Leak Prediction Model for Water Distribution Networks Created Using ...

Water Resour Manage (2016) 30:2719–2733 DOI 10.1007/s11269-016-1316-8

Leak Prediction Model for Water Distribution Networks Created Using a Bayesian Network Learning Approach Sou-Sen Leu 1 & Quang-Nha Bui 1

Received: 13 December 2014 / Accepted: 31 March 2016 / Published online: 11 April 2016 # Springer Science+Business Media Dordrecht 2016

Abstract Water leakage in water distribution systems (WDSs) can bring various negative economic, environmental, and safety effects. Therefore, predicting water leakage is one of the most crucial tasks in water resource management; however, it is also one of the most challenging ones. Previous leakage-related studies have only focused on detecting existing leaks. This paper presents a novel model using expert structural expectation–maximisation, for predicting water leakage in WDSs. The model can take into account the uncertainty of leakage-related factors and balance the contribution of monitoring data and prior information in a Bayesian learning process to maximise leakage prediction accuracy. Moreover, the proposed method can indicate the most crucial factors affecting water leakage. The results of this study could benefit water utilities by aiding them in establishing an effective leakage control plan to minimise the risk of water leakage. A case study is presented to demonstrate the robustness and effectiveness of the proposed method. Keywords Water distribution system . Leak prediction . Water leakage . Bayesian network

1 Introduction Water leakage in urban water distribution systems (WDSs) is a major challenge for water utilities worldwide. Depending on factors such as location, water network systems, and maintenance condition, the amount of water loss attributable to leaks in WDSs may be as much as 50 % of the distribution input (Araujo et al. 2006; Puust et al. 2010). Water leakage

* Quang-Nha Bui [email protected]

1

Department of Construction Engineering, National Taiwan University of Science and Technology, 43, section 4, Keelung Road, Taipei 10672, Taiwan

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wastes water resources and energy and threatens environmental and public health (Besner et al. 2011; Malm et al. 2015). Although many studies have considered the problem of water leakage in WDSs, most studies have focused on detecting leaks. Puust et al. (2010) presented a review of leak detection methods. Recently, some of these methods, such as the inverse transient analysis method (Haghighi and Ramos 2012), noise log correlation method (Jin et al. 2007), and computer-aid simulation optimisation method (Wu et al. 2010), have been tested. The common limitations of these methods are cost, complex equipment system, and a heavy dependence on experts; in addition, applying these methods on a large scale is difficult, and they can only be applied to existing leakages. Few researchers have focused on water leak prediction, which warrants more attention. Leakage prediction models are beneficial for active pipe leakage control methods such as leak prevention and detection (Lijuan et al. 2012). Leak prediction methods are used to identify areas and pipes with a high probability of leakage, thereby allowing water utilities to devise an appropriate active leakage control plan, such as pipe replacement, to replace pipes with a high leakage probability. (Delgado-Galván et al. 2010) reported that active leakage control is the most effective alternative for water supply managers to handle water leakage problems when economic, social, and environmental concerns are considered. Only recently have some techniques been developed specifically to address the leak prediction problem. Lijuan et al. (2012) presented a model that was based on the radial basis function (RBF) neural network for pipe leakage time prediction in which leakage influencing factors act as the input vector and pipe leakage time acts as the objective vector of the RBF neural network. In this model, the hidden layers in the RBF neural network are regarded as a black box; therefore, the impact of individual input factors on output events is inestimable. Liang et al. (2012) presented an approach for estimating the risk of third-party interference to a pipeline system by using a fault tree and self-organising maps algorithm. For this approach to be effective, all basic events in the fault tree must be considered mutually independent events; however, this is rarely the case in real water pipe leakage problems. Analysing factors affecting leaks and the relationship between these factors can facilitate predicting water leakage more effectively. Because many factors that lead to water leaks could be interrelated, there should be no assumption of mutual relationships among them. Thus, water leak prediction is a challenging task. Another difficulty in water leakage prediction is that such events are rare and any prediction has large uncertainty bounds. Therefore, a method is required that both considers the relationships between influencing factors and ensures the uncertainty bounds of the prediction. To address the aforementioned problems, this paper proposes a Bayesian framework for water pipe leakage prediction. The Bayesian network (BN) derived using the Bayesian network learning (BNL) model represents the water leakage forming system, which is used to update the probability of each element in the network, and the leak probability of a target pipe is updated subsequently according to the leak probabilities of other elements in the network. To overcome the limitation of available data, a novel BNL algorithm called expert structural expectation–maximisation (ExSEM) is proposed to incorporate prior expert knowledge into the BNL process. In principle, the ExSEM algorithm balances the contribution of monitoring data and prior information. When data are limited, the model estimation can be made primarily according

