Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object characterisation and invariants

The early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterisation information. The magnetic polarizability tensor (MPT) offers an economical characterisation of metallic objects that can be computed for different threat and non-threat objects and has an established theoretical background, which shows that the induced voltage is a function of the hidden object's MPT coefficients. In this article, we describe the additional characterisation information that measurements of the induced voltage over a range of frequencies offer compared with measurements at a single frequency. We call such object characterisations its MPT spectral signature. Then, we present a series of alternative rotational invariants for the purpose of classifying hidden objects using MPT spectral signatures. Finally, we include examples of computed MPT spectral signature characterisations of realistic threat and non-threat objects that can be used to train machine learning algorithms for classification purposes

Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition

The identification of hidden conducting permeable objects from measurements of the perturbed magnetic field taken over a range of low frequencies is important in metal detection. Applications include identifying threat items in security screening at transport hubs, location of unexploded ordnance, and antipersonnel landmines in areas of former conflict, searching for items of archeological significance and recycling of valuable metals. The solution of the inverse problem, or more generally locating and classifying objects, has attracted considerable attention recently using polarizability tensors. The magnetic polarizability tensor (MPT) provides a characterization of a conducting permeable object using a small number of coefficients, has an explicit formula for the calculation of their coefficients, and a well understood frequency behavior, which we call its spectral signature. However, to compute such signatures, and build a library of them for object classification, requires the repeated solution of a transmission problem, which is typically accomplished approximately using a finite element discretization. To reduce the computational cost, we propose an efficient reduced order model (ROM) that further reduces the problem using a proper orthogonal decomposition for the rapid computation of MPT spectral signatures. Our ROM benefits from a posteriori error estimates of the accuracy of the predicted MPT coefficients with respect to those obtained with finite element solutions. These estimates can be computed cheaply during the online stage of the ROM allowing the ROM prediction to be certified. To further increase the efficiency of the computation of the MPT spectral signature, we provide scaling results, which enable an immediate calculation of the signature under changes in the object size or conductivity. We illustrate our approach by application to a range of homogenous and inhomogeneous conducting permeable objects

Understanding the magnetic polarizability tensor

The aim of this paper is to provide new insights into the properties of the rank 2 polarizability tensor M̆ proposed by Ledger and Lionheart for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy-current regime. In particular, we explore its connection with the magnetic polarizability tensor and the Pólya-Szegö tensor and how, by introducing new splittings of M̆, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the Pólya-Szegö tensor and expressions for the low-frequency and high-conductivity limiting coefficients of M̆. We show, for the high-conductivity case (and for frequencies at the limit of the quasi-static approximation), that it is important to consider whether the object is simply or multiply connected but, for the low-frequency case, the coefficients are independent of the connectedness of the object. Furthermore, we explore the frequency response of the coefficients of M̆ for a range of simply and multiply connected objects

Classification of Metallic Targets Using a Walk-Through Metal Detection Portal

Metal detectors have been used for a long time for treasure hunting, security screening, and finding buried objects such as landmines or unexploded ordnance. Walk-through metal detection (WTMD) portals are used for making sure that forbidden or threatening metallic items, such as knives or guns, are not carried into secure areas at critical locations such as airports, court rooms, embassies, and prisons.The 9/11 terrorist act has given rise to stricter rules for aviation security worldwide, and the ensuing tighter security procedures have meant that passengers face more delays at airports. Moreover, the fear of terrorism has led to the adoption of security screening technology in a variety of places such as railway and coach stations, sports events, malls, and nightclubs.However, the current WTMD technology and scanning procedures at airports require that all metallic items be removed from clothing prior to scanning, causing inconvenience. Furthermore, alarms are triggered by innocuous items such as shoe shanks and artificial joints, along with overlooked items such as jewellery and belts. These lead to time- consuming, manual pat-down searches, which are found inconvenient, uncomfortable, and obtrusive by some.Modern WTMD portals are very sensitive devices that can detect items with only small amounts of metal, but they currently lack the ability to further classify the detected item. However, if a WTMD portal were able to classify objects reliably into, e.g., “knives”, “belts”, “keys”, the need for removing the items prior to screening would disappear, enabling a paradigm shift in the field of security screening.This thesis is based on novel research presented in five peer-reviewed publications. The scope of the problem has been narrowed down to a situation in which only one metallic item is carried through the portal at a time. However, the methods and results presented in this thesis can be generalized into a multi-object scenario. It has been shown that by using a WTMD portal and the magnetic polarisability tensor, it is possible to accurately distinguish between threatening and innocuous targets and to classify them into 10 to 13 arbitrary classes. Furthermore, a data library consisting of natural walk-throughs has been collected, and it has been demonstrated that the walk-through data collected with the above portal are subject to phenomena that might affect classification, in particular a bias and the so-called body effect. However, the publications show that, by using realistic walk-through data, high classification accuracy can be maintained regardless of the above problems. Furthermore, a self-diagnostics method for detecting unreliable samples has also been presented with potential to significantly increase classification accuracy and the reliability of decision making.The contributions presented in this thesis have a variety of implications in the field of WTMD-based security screening. The novel technology offers more information, such as an indication of the probable cause of the alarm, to support the conventional screening procedure. Moreover, eliminating the need for removing all metallic items prior to screening enables design of new products for scenarios such as sports events, where conventional screening procedures might be inconvenient, creating thus new business possibilities for WTMD manufacturing companies.The positive results give rise to a variety of future research topics such as using wideband data, enabling simultaneous classification of multiple objects, and developing the portal coil design to diminish signal nonlinearities. Furthermore, the ideas and the basic principles presented in this thesis may be applied to other metal detection applications, such as humanitarian demining

An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization

The magnetic polarizability tensor (MPT) has attracted considerable interest due to the possibility it offers for characterizing conducting objects and assisting with the identification and location of hidden targets in metal detection. An explicit formula for its calculation for arbitrary-shaped objects is missing in the electrical engineering literature. Furthermore, the circumstances for the validity of the magnetic dipole approximation of the perturbed field, induced by the presence of the object, are not fully understood. On the other hand, in the applied mathematics community, an asymptotic expansion of the perturbed magnetic field has been derived for small objects and a rigorous formula for the calculation of the MPT has been obtained. The purpose of this paper is to relate the results of the two communities, to provide a rigorous justification for the MPT, and to explain the situations in which the approximation is valid