction | Measured data | |

Deteriorated pipe ratio | Designed data |

Classification | Unstandardized Coefficients | Significant Probability |
---|---|---|

Constant | 20.488 | 0.000 |

Water supply quantity per demand junction | −0.048 | 0.251 |

No. of leaks | 0.284 | 0.074 |

Deteriorated pipe ratio | 0.347 | 0.003 |

Demand energy ratio | 1.709 | 0.454 |

Mean pipe diameter | −0.064 | 0.036 |

Pipe length per demand junction | 10.456 | 0.379 |

**Table 5.**Results of Accuracy Assessment. Mean absolute error (MAE); mean squared error (MSE); percent of bias (PBIAS); goodness of fit (G).

Classification | Measured NRW Ratio | Multiple Regression Analysis | Non-Linear Multiple Regression Analysis | ANN (12 Neurons) |
---|---|---|---|---|

Sum. | 3279 | 3279 | 3279 | 3297 |

Ave. | 20.1 | 20.1 | 20.1 | 20.2 |

Standard D | - | 23.7 | 23.5 | 21.9 |

MAE | - | 10.0 | 9.9 | 6.2 |

MSE | - | 146.8 | 139.9 | 63.7 |

PBIAS | - | 0.0 | 0.0 | −0.1 |

G | - | 19.5 | 23.2 | 65.1 |

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**MDPI and ACS Style**

Jang, D.; Choi, G.
Estimation of Non-Revenue Water Ratio Using MRA and ANN in Water Distribution Networks. *Water* **2018**, *10*, 2.
https://doi.org/10.3390/w10010002

**AMA Style**

Jang D, Choi G.
Estimation of Non-Revenue Water Ratio Using MRA and ANN in Water Distribution Networks. *Water*. 2018; 10(1):2.
https://doi.org/10.3390/w10010002

**Chicago/Turabian Style**

Jang, Dongwoo, and Gyewoon Choi.
2018. "Estimation of Non-Revenue Water Ratio Using MRA and ANN in Water Distribution Networks" *Water* 10, no. 1: 2.
https://doi.org/10.3390/w10010002