Target detection and characterization from electromagnetic induction data

Abstract

The goal of this paper is to contribute to the field of nondestructive testing by eddy currents. We provide a mathematical analysis and a numerical framework for simulating the imaging of arbitrarily shaped small volume conductive inclusions from electromagnetic induction data. We derive, with proof, a small-volume expansion of the eddy current data measured away from the conductive inclusion. The formula involves two polarization tensors: one associated with the magnetic contrast and the second with the conductivity of the inclusion. Based on this new formula, we design a location search algorithm. We include in this paper a discussion on data sampling, noise reduction, and on probability of detection. We provide numerical examples that support our findings. Mathematics Subject Classification (MSC2000): 35R30, 35B30

Generalised magnetic polarizability tensors

“…The explicit expression for their coefficients is with respect to the standard orthonormal basis rather than the space of harmonic polynomials. They are functions of B , α , σ ∗ , μ ∗ / μ 0 , and ω and can be computed by solving a generalised form of the vectorial transmission problem obtained in Ammari et al and Ledger and Lionheart . Moreover, the leading order term in our new expansion agrees with our previous result, and here, the GMPT agrees with .…”

“…More recently, for the metal detection problem, Ammari et al have obtained the leading order term in an expansion of ( H α − H 0 )( x ) as α →0 for a highly conducting (multiply connected) object placed in a low‐frequency time‐harmonic background field, H 0 ( x ). This expansion was obtained for the eddy current regime of the Maxwell system, which is the relevant case for metal detection, and they showed that the object is characterised by a rank 4 tensor and, therefore, is of a different form to .…”

Electromagnetic induction tomography

“…It should be noted that the engineering adoption of this tensor structure as described by nine elements is a scope of the current investigation in applied mathematics. Recent progress in the area (Ledger & Lionheart, submitted for publication) examined the derivation of an asymptotic formula for the perturbed secondary field due to the presence of a target and suggested that an earlier derivation of tensor represented as a rank four tensor (Ammari, Chen, Chen, Garnier, & Volkov, 2014) with 81 coefficients can reduce to a rank two tensor with only nine coefficients, which provides a solid foundation for the current configuration. These coefficients forming the matrix M are complex valued and frequency dependent.…”

Classification of materials for conducting spheroids based on the first order polarization tensor

“…In applied mathematics and analysis, previous studies by [1,14,15,16,17,18,19] have shown that the perturbation due to the presence of the conducting objects can be represented by asymptotic formulas and PT is actually the dominant term in the formula. The asymptotic formula and the corresponding PT are generally not the same for different systems.…”