# Burst Detection in Water Distribution Systems:
## 4 Conclusions  
This study proposes a methodology to generate water consumption time series affected by bursts for supporting the development of anomaly detection models in WDS. The SHtsG deals separately with water request and water consumption generation. The first consists of modeling the water requests through a superimposition approach, which considers both the different deterministic trends (e.g., seasonal, weekly and daily pattern) and the random components of the variance. The second phase consists of generating consumption with accurate WDS modeling in which background losses and bursts are properly introduced. The two phases methodology allows for providing a synthetic hydraulic dataset close to the real data in terms of both mean and variance. Moreover, the generated time series are not affected by uncertainty and missing data due to measurements and transmission system. These synthetic data concern normal and abnormal data with precise leaking labels including complete information about the bursts. Two different applications are presented to validate and highlight the advantages of the SHtsG. The first consists of a WDS widely used in literature that is called the Apulian network. This test case aims to provide a detailed step by step explanation of the methodology applied to a WDS operating in scarce pressure conditions. The reliability of the SHtsG is underlined by the resulting time series of the WDS inlet flow rate which represents four years of the total consumption. Moreover, the variance of the consumption is shown by means of the random introduction of the different types of bursts properly labelled. It is noteworthy to mention how complex it is to distinguish normal data from abnormal data, i.e., affected by bursts, due to the pressure deficit condition of the analyzed WDS. Therefore, the use of proper pressure-driven hydraulic solver, which is able to properly simulate the different water request components (e.g., demand, background leakages, and bursts), results in being crucial for providing a final suitable dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Hour** & **March** & **March** & **April** & **April** \\  & **Request** & **Consumption** & **Request** & **Consumption** \\ \hline
0:00 & 0.538 & 0.007 & 0.016 & 0.177 \\
1:00 & 0.093 & \(3.42\times 10^{-6}\) & 0.019 & 0.172 \\
2:00 & 0.038 & \(4.20\times 10^{-14}\) & \(4.9\times 10^{-4}\) & 0.078 \\
3:00 & 0.269 & 0.033 & 0.001 & 0.188 \\  
(5.3\times 10^{-5}\) & \(1.52\times 10^{-4}\) \\
23:00 & 0.353 & \(1.11\times 10^{-5}\) & \(2.9\times 10^{-5}\) & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(P\)-values obtained by the \(t\)-student test of the null hypothesis such that the mean of the real data are equal to the mean of the generated by SHtsG data for each hour of the day. Specifically, real data and synthetic data are compared both for the water request and consumption in March (training) and April (validation), separately. The second presents the Egna network which consists of a small mountain WDS with elevated operating pressures. This test case helps to understand how the SHtsG can be used to enlarge a real dataset maintaining the characteristics of the original time series. The accuracy of the methodology in reproducing real data are proven by a \(t\)-student test. Moreover, the elevated network pressures enhanced the different behavior of the burst, which can be more easily distinguished. The SHtsG depicts that it is possible to properly reproduce the variability of the real data and to generate a time series coherent with the real WDS behavior. The importance of the accurate hydraulic solver adopted is also highlighted. To conclude, the presented methodology has shown promising results to generate suitable time series extrapolated from extended period simulations that include both hydraulic and mechanical WDS reliability.