A stochastic model for the speed of leak noise propagation in plastic water pipes
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A good estimate of the speed of leak noise propagation is necessary to pinpoint the location of a leak using acoustic correlators. Models currently exist for this purpose, but they do not consider uncertainties in the pipe geometry and the properties of the pipe and soil. Using the fact that leak noise propagates as a predominantly fluid-borne wave, this paper develops a stochastic model of the speed of leak noise propagation in plastic water distribution pipes that can account for these uncertainties. The model provides confidence limits for the estimate of this wave speed. It is based on the mean and standard deviation of the pipe geometry as well as the pipe and soil material properties, which have strong influence on the speed at which the leak noise propagates in the pipe. Numerical examples, using parameters from water supply systems found in the field, in which the pipe is made from Medium-Density Polyethylene (MDPE) and Polyvinyl Chloride (PVC) are presented to validate the model. Monte Carlo simulations for both in-air and buried pipes are presented to check the 99.7% confidence interval. To verify that the predictions from the stochastic models give realistic results, they are compared with some measurements from different sites, in which nominal properties and tolerances for the pipe and soil properties are assumed.