Particle Filter–Based Model for Online Estimation of Demand Multipliers in Water Distribution Systems under Uncertainty

Accurate modeling of water distribution systems is fundamental for planning and operating decisions in any water network. One important component that directly affects model accuracy is knowledge of nodal demands. Conventional models simulate flows and pressures of a water distribution network either assuming constant demand at nodes or using a short-term sample of demand data. Given the stochastic behavior of water demand, this assumption usually leads to an inadequate understanding of the full range of operational states in the water system. Installation of sensor devices in a network can provide information about some components in the system. However, the requirement for a reliable water distribution model that can assist with understanding of real-time events over the entire water distribution system is still an objective for hydraulic engineers. This paper proposes a methodology for the estimation of online (near-real-time) demand multipliers. A predictor-corrector approach is developed that (1) predicts the hydraulic behaviors of the water network based on a nonlinear demand prediction model; and (2) corrects the prediction by integrating online observation data. The standard particle filter and an improved particle-filter method that incorporates the evolutionary scheme from genetic algorithms into the resampling process to prevent particle degeneracy, impoverishment, and convergence problems, are investigated to implement the predictor-corrector approach. Uncertainties of model outputs are also quantified and evaluated in terms of confidence intervals. Two case studies are presented to demonstrate the effectiveness of the proposed particle-filter model. Results show that the model can provide a reliable estimate of demand multipliers in near-real-time contexts.