Water distribution networks are of paramount importance for maintaining a substantive modern life and economic growth. Underground pipes are susceptible to leakage, due to excavation damage, sabotage, deterioration and aging. Water leakage is a subject of increasing concern across the world because of the potential danger to public health, economic constraints, environmental damage and wastage of energy.

Correlation-based leak detection techniques have been developed over the past half century, and are in common use in water distribution networks. Researcher GAO Yan from the Institute of Acoustics of the Chinese Academy of Sciences together with some researchers from China, Brazil and the UK have been investigating time delay estimation using the cross-correlation of leak noise signals in buried plastic water pipes. They present a procedure in which the shape of the cross-correlation function can be significantly improved, resulting in an unambiguous and clear estimate of the time delay.

Most commercial leak noise correlators utilize the basic cross-correlation via the Fast Fourier transform for time delay estimation. Previous research has demonstrated the effectiveness of the generalized cross-correlation via a pre-whitening process for accentuating the peak in the cross-correlation associated with the time delay.

The presence of the additional phase shifts in the cross-spectrum between the leak detection sensors can, however, cause errors in the time delay estimate. In practical leak detection surveys, such phase shifts have been observed by researcher GAO Yan et al. 

Researchers find that such phenomena are mostly possibly caused by the dynamic behavior of the pipe system. In some circumstances the bandwidth over which the correlation analysis can be conducted is severely restricted due to resonances.

This manifests themselves as peaks in the modulus and deviations from straight-line behavior in the phase of the cross-spectral density between leak signals measured by two acoustic sensors. The result can be a cross-correlation function in which it is difficult to estimate the time delay accurately for the basic cross-correlation, the generalized cross-correlation for example the Phase transform and the ROTH impulse response methods.

Conceptually, the passage of a leak noise signal from the leak to the sensor can be thought of as passing through a pipe filter and then a resonator. GAO et al. first introduced this resonance model, based on which a novel way to improve the shape of the cross-correlation functions for water leak detection has been investigated.

Significant improvement can be achieved by determining the frequency response functions for any resonators responsible for peaks in the cross-spectral density functions. Researchers then process the data using the frequency response functions of these resonators.

The parameters of the resonators are best determined by examining the ROTH correlators as this is similar to the frequency response function of the system, and thus facilitates the identification of both resonances and anti-resonances if they exist. The net effect of processing the data is to remove any deviations of the phase from that expected for a pure time delay and to smooth the modulus of the cross-spectral density.

Using the modified phase spectrum, the Phase transform correlators can be used over the frequency bandwidth in which there is good coherence between the two measured signals. This results in an unambiguous and clear estimate of the time delay. There are thus significant advantages in applying the process described in the updated research.

The current limitation, however, is that the procedure has to be applied manually, which will restrict its application in practical acoustic correlators. The challenge now is to develop an algorithm to carry out the procedure automatically.