# Prediction of Water Leakage in Pipeline Networks Using Graph Convolutional Network Method
## 1 Introduction  
Due to the development of the industry, the need to transport water resources to cities through pipelines has arisen during urbanization, both from dams and underground sources. The demand for water resources is increasing due to population growth, while water resources are decreasing due to global warming. Given the increasing demand and reduced resources, it is essential to transport water resources without loss. Open or closed pipeline networks are used to transport and distribute water resources. Failures in pipeline networks are common and significant and a global problem. Failures in pipeline networks may occur in two ways: leaks and blockages. This study focuses on the detection of water leaks in pipeline networks. Pipeline leaks that arise from pressure or temperature changes,corrosion, wear and tear, and third-party damages [1] may lead to critical problems in pipeline transportation systems. Accurately detecting water leaks in pipeline networks is essential for avoiding the economic impacts of losses and protecting the environment [2]. Therefore, it is crucial to detect and repair pipeline network failures rapidly. Timely and accurate intervention in pipeline failures is a critical decision-making problem. Two main approaches are used to detect failures in pipeline networks: physical inspection and mathematical model simulation. Physical methods are costly due to the production stoppage, although they accurately identify the location and size of the failure. On the other hand, the mathematical approach theoretically detects leaks and is, therefore, much less expensive [3]. Various methods are used to detect leaks in pipeline networks. Some of these methods include acoustic methods [4; 5], negative pressure wave measurement [6; 7], measurement of input and output values of pressure and fluid velocity [8; 9; 10], vibration analysis, distributed fiber optic sensing, infrared cameras, and lidar systems [11]. Many machine learning algorithms based on convolutional neural networks and artificial neural networks are used for leakage detection and classification [12]. Many studies have been conducted to detect and localize pipeline system leaks [13; 14]. A growing body of literature on using machine learning applications for leak detection in pipelines [15; 16]. However, studies on machine learning methods for leak detection in pipelines are still limited and have remained under-researched [17]. A literature review reveals that studies have been conducted on detecting leaks in pipelines using machine learning methods, which can be categorized into five main approaches. Machine learning models employed in the studies in the literature are as follows:  
1. For the negative pressure wave (NPW) method, a wireless sensor network-based machine learning (WML) algorithm was utilized [18]. 2. The acoustic-based model, including support vector machines (SVM) [19], neural networks [20], artificial neural networks (ANNs), as well as SVM [21], and the combination of SVM with Relevance Vector Machine (RVM) [22], was employed for leak detection methods. 3. The thermal infrared (IR) camera-based method utilized the immune neural network [23] and convolutional neural network (CNN) approaches [24] for leak detection. Some studies specifically focused on the application of these methods in petroleum pipelines. 4. Pressure-monitoring methods employed the spa and CNN [25] for leak detection in petroleum pipelines, while a deep-learning method called beeppipe was also used [26]
5. The fluid transient waves method utilized artificial neural networks (ANNs) [27] and a machine learning (ML)-based framework [28]. This academic literature review highlights the utilization of various machine learning algorithms to detect leaks in pipelines, which demonstrates the successful application of different methods and encourages further research to achieve improved results in leak detection techniques. Using machine learning algorithms, accuracy rates for pipeline fault diagnosis have been reported to range from 78.51% to 99%.