Improving accuracy through density correction in guided wave tomography

Abstract

The accurate quantification of wall loss caused by corrosion is critical to the reliable life estimation of pipes and pressure vessels. Traditional thickness gauging by scanning a probe is slow and requires access to all points on the surface; this is impractical in many cases as corrosion often occurs where access is restricted, such as beneath supports where water collects. Guided wave tomography presents a solution to this; by transmitting guided waves through the region of interest and exploiting their dispersive nature, it is possible to build up a map of thickness. While the best results have been seen when using the fundamental modes A0 and S0 at low frequency, the complex scattering of the waves causes errors within the reconstruction. It is demonstrated that these lead to an underestimate in wall loss for A0 but an overestimate for S0. Further analysis showed that this error was related to density variation, which was proportional to thickness. It was demonstrated how this could be corrected for in the reconstructions, in many cases resulting in the near-elimination of the error across a range of defects, and greatly improving the accuracy of life estimates from guided wave tomography.

Guided wave tomography with an improved scattering model

“…The test cases presented here are similar to those used previously in [14,18], so only the key parameters are given here. In all examples, the A 0 mode has been used at 50 kHz on a 10 mm thick steel plate, although results are normalized to be valid for other thicknesses, provided the frequency is adjusted to ensure the same frequency-thickness product.…”

“…This behaviour can, therefore, be captured by the generalized scattering model, and will automatically be accounted for in the coefficients extracted from the simulation. This integrated technique is arguably a more elegant solution for density correction compared with the previous approach [18] where an initial thickness map was generated ignoring density, then iteratively updated with a correction term based on the implied density. This analysis has been performed using the assumption that the thickness variations were small, allowing the equations to effectively be linearized.…”

“…A recent paper [18] discussed the effects of density in guided wave scattering, and highlighted how it can cause critical errors in the reconstruction if neglected. It is noted that this is the effective density that the guided wave experiences, rather than the material density; this effective density term is proportional to thickness.…”

“…This is operated at 50 kHz using parameters from the A 0 mode on a 10 mm thick steel plate; node spacing was 1 mm and 240 elements were used in a circular array around the defect. All defects were axisymmetric Hann defects as described in [18], and had widths of 20, 40, 60, 80 and 120 mm, and depths of 10, 30, 40, 50, 55, 60% of wall thickness, making 26 simulations in total, including a run to obtain the incident field φ 0 . The coefficients are then extracted from these scattered fields using the approach described previously.…”

“…A simple enhancement is to consider density in addition to velocity when inverting [18], which can improve accuracy, but this still fails to capture guided wave scattering fully. In a more sophisticated approach, Rose et al developed Mindlin plate theory [19] for guided wave tomography [20,21].…”