Characterisation and classification of hidden conducting security threats using magnetic polarizability tensors

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. Walk through metal detectors (WTMDs) are commonly deployed for security screening purposes in applications where these attacks are of particular con-cern such as in airports, transport hubs, government buildings and at concerts. However, there is scope to improve the identification of an object's shape and its material proper-ties. Using current techniques there is often the requirement for any metallic objects to be inspected or scanned separately before a patron may be determined to pose no threat, making the process slow. This can often lead to build ups of large queues of unscreened people waiting to be screened which becomes another security threat in itself. To improve the current method, there is considerable potential to use the fields applied and measured by a metal detector since, hidden within the field perturbation, is object characterisation information. The magnetic polarizability tensor (MPT) offers an economical characteri-sation of metallic objects and its spectral signature provides additional object character-isation information. The MPT spectral signature can be determined from measurements of the induced voltage over a range of frequencies for a hidden object. With classification in mind, it can also be computed in advance for different threat and non-threat objects, producing a dataset of these objects from which a machine learning (ML) classifier can be trained. There is also potential to generate this dataset synthetically, via the application of a method based on finite elements (FE). This concept of training an ML classifier trained on a synthetic dataset of MPT based characterisations is at the heart of this work. In this thesis, details for the production and use of a first of its kind synthetic dataset of realistic object characterisations are presented. To achieve this, first a review of re-cent developments of MPT object characterisations is provided, motivating the use of MPT spectral signatures. A problem specific, H(curl) based, hp-finite element discreti-sation is presented, which allows for the development of a reduced order model (ROM), using a projection based proper orthogonal decomposition (PODP), that benefits from a-posteriori error estimates. This allows for the rapid production of MPT spectral signatures the accuracy of which is guaranteed. This methodology is then implemented in Python, using the NGSolve finite element package, where other problem specific efficiencies are also included along with a series of additional outputs of interest, this software is then packaged and released as the open source MPT-Calculator. This methodology and software are then extensively tested by application to a series of illustrative examples. Using this software, MPT spectral signatures are then produced for a series of realistic threat and non-threat objects, creating the first of its kind synthetic dataset, which is also released as the open source MPT-Library dataset. Lastly, a series of ML classifiers are documented and applied to several supervised classification problems using this new syn-thetic dataset. A series of challenging numerical examples are included to demonstrate the success of the proposed methodology.