Acoustic signal propagation characterization of conduit networks

Analysis of acoustic signal propagation in conduit networks has been an important area of research in acoustics. One major aspect of analyzing conduit networks as acoustic channels is that a propagating signal suffers frequency dependent attenuation due to thermo-viscous boundary layer effects and the presence of impedance mismatches such as side branches. The signal attenuation due to side branches is strongly influenced by their numbers and dimensions such as diameter and length. Newly developed applications for condition based monitoring of underground conduit networks involve measurement of acoustic signal attenuation through tests in the field. In many cases the exact installation layout of the field measurement location may not be accessible or actual installation may differ from the documented layout. The lack of exact knowledge of numbers and lengths of side branches, therefore, introduces uncertainty in the measurements of attenuation and contributes to the random variable error between measured results and those predicted from theoretical models. There are other random processes in and around conduit networks in the field that also affect the propagation of an acoustic signal. These random processes include but are not limited to the presence of strong temperature and humidity gradients within the conduits, blockages of variable sizes and types, effects of aging such as cracks, bends, sags and holes, ambient noise variations and presence of variable layer of water. It is reasonable to consider that the random processes contributing to the error in the measured attenuation are independent and arbitrarily distributed. The error, contributed by a large number of independent sources of arbitrary probability distributions, is best described by an approximately normal probability distribution in accordance with the central limit theorem. Using an analytical approach to model the attenuating effect of each of the random variable sources can be very complex and may be intractable. A tractable approach is to develop an empirical model of the attenuation that has a stochastic component of a finite mean and variance to account for the random variable error akin to addition of a normally distributed random variable shadowing component in the path loss models of radio frequency (RF) wireless communication channels. This approach forms the crux of the present study. To develop an empirical model, a large number of measurements in conduit networks were made in the field and in a laboratory test set up to measure the variability of attenuation with variation in four parameters. These parameters include distance of the receiver from the source, frequency, numbers and lengths of side branches. Variation in signal attenuation with distance at each transmitted frequency is predicted by using linear regression through the scatter plot of the measured data. Variations in signal attenuation due to change in frequency, number and lengths of side branches are measured in the field and laboratory tests by comparing the reference transmitted pressure with the received pressure at either the open end or at some distance away from the source along the conduit length. Residuals between measured and predicted sound pressure levels are computed and tested for normal probability distribution through a graphical method as well as a statistical goodness of fit test for quantifiable results. The findings indicate that an empirical model of signal attenuation, which includes a normally distributed random variable component to account for random variable errors in the attenuation measurements, gives a more accurate prediction of received acoustic signal strength in a conduit compared to existing theoretical models.