## 1 Introduction  
The active control of leaks is essential for limiting losses affecting water distribution networks, which may reach a sizeable percentage of the input volume [1; 2; 3]. Accordingly, numerous methods and technologies for detecting and locating leaks have been proposed, each one characterized by its own pros and cons [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. The methods that proved the most effective are briefly summarized. Techniques based on the monitoring of leak-related noise and vibrations are by far the most commonly adopted [4; 5; 6; 7; 8; 9; 10; 15; 16]. These techniques are non-invasive and can be applied without altering the operational conditions of the network. The detection process may be automated by means of proper indices [6; 7; 8; 9]. Automated leak pinpointing can be also achieved by using the cross-correlation of signals measured by two different sensors [4; 5; 16]. Nevertheless, the technique's effectiveness may be reduced in the case of plastic pipes, due to a higher signal attenuation with respect to metallic pipes; moreover, they are typically only effective over a limited distance range. Methods exploitinginduced hydraulic transients can detect and locate leaks within a wide range, but the pressure peaks can potentially damage the pipes [10; 16]. Acoustic emission (AE) monitoring has been proven as an effective method for detecting very small leaks over long distances [11; 16]; however, its effectiveness may depend on the possibility of artificially amplifying the leak noise by injecting gas or increasing the fluid pressure in the monitored pipes (procedures that are not always allowed during normal operation), and it may be less effective with plastic pipes as well. Tracer gas techniques can reliably provide leak detection and location [4; 16]; nonetheless, they are not suitable for all kinds of leaks and the isolation of the monitored pipe from the network is typically required. Thermography can detect and locate leaks over large areas [4; 12], but its effectiveness may be affected by seasonal temperatures and thermal noise (e.g., large urban areas). Ground penetrating radar (GPR) is also characterized by a large monitoring area and high accuracy [4; 13; 14; 15]; nonetheless, the detection may be hampered by underground anomalies and buried objects other than pipes, and also because of the sizeable amount of signal attenuation in wet soil with high clay content. Electrical resistivity tomography (ERT) can provide leak detection and location [14; 15], but has a low resolution and requires inserting electrodes in the ground, which is not always viable. Time domain reflectometry (TDR) and quasi-static magnetic fields [14; 15] are marginally affected by the environmental disturbances, but are basically suitable for metallic pipes only. Leak detection systems based on devices that are temporarily or permanently deployed throughout the pipeline networks to measure vibro-acoustic signals (e.g., noise loggers [15; 17]) are probably the most common in practical applications. These systems, although providing satisfactory results, may present some drawbacks, particularly when no cross-correlation techniques are adopted [18]. Typically, their operation is based on the detection of increments in the vibration levels, which are expected to occur when leaks start and grow [7; 8; 17]. Consequently, the correct definition of threshold values characterizing the background noise associated with the non-leaking state is essential for their effectiveness. In general, such thresholds are closely related to the local boundary conditions of the monitored locations of the pipeline network, hence a costly and time consuming initial setup being possibly required for each measuring unit. In addition, the presence of pre-existent leaks should be checked carefully to avoid missed detections. Finally, without a unique reference value, optimizing the threshold to achieve the desired sensitivity to leaks is problematic, thus possibly leading to an increased risk of false alarms.