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to the prior information; when data are sufficient to be exploited by the model, the model estimation relies mainly on the data. The remainder of this paper is organised as follows: Section 2 reviews the statistics of water leaks in Taiwan and identifies leakage factors. Section 3 introduces the basic concepts of the BN and BNL model, and Section 4 describes the Bayesian framework for water leakage prediction. Section 5 details a case study to demonstrate how the model is applied to predict leaks. In Section 6, conclusions are made on the effectiveness of the proposed model.

2 Leaks in Taiwan and Identifying Leakage Factors Because of the limited land and uneven seasonal distribution of rainfall in Taiwan, concern for the protection and effective use of water resources is increasing, particularly regarding water leakage management. According to a 2011 Taiwan Water Corporation (TWC) report, the total water leakage volume in Taiwan was equivalent to 630 million m3 per year and water leakage rate was approximately 20.51 %, which is higher than the global average leakage rate of 18 % (TWC 2011). Figure 1 shows the distribution of the leakage rate throughout all water network branches in Taiwan; the lowest and highest leakage rates are 11.03 and 35.84 %, respectively. Figure 1 also illustrates that the leakage rate is unevenly distributed across regions, depending on water network conditions and other factors. The TWC report named the three main direct factors leading to water leaks as pipe dislocation, cracks, and corrosion (TWC 2011). According to the report, pipe dislocation causes leaks by extending the joint gap between pipes; factors in pipe dislocation may be pipe length and the number of connected pipes. Pipe cracks can be identified by monitoring for excessively high or uneven internal or external pressures. Pipe corrosion may be affected by water quality, soil condition, and pipe material and age. According to statistics, the pipeline

Fig. 1 Leakage rate in the water network branches in Taiwan

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system in Taiwan has an overage rate of approximately 33 % and PVC pipes account for 59 % of total pipe length. Data provided by Taipei Water Company revealed that some major factors for water leaks are ground movement, construction activities, load vibration, and pipe material, age, depth, and corrosion (Kuo 2014). Some researchers have studied the causes of water leakage. The International Water Service Association (IWSA) reported that some major impact factors of water leakage are movement, corrosion, traffic loading, water pressure, excavation, water temperature, geological conditions, construction quality, and pipe age, fitting, and material (IWSA 1991). However, the influence of each factor varies widely among countries and regions, all of which have different leak impact factors. Ho et al. (2010) summarised the major leakage impact factors in Taiwan as improper pipes, pipe corrosion, overload and vibration, water hammers, ground collapse, and construction damage. Some common leakage impact factors mentioned by Puust et al. (2010) are ground movement, high water pressure, excavation, temperature, ground conditions, poor workmanship, and pipe age and defects. Table 1 summarises leak impact factors from related research. Defining water leak factors is difficult because many factors influence leaks indirectly through other factors. The following sections of this paper present a systematic method of determining the relationships and influence of water leakage factors.

3 Bayesian Network The Bayesian network (also called the belief network and Bayesian belief network), introduced at Stanford University in the 1970s (McCabe et al. 1998), has since been widely applied in various disciplines such as medicine (Antal et al. 2004; Liu et al. 2006), system reliability (Ching and Leu 2009; Doguc and Ramirez-Marquez 2009), risk analysis (Bouejla et al. 2014; Luu et al. 2009; Martín et al. 2009), and more recently environmental assessment (Cha and Stow 2014). The BN is a powerful modelling tool for complex problems because it can describe numerous relevant factors simultaneously and express their relationship effectively, and provides a mechanism to incorporate many kinds of prior information and expert knowledge into learning to solving problems with many uncertainties (Antal et al. 2004).

