## Abstract

Leakage in a water distribution network (WDN) leads to a large amount of water loss and water pipe pollution and affects residents’ domestic water supply. Therefore, network leakage detection significantly saves water resources. The traditional model approach has ample search space in solving large distribution network applications, a challenging and complex leakage detection process and a low detection accuracy. For the above problems, this study proposes a new method of leakage area detection based on gray wolf optimization (GWO). First, the extensive WDN is divided into several virtual areas. Then, the leakage is simulated by the additional water demand of nodes, and the node demand of the distribution network is calibrated based on the GWO algorithm. Finally, the leakage area is identified, and the size of the leakage in that area is estimated. The method was experimented on in two cases, simulating single-point leakage and multi-point simultaneous leakage, respectively. The results show that the method estimates the size of leakage in the corresponding area based on accurate identification of leakage areas, and the detection error of leakage is within 17.14%. The method provides water workers with guidance on leak detection, significantly reducing staff time to repair pipes.

## HIGHLIGHTS

Use a small number of monitoring sensors to detect the leakage status of pipeline networks, identify leakage areas and estimate the leakage amount.

A multi-leakage point detection method based on gray wolf optimization is proposed, which can effectively simulate the actual pipe network leakage situation.

A method of dividing multiple virtual areas for leak detection is proposed, which improves the accuracy of leak detection.

### Graphical Abstract

## INTRODUCTION

Water is a vital resource for human survival, and population growth and climate change are leading to severe water shortages. By 2030, water demand is expected to increase by 40% compared with 2017 (Endo *et al.* 2017). As the overall size of urban water distribution networks continues to expand, water distribution network (WDN) systems thus serve the vital task of transporting water for residential use. However, urban pipes are prone to ageing when buried underground for years. Leakage can easily occur at pipes and their connections, affecting residents’ domestic water use and leading to water loss and energy loss. Therefore, researchers and water workers have been widely concerned about the leakage of water distribution networks in the past decades (Pérez *et al.* 2011; Fang *et al.* 2019; Xie *et al.* 2019).

Commonly used leak detection methods can be summarized as hardware- and model-based methods. The key to hardware-based methods lies in the mutual correlation technique, where specific sensors are placed at both ends of the pipe for leak detection (Hu *et al.* 2021). Due to the complex environment and low signal-to-noise ratio of the actual leakage situation, it is sometimes difficult to collect the leakage signal effectively. Therefore, researchers usually use wave decomposition and transformation techniques to reduce or eliminate the noise of the leakage signal (Brennan *et al.* 2019). Brennan *et al.* (2019) demonstrated that accurate time-delay estimates could also be obtained by using polar co-correlation on simulated and measured data as long as the excess zeros in the noise data are retained. The results show that severe shear has no significant effect on normalized co-cause failure and the location of leaks. This result has important implications for the development of leak noise correlators. Cody *et al.* (2020) addressed the problem of detecting and locating leaks in water distribution pipes using linear prediction techniques. The method uses data-driven pipeline anomaly detection and features extracted from linear programming coefficients representing the underlying acoustic signal. The results show that shorter segments of the linear programming (LP) reconstructed signal can achieve similar levels of accuracy as using longer segments of the original time series, a key advantage in long-term online implementation applications. Gao *et al.* (2006) compared the ability of various time-delay estimators using intercorrelation to localize plastic pipe leaks. The results showed that the error of random noise on the signal measurement was insignificant relative to the resolution of the time-delay estimator for the low-pass filtering characteristics of the pipe. As mentioned above, wave decomposition and transformation techniques are important for signal extraction and noise cancelation. However, the signal measured at the sensor is distorted by wave attenuation and interference in the propagation path. As a result, the leakage signal of small-scale leakage tends to be drowned in the background noise and is difficult to detect. Conversely, model-based approaches are promising and can provide near-complete leakage control solutions for all types of leakage (Vítkovský *et al.* 2000; Zhang *et al.* 2016; Sophocleous *et al.* 2017).

