Multivariate probability of detection (POD) analysis considering the defect location for long-range, non-destructive pipe inspection using electromagnetic guided wave testing

This paper presents a multivariate probability of detection (POD) analysis method for long-range pipe inspection using microwave non-destructive testing (NDT). The proposed two-dimensional (2D) POD model considers both the size and location of pipe wall thinning (PWT) and is thus able to simultaneously characterize the detectability and detection range. First, the propagation of microwaves in a pipe with PWT was modeled through numerical simulation. The simulated S-parameters (S11) were converted into the time domain and were further processed to correlate the amplitude of the reflection signal with the corresponding PWT depth and location. The simulation results indicate that the logarithmic amplitude of the reflection signal is proportional to the PWT location and logarithmic PWT depth. Therefore, a prior multivariate regression model was established for the above three parameters. Second, an experiment was performed using a 14.5-m-long brass pipe. Twelve short pipes with six different inner diameters were used to emulate PWT and were deployed at eight different locations in the pipe. The experimental results suggest that each PWT can be detected with excellent repeatability, and show consistency with the simulation results. The processed experimental signals were subsequently employed for the regression model of the amplitude of the reflection signal, PWT depth, and location. Finally, a 2D POD model was constructed on the basis of the regression model and a dynamic-static threshold, combining in-pipe microwave signal attenuation with instrumental noises. The POD plot and contour give reasonable interpretations of the detection capability of this testing method against PWTs with different depths, considering the PWT locations.