Target Detection and Characterization from Electromagnetic Induction Data

TL;DR

This paper develops a mathematical and numerical framework for detecting and characterizing small conductive inclusions using electromagnetic induction data, advancing nondestructive testing techniques.

Contribution

It introduces a new small-volume expansion formula involving polarization tensors and a location search algorithm for electromagnetic imaging of inclusions.

Findings

Derived a small-volume expansion formula with polarization tensors

Designed a location search algorithm for detection

Numerical examples validate the approach

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.