Global resilience analysis in urban wastewater collection networks (Case study: Valiasr town, Torbat Heydariyeh)

Resilience analysis of urban infrastructures such as sewerage systems due to different stressors is very crucial. Failure in these infrastructures may lead to economic, social, health and environmental consequences. The structural resilience of system can be analyzed in all failure levels based on global resilience analysis (GRA) method. To perform GRA under different scenarios of pipe collapse and blockage, it is required to evaluate the performance of the system in all possible link failure combinations which could take long time in real sewerage networks.Resilience is defined to evaluate system performance in exceptional conditions (Mugume and Butler 2016). Various conditions threaten sewer networks which some of them are unknown. Each event might have several different consequences or different events can lead to the same end states (Johnson et al. 2011). Accordingly, traditional risk analysis is not appropriate to investigate sewer networks, because it emphasizes on defining and evaluating the probability of an event besides its consequences. Therefore, the middle state analysis method is used to evaluate the system performance based on consequences caused by different and unknown threats. In this approach, the consequences of the events are investigated regardless of their type to represent all the potential modes of failure (Butler et al. 2014).Johnson (2011) presented a method for the global vulnerability analysis (GVA) of technical infrastructures and used it for an empirical analysis of the electrical distribution systems. Mugume et al. (2015) introduced global resilience analysis (GRA) in urban drainage network based on the middle state approach. In GRA, network performance is evaluated from zero to 100 percent failure levels and then the resilience is determined for different levels. This method has four steps. Firstly, the failure mode needs to be identified. In the second step, the system stress associated with the failure mode and the simulation manner are identified. Then, the system corresponding strain is detected and determined how to measure it. And finally, the failure mode strains are simulated under increasing stress magnitude up to 100 percent of maximum stress (Mugume et al. 2015).Mugume et al. (2015) used the sequential random link selections method for sewer networks in order to overcome GRA’s computational challenges. Diao et al. (2016) proposed a semi random selection method for GRA and applied it to water distribution systems. In their method, at each stress magnitude a fixed number of failure scenarios are generated randomly and 2⌊c-(c_f-1)⌋ number of failure scenarios are generated in a targeted manner, where c and c_f are total and failed components, respectively. Atashi et al (2020a) also used the same selection method as Diao et al. (2016) to determine the total number of scenarios in order to evaluate the resilience of water distribution systems based on location of isolation valves. In Diao et al. (2016), the total number of scenarios is directly related to the number of network’s links but Mugume et al. (2015) used a convergence analysis method to determine the required number of scenarios. This method is more generalizable to use in each network, because the effect of hydraulic properties is considered to determine the required number of scenarios. They showed that for an urban drainage system (UDS), by considering a sufficient number of random failure sequences the deviation percentage of GRA results are not significant, in all failure level. It means that, for one failure level if a sufficient number of scenarios are selected randomly, the average resilience for them is approximately equal to the average resilience of all scenarios of the failure level. So, to analyze global resilience with less time and computational cost it is necessary to use a scenario selection method which discover the extreme scenarios in different failure levels to obtain more accurate GRA results.

In this study, a scenario selection method is introduced based on roulette wheel to estimate GRA results without simulation all possible scenarios. In the proposed method, scenarios which lead to the minimum and maximum resilience at each failure level are identified as strategical scenarios and participated in generating (selecting) scenarios of the next failure level. In each failure level, the probability of a scenario being strategic is estimated by a Multi-Criteria Decision Making (MCDM) (Mardani et al. 2015). The scenarios with highest probabilities are selected to generating roulette wheel. Finally, scenarios of the next failure level are generated by selecting candidates from roulette wheel and adding a random link to the selected candidates.

The results of the simulations in the case study show that the minimum, mean and maximum resilience values was estimated by the proposed method with RMSE less than 0.025 and 0.022 comparing with simulating all possible scenarios, respectively. Also, the proposed method has been able to perform better than the random selection method in predicting the scenarios of the extreme points of the global resilience function.

In this article, a simple and rapid approach was presented for investigating structural resilience in sewer networks based on GRA. To properly cover the large space of failure scenarios that is a challenge in the real networks, a selection method is proposed based on the roulette wheel to identify the most strategical combination of failed pipes in each failure level.