عنوان مقاله [English]
Water Distribution Networks (WDNs), as one the most important infrastructures, are very vulnerable to accidental or deliberate contamination intrusion, due to their accessibility and extension over urban areas. In recent years, there has been increased interest on protecting these networks from possible contamination risks with the aim of mainly minimizing the harmful effects on public health and security. Attacks on WDNs can be divided into three categories of cyber-attacks, physical attacks, and biological and chemical attacks. One of the most important threats to WND is a deliberate chemical or biological contamination injection due to uncertainty on both location injection and its consequences. Therefore, it is essentially required to take optimal activities for minimizing public health and economic consequences and restoring the system to normal operation conditions. These activities mainly consist of any combination of system isolation, public notification, flushing and finally providing short-term and long-term alternative domestic water supply.
In this study, an embedded approach consists of EPANET simulation model and multi-objective optimization model namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was used to derive the optimal operational response actions following the contamination detection in the network. EPANET 2.0 simulation model is used to calculate the spatial variation of contamination in the network at different time step. EPANET is open free software that easily linked with optimization model via its toolkit. NSGA-II optimization model develops a trade-off between two common objectives functions in consequence management modeling. NSGA-II optimization model sorts the population of different chromosomes based on their non-dominance over the other solutions. According to the number of dominated solutions, a rank was assigned to a particular chromosome in the current population. Moreover, a crowding distance was considered to preserve diversity among chromosomes in a population. In this research, to illustrate the performance of the proposed methodology, Net3 from EPANET 2 was employed. The system consisted of 117 pipes, 92 nodes, three tanks, two pumps, a lake and a river. A deliberate contamination was injected into the network at node 101 for six hours (08:00 to 14:00). As suggested in Ostfeld and Salomons (2004) study, five sensors at nodes 15, 35, 145, 225 and 255 were considered for early warning contamination detection. The first sensor was detected the contamination about 11:00 and one hour was assumed for initiating response actions. Therefore, optimal operational response actions were started at 12:00 and continued until the end of simulation time (24:00). It was assumed that all hydrants were in class C (red) with discharge rate of less than 1900 liter/min (proposed by National Fluid Power Association). Two main objective functions were considered in this study for NSGA-II multi-objective optimization model. The first objective was to minimize the number of operational activities that include open or close the valves and hydrants in the network. To control the consequences of contamination in the network, the polluted area was isolated by the valves to prevent the spread of contamination and the discharge of contaminated water through fire hydrants. Hence, the optimization model had binary decision variables including hydrant opening and valve closing. Total number of decision variables was equal to the potential number of valves and hydrants. In this study, optimal operation activities were selected among 51 potential valves and hydrants. The number of operational activities was limited to 15. The second objective was the minimization of consumed contaminated water by multiplying the concentration of pollutants in consumed contaminated water volume.
Obtained results showed that without any operational response action, consumed contamination mass was equal to 80.38 kg. Whereas, consumed contamination mass was decreased to 58.04 kg with 15 optimal response actions. Optimal values for different parameters of multi-objective model were obtained by sensitivity analysis through the number of populations and genes, as well as crossover and mutation rates. The optimal selected values for the optimization model were 30 populations, 150 genes with a crossover and mutation rate of 0.85 and 0.15, respectively. Moreover, in this study, sensitivity analysis was carried out on start time of consequence management (between 11:00 to 16:00 with one hour time interval) for evaluation of its effect on the second objective function. Consumed contamination mass at different start time of consequence management between 11:00 to 16:00 with hourly time step were equal to 52.20, 59.27, 61.18, 62.17, 67.47 and 70.17 kg, respectively. Ultimately, the earlier the operational activities starts, the more the consumed contamination mass decreases.