# 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

- Rizzo, P. Water and Wastewater Pipe Nondestructive Evaluation and Health Monitoring: A Review. Adv. Civ. Eng.
**2010**, 2010, 818597. [Google Scholar] [CrossRef] - Saldarriaga, J.G.; Ochoa, S.; Moreno, M.E.; Romero, N.; Cortes, O.J. Prioritized Rehabilitation of Water Distribution Networks Using Dissipated Power Concept to Reduce Non-Revenue Water. Urban Water J.
**2010**, 7, 121–140. [Google Scholar] [CrossRef] - Engelhardt, M.O.; Skipworth, P.J.; Savic, D.A.; Saul, A.J.; Walters, G.A. Rehabilitation Strategies for Water Distribution Networks: A Literature Review with a UK Perspective. Urban Water
**2000**, 2, 153–170. [Google Scholar] [CrossRef] - Halhal, D.; Walters, G.A.; Ouzar, D.; Savic, D.A. Water Network Rehabilitation with a Structured Messy Genetic Algorithm. J. Water Resour. Plan. Manag.
**1997**, 123, 137–146. [Google Scholar] [CrossRef] - Frauendorfer, R.; Liemberger, R. The Issues and Challenges of Reducing Non-Revenue Water; Asian Development Bank: Mandaluyong, Philippines, 2010. [Google Scholar]
- Alegre, H.; Hirner, W.; Baptista, J.M.; Parena, R. Performance Indicators for Water Supply Services; IWA Publishing: London, UK, 2000. [Google Scholar]
- Lambert, A.O.; Hirner, W.H. Losses from Water Supply Systems: Standard Terminology and Recommended Performance Measures; IWA the Blue Pages, International Water Association: London, UK, 2000; pp. 1–13. [Google Scholar]
- Lambert, A.O. International Report on Water Losses Management and Techniques; Water Science and Technology Water Supply; IWA Publishing: London, UK, 2002; Volume 2, pp. 1–20. [Google Scholar]
- Liemberger, R. Do You Know How Misleading the Use of Wrong Performance Indicators can be? In Proceedings of the IWA Managing Leakage Conference, Nicosia, Cyprus, 20–22 November 2002. [Google Scholar]
- Park, S.W.; Kim, T.Y.; Lim, K.Y.; Jun, H.D. Fuzzy Techniques to Establish Improvement Priorities of Water Pipes. J. Korea Water Resour. Assoc.
**2011**, 44, 903–913. [Google Scholar] [CrossRef] - Park, Y.S. A Study on Long Term Replacement and Maintenance Plan for Multi-Region Water Pipelines Considering Economics. Master’s Thesis, Seoul National University, Seoul, Korea, 2014. [Google Scholar]
- Park, I.C.; Kwon, K.W.; Cho, W.C.; Cho, K.H. Study on the Decision Priority of Rehabilitation for Water Distribution Network Based on Prediction of Pipe Deterioration. In Proceedings of the Korea Water Resources Association Conference, Jeju, Korea, 18–19 May 2006; pp. 1391–1394. [Google Scholar]
- Mukundi, M.J. Determinants of High Non-Revenue Water: A Case of Water Utilities in Murang’ A County, Kenya. Master’s Thesis, Kenyatta University, Kenyatta, Kenya, 2014. [Google Scholar]
- Shilehwa, C.M. Factors Influencing Water Supply’s Non Revenue Water: A Case of Webuye Water Supply Scheme. Master’s Thesis, University of Nairobi, Nairobi, Kenya, 2013. [Google Scholar]
- Winarni, W. Infrastructure Leakage Index (ILI) as Water Losses Indicator. Civ. Eng. Dimens.
**2009**, 11, 126–134. [Google Scholar] - Wyatt, A.S. Non-Revenue Water: Financial Model for Optimal Management in Developing Countries; RTI Press: Amman, Jordan, 2010. [Google Scholar]
- Jung, J.J. The Primary Factor of Management Evaluation Indicators for Local Public Water Supplies & Suggestion of Alternative Evaluation Indicators. J. Korean Policy Stud.
**2012**, 12, 139–159. [Google Scholar] - Lambert, A.O.; Brown, T.G.; Takizawa, M.; Weimer, D. A Review of Performance Indicators for Real Losses from Water Supply Systems. J. Water SRT Aqua
**1999**, 48, 227–237. [Google Scholar] - Shinde, V.R.; Hirayama, N.; Mugita, A.; Itoh, S. Revising the Existing Performance Indicator System for Small Water Supply Utilities in Japan. Urban Water J.
**2013**, 10, 377–393. [Google Scholar] [CrossRef] - Gwak, J.M. Research and Statistical Analysis; Informa: London, UK, 2013. [Google Scholar]
- Haykin, S. Neural Networks: A Comprehensive Foundation; Macmillan: New York, NY, USA, 1994. [Google Scholar]
- Kwon, S.H.; Lee, J.W.; Chung, G.H. Snow Damages Estimation Using Artificial Neural Network and Multiple Regression Analysis. J. Korean Soc. Hazard Mitig.
**2017**, 17, 315–325. [Google Scholar] [CrossRef] - Park, C.S. A Case Study on Establishment of Block System for the Increase of Revenue Water in Distribution Systems. Master’s Thesis, Chonnam National University, Gwangju, Korea, 2014. [Google Scholar]
- Jo, H.G. Study on Influence Factors of Non-revenue Water for Sustainable Management of Water Distribution Networks. Ph.D. Thesis, Incheon National University, Incheon, Korea, 2017. [Google Scholar]
- Jang, D.W. Estimation of Non-Revenue Water Ratio Using PCA and ANN in Water Distribution Systems. Ph.D. Thesis, Incheon National University, Incheon, Korea, 2017. [Google Scholar]
- Heaton, J.T. Introduction to Neural Networks with Java; Heaton Research, Inc.: London, UK, 2005. [Google Scholar]
- Waterworks Headquarters, Incheon Metropolitan City. Basic Plan of Waterworks Maintenance in Incheon; Incheon Metropolitan City: Incheon, Korea, 2015. [Google Scholar]
- Waterworks Headquarters, Incheon Metropolitan City. Technical Diagnostics Report for Re-Establish Basic Plan of Waterworks Maintenance in Incheon Water Distribution Network; Incheon Metropolitan City: Incheon, Korea, 2015. [Google Scholar]

**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 |

© 2017 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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