Uncertainty Quantification of Water Distribution System Measurement Data based on a Least Squares Loop Flows State Estimator

This paper presents a novel algorithm for uncertainty quantification of water distribution system measurement data including nodal demands/consumptions as well as real pressure and flow measurements. This procedure, referred to as a Confidence Limit Analysis (CLA), is concerned with a deployment of a Least Squares (LS) state estimator based on the loop corrective flows and the variation of nodal demands as independent variables. The confidence limits obtained for the nodal pressures and the inflows/outflows of a water network are determined with the novel algorithm called Error Maximization (EM) method and are evaluated with respect to two other more established CLA algorithms based on an Experimental Sensitivity Matrix (ESM) and on the sensitivity matrix method obtained with the LS nodal heads equations state estimator. The estimated confidence limits obtained for two real water networks show that the proposed EM algorithm is comparable to the other two CLA benchmark algorithms but due to its computational efficiency it is more suitable for online decision support applications in water distribution systems. Both ESM and EM methods work for any operating point whether arbitrarily or randomly chosen for any water network although EM method has the advantage of being computationally superior and working with any sets of measurements. Keywords-uncertainty quantification, confidence limit analysis, water distribution systems, measurement data, loop corrective flows algorithms, modelling and simulation, state estimation