A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

Seoane, M.; Ledger, P.D.; Gil, Antonio J.; Zlotnik, Sergio; Mallett, M. J. D.

doi:10.1002/nme.6369

Cited by 11 publications

(45 citation statements)

References 34 publications

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“…In particular, in Section 4.1, we describe a ROM based on the POD method 21,22,35,40 and, in Section 4.2, apply the variant called projection based POD (which we denote by PODP), which has already been shown to work well in the analysis of magnetomechanical coupling applied to MRI scanners. 22 To emphasize the generality of the approach, the formulation is presented for an arbitrary list of problem parameters denoted by . In Section 4.3 we derive a procedure for computing certificates of accuracy on the ROM solutions with negligible additional cost.…”

Section: Reduced Order Model (Rom)mentioning

confidence: 99%

“…Note, since M < N ≪ N d , this is significantly smaller than (16) and, therefore, substantially computationally cheaper to solve. After solving this reduced system, and obtaining p M ( ), we obtain an approximate solution for (1,hp) ( , ) using (22).…”

Section: Projection-based Proper Orthogonal Decomposition (Podp)mentioning

confidence: 99%

“…Thus, reducing both the computation cost and time to produce a solution for each new

ω

. In particular, in Section 4.1, we describe a ROM based on the POD method 21,22,35,40 and, in Section 4.2, apply the variant called projection based POD (which we denote by PODP), which has already been shown to work well in the analysis of magnetomechanical coupling applied to MRI scanners 22 . To emphasize the generality of the approach, the formulation is presented for an arbitrary list of problem parameters denoted by

ω

.…”

Section: Reduced Order Model (Rom)mentioning

confidence: 99%

“…Reduced order models (ROMs) based on POD have been successfully applied to efficiently generate solutions for new problem parameters using a small number representative full order model solutions (often called snapshots, e.g., References 21,22) in a range of engineering applications including mechanics, 28,29 thermal problems, 30,31 fluid flow 32,33 as well as electromagnetic problems with application to integrated circuits 34 and recently to coupled magnetomechanical problems. 22 However, ROMs have not been applied to the computation of MPT spectral signatures. A review of current POD techniques is provided in References 21,35. The main novelty of the work is the application of a POD approach to the efficient and accurate computation of the MPT spectral signature and the derivation of a posteriori error estimates of the accuracy of reduced order predictions of the MPT coefficients with respect to those obtained with FEM.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Wilson

Ledger

2021

Numerical Meth Engineering

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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.

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Section: Reduced Order Model (Rom)mentioning

confidence: 99%

Section: Projection-based Proper Orthogonal Decomposition (Podp)mentioning

confidence: 99%

“…Thus, reducing both the computation cost and time to produce a solution for each new

ω

ω

.…”

Section: Reduced Order Model (Rom)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Wilson

Ledger

2021

Numerical Meth Engineering

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Reduced order modelling using neural networks for predictive modelling of 3d-magneto-mechanical problems with application to magnetic resonance imaging scanners

Miah,

Sooriyakanthan,

Ledger

et al. 2023

Engineering with Computers

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The design of magnets for magnetic resonance imaging (MRI) scanners requires the numerical simulation of a coupled magneto-mechanical system where the effects that different material parameters and in-service loading conditions have on both imaging and MRI performance are key to aid with the design and the manufacturing process. To correctly capture the complex physics, and to obtain accurate solutions, finite element simulations with dense meshes and high order elements are needed. Reduced order model approaches, based on the established proper orthogonal decomposition (POD) approach, are attractive as they can rapidly predict the numerical simulations needed under changing parameters or conditions. However, the projected (PODP) approach has an invasive computational implementation, whilst the interpolated (PODI) approach presents challenges when the dimension of the space of parameters to be investigated becomes large. As an alternative, we investigate a POD technique based on using a neural network regression, which is not as invasive as PODP, but has superior approximation properties compared to PODI. We apply this to the coupled magneto-mechanical system to understand three pressing industrial problems: firstly, the accurate and rapid computation of the resonant frequencies associated with this coupled magneto-mechanical system, secondly, the effects of magnet motion on the Ohmic power and kinetic energy curves, and, thirdly, the prediction of the uncertainty in Ohmic power and kinetic energy curves as a function of exciting frequency for uncertain material parameters.

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A staggered high-dimensional Proper Generalised Decomposition for coupled magneto-mechanical problems with application to MRI scanners

Barroso

Seoane

Gil

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Manufacturing new Magnetic Resonance Imaging (MRI) scanners represents a computational challenge to industry, due to the large variability in material parameters and geometrical configurations that need to be tested during the early design phase. This process can be highly optimised through the employment of user-friendly computational metamodels constructed on the basis of Reduced Order Modelling (ROM) techniques, where high-dimensional parametric offline solutions are obtained, stored and assimilated in order to be efficiently queried in real time. This paper presents a novel Proper Generalised Decomposition (PGD) based metamodel for the analysis of electro-magneto-mechanical interactions in the context of MRI scanner design, with three distinct novelties. First, the paper derives, from scratch, a five-dimensional parametrised offline solution process, expressed in terms of (axisymmetric) cylindrical coordinates, external excitation frequency, electrical conductivity of the embedded shields and strength of the static magnetic field. Second, by exploiting the staggered nature of the coupled problem at hand, an efficient sequential PGD algorithm is derived and compared against a previously published monolithic PGD algorithm. As a third novelty, the paper draws some interesting comparisons against an alternative tailor-made ROM technique, where the electromagnetic equations are solved using a Proper Orthogonal Decomposition model. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and potential of the considered approach, especially in terms of cost reduction.

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A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

Cited by 11 publications

References 34 publications

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

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

Reduced order modelling using neural networks for predictive modelling of 3d-magneto-mechanical problems with application to magnetic resonance imaging scanners

A staggered high-dimensional Proper Generalised Decomposition for coupled magneto-mechanical problems with application to MRI scanners

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