## 1 Introduction  
Water distribution networks (WDNs) are complex systems that are prone to significant water loss, and this loss is mainly due to pipe leakage [1, 2]. It is estimated that leaks can contribute up to 70% of water losses in transmission systems [3]. Leakages in these WDNs are mainly caused by pipe damage or by the network's inability to control pressure due to uncertain demand and operating conditions [4]. Leaks in pipelines are an issue of increasing concern in WDNs as they have negative environmental, economic, and social impacts. Pipe leakages have detrimental effects on natural water resources, nearby infrastructure, and the environment, as they cause pipes to burst and enable the entry of harmful contaminants into the network [4, 5]. The loss of a substantial volume of water that has undergone costly treatment is, for one, a serious economic issue [6]. Moreover, leaky pipes cause an increase in pumping energy and system rehabilitation costs, which compromise water quality by enabling the entry of contaminated groundwater, pathogens, and soil constituents [7]. Leaks also have the potential to erode soil and recharge aquifers beneath urban areas, which puts building foundations at risk [8]. Not only will mitigating leakages reduce operating costs and increase revenues, but it will also improve water efficiency, minimize infrastructure damage, and prevent adverse effects on human health [9]. Detecting these leakages poses a great challenge to engineers since the pipes are usually buried underground. For this reason, constant monitoring is required to identify and prevent potential water leakages in pipes. Traditional leak detection methods, which are disruptive techniques, would change the structure of the WDN, disrupting the serviceability of the network [10]. However, research on novel non-destructive methods has shown the potential for leak detection without altering the chemical composition or geometry of the materials being investigated. The advent of technology has led to developments in non-destructive leak detection techniques for WDNs. For instance, innovative non-destructive techniques (NDT) like infrared (IR) cameras, spectrometers, and ground penetration radar (GPR) have been used to identify leaks in different types of pipes at different moisture contents [10; 11]. The study deduced that all three NDTs could identify leaks in PE, PPR, and PVC pipes, but the detection effectiveness decreased as the moisture content of the soil increased. A recent study has shown the use of GPR and IR cameras simultaneously to effectively determine water leaks in both cold and hot weather conditions [12]. Since GPR is a geophysical imaging technique used for subsurface monitoring, it can accurately identify the pipe's location underground [12]. The IR camera is then able to determine leakage locations and estimate the leakage area [12]. Thermal imaging has also been successful in leak detection [12; 13]. In addition, acoustic emission methods are another NDT suitable for detecting leaks, as they collect sound signals generated by the cavitation and turbulence that occur in a leak [14; 15]. It is important to note that signal processing and classification methods are required to verify that the noises formed are due to leaks [14]. Therefore, integrated approaches are proven to be the most effective for accurate and efficient real-time monitoring. Therefore, using a combination of NDTs has proven to enhance the effectiveness of leak detection methods to help mitigate leakages. Several studies have proposed techniques for leak detection in pressurized transmission mains (TMs). These techniques can be used on WDNs as well; however, more studies are focusing on TMs as the current technology for fault detection on TMs is lacking [16]. This issue is being addressed because research has shown that TMs with relatively larger diameters have larger leaks than expected, and the costs of replacing deteriorating TMs are higher than those of WDNs [17].