The modeling method is a crucial detection technique in the leakage detection method. Its basic principle is to construct a hydraulic model to simulate the operation of the pipeline, and the model simulation to obtain characteristic data under different leakage conditions, and formulate and solve the inverse problem based on the steady-state model by minimizing the difference between the actual and simulated values (Vítkovský *et al.* 2001; Blocher *et al.* 2020). The method was first proposed by Pudar & Liggett (1992) to solve the inverse problem of pipeline network leakage using parameter identification. In order to try to locate the leakage using pressure data, the method represents the equivalent orifice area of possible leakage as an unknown quantity. The results show that the method can represent the location of the most likely leaky node with probability, although the error is significant. Wu *et al.* (2010) further proposed a leak detection method that calibrates the nodal injector coefficients. The method considers the pressure changes in the pipeline network due to leakage. The simulated leakage amount is related to the node pressure and is solved using a genetic algorithm (GA). The results show that the method can reduce the leakage area to several leakage nodes and their connected nearby pipes. Berglund *et al.* (2017) identify linear combinations of individual simulated leaks capable of simulating pressure variations between normal operating conditions and the leaky pipe network, i.e., the interaction of multiple leaks assumed to be nonlinear can be approximated as linear. The method considers mathematical programming to describe the leakage characteristics of the pipe network efficiently. The results show an approximately linear relationship between the pressure variation and the amount of leakage for leakage coefficients below 20 (two leaks) and 7 (five leaks). Sanz *et al.* (2015) proposed comparison of the calibration parameters with their historical values and determination of the presence of leakage in the pipeline network based on the variation of the parameters. The results show that even considering a small number of sensors, leakage losses that affect the parameter more than the uncertainty of the parameter can be located within 200 m. Hajibandeh & Nazif (2018) considered the different probabilities of leakage occurring for different leakage amounts during the leakage detection process, i.e., areas with high operating pressure are more prone to severe leakage. The results showed that the method could accurately find the leak location or its adjacent joint location. However, the traditional modeling method has an ample search space applied to large distribution networks during the solution process. The leakage detection process is complicated, with low detection accuracy (Zhang *et al.* 2016). Therefore, developing a practical leak detection technology is an urgent task nowadays.

In response to the above questions, a new method of leak detection based on gray wolf optimization (GWO) is proposed in this study. In order to achieve the leakage area identification, the leakage is represented as a combination of leakage of different water demand types. The nodal water demand calibration process is completed based on the GWO algorithm to minimize the difference between the observed and simulated pressures. Finally, the leakage area of the network is identified, and the leakage volume of the corresponding area is estimated. Unlike most previous methods, this method can detect large-scale network leaks, and the number of simultaneous leaks during the simulated leak is unknown.

## METHODOLOGY

The current study proposes a method to identify leakage areas in the distribution network, which treats the leakage detection problem as an inverse problem-solving process of parameter identification, i.e., a calibration process. The calibration process is achieved through GWO. In particular, this study uses a small number of monitoring sensors to detect the leakage status of the pipe network and identify the leakage areas and estimate the corresponding leakage volume.

### Calibration process

The method consists of several steps: first, the network is divided into several virtual areas based on the topology of the distribution network and the location of the monitoring points. Secondly, the leakage is represented as a combination of leakage of water demand types, and the leakage is simulated with the additional water demand of nodes. The EPANET Toolbox is called to perform hydraulic analysis and obtain simulated pressure data. Finally, the GWO is used to construct a leakage detection model to estimate the leakage size in each area.

denotes the total leakage in calculation area *z*, denotes the leakage of leakage node *n* in area *z*, *n* denotes the leakage node index and denotes the total number of leakage nodes in area *z*.

*N*denotes the total number of leaky nodes in the pipe network.

### Optimization process

GWO is a novel population intelligence optimization algorithm proposed by Mirjalili *et al.* (2014), and which is an optimization method that simulates the prey predation process of gray wolves. The GWO algorithm has a simple structure, with few parameters to be adjusted. It is easy to implement, in which there are convergence factors that can be adaptively adjusted and an information feedback mechanism that can balance local optimum and global search. The results show that the GWO algorithm has high performance in solving unknown, challenging search spaces and can effectively balance exploration and exploitation capabilities (Ansari *et al.* 2020; Vashishtha & Kumar 2022).

