Directional wave separation in tubular acoustic systems - The development and evaluation of two industrially applicable techniques

An acoustic device is used to evaluate internal features and defects within tubes by determination of the acoustic impulse response. This paper concerns methods of separating the total pressure wave measured in the device into its forward and backward travelling components, which facilitates computation of the acoustic impulse response. The device comprises a tube that has a speaker at one end and is axially instrumented with microphones. Unlike similar works, the methods presented in this paper were designed to be applied in an industrial context, they allow simple calibration and implementation using readily transportable equipment. Two wave separation algorithms are presented; the first is a known method that has been improved to provide simplified calibration and the second is a computationally inexpensive technique that has been adapted to improve its operational bandwidth. The techniques are critically evaluated using a custom built test rig, designed to simulate realistic tube features and defects such as constrictions, holes and corrosion. It is demonstrated that, although inter-microphone attenuation is not accounted for in the second algorithm, both algorithms function well and give similar results. It is concluded that the added sophistication of the first method means that it is less affected by low frequency interference and is capable of yielding more accurate results. However, in practical use as an evaluation tool, the benefits of including inter-microphone attenuation are outweighed by the additional calibration and computational requirements. Finally the output of the wave separation techniques is validated by showing agreement between experimental impulse response measurements and those obtained from a theoretically derived acoustic tube simulator.