Transient-based frequency domain method for dead-end side branch detection in reservoir pipeline-valve systems

Unexpected, unknown or unused side pipe branches, termed dead-end side branches in this study, commonly exist in water pipe systems because of incorrect device installations or illegal connections. These connections are detrimental to the water quality and the operation and management of pipe networks. This paper investigates a transient-based frequency domain method for detecting side branches in pipe systems. The frequency response function for a pipe system with a single dead-end side branch is first derived by the transfer matrix method and the side branch was found to cause shifts in the system resonant frequencies. The nature of the resonant frequency shifts can be used to inversely determine the location and size of the side branch. A two-step genetic algorithm based optimization is proposed in this study to efficiently solve the derived analytical expression for the resonant frequency shifts. The developed method is validated through numerical simulations, and the results demonstrate the feasibility of this method for detecting side branches. The accuracy for locating the side branch is higher than the accuracy in sizing the branches. The sensitivity of the method to the magnitude and bandwidth of the transient wave signal is also discussed in the paper.