Like other optimization methods, this algorithm simulates the predatory behavior of gray wolf packs by basing on the wolf pack. The mechanism of body collaboration is used to achieve optimization. Four types of gray wolves, the alpha, beta, delta and omega, were used to simulate the leadership hierarchy and hunting mechanism in nature. In addition, three main steps of searching for prey, surrounding prey and attacking prey are implemented for optimization (see Figure 2 for the specific steps).

denotes the leakage matrix of the *w* gray wolf individual; denotes the leakage volume of the *j* node of the simulated pipe network and *J* is the total number of nodes of the pipe network.

denotes the updated leakage matrix of the *w* gray wolf, where *t* is the number of generations of the current iteration; and define the step length and direction of the wolf pack *w* individuals toward and , respectively; and represent the current leakage matrices of and , respectively; *A* is the coefficient vector.

is denoted as the distance between individual gray wolves and their prey, where *t* is the number of generations of the current iteration, is the coefficient vector and and are the position vector of the prey and the position vector of the individual gray wolf, respectively.

## RESULTS AND DISCUSSION

In this section, we will study the method's performance in two cases of pipe networks. The first is the publicly available simple pipe network model Hanoi network, and the second is the publicly available NET3 benchmark model pipe network by Rossman's team. The hydraulic model of the network is used to simulate each scenario, collect the field pressure data and compare it with the pressure of the model-simulated leakage, which determines the pipe network's actual leakage.

### Case 1: Hanoi network

The Hanoi network is an example of a typical WDN, initially proposed by Fujiwara & Khang (1990) and built on the planned backbone network in Hanoi, Vietnam. The Hanoi network contains 31 water nodes, 34 pipes and one pump. The total demand of the system is about 5,556 L/s and the total pipe length is 36.61 km. The network was analyzed in a single steady state without delayed simulation, with simulated leakage in litres per second.

Leakage location . | 7 . | 13 . | 21 . | 26 . | 29 . | Average accuracy (%) . |
---|---|---|---|---|---|---|

GA (%) | 82 | 77 | 66 | 81 | 76 | 76.4 |

ACO (%) | 78 | 71 | 65 | 76 | 76 | 73.2 |

GWO (%) | 96 | 91 | 85 | 92 | 99 | 91.2 |

Leakage location . | 7 . | 13 . | 21 . | 26 . | 29 . | Average accuracy (%) . |
---|---|---|---|---|---|---|

GA (%) | 82 | 77 | 66 | 81 | 76 | 76.4 |

ACO (%) | 78 | 71 | 65 | 76 | 76 | 73.2 |

GWO (%) | 96 | 91 | 85 | 92 | 99 | 91.2 |

In the optimization process, the solution to each optimization problem is abstracted as the individual gray wolves in the population. In this case, the number of gray wolf populations is set to 80 and the maximum number of iterations is set to 50. Also, we mention that the GWO requires fewer parameters to be adjusted. This is because the two main adjustment parameters, *a* and *C*, are adaptive and do not need to be set artificially. They are shown in Table 2.

Parameters . | Number of gray wolves . | Max iterations . | r1
. | r2
. | a
. | . |
---|---|---|---|---|---|---|

Value | 80 | 50 | [0,1] | [0,1] | 2 → 0 | 1 |

Parameters . | Number of gray wolves . | Max iterations . | r1
. | r2
. | a
. | . |
---|---|---|---|---|---|---|

Value | 80 | 50 | [0,1] | [0,1] | 2 → 0 | 1 |

*et al.*(2021). Based on the geographic location of the network and the measurement field tools, they divide the network area into several virtual areas and then estimate the leakage probability of the virtual areas. Similarly, we divide the network evenly into several virtual areas based on the topology of the network, with a similar number of water-using nodes in each virtual area. To investigate the effect of the division method of virtual areas on the detection results, two different sets of virtual areas are designed. Figure 4(a) and 4(b) indicate the horizontal division and the vertical division. This also includes three pressure monitoring points and four virtual areas, denoted as red triangles and areas delimited by red boundaries.

