Impedance Method for Abnormality Detection of a Branched Pipeline System

In this paper, an integrated detection scheme is developed to simultaneously address a leakage, a partial blockage and unknown branched pipeline elements. Expressions for the pressure head and discharge for a branched pipeline system having both a leakage and a blockage are derived in frequency domain. Boundary conditions for a reservoir and a branched dead-end allow the development of impedance formulations. The condition for a pipeline junction can be addressed using either a common condition for the pressure head combined with a continuity condition of discharge or a connectivity condition for impedance. In order to consider the unsteady friction’s impact, the impedance development process studied both the impact resulting from velocity profiles with two-dimensional distributions and the impact resulting from local and convective accelerations. Impedance expressions are derived for two distinct branched pipeline systems at different abnormality conditions. Based on drived formulations describing these systems, response functions were derived in the frequency domain and their corresponding time domain representations were integrated into a meta-heuristic calibration scheme for inverse transient analysis. Using an objective function for minimization of root-mean-square-errors between the observed and computed pressures, the calibration based one impulse response can simultaneously predict locations and magnitudes of abnormalities as well as parameters for a branched pipeline. The strength of the impedance-based approach for inverse transient analysis arises mainly from its feasibility to address different conservation conditions for pressure and discharge and for combining these conditions into a unified impedance connectivity condition.