# Leveraging Urban Water Distribution Systems with Smart Sensors for Sustainable Cities
## 5 Experimental Results
### Balerna Scenario  
Figure 11 displays the performed linear regression between the base demand and pipe diameter. Varying the pipe diameter between 120, 140, and 165 mm, it is found that the base demand tends to stabilize at a single value for any one diameter, establishing that base demand=k, implying that pipe diameter does not have a significant impact on the base demand in the range of values considered. A base demand of 5.53 L/s was calculated, oscillating between [4.7, 6.35]. The linear regression between base demand and lps demand (Figure 12) shows a negative trend. Of 445 nodes, 430 were optimized, achieving an MAE of 0.049. The stabilization of base demand across varying pipe diameters in Balerna reflects the relatively uniform demand patterns within its water distribution network. This is likely due to the town's smaller size and more consistent water usage across its nodes. The flat slope (0.0007) indicates a minimal change in base demand with increasing diameter, suggesting that pipe size is less critical in this scenario than in other cities. This stability is ideal for predictive modeling as it simplifies resource planning and optimization efforts. The distribution of resource savings in Balerna reveals that certain nodes, particularly those with higher local demand, offer greater opportunities for water conservation. The top-saving node (186,840 L/day) demonstrates the effectiveness of the optimization strategy in reducing water wastage. This trend suggests that optimizing nodes in high-demand areas disproportionately positively impacts overall network efficiency. Additionally, the range in savings across nodes reflects the heterogeneity of water usage within Balerna's network, which is influenced by the varied topography and population density. The linear  
Figure 10: Resource savings per node optimized in Moratalla. regression between base demand and pipe diameter (Figure 12) shows stabilization of base demand values across diameters. \[B_{D}=0.0006776\times\text{diameter}+5.3639962 \tag{5}\]  
Figure 11 shows resource savings per node, respectively, with the highest saving node achieving 311,040 L/day. In Balerma, the highest resource-saving node saves 311,040 L/day, indicating that substantial water savings can be realized through targeted optimization even in smaller cities. The relatively high number of optimized nodes (430) reflects the potential for  
Figure 12: Linear regression between \(B_{D}\) and \(L_{D}\) in Balerma. Figure 11: Linear regression between \(B_{D}\) and pipe diameter at Balerma. widespread efficiency improvements across the network. The consistency in node savings indicates a more homogeneous distribution of water demand, likely due to the town's uniform population density and lower overall water consumption compared to larger urban areas. Table 3 presents the results obtained from Algorithm 1, showing key performance indicators for the three cities Lugo, Moratalla, and Balerma. This table highlights the performance of the optimization algorithm across the three cities--Lugo, Moratalla, and Balerma--based on key metrics such as mean absolute error (MAE), the number of optimized nodes, and total resources optimized. The differences in MAE values across the cities are likely due to the unique characteristics of their water distribution networks. Balerma, with a smaller, less complex network and more uniform water demand patterns, allows for more accurate predictions. The near-perfect MAE of 0.05 suggests that the optimization algorithm can capture demand variations with minimal error in such environments. Conversely, Lugo has a more complex network, higher population density, and greater variability in demand between nodes. This complexity likely contributes to the higher MAE (46.10), as the algorithm struggles to predict demand in a more dynamic system accurately. Future iterations of the algorithm could include more advanced modeling techniques, such as clustering similar demand nodes, to reduce error in complex systems like Lugo.