Comprehensive study on microwave inspection of internal pipe wall thinning: Discontinuities, reflections and signals

Microwave inspection of internal pipe wall thinning (PWT) relies on reflections occurring at locations where inner radius changes. Reflections also occur at other discontinuities, such as air gaps and the pipe end, which seriously contaminate the measurement signals for PWT and pose challenges to PWT characterization. This study clarified the mechanism of reflections from different types of discontinuities using theoretical, analytical, and numerical solutions. By establishing a formula to calculate the characteristic impedance of a circular waveguide, we were able to analytically compute the scattering parameter $S_{11}$ for a waveguide with a full-circumferential PWT, providing insights for PWT characterization. Furthermore, we defined the number of repetitions per unit of frequency as $\Omega$ and represented the measured $S_{11}$ signals in the $\Omega -$ domain. The correspondence between $\Omega$ and traveling distance enables localization of discontinuities without considering frequency-dependent propagation velocity. The $\Omega$ domain representations primarily associated with PWT were isolated by band and converted back to the frequency domain, allowing for more effective PWT characterization.