Cross-spectral phase method for time delay estimation in acoustic leak detection

This paper introduces a method for estimating time delays in acoustic/vibration leak signals within water distribution systems, using linear segmentation of the cross-spectral phase. The method applies linear regression to undistorted regions of the phase, automatically identified by a simple algorithm, to calculate the time delay. Simulation and experimental results demonstrate that the method accurately estimates time delays without the need for pre-filtering, even in the presence of multiplicative noise that distorts the cross-spectral phase—offering a significant improvement over correlation-based techniques. Furthermore, the method provides a confidence interval that quantifies the uncertainty in the estimated leak location, thereby enhancing the reliability of leak localisation. • Multiplicative noise such as resonance introduces additional shifts in the cross-spectral phase of leak signals. • Phase shifts reduce the accuracy of the time delay estimate. • Accurate time delay estimates are given by the slope of linear sections of the cross-spectral phase. • Linear segments are identified in the cross-spectral phase using a simple divide-and-conquer algorithm. • A confidence interval is used to quantify the uncertainty in the leak location.