Both networks (a) and (b) have been used to study the proposed method under two operating conditions in this case. The two operating conditions represent one leakage and three simultaneous leaks, as marked by the green and blue arrows in Figure 4. The first condition simulated node 30 with a leak of 15 L/s. The second condition simulated three simultaneous leaks at nodes 7, 14 and 27 with leakages of 13, 7 and 10 L/s. It is assumed that the total leakage of the pipe network is known, and the reservoir is directly connected to the network from a single node (Maghrebi *et al.* 2014). Leakage under all operating conditions is considered a variation in demand between 0 and 20 L/s with an interval of 1 L/s and leakage within 0.36% of the total water demand. The results of the ten independent experimental tests in the first case study are given in Tables 3 and 4, and the results are expressed as the estimated leakage in the corresponding areas.

Division method . | Experimental conditions . | 1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | 1 | I | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |

2 | I | 10 | 10 | 10 | 8 | 12 | 10 | 10 | 8 | 7 | 10 | 11 | |

II | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | ||

III | 20 | 20 | 20 | 19 | 18 | 20 | 20 | 22 | 19 | 20 | 19 | ||

b | 1 | I | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |

2 | II | 10 | 10 | 10 | 10 | 12 | 12 | 10 | 14 | 10 | 10 | 11 | |

III | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | ||

IV | 20 | 20 | 20 | 20 | 18 | 17 | 19 | 16 | 20 | 20 | 19 |

Division method . | Experimental conditions . | 1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a | 1 | I | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |

2 | I | 10 | 10 | 10 | 8 | 12 | 10 | 10 | 8 | 7 | 10 | 11 | |

II | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | ||

III | 20 | 20 | 20 | 19 | 18 | 20 | 20 | 22 | 19 | 20 | 19 | ||

b | 1 | I | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |

2 | II | 10 | 10 | 10 | 10 | 12 | 12 | 10 | 14 | 10 | 10 | 11 | |

III | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | ||

IV | 20 | 20 | 20 | 20 | 18 | 17 | 19 | 16 | 20 | 20 | 19 |

Division method . | Experimental conditions . | Detection result . | ||||
---|---|---|---|---|---|---|

. | Leakage area . | Leakage amount (L/s) . | Leakage area . | Leakage amount (L/s) . | Error . | |

a | 1 | I | 15 | I | 15 | 0 |

2 | I | 10 | I | 10.125 | 1.25% | |

III | 20 | III | 19.875 | 0.63% | ||

b | 1 | I | 15 | I | 15 | 0 |

2 | II | 10 | II | 10.875 | 8.75% | |

IV | 20 | IV | 19.125 | 4.37% |

Division method . | Experimental conditions . | Detection result . | ||||
---|---|---|---|---|---|---|

. | Leakage area . | Leakage amount (L/s) . | Leakage area . | Leakage amount (L/s) . | Error . | |

a | 1 | I | 15 | I | 15 | 0 |

2 | I | 10 | I | 10.125 | 1.25% | |

III | 20 | III | 19.875 | 0.63% | ||

b | 1 | I | 15 | I | 15 | 0 |

2 | II | 10 | II | 10.875 | 8.75% | |

IV | 20 | IV | 19.125 | 4.37% |

The results show that the detection model can accurately simulate leakage assuming only one leakage in the network. Each experiment identifies a 15 L/s leakage occurring in the simulated leakage area I. Assuming multiple leaks in the network, the detection model identifies the occurrence of leaks in the simulated leaky areas I and III of the network (a), and the occurrence of leaks in the simulated leaky areas II and IV of the network (b). In addition, the third and eighth experiments of network (a) identified leakage in area II, and the fifth and sixth experiments of network (b) identified leakage in area III. This is because the detection model locates the upstream and downstream nodes of the actual leakage, which are classified as other leakage regions.

