A multi-level spectral clustering process to ascertain sensor location for mitigating effects of a potential contamination in a water supply network

In this paper, we introduce a multi-level methodology based on the iteration of successive processes of spectral clustering to divide a water supply network (WSN) into metric subsystems, also called district metered areas (DMAs). Each one of the abovementioned divisions is approached by spectral clustering. This is a graph clustering methodology in data analysis that improves the straightforward application of K-means, works well in non-convex spaces, and takes into account the underlying graph structure under study. Spectral clustering uses information obtained from computing the eigenvalues and eigenvectors of the Laplacian matrices obtained from partitioning the graphs and searches a minimum number of cut edges to achieve it. Our aim is to propose suitable conditions to approach useful characterizations of DMAs. In addition, we try to take advantage from this reduction of the inspection area in technical management tasks, such as sensor location. In this work, an experimental study based on a real WSN is proposed. An iterative nested division into DMAs is used to locate sensors throughout the whole network and to perform inference tasks on the presence of contamination events based on those sensor signals. If the sensors are located in separated areas weakly interconnected with each other, it will be easier to mitigate the effects of potential contamination, having at one's disposal a minimal number of cut-off valves for security. In addition, the nested nature of the proposed cluster construction increases reliability in mitigation plans. The method is scalable and can be generalized to address other managerial issues related to water quality and leakages, among others