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Article

A Novel Intelligent Leakage Monitoring-Warning System for Sustainable Rural Drinking Water Supply

by
Xiaoqin Li
1,2,*,
Xiaomei Wu
1,2,
Mingzhuang Sun
3,
Shengqiao Yang
4 and
Weikun Song
1,2
1
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
2
Department of Irrigation and Drainage, China Institute of Water Resources and Hydropower Research, Beijing 100048, China
3
School of Environment, Tsinghua University, Beijing 100084, China
4
School of Energy and Environmental Engineering, Hebei University of Engineering, Handan 056038, China
*
Author to whom correspondence should be addressed.
Sustainability 2022, 14(10), 6079; https://doi.org/10.3390/su14106079
Submission received: 13 April 2022 / Revised: 12 May 2022 / Accepted: 13 May 2022 / Published: 17 May 2022
(This article belongs to the Section Sustainable Urban and Rural Development)
Browse Figures
Versions Notes

Abstract

:
Leakage occurs in rural water supply pipelines very often and its locating is quite demanding even for specialists, which could result in a poor operation efficiency of rural water supply projects and thus a low rural water supply guarantee rate. In view of this problem, the detection of leakage, as well as its prediction, is of great significance for the operation, maintenance, and administration of rural water supply projects. The traditional monitoring-warning systems for urban water distribution networks cannot be applied to rural water distribution networks, due to various limitations. Meanwhile, as with the traditional models, most new approaches based on machine learning such as the artificial neural network (ANN), probabilistic neural network (PNN), and statistical learning theory (SLT) do not fit rural water distribution networks much better, being unable to converge and force high-accuracy results with small sample sizes, which is a crucial demand to meet when dealing with rural water supply pipelines. Extreme gradient boosting (XGBoost), a model that specializes in small sample sizes and has a high generalization ability, was applied to a rural water supply project in Ningxia, China. In this study, a monitoring-warning system featuring both leakage locating and quantity estimation was established based on XGBoost. The accuracy and F1-score of the leakage locating model were 95% and 93%, respectively, while those of the leakage quantity model reached 96% and 97%, respectively. Furthermore, the pressure of monitoring stations could be obtained through the feature importance analysis enabled by XGBoost, which is essential for leakage warning. These results indicate that this system based on XGBoost could be a promising solution to the leakage issue in rural water supply projects, as a great inspiration for future developments in intelligent monitoring-warning systems, thus providing reliable approaches for the sustainable development of rural drinking water supply projects.

