# Qualification of Hydraulic Analysis Models for Optimal Design of Water Distribution Systems
## 1 Introduction  
In the hydraulic analysis of water distribution systems (WDSs), there have been several approaches throughout the decades for designing and representing the behavior of these systems more realistically, especially in case of abnormal operating conditions. Generally, the risk of an abnormal condition can define a measure with which a hazard or threat resulting either from probable events beyond our control or from the possible consequences of a decision may be assessed [1, 2]. This abnormal condition can be generated frequently in WDSs fields such as pipe breakage, leakage, extreme demand e.g., fire flow, and for this reason, the realistic quantification of damage via efficient hydraulic analysis approaches is needed. There are two main approaches for hydraulic analysis such demand-driven analysis (DDA) and pressure-driven analysis (PDA) with different characteristics and levels of complexity. The conventional hydraulic analysis of WDSs corresponds to a demand-driven analysis, in which the energy equation is nonlinear. Because of this, some iterative method is needed to solve a set of hydraulic equations (nonlinear energy equation and linear mass balance equation). The history of the development of these iterative methods is long and wide; finally, it was [PERSON] and [PERSON] [3] who suggested the gradient method, an improved version of the Newton-Raphson approach that assumes and obtains unknown values of nodal head and pipe flows simultaneously. This approach does not need a balance of equations at the beginning of the method, which is a big improvement compared with previous methods, becoming the most prominent iterative method for simple formulation and computational benefits. The accurate results of this method under normal operation conditions (no leakage, pipe breaks, or unexpected fire demands) were enough reason to implement it in commercial hydraulic solvers, such as EPANET [4] and KYPipe [5]. However, these simulators, which are applied DDA as a hydraulic analysis approach, can be appropriately hydraulically analyzed only under abnormal system conditions, such as a sudden increase in demand flow due to a fire, the effect of a network condition during the system for damaged pipe reparation, rehabilitation, and replacement. In reality, when there is a problem in the network, usually, the water pressure in each head might be less than the minimum required to satisfy the nodal demands. As a consequence, the simulation will give a negative or unacceptably low nodal pressure compared with the nodal pressure head in normal conditions [6; 7; 8]. In other words, it is necessary to accurately predict the water supply and water pressure shortage area according to abnormal conditions through hydraulic analysis, approximating the behavior of the actual system, and through this, design and operation techniques should be performed in consideration of each abnormal situation. To overcome this negative pressure and other unrealistic results, a pressure-driven analysis (PDA) was developed to solve the unrealistic hydraulic analysis problem of DDA. PDA identifies the nodes where the pressure head can satisfy the current demand; otherwise, the nodal demand can be partially satisfied and becomes dependent on the available pressure head. Traditional hydraulic analysis of WDSs based on DDA considers the fixed demand that applies the whole of the nodal demand regardless of the normal and abnormal system condition. However, the paradigm of WDSs has changed from delivering the required amount of water to a stable water supply similar to normal conditions, even under abnormal system conditions. Therefore, the WDSs design is performed by considering the cost, system resilience, and robustness for a stable water supply and to prepare for uncertain future system conditions. Some studies have applied an evolutionary optimization approach for the optimal design of WDSs under various system failure scenarios (e.g., pipe failure, fire flow, and isolation of connections to all water sources) [9; 10; 11; 12; 13].