Sector Identification and Graph Decomposition

  • Last Update
  • December 12, 2016

The development of software for water network analysis and design makes possible today to visualize networks with several thousand of pipes without big efforts. Nevertheless, for a person who does not know the model a priori, it can be difficult to understand what are the main parts of the network and how those parts are interconnected, as the number of elements in the model increases. Let´s take a look to the following example taken from the Battle of Water Networks DMAs (BWNDMA) as part of the Water Distribution System Analysis Conference (WDSA) 2016:


Image a) represents the original network as it can be seen in EPANET. Image b) provide visualization after running a graph decomposition algorithms. Several interesting works related to applications of graph decomposition in hydraulic networks have been done by (Deuerlein, 2008). Graph decomposition can basically help to identify trees in water networks and also the largest set of components (blocks) connected to the rest of the network by one single link (bridge). This idea is very useful to get a better visualization of the water network and identify potential layout mistakes when creating a model. In the following example, it can be easily identified that component A is only connected to the rest of the network through the bridge B1 and component B is only connected to the rest of the network through the bridge B2. Note that if B1 is cut, component A will get separated from the rest of the network and the same would happen for component B if bridge B2 is cut.

Despite graph decomposition is a powerful tool, it is not enough to identify potential sectors in a water network considering that a sector can be potentially a “block” connected to the rest of the network by more than one link. In the following example the graph decomposition would identify one big component but it won´t identify the “sectors” in the network:

Here it is useful to introduce some modifications combining graph theory with hydraulic engineering to associate sectors with the presence of valves or water meters in the frontier of a graph component. The following images represent a visualization comparison between the original visualization of a network layout in EPANET, the graph decomposition of the network and the sector identification. The sector identified corresponds to one of the solutions created for the Battle of Water Networks DMAs mentioned before.

Note that here the sectors are not created but identified based on the presence of valves. In (Gilbert et al., 2016) valves were added to the system for creating sectors, the position of those valves and the rest of the network were imported in Water-Ing and the software was able to check, identify and visualize the sectors created. Both graph decomposition and the identification of sectors can be executed efficiently in Water-Ing with almost no waiting time for the user. The source code of both graph decomposition and sector identification was written in c# and It is available for all Water-Ing subscribers. If you are executing the software directly you just need to import your .INP file and execute the functions for graph decomposition or sector identification that you will find in the main menu. Do not hesitate in contacting us if you require additional support.


References

Deuerlein, J., Decomposition Model of a General Water Supply Network Graph. Journal of Hydraulic Engineering 134(6), 822-832, 2008


Gilber, D., Abraham, E., Piller, O., Montalvo, I. Iterative Multi-Level algorithm for network sectorization into DMAs using ASO and deterministic optimization tools in a multi-objective design setting. Battle of Water Networks DMAs, Water Distribution Systems Analysis Conference 2016, Cartagena de Indias, Colombia.


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