Estimating the spectrum of leak noise in buried plastic water distribution pipes using acoustic or vibration measurements remote from the leak

An appropriate model of leak noise at source is necessary in analytical and numerical approaches to investigate the characteristics of leak noise measured remotely from the leak in buried water pipes. It is extremely difficult to measure leak noise at source in practice, so an inverse method is needed to predict this from measurements made either side of the leak at convenient access points. This paper presents such a method, and illustrates the approach using four data sets from three different test sites. The method requires that the noise propagates in the pipe according to a simple model of wave propagation within the frequency range over which leak noise is detected at the sensors. Using the measured data, the real and imaginary parts of the wavenumber are estimated, and these, together with an estimated position of the leak between the two sensors, the frequency response functions corresponding to the sections of the pipe either side of the leak position are estimated. If pressure measurements are made, then both the level and shape of the leak noise spectrum can be estimated, but if accelerometers are used then only an estimate of the shape of the spectrum is possible. From the measurements presented, it is found that it is not possible to state categorically that the leak noise spectra decays according to a particular frequency power law. There is some evidence that it decays with a frequency power law of ω-1, which agrees with previous laboratory based experiments, but this is not definitive in all cases.