1. Introduction

By the end of 2020, there were around 580,000 concentrated rural water supply projects in China, providing safe tap water to 909 million rural residents [1]. However, according to the rural water supply plan in the 14th five-year plan of China, around 10% of the concentrated rural water supply projects were constructed before 2005, most of which are facing issues such as aging pipelines and high leakage rates. Reports show that in some regions, the leakage rate of the rural water supply pipeline has surpassed 30%, menacing the rural tap water safety. Pipeline leakage could be due to various reasons, such as pipe cracking, low construction quality, and great maintenance difficulties caused by the depth of buried pipes. In the northeast of China, the pipes are buried relatively deep and the temperature in winter could be low. The leakage rate there could reach 20% in some cities [2].
As stated above, leakage is a serious issue in rural water supply projects and restricts the sustainable development of rural water supply projects. The existing leakage detection approaches are mostly developed from the passive testing method, MNF (minimum night flow), or warning mechanism based on the upper and lower pressure limits. Negharchi and Shafaghat (2020) [3] carried out research on a rural network in the north of Iran using two leakage calculation methods, including background and bursts estimates (BABE) and MNF; the average leakage was found to be 1.45 L/s and 1.105 L/s, respectively. The effects of the legitimate night-time consumption (LNC) and leakage exponent (N) have been evaluated. Norouzi et al. (2019) [4] proposed that employing suitable techniques for specifying the right domestic night-time consumption values is essential when applying the MNF method. Flow measurement by loggers was used to determine real losses through MNF analysis in the Juru Rural Service Centre by Chawira et al. (2022) [5]. Dandansaz et al. (2020) [6] minimized network leakage by applying minimal pressure on network nodes and analyzed the water distribution network using WaterGEMS and ArcGIS, aiming to determine the optimal pressure in the network.
The methods listed above are apparently much less efficient than those applied to urban water distribution networks. A compatible monitoring model for the rural water distribution network is in need. Traditional monitoring models already applied to leakage detection in urban water distribution networks usually rely on sufficient historical data, a hydraulic model of the pipeline, and real-time online monitoring data. However, when developing monitoring-warning systems for rural water distribution networks, researchers would face a lack of online monitoring stations, a limited variety of monitoring indicators, and insufficient historical data, which would result in the low accuracy of the hydraulic model of pipelines and thus a poor leakage detection model. New methods, different from those adopted in monitoring models for urban water distribution networks, need to be introduced and assessed in rural water supply projects.
With the development of network technology, the Internet of Things, and a cloud platform, real-time monitoring data of high quality could be obtained and transmitted by online sensors, enabling the application of artificial intelligence and machine learning to the analysis of online monitoring data. During the last decade, much progress has been made in researching new algorithms such as the artificial neural network (ANN) and fuzzy inference system (FIS). Mounce et al. (2002) [7] first proposed the application of artificial intelligence to water distribution networks. Mounce et al. (2006) [8] utilized multi-layered perceptrons (MLP) and the time delay neural network (TDNN) when studying the process where a fire hydrant was applied to a simulated burst in a pipeline. In the following research of Mounce et al. (2003, 2008, 2010, 2007) [9,10,11,12], an artificial intelligence system was established for the detection of bursts and flow meter data analysis, enabled by continuously updated historical data.
Many other researchers also developed a variety of ANN models. Caputo and Pelagagge (2002, 2003) [13,14] proposed a leakage monitoring approach based on a multi-layered neural network. Feng and Zhang (2006) [15] proposed a leakage monitoring approach based on a fuzzy neural network that could also identify anomalies in a pipeline. Aksela et al. (2009) [16] established a pipeline leakage detection model based on a self-organizing map, where the leakage function consisted of a distance function and a confidence function. Tao et al. (2014) [17] proposed a burst detection method based on an artificial immune network, where a burst could be located by the algorithm of nearest neighbors after monitoring data were inputted into the artificial immune network. Liang et al. (2001) [18] established a model based on the ANN, able to describe the relationship between three pressure monitoring stations and leakage-concerning parameters such as leakage location, intensity, and influence. Huang et al. (2007) [19] developed a method based on supervisory control and data acquisition (SCADA) that could locate a leakage through a fuzzy similar priority comparison. The industrial application of an ANN to leakage detection has also been reported with satisfying outcomes. However, it is not easy for such models to converge and their convergence would require large training sample sizes, thus making them unfit for rural water supply projects.
Bayesian analysis (BA) was introduced to solve the convergence problem of the ANN, where the probability distribution could describe all forms of uncertainty. Poulakis et al. (2003) [20] established a Bayesian probabilistic framework for leakage detection. Costanzo et al. (2014) [21] also realized leakage area determination through BA. Romano et al. (2010) [22] integrated an ANN, statistical process control (SPC), and BA into a burst-leakage detection framework and tested its applicability in a district metered area (DMA) of the UK. The results showed that this framework could successfully locate bursts and leakage. Despite the satisfying results obtained with BA, the Bayesian models have to make assumptions on the probability distribution of training samples, which would often cause a low identification accuracy. Large training sample sizes are required to improve accuracy, which is not practical in rural water supply projects.
Efforts have been made to solve the problem of sample size requirement. Vapnik et al. (1982) [23] developed a statistical learning theory (SLT) that could be applicable to small sample sizes. Mounce et al. (2010) [24] utilized support vector machines (SVMs) to analyze the time-series data obtained from monitoring stations and realized online monitoring of abnormal events such as burst-leakage, pipe cleaning, and sensor malfunction. Mamo et al. (2014) [25] developed a leakage detection and classification technique based on multi-class SVMs (M-SVMs). The operation state of the pipeline was classified into six categories according to the degree of leakage. M-SVMs could then be applied to identify the operation state of the DMA, based on the flow and pressure data obtained from monitoring stations. Zhang et al. (2016) [26] proposed a leakage zone identification model that could be suitable for large-scale pipe networks. Compared to ANN and FIS, this method could send warnings much faster. The weakness of this method is that it fails to consider the optimization of parameters, which could greatly influence the classification accuracy.
Another famous algorithm specialized in small sample sizes is gradient boosting, developed by Friedman, as an approximate of gradient descent. The gradient boosting decision tree (GBDT) is one of the best-performing models derived from this algorithm. It is a recursive model, consisting of multiple decision trees. GBDT could deal with all types of data, achieve high accuracy, and stay robust against anomalies. Extreme gradient boosting (XGBoost) is an enhanced version of GBDT, where regularizers have been introduced to avoid overfitting. XGBoost has a great generalization ability, widely used for various aims such as parameter anomaly detection in satellite engineering, personal credit risk assessment, water depth inversion based on remote sensing, determination of urban water sustainability index, and predicting the quantity of the urban water supply (Chen et al., 2016, Devan et al., 2020, Clercq et al., 2018, He et al., 2020) [27,28,29,30]. XGBoost has been applied to pipeline maintenance in several studies. Snider and McBean (2020) [31] used XGBoost to predict pipeline rupture. Wu et al. (2022) [32] adopted XGBoost to study the influence of the count of leakage occurrence and its location on model performance. Artificial leakage data were generated using a hydraulic model simulation and the prediction accuracy could reach 90.4%. The research of Mohsen (2021) [33] showed that SVM and XGBoost ranked first in predicting leak and nonleak samples in a laboratory-scale water distribution system. Moreover, Wang et al. (2021) [34] found that XGBoost had a better generalization ability than SVM, as XGBoost could improve its prediction accuracy via the decontamination effect. Nagaraj and Lakshmi (2021) [35] reported that the XGBoost classifier outperformed the other machine learning algorithms assessed in their study in terms of water body extraction.
As a model applicable to small sample sizes, XGBoost has a high potential for leakage detection in rural water distribution networks. The validation of its feasibility would be of great value to the better development of rural water supply projects, which has not been carried out to the best of our knowledge. In this study, XGBoost was applied in a rural water supply project in Ningxia, China. A novel intelligent monitoring-warning system for leakage detection was established, consisting of a leakage locating model and a leakage quantity model, aimed to provide valuable insight into the construction and maintenance of future rural water supply projects.

