Comparison of Imputation Methods for End-User Demands in Water Distribution Systems

This study examines the impact of advanced metering infrastructure (AMI) end-user demand metering failure on water distribution system (WDS) operation and management. To address this issue, our first step is to develop a burst detection algorithm that compares total end-user demands with system inflow rates. Western Electric Company (WEC) rules are applied to test for anomalies in the time series of normalized differences between supply and withdrawal. Then, hydraulic model prediction and burst detection performance are evaluated for fully reporting and missing AMI demand conditions using synthetically generated end-user demands for a network in Tucson, Arizona. Three imputation methods [zero, historical mean (HM), and distribution sampling (DS) method] are applied to replace missing AMI data and are compared for a range of missing data percentages. Based on the numerical experimental results, HM imputation method is the most useful tool to replace missing WDS AMI data. This scheme resulted in the lowest hydraulic model prediction errors and low false-alarm rates while maintaining high burst detection probability. However, more false alarms are raised as the percentage of missing data increases. To solve the problem, the guidelines for optimal WEC rule application are identified for a range of missing demand levels.