# Qualification of Hydraulic Analysis Models for Optimal Design of Water Distribution Systems
## 4 Conclusions and Future Studies  
The hydraulic analysis of WDSs is categorized into two types of the demand-driven hydraulic analysis, which should be supplied by the fixed demand and the pressure-driven hydraulic analysis, which considers the head-outflow relationship for abnormal conditions. Previous studies have demonstrated that DDA is appropriate in normal conditions, and PDA presents realistic hydraulic results under abnormal system conditions. Therefore, this study quantified the hydraulic results of DDA and PDA under various single/multiple abnormal situations applied to three WDSs that have different characteristics (e.g., network size and configuration), and according to the results of hydraulic analysis, the DDA-based design model and the PDA-based design model were compared, and their design characteristics were analyzed to identify the efficiency of an WDSs design under abnormal system conditions. To verify the characteristics of the two hydraulic analysis approaches, two scenarios combined with abnormal conditions (i.e., fire flow and pipe breakage situation) for single/multiple conditions were generated, and these scenarios were applied to three benchmark networks. In the system abnormal conditions of the benchmark networks, PDA showed practical quantification, such as identifying the nodes with the most variations in pressure and analyzing the critical pipes that have the greatest impact on the hydraulic results under abnormal situations (e.g., fire flow and pipe breakage). Identified critical nodes and pipes can be reinforced by the planning and management of WDSs. Moreover, for a comparison of WDSs designs using the DDA-/PAD-based design model, GA was applied as an optimization technique to consider the minimum construction cost. To efficiently compare the optimal design, depending on the different minimum thresholds (20, 30, and 40 m), the percentage of PDA was considered (0%; DDA, 20%, 40%, 60%, and 100%). As a result of an optimal design with various PDA% values under the minimum threshold, increasing the percentage of PDA in the hydraulic design of the network, the construction cost decreased for the quantity of the demand change with the actual demand based on the pressure-driven model. Moreover, the design cost variance showed that a larger network is more different, and also the higher minimum threshold affected the lower design cost. Therefore, this study will help to select a reasonable hydraulic analysis technique for WDSs design through the application of the DDA and PDA techniques, which are actively used as hydraulic analysis techniques in WDSs design considering abnormal situations. It can be used as a reference research in the WDSs design field in the future. Additionally, a PDA model with uncertainty quantification can be used for reliability and resilience analyses of an actual WDN considering abnormal system conditions. A future study may refer to the results of this study to consider the optimal design of WDSs. For this work, various kinds of objective functions (e.g., energy consumption, water \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Threshold (m)**} & \multirow{2}{*}{**PDA (\%)**} & \multicolumn{4}{c}{**Cost (5)**} \\ \cline{3-5}  & & **Two-Loop Network** & **Hanoi Network** & **Balerma Network** \\ \hline \multirow{4}{*}{20} & 20 & 450,000 & - & 19,025,704 \\  & 40 & 438,000 & - & 20,499,368 \\  & 60 & 614,000 & - & 20,889,470 \\  & 100 & 636,000 & - & 20,430,582 \\  & 20 & 438,000 & 6,101,325 & 18,661,006 \\  & 40 & 424,000 & 6,040,182 & 20,061,426 \\  & 60 & 419,000 & 6,028,117 & 20,013,434 \\  & 100 & 450,000 & 5,986,931 & 20,054,226 \\  & 20 & 459,000 & 6,026,302 & - \\  & 40 & 493,000 & 5,869,400 & - \\  & 60 & 566,000 & 5,731,202 & - \\  & 100 & 596,000 & 5,471,554 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Cost results for certain % of PDA for the benchmark networks.