2. Materials and Methods

2.1. Leakage Simulation and Monitoring

The water supply plant where this study was carried out is in Zhongwei, Ningxia, China, with a capacity of 20,000 m3/d. It has been under operation since May 2019, supplying water to 120,000 residents. Ground water pumped through 4 wells is treated in this plant and then pumped to the secondary booster pump station. As shown in Figure 1, the water distribution system is established as a branching network. On each main branch, multiple monitoring and test points were set-up. In this study, four additional monitoring points were set-up at Jingtai, Yanggou, Shuangda, and Caoshan, where pipe flow and pressure could be measured and transmitted in real time. Test points were set-up between monitoring points as simulated leakage locations. Controlled leakage could be realized by a three-way valve or an effluent pipe with a valve.
The parameters considered in the experiment plan included water usage period, leakage location, and leakage quantity. Table 1 shows the parameter settings for water usage period. The distribution of test points was as displayed in Figure 1. Table 2 shows the parameter settings for leakage quantity. When leakage quantity surpasses 30% of the flow in pipeline, the pressure change could be obvious and thus easy to identify. As this study focused on occasions where leakage could be difficult to identify, the leakage quantity was set to be smaller than 30% of the flow.
Before each test, a handheld ultrasonic flowmeter (TDS-100H, Dalian Haifeng Development Co., Ltd., Dalian, China) was installed on the pipe. The duration time of each test started recording when the valve was opened. The designed leakage quantity could be realized by adjusting the valves. After recording the results of the flowmeter for 5 min, the valves were closed. The valves would then be opened and adjusted again for another leakage quantity. The same procedure was repeated for each preset experimental condition until all desired data were collected.

