Bayesian Approach for Joint Estimation of Demand and Roughness in Water Distribution Systems

Abstract

A combined demand and roughness estimation is a critical step in order for the water distribution system model to represent the real system adequately. A novel two-level Markov chain Monte Carlo particle filter method for joint estimation of demand and roughness is proposed in this paper. First, an improved particle filter with ensemble Kalman filter modification to proposal density is adopted to track the non-Gaussian system dynamics and estimate demands. Then, the improved particle filter for demand estimation is nested into the Markov chain Monte Carlo simulation for roughness estimation. The method is very capable of quantifying the uncertainties associated with estimated or predicted values without requiring any assumptions of linearity and Gaussianity or any derivatives to be calculated. A strong nonlinear benchmark network with synthetically generated field data is utilized to validate the performance of this method. The results suggest that the proposed method is demonstrated to provide satisfactory demand and roughness values with reliable confidence limits. Some practical issues are also discussed to enhance the application potential of this method.