Sensitivity Analysis for Sampling Design and Demand Calibration in Water Distribution Networks Using the Singular Value Decomposition

Abstract

Research in water distribution networks during recent decades has often focused on calibration. There is no unique solution for this problem as the methodologies are developed depending on which parameters have to be calibrated and the final use of the model. This work presents a demand calibration methodology that identifies a set of patterns that minimize the error in predicted measurements. The singular value decomposition (SVD) of the sensitivity matrix is a powerful tool for solving the optimization problem. Additionally, in this work, the deep understanding of the SVD allows the selection of an alternative to the classic patterns. Each individual demand is defined as a combination of geographically distributed patterns. The membership of each demand to every pattern is produced naturally through the analysis of the SVD of the sensitivity matrix. Three types of memberships are considered: binary, positive, and free. The SVD analysis is also used to define the location of sensors for the calibration. The performance of the methodology proposed is tested on a real water distribution network using synthetic data. Results show that the use of positive memberships to define individual demands is the best option to reduce the error in predicted pressures and flows.