Leakage diagnosis using closed-form solution and linear observer

In this paper, an approach is proposed to estimate the location of leakages in liquid transmission lines with a high accuracy. First, the mathematical model is analyzed and a closed-form solution is provided for the partial differential equations of the pipeline. Next, the leakage location is calculated using the closed-form solution. The calculations are applied to various leakages and are extended to a case in which the pressure and flowrate do not converge to constant values. Considering a singleleakage pipeline system, a linear observer is utilized to estimate the leakage location with reduced errors. The simulation results are presented and the proposed method is verified by changing the location of the leak.