Reliability assessment of water distribution networks under uncertain nodal demand and pipe roughness

The reliability of a water distribution network (WDN) is defined as the probability that WDN is able to provide sufficient flow and pressure at all consumption nodes of the network under predicted and unforeseen conditions during a specified period of time. Uncertainty in projected nodal demands and estimated pipe roughness coefficients of each year of operation is the major cause of fluctuation in pipe flows and nodal pressures of the WDN. Since WDN is one of the most important and expensive components of water supply systems, safeguarding the reliability of WDNs under uncertain demand and pipe roughness is the aim of water agencies or authorities dealing with design, maintenance, and the operation of WDNs.<br><br>There are two main approaches in the current literature for safeguarding the reliability of a WDN: applying reliability theory as a probabilistic approach; and, using resilience index as a deterministic approach. To assess the reliability of a WDN, the nodal demands and pipe roughness coefficients are modeled probabilistically, and the performance of the water distribution network in terms of probabilistic nodal pressures is assessed using various methods, such as Monte Carlo Simulation (MCS). On the other hand, the resilience index is a surrogate deterministic measure for the reliability of the WDN which has been widely used in recent years to improve the reliability of WDN design.<br><br>In this study, MCS is applied to compute the reliability of the nodes and the network under uncertain demand and roughness, and to determine how reliability is distributed among the various nodes of WDN, as well as assessing the reliability of the network as a series or parallel system. The effect of the resilience index on the nodal and network reliability is also assessed. This research investigates the relationship between the reliability and resilience index at two levels of nodes and networks; thus, it fills the knowledge gap that exists in a process where only the resilience index is used, thereby providing a more comprehensive measure for the WDN operating under uncertain conditions.<br><br>The results showed that the impact of uncertainty in projected demands and estimated pipe roughness – which is not considered in the term of the resilience index – can be assessed on performance of a WDN using the reliability theory. The results of the reliability assessment of different nodes of a WDN showed that the value of reliability at each node depends on the location of the node, and it decreases as the distance of nodes from the supply node increases. Results of sensitivity analysis of reliability to the degree of uncertainty in design parameters also show that an increase in the coefficient of variation (COV) of random nodal demands and random pipe roughness coefficients decreases the nodal and network reliability of a WDN.<br><br>Furthermore, a mathematical formula was developed between the reliability and resilience index to determine the thresholds of the resilience index that are able to meet a desired level of nodal and network reliability under a designated uncertainty in nodal demands and pipe roughness coefficients.