Modeling of axisymmetric ultrasonic waves reflected from circumferential cracks in a pipe based on a rigorous analytical theory and implementation on distributed devices

Abstract

Inspection of defects in pipelines can be materialized by measuring ultrasonic guided waves the properties of which are conventionally analyzed with complicated finite-element methods (FEM). They require complete geometric discretization and result in large memory consumption in a single analysis, thus are clumsy and inapplicable on distributional devices. This work developed a comprehensive analytical modality to perform rapid assessment of reflection for guided waves in a pipe and used low-cost microprocessors. The mechanism of crack reflection was modeled with the reciprocity theorem and novel rigid-ring dynamic approximation. The analytical approach successfully estimated the coefficient dependence of crack depth with an accuracy comparable to that from FEM. The reflection coefficient dependence of the crack-depth was estimated correctly with up to 0.037 error. The developed algorithm was further implemented on an embedded device for calculation estimation. It shows the complete analytical theory sufficiently reduces computational complexity by orders of magnitude while retaining good accuracy for in-situ pipeline management.