2.2. Model Setup and Analysis

2.2.1. Data Preparation

The models developed in this study were based on XGBoost, the mechanism of which was as described in Appendix A. Data preparation consists of four steps: data acquisition, data transfer, generation of positive and negative samples, and data pre-treatment. Data transfer refers to the process of transferring the results of tests carried out at a couple of water usage periods to those of tests carried out at different water usage periods, as there were certain limitations during the experiment and sample sizes were relatively small. The generation of positive and negative samples could then be completed based on the expanded database. Data pre-treatment mainly concerns the determination of x features and y features, as well as the mapping of several nonnumerical data sources.
The x features are water usage period, pipe depth, pipe flow, pre-test pressure of Jingtai (Jingtai 1st), pre-test pressure of Yanggou (Yanggou 1st), pre-test pressure of Shuangda (Shuangda 1st), pre-test pressure of Caoshan (Caoshan 1st), test pressure of Jingtai (Jingtai 2nd), test pressure of Yanggou (Yanggou 2nd), test pressure of Shuangda (Shuangda 2nd), and test pressure of Caoshan (Caoshan 2nd), labeled as x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, and x11, respectively. Among the x features, two of them, x1 and x2, are nonnumerical and thus need to be transformed, as shown in Table 3. The y features are leakage location and leakage quantity, which are represented by the percentage of leakage in pipe flow. Both features are nonnumerical and their corresponding numerical labels are as shown in Table 4.
After data pre-treatment, the samples were ready for training. The sample distribution of the leakage locating model and that of the leakage quantity model were as shown in Table 5 and Table 6.

2.2.2. Iteration Setup

Proportions of 80%, 10%, and 10% of the total samples were used for training, validation, and testing, respectively. The data distribution of the two models was as shown in Table 7.
The parameter optimization was based on the greedy algorithm as explained in Section 2.2. At every iteration, only one parameter would be modified until no improvement could be made. After finishing the establishment of the leakage locating model, the input of the leakage quantity model could be obtained and iterations for the leakage quantity simulation would be started until optimized parameters were found. The hyper-parameters selected in this study and their default values were as shown in Table 8.

2.2.3. Results Analysis

The assessment of model performance was based on the F1-score, accuracy, and AUC-ROC (Area Under the Curve-Receiver Characteristic Operator) curve, as calculated in Equations (1)–(6). The F1-score and accuracy have been used in many studies on XGBoost, such as Mohsen (2021) [33] and Zhong et al. (2018) [36].
Accuracy = (TP + TN)/(TP + FN + FP + TN)
F1-score = 2 × Precision×Recall/(Precision + Recall)
Precision = TP/(TP + FP)
Recall = TP/(TP + FN)
TPR = Recall
FPR = FP/(TN + FP)
TP/TN stands for true positive/negative, which means that a positive/negative class is predicted as positive/negative. FP/FN stands for false positive/negative, which means that a datapoint of one class is predicted as that of the other class.
The AUC-ROC curve is the preferred method to assess the performance of classification models. ROC is a probability distribution curve, whose x-coordinate and y-coordinate are TPR and FPR, respectively. Ranging from 0 to 1, AUC is calculated from ROC, representing how well the different classes have been separated from each other. The higher the AUC, the better the performance is, with AUC values between 0.5 and 1. When AUC is less than 0.5, the model performance would be considered poor.
To examine the sensitivity of results to the parameters, sensitivity analysis was realized by IBM SPSS Statistics (Version 27.0, IBM, New York, NY, USA). Feature importance analysis was also carried out as XGBoost could obtain the importance of each feature. The more one feature participates in the construction of the decision tree, the higher its importance.

