Structure Preserving Model Reduction of Low-Frequency Electromagnetic Problem Based on POD and DEIM

Montier, Laurent; Pierquin, Antoine; Henneron, Thomas; Clénet, S.

doi:10.1109/tmag.2017.2663761

Cited by 12 publications

(13 citation statements)

References 12 publications

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“…Among these methods, the POD is one of the most known and is applied to our problem. In order to conserve the structure of the matrix system during the reduction and to insure the stability, a structure preserving MOR [6] is performed: only the magnetic part of the problem is reduced. Then, a is approximated by means of a reduced basis Ψ such that a Ψa r where the size of a r is much smaller than this of a.…”

Section: A Proper Orthogonal Decompositionmentioning

confidence: 99%

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Data-Driven Model-Order Reduction for Magnetostatic Problem Coupled With Circuit Equations

2018

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Among the model order reduction techniques, the Proper Orthogonal Decomposition (POD) has shown its efficiency to solve magnetostatic and magneto-quasistatic problems in the time domain. However, the POD is intrusive in the sense that it requires the extraction of the matrix system of the full model to build the reduced model. To avoid this extraction, nonintrusive approaches like the Data Driven (DD) methods enable to approximate the reduced model without the access to the full matrix system. In this article, the DD-POD method is applied to build a low dimensional system to solve a magnetostatic problem coupled with electric circuit equations.Index Terms-Data driven, finite element model, model order reduction.

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Section: A Proper Orthogonal Decompositionmentioning

confidence: 99%

“…One of these approaches (DD-POD) [3], builds an approximation of the reduced model from the known inputs and outputs of the full model. In low frequency, a significant number of magnetostatic or magnetodynamic problems have been studied with POD [4], [5], [6], [7] but not with nonintrusive approaches.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Model-Order Reduction for Magnetostatic Problem Coupled With Circuit Equations

2018

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“…To overcome this difficulty, methods such as EIM and DEIM were implemented along with POD [ 19 , 20 ]. Magnetostatic and magnetodynamics nonlinear systems were analyzed using the POD-DIEM method previously.…”

Section: A Formal Mor Framework For Nonlinear Systemmentioning

confidence: 99%

“…Also, Far et al introduced a multiple input case for an electrical machine in [ 18 ]. To incorporate the nonlinearity in the electromagnetic systems, references [ 19 , 20 ] presented the use of the so-called Empirical Interpolation Method (EIM) and Discrete Empirical Interpolation Method (DEIM) along with POD. These methods give a good approximation, but DEIM is a numerically complicated method.…”

Section: Introductionmentioning

confidence: 99%

Design and Parametric Study of the Magnetic Sensor for Position Detection in Linear Motor Based on Nonlinear Parametric model order reduction

Paul

Chang

2017

Sensors

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This paper presents a design approach for a magnetic sensor module to detect mover position using the proper orthogonal decomposition-dynamic mode decomposition (POD-DMD)-based nonlinear parametric model order reduction (PMOR). The parameterization of the sensor module is achieved by using the multipolar moment matching method. Several geometric variables of the sensor module are considered while developing the parametric study. The operation of the sensor module is based on the principle of the airgap flux density distribution detection by the Hall Effect IC. Therefore, the design objective is to achieve a peak flux density (PFD) greater than 0.1 T and total harmonic distortion (THD) less than 3%. To fulfill the constraint conditions, the specifications for the sensor module is achieved by using POD-DMD based reduced model. The POD-DMD based reduced model provides a platform to analyze the high number of design models very fast, with less computational burden. Finally, with the final specifications, the experimental prototype is designed and tested. Two different modes, 90° and 120° modes respectively are used to obtain the position information of the linear motor mover. The position information thus obtained are compared with that of the linear scale data, used as a reference signal. The position information obtained using the 120° mode has a standard deviation of 0.10 mm from the reference linear scale signal, whereas the 90° mode position signal shows a deviation of 0.23 mm from the reference. The deviation in the output arises due to the mechanical tolerances introduced into the specification during the manufacturing process. This provides a scope for coupling the reliability based design optimization in the design process as a future extension.

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“…For example, the entire problem region can be subdivided into air and the laminated media on the one hand and, on the other, the total solution is composed of a large scale and fine scale part. This work focuses on the second aspect which will be called structural model order reduction (SMOR), see also [3,7].…”

Section: Introductionmentioning

confidence: 99%

MOR for the MSFEM of the Eddy Current Problem in Linear Laminated Media

Hollaus¹,

Schöberl²,

Schobinger³

2020

SNE

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The multiscale finite element method has proven to be a powerful method in the simulation of eddy currents in laminated cores. However, the resulting equation systems of the problems relevant in electrical engineering are still too large to be solved conveniently. The use of model order reduction methods to overcome this shortcoming is obvious. The feasibility to exploit the specific approach of the multiscale finite element method in terms of a structural model order reduction method has been studied in this work. A small numerical example shows satisfactory results.

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Structure Preserving Model Reduction of Low-Frequency Electromagnetic Problem Based on POD and DEIM

Cited by 12 publications

References 12 publications

Data-Driven Model-Order Reduction for Magnetostatic Problem Coupled With Circuit Equations

Data-Driven Model-Order Reduction for Magnetostatic Problem Coupled With Circuit Equations

Design and Parametric Study of the Magnetic Sensor for Position Detection in Linear Motor Based on Nonlinear Parametric model order reduction

MOR for the MSFEM of the Eddy Current Problem in Linear Laminated Media

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