# Burst Detection in Water Distribution Systems:
## 3 Application
### Egna
The fourth plot represents the random components and the fifth the resulting water request. It shows a few outliers regarding the normal data, while the abnormal data, indicated with the red color, appears to be more diffused in the outlier zone. This behavior is different from the Apulian test case (see Figure 6). In fact, the Egra network does not suffer from the pressure deficit condition. This means that the available pressure is always enough to suffice at both users' water request and bursts. These observations underline even more the crucial role played by the proper hydraulic solver adopted in the simulations. In fact, the generation of a time series of consumption for burst detection can not be made regardless of the pressure behavior of the WDS. To show the robustness of the proposed methodology, the original time series and the data generated by SHtsG have been tested by means of the \(t\)-student test. Figure 12 and Table 1 display the corresponding results. Thus, the reliability of the consumption time series generated by SHtsG has been tested for both March and April, which are the months used for the model training and  
Figure 11: Box & Whiskers plot for each hour of the day of the 10 generated samples of April consumption of the Egra WDS. Figure 10: Total generated consumption of the Egra network for the March month, including the bursts and the calibrated background losses. validation, respectively. The \(t\)-student test enables to define if there is a consistent difference between the original and the generated data at each hour of the day. In particular, the null hypothesis states that the mean of the real data are equal to the mean of the generated by SHtsG data. The results of the test are displayed through the bounds of Figure 12, which are defined according to a significance level of 1%, allow to easily identify the rejected hours, i.e., real values out of the limit lines. Firstly, Figure 12a,b report the results of March data adopted in the training of the SHtsG. In this month, the null hypothesis is never rejected for the water request, while only 5 times the null hypothesis is rejected for the consumption. This means that the generated time series are able to well resemble the real data with 1% significance level. Secondly, Figure 12c,d show the results of the \(t\)-student test of April data. It is worth noting that the statistical test has been made between 1 month of real data and the 10 sample of the generated April data. The performance of 10 samples representing April data has been adopted in order to have a more robust evaluation of the SHtsG. In case of a single sample, the random part of the bursts modelling excessively affects the variability of the results even if the procedure has been properly set up. The test gives positive results even in the severe case of the validation dataset of April. Only in a few hours, the two dataset are significantly different from each other. It mainly happens during the night, where the difference between March and April is more significant. Table 1 lists the \(p\)-values of the \(t\)-student test applied on the 4 cases described above. \[\widetilde{\overline{W}t}=\widetilde{\overline{W}d}+\widetilde{\overline{W}l}+ \widetilde{\overline{W}b}, \tag{20}\]0 T-student test between generated and real data of March and April for both water request and consumption.