Response Surfaces for Water Distribution System Pipe Roughness Calibration

Water distribution system (WDS) model calibration research has focused on estimating model input/output parameters and analyzing several uncertainties (e.g., model uncertainty) to improve models with best-fit parameters. Numerous studies have shown that optimization algorithms generally quickly converge to very good parameter solutions. However, the generality and reasoning behind this have not been identified. This paper examines the shape and convexity of WDS response surfaces (i.e., objective function surfaces) and whether the surfaces have single global or multiple local optima. To that end, three networks with different network topologies are evaluated: (1) the Modena network as presented, (2) a modified form of the Modena network, and (3) a real Austrian network. Various conditions were evaluated to consider field measurement error, parameter uncertainty through pipe grouping, and model uncertainty. Results demonstrate that the response surfaces remained smooth and convex even when uncertainties are introduced, but the best parameter solutions are shifted from the true solution. The impact and sensitivities of the uncertainties are evaluated by examining the change in best-fit parameter estimates.