3. Results and Discussion

3.1. Sensitivity Analysis

As can be seen in Table 9, Max_depth and Learning_rate had the highest F-value, at 10.458 and 7.407, respectively. This means that the results were most sensitive to these two factors. Max_depth had great influence on the model complicity, while Learning_rate controlled the steps of each iteration, thus highly relevant to model robustness. Their relatively high sensitivity could be explained while the p-values of all the factors were greater than 0.05, indicating poor statistical significance.

3.2. Model Performance

Training samples were used for model establishment, which would then be used to predict testing samples. The accuracy and F1-score of the two models, applied to training samples and testing samples, were as shown in Table 10. The results obtained from testing samples were almost as good as those obtained from training samples.
The fluctuation in the results along the iterations were also studied. As can be seen in Figure 2, the F1-score and accuracy of the leakage locating model were both satisfying. During iterations, most leakage could be identified. The lowest accuracy and F1-score were 74% and 72%, respectively. At iteration 15, the accuracy and F1-score could already reach 95% and 93%, respectively, indicating that the leakage could be accurately located by the leakage locating model in this study.
The leakage quantity model could predict the quantity of leakage at the location where leakage occurs according to the leakage locating model. The performance of this model was as shown in Figure 3. At iteration 8, the accuracy and F1-score could reach 96% and 97%, respectively, while the error of leakage quantity did not surpass 10% of the pipe flow, indicating that this model predicted leakage quantity with high accuracy and sensitivity. Farley et al. (2008, 2010, 2013) [37,38,39] used a dynamic hydraulic model to locate leakage and noted that the leakage quantity had to be at least 1.5 L/s to cause a pressure change measured at monitoring points. In this study, the leakage quantity model could predict a leakage of less than 1 L/s. Mounce et al. (2006, 2010, 2007) [8,11,12] developed a leakage quantity model based on ANN and the error of its estimate was around 10% of the pipe flow, which was comparable to the performance of the XGBoost model developed in this study.
The results obtained from the AUC-ROC curve were as shown in Figure 4. Class 0, 1, 2, 3, and 4 in the leakage locating model represented “No leakage”, “Yanggou”, “Chengnong”, “Shuangda”, and “Caoshan”, respectively, while Class 0, 1, 2, and 3 in the leakage quantity model represented “y2 < 10%”, “10% ≤ y2 < 20%”, “20 ≤ y2 < 30%”, and “y2 ≥ 30%”, respectively. As can be seen in Figure 4, the AUC of each curve was close to 1. The micro- and macro-average were both over 0.99. The results of Figure 4 further demonstrated the promising performance of the models established in this study.

3.3. Feature Importance Analysis

By calling the function of xgb.feature_importances, the importance of each feature could be obtained, as shown in Figure 5.
It could be seen that in the leakage locating model, the pressure of monitoring points had great importance, whereas neither the influence of water usage period nor that of pipe depth surpassed 5%. Among the four pressure monitoring points, Yanggou, which was situated at a low position, and Shuangda, which was situated at a high position, were very sensitive to pressure and their pressure proved to have greatest importance according to the feature importance analysis. In the leakage quantity model, the most important features were still pressure of the monitoring points, but the importance of pipe flow was lower in the leakage quantity model than that in the leakage locating model. In addition, in both models, the importance of second tests was higher than that of first tests, which indicates that the accurate and timely update of monitoring data is vital to monitoring and warning of leakage.
After further analysis, it could be concluded that monitoring points near the end of the pipeline were more sensitive to pressure than those near the start of the pipeline. Jingtai was located at the start, where the pressure measured had much less importance than that measure elsewhere. Both the importance of pipe depth and that of water usage period were under 10% in both models. The two features mentioned above should not be included in future studies. The feature importance analysis found that the pressure of the nodes could have profound influence on the operation of water distribution networks, thus being among the most important factors to consider when dealing with leakage issues. Extra attention should be paid to pressure management, especially that of nodes near the end of the pipeline, so as to better deal with existing and potential leakage issues.

