An eddy current transducer model for image restoration

Abstract

We describe in this short paper a new imaging model for the spatial magnitude response of an absolute eddy current transducer to a flaw. This model is appropriate for image restoration purposes in that it captures the transducer response with sufficient accuracy for image restoration, yet is simple enough to be computationally practical.The model described in this paper is based on a simple resistive loop approximation to the transducer impedance changes induced by a flaw, and is efficiently implemented as layers of linear blurring functions and nonlinear point operations. The model is shown to accurately reflect the magnitude response of an absolute transducer to an EDM slot in a non-ferrous alloy. Furthermore, the model is shown to produce good restoration results for synthetic images of flaws. The model may be adapted to a particular combination of absolute transducer and surface flaw type by optimizing the model parameters, either by forming the partial derivatives with respect to the parameters and minimizing by gradient descent, or by a straightforward implementation of a neural net back-propagation algorithm. Other types of eddy current transducers may be modeled by simply modifying the spatial layers to combine the local terms appropriately for the geometry of the transducer.

Eddy Current Imaging, Array Sensors and Flaw Reconstruction

“…At each step of the iterative flaw reconstruction process the perturbed field should be updated by solving the forward problem (7)- (10). In a general case the above mentioned problem is difficult to solve, because usually eddy current probes contain ferromagnetic cores and the exact field analysis has to be done by means of sophisticated 3-D finite element codes.…”

Eddy Current Image Restoration Using the Groshong Parametric Model

“…The Groshong EC transducer model [1,2] is simply based on a weighted sum of the path lengths of an annulus of eddy current filaments flowing on the component surface and is suitable for axially symmetric probes. In a general form, the transducer response can be written as: (1) where G is the image obtained from the probe impedance changes when scanned over the component surface, Hp the nonlinear transfer function of the probe defined by the parameters p, F the original flawed surface image and N the noise.…”

“…In a general form, the transducer response can be written as: (1) where G is the image obtained from the probe impedance changes when scanned over the component surface, Hp the nonlinear transfer function of the probe defined by the parameters p, F the original flawed surface image and N the noise. The noise is assumed to be additive in Groshong's publications and in the work presented here.…”

“…The summation over k is the discrete formulation for the angular integration of the current path lengths. Detailed formulations of these functions are given in Groshong's Ph.D. thesis [3]. The function sl defined by Groshong has been modified to remove the DC component:…”

NDE data fusion using phenomenological approaches

“…As a result, many indirect inversion methods have been proposed. One commonly used technique is to employ calibration curves [105][106][107]. Such curves, relating the measurement variable and specific defect characteristic of interest, are derived using experimental data or results generated using forward models.…”