An Enhanced Sensor Placement Strategy to Quantify Small Leaks in Water Distribution Networks using Weighted Lean Graphs

Small leaks have been a severe problem for years due to their undetected characteristic. We characterize small leaks at different locations by observing their signatures indicated by flow changes in pipes. We characterize small leaks using a weighted directed acyclic graph, called the Weighted Lean Graph, and use it to develop a sensors placement strategy. We partition a Water Distribution Network into clusters based on the similarity of lean graphs. A cluster inlet is selected from pipes at the boundary of each cluster to place a sensor. We combine the use of lean graph similarity and weights of lean graph edges in the cluster inlet selection and compare the performance to the use of lean graph similarity only. We evaluate our sensor placement strategy by calculating the cosine similarity and the partition balance based on the sensor readings and the cluster sizes, respectively. Experiment results indicate that the use of weighted lean graph has successfully lowered the cosine similarity scores while maintaining the partition balance of clusters. The use of weighted lean graphs has more impact on sparse networks or networks with low connection degree.