A Stochastic Based Approach to Model Acoustic Propagation in Pipes with Laterals

Newly developed applications for condition monitoring of piping networks (e.g. sewer pipes) depend on measuring acoustic signal attenuation through tests in the field. In many cases, the exact layout of the installed pipelines is not accessible or actual installation differs from documented layout. This lack of exact knowledge of numbers and lengths of side branches (laterals) introduces a random variable error between measured attenuation and that predicted from theory. As the sources of this random variable error can be considered independent and arbitrarily distributed, it is reasonable to assume that the error also follows an approximately normal probability distribution in accordance with Central Limit Theorem. Using an analytical approach to model signal attenuation due to random variable sources can be complex and may be intractable. A tractable approach is to develop an empirical model of attenuation with a stochastic component to account for random variable sources of attenuation. This approach forms the crux of work reported in this paper. Extensive field and laboratory measurements were made in pipes to measure acoustic attenuation with change in numbers and lengths of side branches. Results show that an empirical model of signal attenuation, that includes a stochastic component, gives a better prediction of received sound pressure level in a pipe with side branches compared to the existing theoretical models.