## 4 Discussion  
On the basis of the above analysis, the use of pressure signals does not seem suitable for the proposed technique, due to the excessive variability of the adopted index (i.e., a high standard deviation) and also in light of the superior performance of the hydrophone in the previous experiments reported in Section 3.4. The experimental results proved the effectiveness of the proposed leak detection method when using accelerometers with a sensing direction parallel to the pipe axis. Indeed, a remarkable performance could be achieved in all the tests through the analysis of the longitudinal vibration signals, in terms of both a high sensitivity to the leak and the robustness of the detection. Moreover, the new technique is still in an early stage of development and promising future investigations may show that this technique can outperform other approaches, in terms of the sensitivity to the leak (cf. Section 3.4). Conversely, the monitoring of radial vibrations provided inadequate results, since leaks could not be identified at all in one of the tests and the experiments revealed a significant influence of the modifications in the properties of the surrounding medium. This behavior may represent a critical limitation of the proposed method. Indeed, the presence of elbow fittings between the leak and the transducer (possibly characterizing the layout of actual service pipes near the connections of the customers' water meters) may significantly alter the transmission path of vibrations, thus hindering direct measurements of the longitudinal vibrations generated by leaks. Hence, further verification of the actual detection capabilities in the case of radial accelerometers is recommended. In particular, filtering the acquired raw signals in proper frequency bands may be investigated as a possible solution to solve this issue. In fact, in the previous studies reported in Section 3.4, the sensitivity to the leak  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Sensor**} \\ \cline{2-10}
**Leak** & \multicolumn{3}{c}{**Ard**} & \multicolumn{3}{c}{**Aax**} & \multicolumn{3}{c}{**Hyd**} \\ \cline{2-10}  & **Test-1** & **Test-2** & **Exp-0** & **Test-1** & **Test-2** & **Exp-0** & **Test-1** & **Test-2** & **Exp-0** \\  & **(K\({}_{R}\)ratio)** & **(K\({}_{R}\)ratio)** & **(MIE)** & **(K\({}_{R}\)ratio)** & **(K\({}_{R}\)ratio)** & **(MIE)** & **(K\({}_{R}\)ratio)** & **(K\({}_{R}\)ratio)** & **(MIE)** \\ \hline L1 & 1  
for the radial accelerometer could be remarkably enhanced by using a convenient band-pass filter. Accordingly, extending the database with additional measurements (possibly from real service pipes) is considered mandatory in order to properly test and optimize the desired filter. Reasonably, achieving a sufficient performance is deemed feasible, in light of the good results provided by Test-2. A second limitation of the proposed method may be the distance range of detection, which appeared modest in the experiments, since the farthest leak (exhibiting a sizeable flow rate) could not be detected with any of the tested transducers. On one side, the possibility of further improvements appears hardly achievable, due to the expected significant attenuation of vibration signals [19]. On the other side, it should be noted that this is not a real problem in practice, where the targeted application requires monitoring service pipes which are shorter than 10 m in the networks of interest. Increasing the acquisition duration appears to be a viable strategy in improving detection reliability. It is worth noting that long acquisitions may be deemed undesirable, due to the increasing probability of transients and external disturbances affecting the measured signals. However, signals with the required duration may be attained by simply aggregating shorter signals, as proven by the procedure adopted in the presented analysis.