Table 1 Summary of leak impact factors by relevant researches research/source

Leak impact factors

TWC (2011)

pipe cracked, pipe dislocation, pipe corrosion, pipe length, number of connected pipes

IWSA (1991)

ground movement, pipe corrosion, traffic loading, water pressure, excavation, pipe age, water temperature, pipe material, pipe fitting, geological condition, construction quality

Ho et al. (2010)

improper pipe, pipe corrosion, overload and vibration, water hammer, ground collapse, construction damage

Puust et al. (2010)

ground movement, high pressure, excavation, pipe age, temperature, pipe defects, ground conditions, poor quality of workmanship

Kuo (2014)

ground movement, pipe material, pipe age, construction activities, pipe depth, load vibration, pipe corrosion

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3.1 Bayesian Network Representation A BN can be represented as a directed acyclic graph (DAG) in which nodes represent factors of concern and edges represent casual relationships between nodes. In addition to the graph, a BN has a set of conditional probability tables (CPTs) Θ = {θijk} specifying the probability of each possible state of the node Xi according to each combination θijk of the states of its parents Pai. A node without parents is called a root node and a node without children is a leaf node. Given the parents Pai of the node Xi, node Xi is conditionally independent of all its nondescendant nodes. When the structure and parameters are already known, a BN defines uniquely a joined probability distribution over all nodes in the graph, which can be expressed as n 

PðX 1 ; X 2 ; …; X n Þ ¼ ∏ P X i
Pai

ð1Þ

i¼1

Once the joined probability distribution in Eq. 1 is known, many inference algorithms can be used for reasoning probabilities of nodes that have not been observed conditionally to the values of observed nodes. A review of these inference algorithms can be found in the study by Murphy (2001).

3.2 Basic Structural Expectation–Maximisation Algorithm for Bayesian Network Learning A BN model can be constructed on two general bases: information from domain experts or from historical data. The first method requires meticulous and exhaustive research by experts and is susceptible to errors caused by subjective assessment. The second approach generally requires a large amount of data to be effective (Chickering et al. 2004). Many methods have been proposed to create BNs from data (Bui and Jun 2012; Eerola et al. 2011; Schulte et al. 2009; Wong and Guo 2008). Among these BNL algorithms, structural expectation–maximisation (SEM), proposed by Friedman (1998), is one of the most popular and can manage incomplete data. The SEM method is an extension of the expectation–maximisation (EM) algorithm proposed by Dempster et al. (1977) for BN parameter learning. In contrast to EM, SEM is employed to find both the structure M and parameters Θ of the BN. The parameter maximisation in EM is replaced by maximisation in the joint space {M, Θ}, which alternately searches for the optimal structure and the optimal parameters corresponding to this structure. To compensate for missing values, the exact score of BN is approximated according to the expected values of the statistics.

4 Bayesian Framework for Water Leakage Prediction The ExSEM algorithm serves as the basis of the proposed leakage prediction system. The most challenging task in executing the proposed model is combining expert information and monitoring data. There are several means of combining expert knowledge into the BNL process, in which each method requires experts to provide different types of information (Feelders and van der Gaag 2006; Heckerman et al.

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1995; Liao and Ji 2009). In this study, experts provided feedback on the structure of the true BN. A predefined network BN0 was given to experts to obtain their opinions on how it should be modified, and the final modified network was designated as expert network BNEx. To integrate this expert network into the ExSEM, a score function called Bexpert Bayesian information criterion^ (ExBIC) was developed for integrating two information sources (i.e. limited data and an expert network).

4.1 Expert Bayesian Information Criterion Score The Bayesian information criterion (BIC) is often adopted to score a candidate network in the BNL problem and can be expressed as follows:   1     BIC ¼ logP B* þ logP B* jD − Dim B* logðnÞ 2

ð2Þ

where n ri qi X 
 X X   *
N *ijk log θi jk log B
D ¼ i¼1

ð3Þ

j¼1 k¼1

is the log-likelihood of candidate network B* given the data D; N*ijk is the occurrence number {Xi = xk, Pai = paj} in D obtained by inferring from the current optimal network in the case of incomplete data or otherwise by mere counting (Leray and Francois 2005). The term log P(B*) in Eq. 2 represents the prior probability of candidate network B*; 0.5Dim(B*)log(n) is the penalty for the complex model in which Dim(B*) is the number of parameters used for BN representation and calculated as 

