## 3 Results
### Analysis on the Influence of the Signal Duration  
On the basis of the comparison between the two tests, sensor Aax provides a satisfactory performance. Conversely, sensor Ard appears overly affected by the modifications occurring in the soil conditions, therefore exhibiting inadequate reliability. The performance of the hydrophone can be deemed poor as well, due to the high variability associated with leak L1, which was the nearest leak. Hence, potential strategies for enhancing the reliability of sensors Ard and Hyd, and for possibly further improving the sensitivity of sensor Aax, are investigated. In particular, since the value of \(K_{R}\) may depend on the signal length, as shown by Equation (10), the possibility of enhancing the leak detection performance by optimizing the acquisition duration was assessed in this study.  
Figures 6-8 show the trend of \(K_{R}\) as a function of the acquisition duration. For the sake of clarity, a single \(K_{R}\) value was reported for the non-leaking conditions, referred to as NL, and computed as the mean of the three values related to conditions NL1, NL2 and NL3.  
As expected on the basis of the behavior observed for the Gaussian noise (Section 2), the curves associated with leaks L1 and L2 exhibit a sizeable growth as the duration was increased, except for one case (namely the Hyd sensor, with duration of 60 s). The curves related to the non-leaking condition were characterized by an increment as well, but the growth rate appeared lower. As for leak L3, it exhibited a trend similar to the non-leaking condition, hence confirming that such a leak can not be distinguished from the environmental noise on the basis of the parameter \(K_{R}\).  
Figure 5: Mean values of \(K_{R}\) in Test-2 (\(\pm\sigma_{R}\) intervals indicated by the orange vertical bars), for sensors: (**a**) Ard; (**b**) Aax; (**c**) Hyd.  
In order to better appreciate the effects of the observed behavior on detection performance, the ratios between the \(K_{R}\) values of the \(k\)-th leak (Lk) and of the non-leaking condition (NL), respectively, were computed as:  
\[K_{R}ratio\big{(}T_{j},Lk\big{)}=\frac{K_{R}\big{(}T_{j},Lk\big{)}}{K_{R}\big{(} T_{j},NL\big{)}}, \tag{11}\]  
where \(j=1,\,\ldots,\,3\) and \(\mathbf{T}=\{T_{j}\}=\{10;\,30;\,60\}\), reported in Figures 9-11. The \(K_{R}\) ratio index is meant to quantify the sensitivity of the method to a specific leak; the higher its value, the higher the sensitivity to the corresponding leak. Hence, an increment in the ratio indicates an improved leak detection performance. Due to the trend of \(K_{R}\) characterizing the leaking and non-leaking conditions, a general growth was observed for the \(K_{R}\) ratio. For the Aax sensor, an actual improvement of the performance  
Figure 8: Trend of \(K_{R}\) as function of the acquisition duration for Hyd signals: (**a**) Test-1; (**b**) Test-2.  
Figure 6: Trend of \(K_{R}\) as function of the acquisition duration for Ard signals: (**a**) Test-1; (**b**) Test-2.  
Figure 7: Trend of \(K_{R}\) as function of the acquisition duration for Aax signals: (**a**) Test-1; (**b**) Test-2.  
can be achieved by using longer acquisitions. Conversely, both the Ard and the Hyd sensors still could not provide a satisfactory identification of the leaks in Test-1.