Local Sensitivity of Pressure-Driven Modeling and Demand-Driven Modeling Steady-State Solutions to Variations in Parameters

Abstract

AbstractThe first-order sensitivity matrices (matrices of sensitivity or influence coefficients) have application in many areas of water distribution system analysis. Finite-difference approximations, automatic differentiation, sensitivity equations, and the adjoint method have been used in the past to estimate sensitivity. In this paper new, explicit formulas for the first-order sensitivities of water distribution system (WDS) steady-state heads and flows to changes in demands, resistance factors, roughnesses, relative roughnesses, and diameters are presented. The formulas cover both pressure-dependent modeling (PDM) and demand-dependent modeling (DDM) problems in which either the Hazen-Williams or the Darcy-Weisbach head-loss models are used. Two important applications of sensitivity matrices, namely calibration and sensor placement, are discussed and illustrative examples of the use of sensitivity matrices in those applications are given. The use of sensitivity matrices in first-order confidence estima...