# Burst Detection in Water Distribution Systems:
## 3 Application
### Apulian  
The first application used to test the performance of the SHtsG is the Apulian WDN, a well-known test case in literature. This WDS has been selected due to its scarce hydraulic pressure behavior, which ensures pressure driven conditions, and, due to the simple layout, which potentially emphasizes the weakness and strengths of the SHtsG. Figure 2 shows the network layout which consists of 34 pipes and 23 nodes. More details about the Apulian network can be found in [31]. In addition, the Apulian network is divided into five districts for highlighting the SHtsG capability in generating variable water requests for different parts of the network. In order to properly model the WDS, the total amount of water request has been reduced as in [44]. This means that the yearly average total users request results in 70 L/s. Therefore, this water request has been distributed along the pipes of the network. Then, the Apulian WDS has been simulated with a fully pressure driven approach according to Section 2.2. Nonetheless, the modeling of the stochastic behavior of the water requests in time is crucial for performing a realistic extended period simulation. Hence, the water request has been generated according to Section 2.1 by modelling the deterministic and the random components for each pipe of the network over a period of 4 years. These components for a single month are reported in Figure 3.  
Starting from the top, the first plot in Figure 3 represents the dimensionless daily behaviour. To specifically model the water behaviour of each district, 5 different daily pattern time series have been generated and distributed in the corresponding district of the network (see the districts in Figure 2). Each daily district time series has been generated by randomly selecting different pattern combinations according to the main characteristics of the district water request, e.g., number of peaks (two or three),  
Figure 2: Layout of the Apulian network and its five districts. main peak (morning, midday or evening) and occurrence time. The use of different district daily patters helps to increase the variance of the final WDS water request, making it more realistic [45]. The second plot in Figure 3 represents the weekly patterns, and the third plot the monthly one, which is constant in the plot since only one month is displayed. The yearly pattern adopted corresponds to that of a typical seaside tourist region, characterized by a high water request during the summer (more details [44]). The fourth plot instead represents the dimensional random component of the water request (L/s), which is specific of each user aggregation (i.e., the water request is aggregated for each pipe of the WDS). Having the Apulian 34 pipe, the random components have been calculated for the distributed water request of each pipe. In this way, the random nature of the request is guaranteed together with a temporal and spatial variability of the request time series. Finally, the fifth plot shows the total water requests of the entire network in L/s. Calculated the water request in the first phase of the SHtsG, hereafter, the second phase is described. Therefore, the water request is the input of the DFPDM which, together with the bursts and the background losses, allows for producing a realistic time series of the water consumption. The total WDS consumption divided for its components is reported in Figure 4.  
Figure 3: Water request components of the Apulian test case. Starting from the top, the first plot represents the daily pattern, the second the weekly pattern, and the third the yearly pattern. The fourth plot represents the random component and the fifth the resulting water request. The first step of this second phase is the calibration of the background losses. In this work, it was assumed that the average background leakage corresponds to the 40% of the yearly average request. These type of losses have been uniformly spread along the network by distributing the same amount of water losses per unit length along each pipe.