Simultaneous Extraction of Multiple Parameters From a Transmit–Receive Eddy Current Probe Above a Layered Planar Conductive Structure

Abstract

A validated analytical model of a transmit–receive coil pair situated above two parallel plates, separated by an air gap, was used as the basis for an inversion algorithm (IA) to extract probe liftoff, second layer plate resistivity, and plate-to-plate gap from multi-frequency eddy current data. The IA was tested over a large range of first layer wall thickness (3.80–4.64 mm), second layer plate resistivity (1.7–174 µΩ cm), second layer wall thickness (1.20–4.85 mm), probe liftoff (2.8–7.9 mm), and plate-to-plate gap (0–13.3 mm). At nominal liftoff (2.8 mm), the IA achieved a gap measurement accuracy of ±0.7 mm and was able to return good estimates of the second layer resistivity within ±1 μΩ cm for low resistivity samples, but with decreasing accuracy for higher resistivities. When the gap was fixed, the IA was able to measure changes in probe liftoff (relative to nominal) to an accuracy of ±0.2 mm. The reported accuracy and a demonstration for the ability to accurately estimate parameters outside of the calibration range provide confidence in the potential utility of the algorithm.

Analytical model of eddy current bobbin coil probe responses at support plates in steam generator and heat exchanger tubes

“…Analytical models show potential for use in model based inverse algorithms, either derivative free methods such as the Nelder-Mead simplex method [15,16], or methods that utilise derivatives, such as Newton's method [17], the Gauss-Newton method [18]. Inverse models have also been developed using error minimisation algorithms [15,16]. The models may also be used to generate training data for artificial neural networks [15,19].…”

Pulsed eddy current testing for gap measurement of metal casing

“…In addition, all electromagnetic coupling coefficients produced by the probe and layered conductors, which were used for calculating the induced voltage of receive coil, were determined. In [5], the analytical solution of the detection model was derived using truncated region eigenfunction expansion solutions with simplified calculation. This new analytical model was used as the basis for inversion algorithm, which could simultaneously extract the probe lift-off, plate resistivity and casing gap from multi-frequency measurement data.…”

“…Both the RFEC method in [1] and the multi-frequency eddy current method in [2][3][4][5][6] proposed for gap measurement of metal casing belong to the sinusoidal eddy current method excited by a sinusoidal current. The main purpose of this paper is to theoretically compare the detection sensitivity of sinusoidal eddy current method and pulsed eddy current method for the casing gap measurement.…”