Estimating Distribution System Water Demands Using Markov Chain Monte Carlo

The use of drinking water distribution system models has been around for decades and requires good demand estimates to ensure adequate hydraulic and water quality representation. Traditional demand estimation processes are capable of estimating demands, often for highly skeletonized systems, with approximations to represent uncertainties in demand estimates and hydraulic states. This study implemented a Markov chain Monte Carlo (MCMC) algorithm to estimate hourly demand multipliers and uncertainties for a synthetic network using a previously developed clustering algorithm to reduce the number of unknowns. The MCMC approach also provided the flexibility to accommodate potential spatial correlation in demand multipliers through, for example, the use of a Markov Random Field (MRF) prior. The MCMC algorithm produced adequate representation of demand multipliers, similar to weighted least squares (WLS), and improved representation of the uncertainties relative to the approximations based on WLS results. The incorporation of the MRF prior resulted in more spatially correlated demand multipliers but did not provide any significant benefits for representing the network being studied. Increasing the number of clusters, reducing measurement uncertainty, and including additional flow measurements (rather than pressure) improved the ability to represent system-wide flows. However, increasing the number of clusters also resulted in larger uncertainties in the demand multiplier estimates as the estimation problem became more ill-conditioned. A generalized discussion associated with clustering approaches and measurement locations is included to provide a broader perspective on demand estimation.