## Materials and Methods  
The experiments were conducted in a test facility that replicates a typical portion of a water distribution network (Figure 1), which had already been used by the authors previously for investigating and developing other leak detection algorithms [19]. One polyvinyl chloride (PVC) pipe with an outer diameter of 90 mm (DN 90) was used as water main. Several plastic pipes of smaller diameter (DN 32) were connected to the larger one as customer service pipes. A two-way shut-off valve was installed at each termination of each service pipe, inside manholes. All the pipes were buried under \(\sim\)0.5 m of backfill soil. A pressure tank fed the rig at constant (and adjustable) water pressure. All measurements were performed on a HDPE pipe of length 28 m. Pressure was kept constant at 350 kPa, which is a common operating condition in the networks of interest. Leaks were artificially induced at three different locations along the pipe, accessible through manholes (Figure 1), in order to assess the detection performance for different distances between the leaks and transducers. The distance values from the terminal valve port are reported in Table 1. The \(k\)-th leak (Lk) was generated by damaging the pipe wall with a single longitudinal cut of 20 mm (parallel to the pipe axis), which simulates one the most common kind of cracks characterizing burst leaks occurring in HDPE service pipes [19]. Each crack was expected to generate a leaking flow of about 200 L/h at 350 kPa, which is the minimum leak rate to detect. Pipe repair clamps were installed  
Figure 1: Test facility: (**a**) Pipeline schematics; (**b**) clamped leak; (**c**) active leak. for each leak to allow rapid switching between leaking and non-leaking conditions (Figure 1b,c). A static electromagnetic flow meter, namely a SENSUS iPERL (Xylem Inc., Rye Brook, NY, USA) with a low starting flow rate (about 4 L/h) was installed at the pipe T-joint, monitoring the leaking flow (Figure 1a). This kind of flow meter does not include mechanical moving parts, hence it does not affect the measurements with additional undesired noise/vibrations. The measured flow rates are reported in Table 1. Leak L3, generated for previous experiments and having a flow rate more than an order of magnitude greater than the other two leaks, is included in the measurements to test the proposed method on a large but relatively distant leak. Three sensors were installed on the pipe terminal valve (Figure 2), to simulate a possible setup of real distribution networks (where the transducers should be located some meters away from the water main, near the customer water meter). Two integrated electronic piezoelectric excitation (IEPE) monoaxial accelerometers (PCB 333B55, PCB Piezotronics, Depew, NY, USA, sensitivity 1 V/g) detected radial (referred to as Ard) and axial (i.e., longitudinal, referred to as Ax) shell/wall vibrations, respectively. A piezoelectric hydrophone (Wilcoxon Research H571 LD-1A, Meggitt PLC, Christchurch, UK, sensitivity \(-187\) dB, ref. 1 V/uPa) measured fluid-borne leak-related noise (referred to as Hyd). The hydrophone was fastened to the threaded port of the terminal valve, thus causing no water flow to exit the pipe when the valve was open, also. It is worth noting that the axial accelerometer (Aax) was expected to be more sensitive to the presence of leaks than the radial one (Ard). Indeed, in the frequency band of interest, vibration energy propagates along the pipelines mainly with the axisymmetric waves, termed s = 1 and s = 2, whose displacements are normally characterized by preponderant axial components [23]. However, in actual pipelines the presence of elbow fittings between the leak and the transducer may alter the vibration transmission path and/or the monitoring of axial vibrations may be unpractical. Therefore, radial vibrations of the pipe wall were examined as well.