*

Dim B



¼

n X

ðri −1Þqi

ð4Þ

i¼1

To incorporate the prior information from expert network BNEx into the BNL process, a new ExBIC score is proposed to replace the original BIC score. The uniform prior probability log P(B*) in the BIC score is replaced by the prior probability of the candidate network given the expert network log P(B*|BNEx); therefore, Eq. 2 becomes   1   
 ExBIC ¼ logP B*
BN Ex þ logP B* jD − Dim B* logðnÞ 2

ð5Þ

The calculation of log P(B*|BNEx) is performed using the prior probability concept of a candidate network. The conditional probability of a candidate network given the expert network is estimated by calculated the similarity of its DAG with BNEx as follows: 

P B*
BN Ex ¼

1 Ex ½nðn−1Þdiff ðBN Þ

ð6Þ

where diff(BNEx) is the number of different edges (including added, deleted, and reversed edges) between B* and BNEx, and n(n-1) is the number of possible directed edges in n nodes BN. Equation 6 shows that diff(BNEx) = 0, B* is the same as BNEx; therefore, P(B*|BNEx) = 1. When diff(BNEx) increases, the probability assigned to B* decreases, signifying that the more

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or less similar to the BNEx the candidate network is, the higher or lower, respectively, the score given to the candidate network will be. The contribution of the prior network to the learning process is measured by including a prior weight α in the ExBIC score function:   1   
 ExBIC ¼ αlogP B*
BN Ex þ logP B* jD − Dim B* logðnÞ 2

ð7Þ

where α ranges from 0 to 1 and represents the prior weight of expert information; α = 0 corresponds to the uniform prior and α =1 corresponds to the full log prior probability given by the prior network in the ExBIC score.

4.2 Expert Structural Expectation–Maximisation Algorithm for Predicting Water Pipe Leakage The proposed ExSEM algorithm is a modification of the original SEM, adapting the new ExBIC score into the BNL process. Accordingly, the inputs for the ExSEM algorithm include initial network BN0, expert network BNEx, and leakage monitoring data. To search for the structure and parameters {M, Θ} of the BN, a greedy hill-climbing search is employed in the ExSEM, which is also applied in the original SEM. This is a simple and effective heuristic search tool. Although the greedy hillclimbing search does not guarantee an optimal result, many previous studies have shown that it obtains satisfactory solutions (Gámez et al. 2011). To increase the efficiency of the hill-climbing search in ExSEM, the search engine is provided with a Bgood^ initial network BN0 to reduce search time and avoid local optima. Figure 2 presents the generalised framework of the ExSEM algorithm.

Initial BN: BN0

Fig. 2 ExSEM algorithm flowchart

Current best BN:

M,

EM parameter learning Current best BN:

M,

monitoring data

*

Search engine

ExBIC score

Improve score?

Expert network

yes

no Return best BN:

M *,

*

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5 Case Study 5.1 Input Data and Experimental Setup The proposed approach was applied to predict water leakages in the Taipei water distribution system. Data were collected for two district meter areas (DMAs) for 2 months by field engineers. Sampling points were distributed evenly among the two DMAs to ensure impartiality. To optimise the learning process of the ExSEM algorithm, continuous data were discretised into discrete states. Finally, a data set comprising 2633 cases was input into the model. Table 2 shows all the input factors and their states after discretisation. In addition to a data set, ExSEM requires an expert network BNEx for the learning process. To fulfil this requirement, an initial BN structure BN0 was built according to the leakagerelated factors in the dataset and a survey of previous studies. Figure 3a shows the BN0 structure. This BN0 was then presented to three experts, who suggested deleting one factor and three edges and adding six edges. Figure 3b presents the final, expert-approved network BNEx. After sufficient data was inputted, the system was implemented using the Bayes Net Toolbox developed by Murphy (2001). To evaluate the contribution of the expert network to the ExSEM learning result and the predictive ability of the system, we applied SEM for the learning BN with the same data source and compared the structure of the two learned BNs and their predictive ability. The following comparison demonstrates the superiority of ExSEM over SEM.

