Pipe roughness calibration in water distribution systems using grey numbers

摘要

This paper presents a procedure based on the use of grey numbers for the calibrationn(with uncertainty) of pipe roughness in water distribution systems. The pipe roughnessnuncertainty is represented through the grey number amplitude (or interval). The procedurenis of a wholly general nature and can be applied for the calibration (with uncertainty) of othernparameters or quantities, such as nodal demands. In this paper, for the purpose of roughnessncalibration, a certain number of nodal head measurements made under different demandnconditions is assumed to be available at different locations (nodes); all other topologicalnand geometric characteristics of the system are considered to be known exactly.nThe general approach to pipe roughness calibration (taking account of uncertainty) focusesnon identifying the grey roughness values which produce grey head values at the measuringnnodes such as to encompass the observed values grouped on the basis of the differentndemand scenarios and, at the same time, have as small an ‘amplitude’ as possible.nThe proposed procedure was applied to two synthetic case studies and to one real network.nThe tests on the synthetic case studies show that the proposed procedure is able to correctlynsolve the inverse problem, i.e. it can identify the known grey roughness numbers evennwhen they overlap; the same applies when the known grey roughness numbers collapse intonknown white roughness numbers. The test on the real case offers the possibility of highlightingnthe potentials of the procedure when applied within a context where measurement errorsnand other uncertainties are present. The procedure entails computing times that may becomenlengthy. However, it is possible to reduce these computing times considerably by replacingnthe hydraulic simulator—to which a number of calls must be made during the calibrationnprocedure (for objective function evaluation)—with an approximation based on a first-ordernTaylor series expansion. This approach introduces acceptable approximations within thencontext of the problem considered.