Frequency domain response characteristics and localization of transient wave-based water pipeline leakage

The innovation and advancement of pipeline leakage detection technology are crucial for ensuring water supply safety and the effective utilization of resources. Currently, transient wave-based leakage detection methods face challenges such as signal attenuation in complex pipeline systems, difficulties in identifying multiple leakage points, and insufficient real-time performance, which limit their localization accuracy and reliability. Therefore, this paper revisits the fundamental principles which form the basis for transient-based leak detection methods, systematically exploring the influence of leakage on the characteristics of the frequency response function (FRF) and its intrinsic relationship with the standing wave-leak interactions through experimental verification and theoretical analysis. The experiments reveal that leakage significantly alters the peaks and amplitudes of the FRF, with factors such as leakage volume, background pressure, transient pressure, and leakage location affecting its characteristics. Changes in leakage location can cause shifts in the FRF peak patterns through the standing wave-leak interactions, this phenomenon is similar to the Bragg effect, but the mechanism is not entirely the same. This study successfully constructs a frequency-domain mathematical model of transient wave-leakage coupling, innovatively introducing the precise and efficient Trikha-Vardy-Brown (TVB) unsteady friction model combined with viscoelastic theory to accurately simulate FRF characteristics under different pipe materials and operating conditions. Additionally, the study employs the matched-field processing (MFP) method to achieve accurate estimation of the location and size of single and multiple leaks, the single leakage error is within 0.6 m for steel pipes, within 4 m for acrylic pipes, and the multiple leakage errors are all within 4 m. In conclusion, this study confirms the effectiveness and accuracy of transient wave propagation technology in pipeline leakage detection, providing a new technical approach for the rapid diagnosis and localization of water pipeline leaks.