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Characterisation, computation and classification of conducting magnetic objects for safety and security

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RNT - Rich and Nonlinear Tomography - a multidisciplinary approach

The location and identification of hidden conducting magnetic threat objects using metal detection is an important yet challenging task. Applications include security screening at transport hubs as well as finding landmines and unexploded ordnance in areas of former conflict, which often involve objects whose materials are both conducting and magnetic. The talk will begin with an introductory example of characterising an isolated non-conducting magnetic object by a real symmetric rank 2 polarizability tensor, whose coefficients are a function of the object’s size, shape and permeability contrast. The explicit formulae of this economical characterisation will be obtained by deriving an asymptotic formula for the perturbed magnetic field due to the presence of a small object. Then, the asymptotic expansion of the perturbed magnetic field for the eddy current problem, which is relevant for characterising conducting magnetic objects for the metal problem, will be presented. The explicit formulae for computing the corresponding coefficients of the complex symmetric magnetic polarizability tensor (MPT) characterisation, which is a function of the object’s size, shape, material properties and the exciting frequency, will be discussed. The computation of the MPT coefficients requires the solution of a vectorial transmission problem. For this, we will discuss how a high order H(curl) conforming finite element method (FEM) can be applied. To rapidly compute MPT coefficients as a function of frequency (known as the MPT spectral signature), we will accelerate the FEM computation with a proper orthogonal decomposition reduced order model (ROM). We will use an a-posteriori error estimate to adaptively choose new snapshots to further improve the efficiency of the ROM . In the case of conducting magnetic objects, which have very thin skin depths, we will use prismatic boundary layers to ensure exponential convergence of the FEM solution and accurate MPT coefficient computations. Combining our computational approaches with scaling results will allow us to obtain a large dictionary of MPT spectral signature characterisations of realistic threat and non-threat objects. The talk will also discuss how probabilistic and non-probabilistic machine learning classifiers can be applied to identify hidden objects learnt from our dictionary. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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