**5. Conclusions**

In this work, a methodology that combines WNP and optimal sensor installation was proposed, to investigate the benefits of the "divide and conquer" technique for the monitoring of WDNs from contamination events (direct action), and for the effectiveness of optimal sensor placement (indirect action). The applications concerned a real Italian WDN, which was first partitioned into 5 DMAs. Optimal sensor solutions were searched for on the original un-partitioned WDN and on the partitioned layout, in the trade-off between number of installed sensors and affected population for an assigned set of contamination events. Further optimizations were carried out by restricting sensor installation to some pre-selected nodes (nodes hydraulically upstream from the flow meter-fitted boundary pipes and central nodes). The results showed that, for a given number of installed sensors, the monitoring stations installed in the partitioned layouts offer better monitoring performance. On the other hand,

the option of considering locations in proximity to flow meters and at most central nodes as the only potential locations in the context of optimal sensor placement has the following advantages:


With regards to the last issue, it must be noted that the calculations of the present work were carried out on a simple though real WDN. Therefore, the benefits are expected to be much larger in the case of big-size WDNs, for which the problem of optimal sensor placement may become computationally infeasible. Indeed, the topics analyzed in this paper fully match the future research directions identified by Ostfeld et al. (2008) [20] during the Battle of the Water Sensor Networks. In fact, specific reference was made to the problems of aggregation, i.e., the possibility of using a reduced but still significant sample of nodes for investigations into water quality, multi-criteria analysis of sensor performance, choice of optimal number of sensors and multiple use of boundary pipes (for both monitoring flow between DMAs and detecting potential contaminations).

Though topologically central nodes have been considered in this analysis along with DMA entry points, another attractive option is made up of critical sink nodes with lowest head inside DMAs, in which water quality parameters are already monitored. Future works will be dedicated to exploring the solution of critical sink nodes. Future work will be dedicated to investigating how results change when other objective functions from those used in the present work are considered. The methodology presented in this paper will be refined in the future considering also other benchmark networks. Adopting different clustering algorithms and centrality metrics could affect the results; to better investigate the influence on the solutions, new algorithms will be applied. Another aspect that deserves to be further investigated concerns the assumptions made for the definition of the representative set of contamination scenarios. Other prospects could concern the issues of restoration after the generic contamination and of constructing mega-monitoring stations on which to locate all the management devices (chlorine stations, pressure valves, etc.). This will be done with reference to specific real contaminants, while abandoning the simplifying assumption of unreactive and conservative contaminant adopted so far.

**Author Contributions:** E.C. and A.D.N. wrote the manuscript, C.G. and G.F.S. developed the coding and performed the analysis, C.C., D.M., and M.D.N. revised the paper.

**Funding:** This research received no external funding.

**Acknowledgments:** This research is part of the Ph.D. project "Water distribution network management optimization through Complex Network theory" within the Doctoral Course "A.D.I." granted by Università degli Studi della Campania "L. Vanvitelli".

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**


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