4. Conclusions

XGBoost, a model that has a great generalization ability and specializes in small sample sizes, was applied to the leakage detection of a rural water supply project in Ningxia, China. A novel intelligent monitoring-warning system was established, consisting of a leakage locating model and a leakage quantity model. The accuracy and F1-score of the leakage locating model were 95% and 93%, respectively, while those of the leakage quantity model were 96% and 97%, respectively. The AUCs of the AUC-ROC curves were all close to 1, while both micro- and macro-F1 were over 0.99. The model performance was satisfying. In addition, with the help of feature importance analysis, enabled by XGBoost, the most important feature for leakage detection was discovered to be the pressure of monitoring points, and it was found that the importance of second tests was greater than that of first tests, indicating that the stable and timely transmission of online monitoring data could be crucial for the establishment of an intelligent monitoring system for rural water distribution networks.
The local water management authorities were also satisfied by the results. The intelligent system established in this study could not only help with major leakage incidents but also minor leakage issues that are difficult to notice. The main holdback of this system found by managers is that the reliable leakage warning service is based on the stable operation of the warning system, which requires the timely upload of pressure data and stable internet access. Certain efforts must be made to the maintenance of pressure monitoring devices.
The successful application of XGBoost in this study shows that a highly intelligent monitoring system for leakage detection in rural water supply projects is not impossible. To further improve the models developed in this study, the system could be enabled to constantly learn from new samples while conserving existing knowledge. Hopefully, the leakage locating model could become even more precise. A future study on the application of this model in rural water supply projects could eventually realize the efficient and accurate identification of leakage, early prediction, timely treatment, and hence significant improvement of rural water supply services.

Author Contributions

Conceptualization, X.L.; data curation, X.L. and S.Y.; formal analysis, X.L., M.S. and W.S.; funding acquisition, X.W.; investigation, X.W.; methodology, X.L.; validation, W.S.; visualization, S.Y.; writing—original draft, X.L.; writing—review and editing, X.L., X.W. and M.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by a cooperative research project of academician workstation (No.2020.C-003).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

Thanks to Zhang Yanhua from the Zhongwei Water Limited Company of Ningxia Water Investment Group and Yang Pengwei from the China Institute of water resources and Hydropower Research, for providing support in the leakage simulation.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

