Generalised Magnetic Polarizability Tensors: Invariants and Symmetry Groups
Lead Research Organisation:
Keele University
Department Name: Faculty of Natural Sciences
Abstract
Characterising and identifying hidden metallic objects has important applications in:
1. Security screening at border controls, public events and transport hubs and detecting threats such as knives and firearms. Knife crime is at its highest recorded level in 10 years in the UK and firearm offences are seeing an increase, many being smuggled into the UK from Europe via ferry routes.
2. The identification of the 110 million current unexploded anti-personal landmines, unexplored ordnance (UXO) such as mortar and cluster bombs in areas of former conflicts. Using current techniques, it has been estimated to take over 1000 years to clear them so that the land can be returned to normal use.
3. Improvements to scrap sorting, which has the potential to improve the recycling of valuable metals.
Going beyond the planned work in the EPSRC funded project EP/R002134/1, a new form of object charactization called a generalised magnetic polarizabilty tensor (GMPT) has been established for highly conducting objects, offering significant advantages over existing small object characterisations. Specifically:
1. Offering the possibility to better discriminate between objects and, hence, the potential to achieve better classification and identification of objects.
2. Being able to use the non-uniform fields generated by a metal detector in a creative way, overcoming the assumption that field is uniform over the object in current small object characterisations, and, hence, achieving better 1.
There is much still to learn about GMPTs and there are open mathematical questions about the appropriate choices of invariants (required for object classification) and using representation theory to determine symmetry groups for symmetrical metallic objects (such as mortar bombs). This project will seek to address these questions, which are required before a revolutionary new type of metal detector offering substantial improvements in the above applications can be built.
1. Security screening at border controls, public events and transport hubs and detecting threats such as knives and firearms. Knife crime is at its highest recorded level in 10 years in the UK and firearm offences are seeing an increase, many being smuggled into the UK from Europe via ferry routes.
2. The identification of the 110 million current unexploded anti-personal landmines, unexplored ordnance (UXO) such as mortar and cluster bombs in areas of former conflicts. Using current techniques, it has been estimated to take over 1000 years to clear them so that the land can be returned to normal use.
3. Improvements to scrap sorting, which has the potential to improve the recycling of valuable metals.
Going beyond the planned work in the EPSRC funded project EP/R002134/1, a new form of object charactization called a generalised magnetic polarizabilty tensor (GMPT) has been established for highly conducting objects, offering significant advantages over existing small object characterisations. Specifically:
1. Offering the possibility to better discriminate between objects and, hence, the potential to achieve better classification and identification of objects.
2. Being able to use the non-uniform fields generated by a metal detector in a creative way, overcoming the assumption that field is uniform over the object in current small object characterisations, and, hence, achieving better 1.
There is much still to learn about GMPTs and there are open mathematical questions about the appropriate choices of invariants (required for object classification) and using representation theory to determine symmetry groups for symmetrical metallic objects (such as mortar bombs). This project will seek to address these questions, which are required before a revolutionary new type of metal detector offering substantial improvements in the above applications can be built.
People |
ORCID iD |
| Paul Ledger (Principal Investigator) |
Publications
Ledger P
(2022)
Minimal Object Characterizations Using Harmonic Generalized Polarizability Tensors and Symmetry Groups
in SIAM Journal on Applied Mathematics
Ledger P
(2022)
Properties of generalized magnetic polarizability tensors
in Mathematical Methods in the Applied Sciences
Ozdeger T
(2022)
Measurement of GMPT Coefficients for Improved Object Characterisation in Metal Detection
in IEEE Sensors Journal
Wilson B
(2022)
Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object classification
in International Journal for Numerical Methods in Engineering
Özdeger T
(2023)
Measuring the Magnetic Polarizability Tensor of Nonsymmetrical Metallic Objects
in IEEE Sensors Journal
| Description | New mathematical results were developed to underpin future new types of metal detection technology, which has the potential to detect threat items (such as firearms and knives) in security screening at border controls, public events and transport hubs, as well as important application in the clearance of anti-personal landmines and unexploded ordnance and the sorting of scrap to recover valuable metals. This involved developing new forms of object characterisations with minimal representations in terms of harmonic polynomials first for a scalar problem relevant for finding hidden magnetic objects in magnetometry and then for the vectorial eddy current problem relevant for finding hidden conducting magnetic objects with metal detection. For the latter, the behaviour of the new forms of object characterisation with frequency was investigated. Computational approaches for computing the basis needed for new forms of minimal object characterisation were released as open source scripts on github. In collaboration with group led by Professor Peyton, The University of Manchester, measurement of the new forms of object characterisation were undertaken and their spectral (frequency behaviour) was shown to be in close agreement with the computed characterisations for a range of different materials. |
| Exploitation Route | This award has shown for the first time that generalised magnetic polarizability tensors can be both measured and computed. These new forms of object characterisation have the potential to lead to new forms of metal detection technology aimed at identifying hidden conducting objects with greater accuracy. This has potential important uses in the defence, manufacturing and security industries. |
| Sectors | Aerospace, Defence and Marine,Manufacturing, including Industrial Biotechology,Security and Diplomacy |
| Description | This project has developed new minimal object characterisations using harmonic polynomials. Compared to previous generalised polarizabilty tensor characterisations, these require fewer coefficients to characterise an object to a given rank. Furthermore, an approach has been developed to determine those coefficients that are invariant to object rotation when an object is a member of a given symmetry group. This approach has the potential to provide invariants for object characterisations using higher polarizabilty tensors and has the potential to be used in the next-generation of detection technology for finding unexploded ordnance and landmines. The results of this research have been published in a number of research articles and have been promoted in research seminars and at conferences. The mathematical developments have been used to develop the Mathematica notebooks that are released as open software on a GitHub page. |
| First Year Of Impact | 2022 |
| Sector | Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Manufacturing, including Industrial Biotechology,Security and Diplomacy |
| Impact Types | Economic |
| Title | HGPTSymmetries |
| Description | Mathematica functions for computing symmetric products of harmonic polynomials invariant under a symmetry group for investigating the symmetries of higher order harmonic generalised polarizability tensor characterisations of objects. |
| Type Of Technology | Software |
| Year Produced | 2022 |
| Impact | Software led to the research article Minimal Object Characterizations Using Harmonic Generalized Polarizability Tensors and Symmetry Groups P. D. Ledger and W. R. B. Lionheart SIAM Journal on Applied Mathematics 2022 82:6, 2057-2079 and a presentation at the IMA Conference on Inverse Problems at the University of Edinburgh in 2022. |
| Description | Talk at IMA Conference on Inverse Problems from Theory to Application 2022 |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Around 50 attendees from academia and industry attended my talk at the IMA Conference on Inverse Problems from Theory to Application that was held in Edinburgh, which sparked questions and discussion afterwards, and led to requests for further information. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Talk at Swansea University |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Postgraduate students |
| Results and Impact | Around 30 attendees listed to the talk at Swansea University, which sparked questions and discussion afterwards, and led to several requests for further information on the material presented. |
| Year(s) Of Engagement Activity | 2022 |