Pulsed Eddy Current: Feature Extraction Enabling In-Situ Calibration and Improved Estimation for Ferromagnetic Application
Faris Nafiah, M. O. Tokhi, S Majidnia, John Rudlin, Zhanfang Zhao, Fang Duan
Abstract
Abstract Steel pipes in process plant applications are often covered with insulation or weather protection that make inspection difficult because the additional layers need to be penetrated to inspect the pipes’ structure. The pulsed eddy current (PEC) method was devised as a means of inspection through the surface layers. However, the performance of a PEC system is dependent on the electrical and magnetic properties of the pipe material, which are generally unknown. Therefore, the use of a calibration block from a different steel will give inaccurate results. The concept of calibrating using $$\tau _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> values obtained during inspection has undoubtedly been discussed in the literature. However, no comprehensive work was dedicated to using $$|\nabla |^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>∇</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> to carry out calibration on inspected structure. The linear relationship of the $$|\nabla |^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>∇</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> feature with the thickness squared, $$d^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>d</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , is first established using analytical solutions, and the calibration is carried out using the feature values obtained in air and the reference signal. The performance of this technique is assessed and compared with the conventional $$\tau _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> technique. Although both features exhibit similar immunity towards lift-off, $$\tau _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> technique requires normalisation procedure, which contributes to determining more configuration parameters. Experimental results also suggest the relative advantage of using $$|\nabla |^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>∇</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> feature in both wall thickness estimation and influences of noises.