**3. Application**

The proposed ONG model is applied to estimate the Austin network demand [36] with modifications [8]. The Austin network is a non-district metering area (DMA) structured loop-dominated network. As shown in Figure 6, the modified system comprises 126 nodes and 90 pipes supplied by two reservoirs and one pumping station. Similar to the original network, the modified Austin network is solely supplied by a single reservoir (Source 1) with a fixed source head

(306 m). The second reservoir (total head = 366 m) in the middle of the loop in the east corner of the system is not operated.

**Figure 6.** Study network layout. A thicker pipe represents a larger diameter, while a larger node represents a larger demand.

Only 47 nodes have external demands. Therefore, the total number of unknown demand nodes is 47. The rest of the nodes (*i.e.*, 79 nodes) are pipe connections with no external demands. A total of 14 pipe flowmeters are assumed to be installed throughout the system. The meters are assumed to be installed at the same locations selected by Jung and Lansey [8]. The number of node groups is set equal to the number of meters to realize high demand estimation accuracy. Therefore, the 47 demand nodes are assumed to be aggregated into 14 node groups (*i.e.*, *m* = 14).

A two-day series of node group demands and pipe flow rates is generated at 5-min time steps using the network's hydraulic model based on the methodologies described in Section 2.1. Similar to Jung and Lansey [8], the Kang and Lansey approach [2] is applied to demand aggregation and disaggregation. The method is briefly described here. The forecast node group demands at the current time (aggregated demands) are estimated from the transition of the updated demand of the previous time step (Equation (1)). The forecast node group demands are then disaggregated to individual nodes under the assumption that the nodal demands (disaggregated demands) in the same group are perfectly correlated. During the disaggregation, the ratio of the individual nodes' base demands to the total node group base demand is multiplied by the forecast node group demands to obtain the individual nodal demands.

The demands are normally distributed with a coefficient of variation (CV) of 0.1 (*<sup>σ</sup>q* " 0.1*μq*). The measurement errors are random variables *N*p0, *σ*), where *<sup>σ</sup>Q* " 0.1*μQ*{3.27 (corresponding to a measurement error of 10%) for pipe flow measurements. All nodes are considered to be residential users in apartments.

eGA is used to find an optimal solution for the ONG problem, wherein the number of possible solutions is 7.379 ˆ 10<sup>53</sup> (= 1447). Note that the well-known Hanoi network design problem has 2.865 ˆ 10<sup>26</sup> (634) possible solutions [37]. The crossover and mutation processes are conducted with probabilities of 85% and 5%, respectively. The genetic traits of the chromosomes are shared at multiple scattered points, while the standard mutation is employed. The node grouping determined by the

engineering decision of Jung and Lansey [8] (*i.e.*, a node group comprising nodes of the same user type) is seeded as an initial solution, whereas the other initial solutions, where the population is 100 (*ni* = 100), are randomly generated by uniform sampling among 1–14 integer values. The eGA returns the best solution when the solution is not changed over 300 iterations.