5.2 Bayesian Learning Results ExSEM was applied to learn BN with expert prior weight α = 1 and then compare the learned BN with the result of the SEM algorithm (corresponding to α = 0 in ExSEM). Figure 4 Table 2 All leakage related factors and their states Node

Factors

states

X1

Leakage

0 (no), 1 (yes)

X2

Pipe corrosion

0 (no), 1 (yes)

X3

Pipe cracked

0 (no), 1 (yes)

X4

Pipe dislocation

0 (no), 1 (yes)

X5

Pipe depth

A(1.2 m)

X6 X7

Pipe material Pipe diameter

PB, PVC, SSP A( 150 mm)

X8

Pipe age

A(0 ~ 10), B(10 ~ 20), C(20 ~ 30), D(>30)

X9

Pipe length

A(80 m), B(80 ~ 150 m), C(150 ~ 300 m), D(>300 m)

X10

Construction activities

A (small), B(medium), C (large)

X11

Number of connected pipes

A(0 ~ 10), B(11 ~ 20), C(20 ~ 30), D(>30)

X12

Soil class N value

A(0 ~ 2), B(2 ~ 4), C(4 ~ 8), D(8 ~ 15), E(>15)

X13

Pressure surge

A(0), B(0 ~ 5), C(>5)

X14 X15

Ground movement Road width

0 (no), 1(yes) A(0 ~ 6 m), B(6 ~ 8 m), C(8 ~ 12 m), D(>12 m)

X16

Pump station radius

A(0 ~ 2 km), B(2 ~ 4 km), C(4 ~ 6 km), D(>6 km)

X17

District meter area

A, B

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(a) Initial Bayesian network BN 0

(b) Initial Bayesian network BN Ex Fig. 3 Input BNs for ExSEM model: a Initial network BN0 and b Expert network BNEx

presents the BNs BNExSEM and BNSEM learned from the ExSEM and SEM algorithms, respectively. Comparing structural differences between BNExSEM and BNSEM in the results in Fig. 4 reveals that the expert network recovered some relationships in BNExSEM, such as X8-X6, X4-X3, X15-X5, and X7-X3, and restored some factors that were missing in BNSEM, such as X7 and X15. Other relationships were not supported by BNEx but were recovered by monitoring data, such as X17-X8, X17-X12, and X12-X14. Some relationships appeared in BNEx, such as X13-X11, X5-X7, and X6-X2, but were excluded in BNExSEM because they were unsupported by the data. Table 3 shows a comparison of structural difference between BNExSEM and BN0, BNEx, and BNSEM. Although relationships in BNs do not constantly represent a real relationship in practice, most of them are easily explained. The same is true of relationships in BNExSEM because they can be interpreted when considering monitoring data, a literature survey, or opinions from experts. For example, the relationship between pipe age (X8) and pipe material (X6) can be explained using observations from data and comments from experts. Stainless steel pipes (SSP) can last longer than 30 years, whereas pipes made with materials such as PVC or PB are normally replaced within 30 years. Another example is the relationship between pipe diameter

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(a) Bayesian network learned from ExSEM algorithm: BN ExSEM

(b) Bayesian network learned from SEM algorithm: BN SEM Fig. 4 BNs learning result from ExSEM and SEM algorithms: a BNExSEM and b BNSEM

(X7) and pipe cracks (X3); most pipes in our database had diameters of at least 150 mm; larger pipes such as these are more crucial and will be monitored more closely. However, this overrepresentation of large pipes created difficulty for SEM to determine the relationship Table 3 Comparison of structural differences between BNExSEM and other BNs Compares with BN0

Compares with BNEx

Compares with BNSEM

Added edge

Added edge

Removed edge

Added edge

Removed edge X11-X3

Removed edge

X4-X3

X17-X8

X13-X11

X15-X5

X14-X3

X17-X12

X5-X7

X8-X6

X12-X14 X11-X6

X12-X14 X6-X2

X6-X12

X4-X3 X7-X3

X8-X6

X6-X4

X17-X8

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between pipe diameter and cracks. By using the expert network, ExSEM could recover this relationship more accurately and produce a more complete network. A possible explanation of the two aforementioned phenomena is that strong relationships could not be recognised and recovered by SEM because of insufficient data; however, these relationships were restored by ExSEM with the assistance of the expert network. This reveals the importance of integrating expert knowledge into the Bayesian learning process and the manner in which expert knowledge and monitoring data are combined to optimise the learned network. This optimisation affects the structure of BNExSEM and enhances the prediction accuracy. The next section describes how BNExSEM exceeded BNSEM in predictive capability.

