Integration of multiple wall thinning parameters into the probability of detection analysis for long-range pipe inspection using microwaves

Abstract

A three-dimensional probability of detection (POD) model integrating the depth, circumferential angle, and location of pipe wall thinning (PWT) was proposed for the probabilistic analysis of long-range pipe inspection using microwaves. Microwaves in TM01 mode were used to detect PWT with different sizes and locations (up to 13.5 m). The microwave signals reflected from the PWT were measured and processed, and their amplitudes were extracted and treated as the signal response. The results showed that the signal response was rarely influenced by the axial length of the PWT, while its natural logarithm was proportional to the natural logarithm of the PWT depth and circumferential angle. In addition, the signal response decreased exponentially with the PWT location. Subsequently, a multivariate regression model was established, and the related coefficients were estimated using the maximum likelihood method. The POD calculated from the regression model suggests that a small PWT at a far distance (e.g., 36.0 m) can be reliably detected using microwaves. Compared with a two-dimensional POD model that considers only the PWT cross-section area as the size parameter, the proposed POD model clearly shows that the POD is more dependent on the circumferential angle than on the depth of the PWT.