Calibration of Water Distribution Hydraulic Models Using a Bayesian-Type Procedure

Abstract

Estimating model parameters is a difficult, yet critical step in the use of water distribution system models. Most of the optimization-based approaches developed so far concentrate primarily on efficient and effective ways of obtaining optimal calibration parameter values. At the same time, very little effort has been made to determine the uncertainties (i.e., errors) associated with those values (and related model predictions). So far, this has typically been done using the first-order second moment (FOSM) method. Even though reasonably computationally efficient, the FOSM approach relies on several restrictive assumptions and requires computationally demanding calculation of derivatives. To overcome these limitations, the recently developed shuffled complex evolution metropolis (SCEM-UA) global optimization algorithm is linked to the Epanet2 hydraulic model and used to solve a least-squares-type calibration problem. The methodology is tested and verified on the Anytown literature case study. The main advantage of the SCEM-UA algorithm over existing approaches is that both calibration parameter values and associated uncertainties can be determined in a single optimization model run. In addition, no model linearity or parameter normality assumptions have to be made nor any derivatives calculated. The main drawback of the SCEM-UA methodology is that it could, potentially, be computationally demanding, although this is not envisaged as a major problem with current computers.