In Table 4, a summary of the experimental results simulating both conditions of the above networks (a) and (b) is given. The leakage area is the detection result with the most frequent occurrence under ten independent experiments, and the leakage amount is the average value of the leakage amounts for the correctly identified leakage area in ten independent tests. The error calculates the magnitude of the direct difference between the simulated leakage amounts and the detection results. An error of zero means that the leakage estimated by the detection model is equal to the leakage simulated by the experimental condition in all results where the leakage area is correctly identified. The results show that both the network divided horizontally (a) and vertically (b) were able to correctly identify the leakage areas, and the error in the estimated leakage was within 8.75%. Therefore, the way the virtual area is divided is not unique and has no necessary impact on the good or bad detection results.

### Case 2: NET3 network

In this case, the network has been used to study the proposed method under different operating conditions, including one, three and five simultaneous leakages. In these service condition experiments, five pressure monitoring points were placed at 111, 157, 213, 269 and 273, as shown in the red triangles of the figure. Figure 5 shows the Working Condition 1 simulation. The leakage at a single node of the pipe network is 5 L/s, indicated by the black arrow. Conditions 2 and 3 indicate three and five simultaneous leaks, respectively. The green arrows indicate the three leakage amounts of 4 and 6 L/s for area V and 5 L/s for area VII. Five simultaneous leakage simulations of 7 and 8 L/s in area II, 4 and 6 L/s in area III and 5 L/s in area VI are indicated by blue arrows. Assuming that the total network leakage is known, that the river is directly connected to the network from a single node, and that the lake water supply valve is closed, the node leakage for all operating conditions is considered to vary between 0 and 10 L/s with an interval of 1 L/s. Leakage is within 5.2% of total water demand. In the optimization process, the number of gray wolf individuals is set to 100, the maximum number of iterations is set to 50 and the rest of the parameters are the same as the first case network. The results of the ten independent experimental tests in the second case study are given in Tables 5 and 6, and the results are expressed as the estimated leakage in the corresponding areas.

Conditions . | Experimental conditions . | 1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | I | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

2 | V | 10 | 11 | 11 | 11 | 12 | 10 | 10 | 10 | 10 | 11 | 11 |

VI | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | |

VII | 5 | 3 | 4 | 4 | 3 | 4 | 5 | 4 | 5 | 4 | 4 | |

3 | II | 15 | 16 | 15 | 14 | 16 | 11 | 12 | 15 | 15 | 16 | 11 |

III | 10 | 9 | 9 | 11 | 9 | 14 | 11 | 10 | 10 | 7 | 14 | |

IV | 0 | 0 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 0 | |

VI | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

Conditions . | Experimental conditions . | 1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | I | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

2 | V | 10 | 11 | 11 | 11 | 12 | 10 | 10 | 10 | 10 | 11 | 11 |

VI | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | |

VII | 5 | 3 | 4 | 4 | 3 | 4 | 5 | 4 | 5 | 4 | 4 | |

3 | II | 15 | 16 | 15 | 14 | 16 | 11 | 12 | 15 | 15 | 16 | 11 |

III | 10 | 9 | 9 | 11 | 9 | 14 | 11 | 10 | 10 | 7 | 14 | |

IV | 0 | 0 | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 0 | |

VI | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

Experimental conditions . | Detection result . | ||||
---|---|---|---|---|---|

. | Leakage area . | Leakage amount (L/s) . | Leakage area . | Leakage amount (L/s) . | Error . |

1 | I | 5 | I | 5 | 0 |

2 | V | 10 | V | 10.857 | 8.57% |

VII | 5 | VII | 3.857 | 17.14% | |

3 | II | 15 | II | 14 | 6.67% |

III | 10 | III | 11 | 10% | |

VI | 5 | VI | 5 | 0 |

Experimental conditions . | Detection result . | ||||
---|---|---|---|---|---|

. | Leakage area . | Leakage amount (L/s) . | Leakage area . | Leakage amount (L/s) . | Error . |

