Accuracy of First-Order Second-Moment Approximation for Uncertainty Analysis of Water Distribution Systems

Abstract

This study performs an extensive investigation to explore critical factors that affect the accuracy of the first-order second-moment (FOSM) approximation when it is used as a nodal pressure head uncertainty estimation method for a water distribution system (WDS). The applicability of FOSM for WDS calibration, abnormality detection, and network design is examined. Uncertainties are considered in nodal demands, peak demand factors, and pipe roughness coefficients. To quantify the accuracy of FOSM, results are compared with those from Monte Carlo simulation (MCS). The accuracy of FOSM is tested based on WDS peak demand conditions, topology, and pipe diameter by applying it to 21 real and hypothetical WDSs. Results reveal that FOSM provides accurate variances estimation of nodal pressure heads and the extreme values of 1st and 99th percentile nodal pressure heads compared to MCS. In addition, accurate uncertainty estimations are obtained from FOSM even under the peak demand conditions. FOSM accuracy is lower for a branched system relative to looped and gridded systems and independent of the pipe size.