XGBoost model: the main mechanism of the XGBoost model is integrating boosted trees as a kind of additive model (i.e., training process) [40]. It can be written as follows:
Y ^ i = ∑ κ − 1 Κ ƒ κ ( x i ) ,   ƒ κ ϵ ℱ
ƒ κ ( x i ) = ω q ( x i ) ( q : R m → T , ω ϵ R T )
κ is the number of trees and ƒ ( x ) is a function in the function space; the function q ( x i ) divides sample x into a certain leaf node; ω is the leaf score of leaf nodes.
The target function is as described in Equations (A3) and (A4).
ℒ = ∑ i = 1 n ι ( Y ^ i ,   Y i ) + ∑ κ − 1 Μ Ω ƒ κ
where   Ω ( ƒ ) = γ Τ + 1 2 ∥ ω ∥ 2 = γ Τ + 1 2 ∑ j = 1 Τ ω j 2
Here, the function ι is a differentiable convex function that represents the difference between the predicted value Y ^ and the true value Y , measured as the mean squared error. The penalty term Ω is used to ensure that the tree structure does not become too complex. The weights can be smoothed to avoid the problem of overfitting. The error function of XGBoost has L1 and L2 regular terms, where the loss function can be a square loss or a logical loss, and T represents the number of leaf nodes. The introduction of regularizers is to prevent overfitting. More precisely, regularizers could enable preponing as there is a limited number of leaf nodes in the regularizers; meanwhile, the coefficient of the squared L2 modulus of the leaf score in the regularizers could smooth the leaf score.
The objective function is expanded and simplified using Taylor’s second-order formula, as shown in Equations (A5)–(A8).
ℒ ( t ) ≃ ∑ i − 1 n [ ι ( Y i , Y ^ ( t − 1 ) ) + g i ƒ t ( Χ i ) + 1 2 h i ƒ t 2 ( Χ i ) ] + Ω ( ƒ t )
where   g i = ∂ Y ^ ( t − 1 ) ι ( Y i , Y ^ ( t − 1 ) )   and   h i = ∂ Y ^ ( t − 1 ) 2 ι ( Y i , Y ^ ( t − 1 ) )
ℒ ˜ ( t ) = ∑ i − 1 n [ g i ƒ t ( Χ i ) + 1 2 h i ƒ t 2 ( Χ i ) + γ Τ + 1 2 λ ∑ j = 1 Τ ω j 2 ]
= ∑ j = 1 Τ [ ( ∑ i ϵ Ι j g i ) ω j + 1 2 ( ∑ i ϵ Ι j h i + λ ) ω j 2 ] + γ Τ
After the structure of the tree is determined, the objective function can be minimized by setting its derivative to zero. The optimal prediction fraction of each leaf node can be obtained as follows: for continuous attribute features, discretize according to the candidate segmentation points, and select the best one from these candidates.
ω j * = − ∑ i ϵ Ι j g i ∑ i ϵ Ι j h i + λ ,
Substituting this into the objective function, the minimum loss is:
ℒ ˜ ( t ) ( q ) = − 1 2 ∑ j = 1 Τ ( ∑ i ϵ Ι j g i ) 2 ∑ i ϵ Ι j h i + λ + γ Τ
After the determination of the objective function and the best solution, the nodes should be split according to the node segmentation algorithm. A greedy algorithm is where all splitting points are identified using an exhaustive method, and then the splitting point with the largest information gain is selected. The greedy algorithm is as described in Figure A1.
Sustainability 14 06079 g0a1 550
Figure A1. Mechanism of greedy algorithm.
Figure A1. Mechanism of greedy algorithm.
Sustainability 14 06079 g0a1

