Acoustic Leak Localization Study Based on MVDR Time-Delay Estimation Algorithm in a Cross-Spectral Domain for Water Pipeline Systems

To address the problem of multipeak interference in traditional cross-correlation–based pipeline leak localization caused by signal reflections and transmissions, this paper proposes an improved leak localization method based on the cross-spectral domain minimum variance distortionless response (CSMVDR). Combining beamforming principles with cross-spectral domain signal processing, acoustic emission signals from two sensors are used to directly construct a spatial covariance matrix in the cross-spectral domain. The wideband leakage signals are decomposed into narrowband components via the short-time Fourier transform (STFT), and frequency-domain sub-band optimization together with time-continuity analysis of delay trajectory bright lines significantly enhances the extraction of primary propagation path features. Requiring no prior model information, the approach transforms the physical process of listening for leaks along the water pipeline system into a scanning process between sensors while retaining the energy and temporal continuity of suspected leak peaks to assist practical detection. Experiments were performed on a 100-m galvanized steel pipe (DN20) with a simulated leak generated by a ball valve. Results show that the proposed CSMVDR method effectively sharpens the main peak of the time-delay spectrum and suppresses spurious peaks caused by reflections and multipath interference. Compared with the basic cross-correlation (BCC) method, the CSMVDR method achieves an average localization error of 2.09 m, confirming its feasibility, robustness, and strong engineering applicability for practical water pipeline leak detection.