Modeling of Axisymmetric Ultrasonic Waves Reflected from Circumferential Notches in a Pipe based on a Rigorous Analytical Theory and Implementation on Distributed Devices

Inspection of defects in pipelines can be materialized by measuring ultrasonic guided waves the properties of which are conventionally analyzed with three-dimensional finite-element methods (FEM). They require complicated geometric discretization and memory consumption in a single analysis, thus are clumsy and limited to be used for field fast analysis. This work developed a systematic analytical approach to perform rapid assessment of mode-to-mode reflection for guided waves in a pipe owing to notches and used low-cost microprocessors for calculation. The mechanism of wave reflection was interpreted with the reciprocity theorem and a novel dynamic rigid-ring approximation. The theory successfully estimated the coefficient dependence of notch depths with an accuracy comparable to that obtained from a FEM, with the maximum error being less than 0.044. The developed algorithm was further implemented on an embedded system for computational complexity estimation. It shows the complete analytical theory sufficiently reduces computational memory and time cost by orders of magnitude while retaining good accuracy in determining mode-to-mode guided reflection by notches, which is a useful tool for practical pipeline applications.