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

Ben Wilson, Paul D. Ledger

International Journal for Numerical Methods in Engineering, Volume: 122, Issue: 8, Pages: 1940 - 1963

Swansea University Author: Ben Wilson

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DOI (Published version): 10.1002/nme.6606

Abstract

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, a...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57534
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spelling 2021-09-08T15:13:45.0123153 v2 57534 2021-08-05 Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition 7aad8167510801e63f1b9879d307c2ca Ben Wilson Ben Wilson true false 2021-08-05 REWI 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. Journal Article International Journal for Numerical Methods in Engineering 122 8 1940 1963 Wiley 0029-5981 1097-0207 finite element method, magnetic polarizability tensor, metal detection, object characterization,reduced order model, spectral, validation 22 3 2021 2021-03-22 10.1002/nme.6606 COLLEGE NANME Reaching Wider COLLEGE CODE REWI Swansea University External research funder(s) paid the OA fee (includes OA grants disbursed by the Library) B. A. Wilson gratefully acknowledges the financial support received from EPSRC in the form of a DTP studentship withproject reference number 2129099. P. D. Ledger gratefully acknowledges the financial support received from EPSRC inthe form of grant EP/R002134/1. 2021-09-08T15:13:45.0123153 2021-08-05T13:43:04.3093775 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Ben Wilson 1 Paul D. Ledger 2 57534__20555__cb55ad49a99d4cfbb3a9cfe10a3169a7.pdf 57534.pdf 2021-08-05T13:49:10.6015468 Output 1857679 application/pdf Version of Record true © 2020 The Authors. This is an open access article under the terms of the Creative Commons Attribution License true eng http://creativecommons.org/licenses/by/4.0/
title Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
spellingShingle Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
Ben Wilson
title_short Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
title_full Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
title_fullStr Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
title_full_unstemmed Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
title_sort Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition
author_id_str_mv 7aad8167510801e63f1b9879d307c2ca
author_id_fullname_str_mv 7aad8167510801e63f1b9879d307c2ca_***_Ben Wilson
author Ben Wilson
author2 Ben Wilson
Paul D. Ledger
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 122
container_issue 8
container_start_page 1940
publishDate 2021
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.6606
publisher Wiley
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description 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.
published_date 2021-03-22T04:13:21Z
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score 11.013619

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