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Figure 1. Schematic representation of water distribution network featuring monitoring and test points.
Figure 1. Schematic representation of water distribution network featuring monitoring and test points.
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Figure 2. Performance indicators of leakage locating model along the iterations.
Figure 2. Performance indicators of leakage locating model along the iterations.
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Figure 3. Performance indicators of leakage quantity model along the iterations.
Figure 3. Performance indicators of leakage quantity model along the iterations.
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Figure 4. ROC curve of (a) leakage locating model and (b) leakage quantity model.
Figure 4. ROC curve of (a) leakage locating model and (b) leakage quantity model.
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Figure 5. Feature importance in (a) leakage locating model and (b) leakage quantity model.
Figure 5. Feature importance in (a) leakage locating model and (b) leakage quantity model.
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Table
Table 1. Selection of water usage periods.
Table 1. Selection of water usage periods.
Water Usage PeriodTimeWater Usage PeriodTime
Morning peak hours6:00–8:00Noon off-peak hours15:00–17:00
Morning off-peak hours9:00–11:00Evening peak hours18:00–20:00
Noon peak hours11:00–13:00Evening off-peak hours21:00–23:00
Table
Table 2. Experimental setting of leakage quantity.
Table 2. Experimental setting of leakage quantity.
SequenceDateLeakage LocationLeakage Flow (L/S)Leakage Percentage
(%)
12 August 2021Yanggou2.085
22 August 2021Yanggou4.1710
32 August 2021Yanggou6.2520
43 August 2021Chengnong0.835
53 August 2021Chengnong1.6710
63 August 2021Chengnong2.5015
73 August 2021Chengnong3.3320
83 August 2021Chengnong5.0030
94 August 2021Shuangda1.115
104 August 2021Shuangda2.2210
114 August 2021Shuangda3.3315
121 August 2021Caoshan0.285
131 August 2021Caoshan0.5610
141 August 2021Caoshan0.8315
Table
Table 3. Mapping of nonnumerical x features.
Table 3. Mapping of nonnumerical x features.
FeatureNonnumerical LabelNumerical Label
x1Morning peak hours001
Noon peak hours010
Evening peak hours100
Evening off-peak hours011
Morning off-peak hours101
Noon off-peak hours110
Other111
x21.9 m01
1.8 m10
1.6 m11
Table
Table 4. Mapping of nonnumerical y features.
Table 4. Mapping of nonnumerical y features.
FeatureNonnumerical LabelNumerical Label
y1No leakage0
Yanggou1
Chengnong2
Shuangda3
Caoshan4
Other99
y2y2 < 10%0
10% ≤ y2 < 20%1
20 ≤ y2 < 30%2
y2 ≥ 30%3
Table
Table 5. The sample distribution of leakage locating model.
Table 5. The sample distribution of leakage locating model.
Leakage Locating ModelTotal SamplesNo LeakageChengnongShuangdaCaoshanYanggou
Sample size688439991904587222172
Percentage (%)100.0058.0927.668.533.222.50
Table
Table 6. The sample distribution of leakage quantity model.
Table 6. The sample distribution of leakage quantity model.
Leakage Quantity ModelTotal SamplesPercentage of Leakage in Pipe Flow (Y2)
0123
Sample size295244811331112260
Percentage (%)100.0015.1838.3837.678.81
Table
Table 7. The data distribution of the two models.
Table 7. The data distribution of the two models.
ModelTotal SamplesTrainingValidationTesting
Leakage locating model68845507688689
Leakage quantity model29522362295295
Table
Table 8. Default values of parameters.
Table 8. Default values of parameters.
ParameterDescriptionLeakage Locating Model
-XGBCIassifier		Leakage Quantity Model
-XGBCIassifier
Max_depththe depth of the given tree34
Learning_ratethe learning rate of the model from each iteration0.30.3
N_estimatorsnumber of sub models80200
Objectiveloss functionbinary:logisticbinary:logistic
Boostermodel solving methodgbtreegbtree
Min_child_weightthe smallest sample weight sum in the child node65
Reg_alphaweight of L1 regularization term00
Reg_lambaweight of L2 regularization term11
Table
Table 9. Tests of between-subjects effects.
Table 9. Tests of between-subjects effects.
Dependent Variable: F1_Score
SourceType III Sum of SquaresdfMean SquareFSig.
Corrected Model0.063 a130.00510.8520.234
Intercept7.89117.89117,534.7410.005
Max_depth0.02450.00510.4580.23
Learning_rate0.00720.0037.4070.251
N_estimators0.00430.0012.9390.399
Min_child_weight0.00110.0012.7780.344
Reg_alpha0100.7780.54
Reg_lamba00...
N_estimators * Reg_alpha0100.3970.642
Error010
Total10.48115
Corrected Total0.06414
a. R-squared = 0.993 (adjusted R-squared = 0.901). *. Interaction between two parameters.
Table
Table 10. Performance indicators of training samples and testing samples.
Table 10. Performance indicators of training samples and testing samples.
ModelAccuracy (%)F1-Score (%)
Training SamplesTesting SamplesTraining SamplesTesting Samples
The leakage locating model97959593
The leakage quantity model97969897
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Li, X.; Wu, X.; Sun, M.; Yang, S.; Song, W. A Novel Intelligent Leakage Monitoring-Warning System for Sustainable Rural Drinking Water Supply. Sustainability 2022, 14, 6079. https://doi.org/10.3390/su14106079

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Li X, Wu X, Sun M, Yang S, Song W. A Novel Intelligent Leakage Monitoring-Warning System for Sustainable Rural Drinking Water Supply. Sustainability. 2022; 14(10):6079. https://doi.org/10.3390/su14106079

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Li, Xiaoqin, Xiaomei Wu, Mingzhuang Sun, Shengqiao Yang, and Weikun Song. 2022. "A Novel Intelligent Leakage Monitoring-Warning System for Sustainable Rural Drinking Water Supply" Sustainability 14, no. 10: 6079. https://doi.org/10.3390/su14106079

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