5.3 Leakage Prediction Results and Comparison This subsection compares the prediction results of ExSEM and SEM to evaluate the practical predictive ability of the proposed model. To reduce the bias of the resulting estimator, we used the k-folds cross validation technique introduced by Diamantidis et al. (2000). Accordingly, the dataset was partitioned randomly into five equal folds, each containing 526 data records. In each prediction, four folds were used to train the model. To compute the threshold level of the leakage, the resulted BN was used to predict the data in the training folds and then the predicted results were compared with the real leak condition. The threshold level was determined to give the highest percentage of correct prediction. Finally, the resulting model was used to predict the remaining fold. Figure 5 shows a comparison of the prediction results of ExSEM with those of SEM. The average prediction accuracy percentage of ExSEM was 0.846, which exceeds the SEM average result of 0.726. ExSEM also exhibited stability in its predictions; the standard deviation of its predication results was 0.026. These results are promising, suggesting that the model has practical applications.

5.4 Analysis of the Effects of Leakage-Related Factors Determining the main factors in pipe leakage will aid water utilities in water network design and leakage response planning. An analysis of the effect of each factor on water leakage was performed according to the method presented by Akhtar and Utne (2014). The effects on

Fig. 5 Comparison of leakage prediction results ExSEM vs. SEM

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leakage were validated by setting the evidence on the leakage-related factors to the highest state, one by one, and observing the posterior probability change in the leakage node. This posterior probability change represents the most severe effect of a single factor on water leakage. Figure 6 shows the analysis results. For instance, setting the evidence on Bpipe age^ to state D will increase the marginal probability of water leakage from 0.11 to 0.58, and setting the evidence on Bnumber of connected pipes^ to state D will increase the marginal probability of water leakage from 0.11 to 0.23. The Bno evidence^ factor in Fig. 6 represents the case for which no evidence was entered into the BN; its probability of 0.11 represents the normal leakage probability of the network. Figure 6 also shows that pipe cracks (X4), pipe dislocation (X3), and pipe corrosion (X2) had the highest effects on water leakage, a phenomenon that was expected because these factors are the main factors that cause leakage and the occurrence of each will almost definitely lead to leakage. These factors can be considered to determine the root cause of leakage because their states will be changed by altering the states of their descendant factors. Changing the states of the remaining factors will improve leakage conditions. The mean posterior probability values of these factors was 0.37, indicating that factors with values higher than this threshold severely risks of leakage. As demonstrated, construction activity has the highest effect to leakage, followed by ground movement, pipe age, and pressure surges. This result suggests that one of the most effective methods of preventing leakage is soundly managing construction activities. In addition, the results regarding the phenomenon of subsidence and subsidence prevention measures suggest that the regular replacement of old pipes and the effective design of pumping systems to minimise pressure surges will greatly prevent

Fig. 6 Analysis of effects of leakage-related factors to water leakage

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water leakage. By contrast, pipe diameter has the lowest effect to leakage, followed by the number of connected pipes and road width. That pipe diameter has the lowest effect is somewhat unexpected. As explained above, the diameter of most pipes in our data was the large size (150 mm or 200 mm), possibly affecting the analysis results. Collecting more data on pipes with different diameters will resolve this problem.

6 Conclusions This study proposed a novel leakage prediction system for WDSs that was based on a new Bayesian learning approach, the ExSEM algorithm. In the prediction system, a new ExBIC score was proposed to combine monitoring data and expert knowledge into the BNL process as a balancing solution to enhance prediction results. The system was applied to the Taipei WDS, and the results demonstrated that the proposed approach effectively accounted for extra leakage-related factors and the relationships among these factors. The results also revealed that the system provided more accurate predictions by integrating an expert network into the ExSEM algorithm. Moreover, the predictive accuracy of the system could be continuously improved by updating new data from monitoring systems and experts. This advantage, combined with the quick-response ability of the BN, renders the system suitable for an online leakage prediction and prevention system. Furthermore, an analysis of effects of leakagerelated factors revealed critical factors in water pipe leakage, such as construction activities, pipe age, ground movement, and pressure surges that can be considered to minimise damage during the water network design process. The model has some limitations that must be addressed. Currently, the system cannot handle continuous data; therefore, all data must be discretised before being inputted, potentially affecting the learned network and predictions. Furthermore, the integration of expert knowledge is not necessarily limited to the BN structure, and the integration of other sources of information will enable the BN learn more efficiently. Addressing these limitations can improve our system and its usefulness.

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