# Burst Detection in Water Distribution Systems:
## 3 Application
### Egna
Moreover, the water demand has been estimated considering a water request per habitant for the April month of 131 \(\frac{l}{habitant\cdot day}\). Hence, the time series has been finally decomposed and the result reported in Figure 8.  
Starting from the decomposed time series, the DFPDM has been modeled to properly reproduce the consumption time series of March. The first phase consists of calibrating the water request terms of Equation (1). As previously declared, the calibration of the model has been performed over the March data. An analysis of the March daily pattern has been carried out. Firstly, the structure of the daily pattern has been studied. In particular, the working days, which ranges from Monday to Friday, always show a 3 peaks behavior, while the Saturdays have three peaks in 60% of the cases and two peaks in the others. Differently from the previous, the Sundays always show two peaks. Secondly, an analysis of the peaks level and their occurrence has been performed. It was found that the main peak happens in the morning in 80% of the cases for the working days, and the remaining 20% happens in the evening. In particular, when the main peak is in the morning, it happens in 75% of the cases at 7.00 a.m. and in 25% of the cases at 8.00 a.m. Concerning the midday peaks occurrence, in 65% of the cases, the peak happens at 12.00 a.m., and for the remaining 35% at 1.00 p.m. Lastly, the evening peak occurs at 5.00 p.m. in 20% of the cases, at 6.00 p.m. in 30% of the cases and in the remaining 50% at 7.00 p.m.Regarding the Saturdays with a three-peaks structure, the morning, midday and evening peaks occurs at 9.00 a.m., 12.00 a.m., and 6.00 p.m., respectively. Instead, for the Sundays and the Saturdays with a two-peak structure, the first peak happen always at 9.00 a.m., and the second peak is at 5.00 p.m. or 6.00 p.m. in 50% of the cases. Therefore, the aforementioned probabilities have been used to generate the daily pattern coherent with the real data analyzed. This generation has been performed for each district of the network shown in Figure 7. Moreover, the generation of the water requests has been made as described in Section 2.1, omitting the weekly and yearly components. Regarding the random component, it has been calculated for each district of Egra with its different user aggregation. Figure 9 depicts the resulting water request  
Figure 8: The decomposition of the metered flow rate of March and April for the Egraa WDS. Then, the request previously generated has been used as input into the DFPDM with both the bursts and background losses. Figure 10 shows the generated consumption for March month with no bursts and background losses coherent with the real data. The model has been then used to generate the consumption also for the April month. In particular, 10 different generations of the consumption of April have been made to show the reliability of the methodology. Regarding the burst parameters, the geometric parameters \(A_{0}\) and \(L_{c}\) of the cracks in Equations (15)-(17) have been bounded to generate values of outflow between 1.5 L/s and 10 L/s. This decision has been made due to characteristics of the Egra WDS. Regarding the duration, different intervals have been selected depending on the burst magnitude. In addition, the repair time ranges between 3 and 21 days in case of bursts outflow from 1.5 L/s to 4 L/s, while the bigger than 4 L/s leaks last from 12 to 72 h. These long repair times are due to the poor operational management of the small municipality analyzed. Moreover, the age of the pipes is known and the \(c_{1}\) coefficient has been fixed to 7.364. The \(a\) and \(b\) coefficients are set to 0.02577 and 0.0207, respectively. Figure 11 displays the 10 April generations under the Box & Whiskers plot for each hour of the day. Figure 9: Water request components for the Egra test case. Starting from the top, the first represents the daily pattern, the second the weekly pattern, and the third the yearly one.