Optimal Placement of Pressure Sensors in Water Distribution System Based on Clustering Analysis of Pressure Sensitive Matrix

Optimizing the placement of pressure sensors is of great significance for understanding the performance of water distribution systems (WDSs). The pressure sensitive matrix of WDSs contains the gradient information regarding nodal pressure to nodal outflow, which can be regarded as a series of observation vectors reflecting the correlations of nodal pressure change and used for the optimal placement of pressure sensor. This paper presents a method for optimizing the placement of pressure sensor in WDSs based on clustering analysis of pressure sensitive matrix, which aims to use the limited number of pressure sensors to understand the pressure changes of other nodes unmonitored as accurate as possible. To enhance the computing efficiency especially for larger systems with thousands of nodes, the matrix analysis method is developed to calculate the analytical solution of the pressure sensitive matrix. Based on it, the K-means algorithm is applied to solve the optimization problem for cluster analysis and determining the pressure sensors placement, considering it has the advantage of being computational efficient. A real network is applied to illustrate the application of the proposed method. The obtained results indicate that it is reasonable to arrange the pressure senor on the node with the minimum Euclidean distance to the clustering center.