Pipe roughness calibration in water distribution systems using grey numbers

Abstract

This paper presents a procedure based on the use of grey numbers for the calibration (with uncertainty) of pipe roughness in water distribution systems. The pipe roughness uncertainty is represented through the grey number amplitude (or interval). The procedure is of a wholly general nature and can be applied for the calibration (with uncertainty) of other parameters or quantities, such as nodal demands. In this paper, for the purpose of roughness calibration, a certain number of nodal head measurements made under different demand conditions is assumed to be available at different locations (nodes); all other topological and geometric characteristics of the system are considered to be known exactly.The general approach to pipe roughness calibration (taking account of uncertainty) focuses on identifying the grey roughness values which produce grey head values at the measuring nodes such as to encompass the observed values grouped on the basis of the different demand scenarios and, at the same time, have as small an 'amplitude' as possible.The proposed procedure was applied to two synthetic case studies and to one real network.The tests on the synthetic case studies show that the proposed procedure is able to correctly solve the inverse problem, i.e. it can identify the known grey roughness numbers even when they overlap; the same applies when the known grey roughness numbers collapse into known white roughness numbers. The test on the real case offers the possibility of highlighting the potentials of the procedure when applied within a context where measurement errors and other uncertainties are present. The procedure entails computing times that may become lengthy. However, it is possible to reduce these computing times considerably by replacing the hydraulic simulator-to which a number of calls must be made during the calibration procedure (for objective function evaluation)-with an approximation based on a first-order Taylor series expansion. This approach introduces acceptable approximations within the context of the problem considered.

Automated parameter optimization of a water distribution system

“…However, SCADA systems are beyond the reach of most water utilities in developing countries. In recent years, researchers have identified the necessity to include uncertainty in the calibration of WDS models including pipe roughness coefficients and nodal demands (Alvisi & Franchini 2010;Giustolisi & Berardi 2on). Uncertainty quantification of model parameters such as nodal demands implies a profound knowledge of the system and the availability of sufficiently long time series data.…”

Model Performance Indicator of Aging Pipes in a Domestic Water Supply Distribution Network

“…Some parameter adjustments have been proposed to obtain a good calibration model. One of the approaches is adjusting the pipe roughness coefficient with sufficiently accurate nodal demand data [10][11][12]. There have also been a few methods suggested to consider adjustment of both the pipe roughness coefficient and the nodal demand [13] in model calibration of water distribution networks.…”

Calibration of water distribution network of the Ramnagar zone in Nagpur City using online pressure and flow data

“…The same number of equations are required as the number of unknowns. The other types of methods for calibration of the model are implicit approaches (e.g., Ormsbee 1989;Lansey and Basnet 1991;Datta and Sridharan 1994;Greco and Giudice 1999;Greco and Di Cristo 1999;Lansey et al 2001;Kapelan 2002;Lingireddy and Ormsbee 2002;Bascià and Tucciarelli 2003;Kapelan et al 2007;Koppel and Vassiljev 2009;Alvisi and Franchini 2010), in which field-observed and measured parameters are treated as known parameters and directly used in the model analysis. The implicit approach requires that the number of flow and pressure measurements exceed the number of unknowns.…”