1 | I | 5 | I | 5 | 0 |

2 | V | 10 | V | 10.857 | 8.57% |

VII | 5 | VII | 3.857 | 17.14% | |

3 | II | 15 | II | 14 | 6.67% |

III | 10 | III | 11 | 10% | |

VI | 5 | VI | 5 | 0 |

The results show that the detection model can accurately identify that the leakage occurs in area I assuming only one leakage in the network. Assuming that the network is leaking in two areas, the model identifies the leaking area and estimates the amount of leakage in the leaking area in all seven experiments. The estimated leakage amount is consistently above or below the actual leakage amount in the area. In contrast, three leaky areas were identified in three experiments. This is because the detection model locates nodes near the actual leak. These nodes are often upstream and downstream of the actual leaky nodes, and therefore meet our expectations. However, the detection model still detected the areas with leakage. Similarly, in the second, sixth and ninth experiments of Condition 3, the detection model additionally identified area IV as leaking, with the amount of leakage ranging from about 1 to 2 L/s.

Specifically, under the assumption that there is one leakage in the network, the model identifies the leakage area of the network as area I and estimates the leakage volume of the corresponding area as 5 L/s. The model can accurately identify the leakage area and estimate the corresponding leakage amount, and the calculation error of the leakage amount is 0. This means that in all the results of correctly identifying the leakage area, the leakage estimated by the detection model equals the leakage simulated by the experimental conditions. Under the assumption that the network has three and five leakage areas, the model can accurately identify the leakage areas as V and VII and II, III and VI, respectively, and estimate the corresponding leakage amounts as 10.857 and 3.857 L/s and 14, 11 and 5 L/s, respectively. The leakage in area II is more severe, but the error is within a certain range. This is because the hydraulic model more accurately simulates the situation where there is a large amount of leakage in the network. The pressure changes in the network caused by large leakage are more obvious. The results demonstrate that the model can not only identify areas of leakage in the network but also assess the severity of leakage in each area, guiding staff in developing a leak detection plan.

It should be noted that in the case of simulating multiple leaks in the pipe network, the detection results are subject to errors. These errors are unavoidable and will be detected for each leaky area in the network. The errors arise because the model can detect nodes near the leak location. These nodes are more upstream and downstream nodes of the leaky nodes and are divided into adjacent leaky areas. In particular, detecting only one leak in a single area was good regardless of several leaks in the network. This may be since the pressure variation due to a single leak in an area is better identified and easily detected. It is noteworthy that area VI of the five leakage conditions and areas II and III of the simulated leakage are also not in adjacent spatial locations, and the leakage in area II is more severe than in area III. The test results show that the leakage amount of area II is more significant than that of area III with the same number of leaks, which can determine the area of relatively serious pipe network leakage, as shown in Figure 5.

## CONCLUSION

This paper proposes a new method for leaky area detection based on GWO. The method is based on the calibration of the demand of the pipe network nodes by GWO and is evaluated on two simulation models. In this method, the WDN is divided into several virtual areas, and the network leakage is simulated with a combination of different leakage types of water demand. The pressure variation of the network is calibrated based on the model approach to identify leakage areas and estimate the corresponding leakage volume. The results show that the method can accurately identify the leakage areas and estimate the leakage volume in a single leakage scenario. When there are multiple leakage cases in the network, the method produces errors in estimating leakage in the leakage areas. Likewise, with errors consistently below 17.14%, it can still identify leaky areas and detect the severity between them. It provides a reference for the later field maintenance workers so that a reasonable and practical maintenance plan can be developed.

This paper considers only leakage detection experiments based on an accurate hydraulic model. The hydraulic model calibration part will be further considered in future studies to simulate the leakage of pipe networks more accurately. In addition, the single nature of the data is also a challenge to the leakage detection method. Further research can be conducted later to add the leakage area identification of flow monitoring points to improve the model detection accuracy.

## ACKNOWLEDGEMENTS

This work is supported by the funds: Industry-university-research Project of Anhui Jianzhu University HYB20210116 (Project Name: Development of intelligent integrated system software platform based on BIM technology); Research project of Anhui Jianzhu University jy2021-c-017 (Project Name: research and application of water distribution network leakage detection system based on DMA partition).

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

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