# Real-Time Dynamic Hydraulic Model of Water Distribution Networks

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## Abstract

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## 1. Introduction

#### 1.1. Pressure Management

#### 1.2. Background Leakage Detection

#### 1.3. Demand Forecasting

## 2. Materials and Methods

#### 2.1. System Architecture

#### 2.1.1. Smart Water Network

#### 2.1.2. Active Network Management

#### 2.1.3. Real-time Dynamic Hydraulic Model

#### 2.2. Pressure Management

_{c}in the future. Here T

_{c}is known as the “time-step” (typically of the order of minutes). In principle, information after time t should also be used to determine the actuator setting at time t. The “demand prediction” module (Figure 1) can predict future consumer water consumption. Used in conjunction with the “hydraulic model” module (Figure 1) which inputs consumer water consumption, the “pressure control” module is envisaged to be able to model the state of the WDN after the actuator setting is changed at time t. If the WDN is not subjected to changes that might cause harm to it, and the expected performance of the WDN is acceptable, the actuators are adjusted according to a control signal sent to them (Figure 1). Otherwise the changed settings should be modified. This process will be repeated until it reaches an optimal level.

_{c}from an additional input file. Standard output files are currently: the time-dependent actuator setting, the time-dependent remote node pressure, as well as four files which provide detailed output related to the hydraulic solver, debugging, errors and checks on the correctness of the input file. The program is currently run from the command line.

#### 2.3. Background Leakage Detection

#### 2.4. Demand Forecasting

## 3. Results

#### 3.1. Pressure Management

_{c}, and (c) the scale-independent rate of change of the flow rate in the PCV [37]. In fact, analytical formulae exhibit these factors, and enable a first attempt at predicting the deviation.

#### 3.2. Background Leakage Detection

#### 3.3. Demand Forecasting

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Demand factor (with daily average 1) over one day. Pump speed needed for PM over one day (scaled).

**Figure 3.**Results of the water network analysis: (

**a**) The case study network; (

**b**) Pipe discharge vs. pipe leakage flow; (

**c**) The pipe leakage flow against the leakage threshold; (

**d**) Volume of water loss in each pipe.

**Figure 4.**Outcomes of test dataset: (

**a**,

**b**) forecasting performance of autoregressive-moving average (ARMA), feed-forward neural network (FFBP-NN), hybrid model and the model conditional processor (MCP). In addition, (

**c**) MCP forecast and estimation of its uncertainty and (

**d**) 5% probability acceptance limit plot.

Algorithm 1. The Leakage Detection Algorithm |
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1: Start { 2: Load network parameters 3: Read network parameters and initialise 4: for node i = 1 to n _{t}, (n_{t}: the number of nodes in the network)5: for pipe j = 1 to b, (b: the number of pipes in the network) Run hydraulic analysis and compute leakage vector Compute the background leakage threshold (tolerance) if the pipe leakage vector < tolerance Print “No leaking pipe” else Print “Leaking pipe” Tag leaking pipe as critical pipe and report critical pipe ID Display “PM recommended in areas where the critical pipe with ID. is located” end if 6: end for j 7: end for i 8: Stop} |

Forecasting Performance | RMSE | MAPE (%) | NS Efficiency |
---|---|---|---|

ARMA | 2.42 | 10.3 | 0.84 |

FFBP-NN | 3.46 | 15.7 | 0.68 |

Hybrid | 1.68 | 7.36 | 0.93 |

MCP | 2.00 | 9.29 | 0.89 |

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## Share and Cite

**MDPI and ACS Style**

Abu-Mahfouz, A.M.; Hamam, Y.; Page, P.R.; Adedeji, K.B.; Anele, A.O.; Todini, E.
Real-Time Dynamic Hydraulic Model of Water Distribution Networks. *Water* **2019**, *11*, 470.
https://doi.org/10.3390/w11030470

**AMA Style**

Abu-Mahfouz AM, Hamam Y, Page PR, Adedeji KB, Anele AO, Todini E.
Real-Time Dynamic Hydraulic Model of Water Distribution Networks. *Water*. 2019; 11(3):470.
https://doi.org/10.3390/w11030470

**Chicago/Turabian Style**

Abu-Mahfouz, Adnan M., Yskandar Hamam, Philip R. Page, Kazeem B. Adedeji, Amos O. Anele, and Ezio Todini.
2019. "Real-Time Dynamic Hydraulic Model of Water Distribution Networks" *Water* 11, no. 3: 470.
https://doi.org/10.3390/w11030470