Investigating Prior Parameter Distributions in the Inverse Modelling of Water Distribution Hydraulic Models

Abstract

Inverse modelling concentrates on estimating water distribution system (WDS) model parameters that are not directly measurable, e.g. pipe roughness coefficients, which can, therefore, only be estimated by indirect approaches, i.e. inverse modelling. Estimation of the parameter and predictive uncertainty of WDS models is an essential part of the inverse modelling process. Recently, Markov Chain Monte Carlo (MCMC) simulations have gained in popularity in uncertainty analyses due to their effective and efficient exploration of posterior parameter probability density functions (pdf). A Bayesian framework is used to infer prior parameter information via a likelihood function to plausible ranges of posterior parameter pdf. Improved parameter and predictive uncertainty are achieved through the incorporation of prior pdf of parameter values and the use of a generalized likelihood function. We used three prior information sampling schemes to infer the pipe roughness coefficients of WDS models. A hypothetical case study and a real-world WDS case study were used to illustrate the strengths and weaknesses of a particular selection of a prior information pdf. The results obtained show that the level of parameter identifiability (i.e. sensitivity) is an important property for prior pdf selection.