Numerical Optimization for Electromagnetic Problems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 4250

Special Issue Editors


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Guest Editor
Institute of Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Graz, Austria
Interests: numerical solution of partial differential equations; modeling and numerical simulation of coupled field problems (electromagnetics; magneto-mechanics; piezoelectrics; aeroacoustics; vibro-acoustics); material models and parameter identification (combined experimental and numerical techniques); meta-materials

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Guest Editor
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria
Interests: topology optimization; topological derivatives; shape optimization; optimization of electrical machines

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Guest Editor
Institute of Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Graz, Austria
Interests: optimization; inverse problems; modeling and simulation; biomedical engineering

Special Issue Information

Dear Colleagues,

We cordially invite you to submit your articles to the Special Issue of Mathematics entitled “Numerical Optimization for Electromagnetic Problems”. The title of the Special Issue not only reflects the topicality of the Special Issue itself but is also associated with the 17th International Workshop on Optimization and Inverse Problems in Electromagnetism 2023 that will take place in Graz, Austria from the 17–20 September 2023. Our aim is to discuss and share recent developments in optimization and inverse methodologies and their applications to the design and working principle of electromagnetic devices. A special focus will be put on topology optimization and optimal energy management.

We would like to invite authors to submit an extended version of their conference papers for this Special Issue. However, we want to mention that this Special Issue is also open to submissions from authors who are interested in the topic but did not attend the workshop.

Topics of interest include but are not limited to:

  1. Theoretical aspects and fundamentals
    • Mathematical theory and formulation of inverse and optimization problems;
    • Neural meta-modelling;
    • Regularization techniques;
    • (Model) order reduction;
    • Identification problems;
    • Sensitivity analysis.
  2. Algorithms
    • Machine learning techniques for optimization and inverse problems;
    • Reconstruction techniques;
    • Deterministic, stochastic and hybrid techniques;
    • Multi-objective and multi-level optimization;
    • Heuristic approaches;
    • Design of experiments;
    • Constraints;
    • Robust optimization under uncertainty;
    • Objective functions and direct problems;
    • Numerical efficiency;
    • Numerical problems.
  3. Applications
    • Optimal energy management;
    • Biomedical engineering;
    • Control systems;
    • Coupled problems;
    • Electrical machines;
    • Industrial and biomedical tomography;
    • Information and communication systems;
    • Large-scale systems;
    • Mechatronics;
    • Micro- and nanosystems;
    • Non-destructive evaluation;
    • Design optimization;
    • Sensors and actuators;
    • Smart applications;
    • Transportation and mobility;
    • High frequency and antenna design.

Prof. Dr. Manfred Kaltenbacher
Dr. Peter Gangl
Dr. Alice Reinbacher-Köstinger
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical method
  • numerical techniques
  • Maxwell's equation
  • inverse problems
  • optimization methods
  • regularization techniques
  • (model) order reduction
  • identification problems
  • machine learning
  • multiscale modeling
  • electromagnetic problems
  • magnetohydrodynamics
  • various applications
  • electromagnetic scattering

Published Papers (6 papers)

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Research

13 pages, 6907 KiB  
Article
Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties: Numerical Case Study
by Manfred Kaltenbacher, Andreas Gschwentner, Barbara Kaltenbacher, Stefan Ulbrich and Alice Reinbacher-Köstinger
Mathematics 2024, 12(10), 1586; https://doi.org/10.3390/math12101586 - 19 May 2024
Viewed by 417
Abstract
We are interested in the determination of the local nonlinear magnetic material behaviour in electrical steel sheets due to cutting and punching effects. For this purpose, the inverse problem has to be solved, where the objective function, which penalises the difference between the [...] Read more.
We are interested in the determination of the local nonlinear magnetic material behaviour in electrical steel sheets due to cutting and punching effects. For this purpose, the inverse problem has to be solved, where the objective function, which penalises the difference between the measured and the simulated magnetic flux density, has to be minimised under a constraint defined according to the corresponding partial differential equation model. We use the adjoint method to efficiently obtain the gradients of the objective function with respect to the material parameters. The optimisation algorithm is low-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS), the forward and adjoint formulations are solved using the finite element (FE) method and the ill-posedness is handled via Tikhonov regularisation, in combination with the discrepancy principle. Realistic numerical case studies show promising results. Full article
(This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems)
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18 pages, 1170 KiB  
Article
Robust Design Optimization of Electric Machines with Isogeometric Analysis
by Theodor Komann, Michael Wiesheu, Stefan Ulbrich and Sebastian Schöps
Mathematics 2024, 12(9), 1299; https://doi.org/10.3390/math12091299 - 25 Apr 2024
Viewed by 696
Abstract
In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the [...] Read more.
In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the design of a three-phase, six-pole permanent magnet synchronous motor (PMSM). The geometry is constructed in a two-dimensional framework within MATLAB®, employing isogeometric analysis (IGA) to enable flexible shape optimization. The main contributions of this research are twofold. First, we integrate shape optimization with parameter optimization to enhance the performance of PMSM designs. Second, we use robust optimization, which creates a min–max problem, to ensure that the motor maintains its performance when facing uncertainties. To solve this bilevel problem, we work with the maximal value functions of the lower-level maximization problems and apply a version of Danskin’s theorem for the computation of generalized derivatives. Additionally, the adjoint method is employed to efficiently solve the lower-level problems with gradient-based optimization. The paper concludes by presenting numerical results showcasing the efficacy of the proposed robust optimization framework. The results indicate that the optimized PMSM designs not only perform competitively compared to their non-robust counterparts but also show resilience to operational and manufacturing uncertainties, making them attractive for industrial applications. Full article
(This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems)
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20 pages, 5461 KiB  
Article
Solid Isotropic Material with Penalization-Based Topology Optimization of Three-Dimensional Magnetic Circuits with Mechanical Constraints
by Zakaria Houta, Thomas Huguet, Nicolas Lebbe and Frédéric Messine
Mathematics 2024, 12(8), 1147; https://doi.org/10.3390/math12081147 - 11 Apr 2024
Viewed by 735
Abstract
Topology optimization is currently enjoying renewed interest thanks to the recent development of 3D printing techniques, which offer the possibility of producing these new complex designs. One of the difficulties encountered in manufacturing topologically optimized magnetostatic structures is that they are not necessarily [...] Read more.
Topology optimization is currently enjoying renewed interest thanks to the recent development of 3D printing techniques, which offer the possibility of producing these new complex designs. One of the difficulties encountered in manufacturing topologically optimized magnetostatic structures is that they are not necessarily mechanically stable. In order to take this mechanical constraint into account, we have developed a SIMP-based topology optimization algorithm which relies on numerical simulations of both the mechanical deformation and the magnetostatic behavior of the structure. Two variants are described in this paper, respectively taking into account the compliance or the von Mises constraint. By comparing the designs obtained with those from magnetostatic optimization alone, our approach proves effective in obtaining efficient and robust designs. Full article
(This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems)
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12 pages, 4869 KiB  
Article
Efficient Jacobian Computations for Complex ECT/EIT Imaging
by Markus Neumayer, Thomas Suppan, Thomas Bretterklieber, Hannes Wegleiter and Colin Fox
Mathematics 2024, 12(7), 1023; https://doi.org/10.3390/math12071023 - 28 Mar 2024
Viewed by 667
Abstract
The reconstruction of the spatial complex conductivity σ+jωε0εr from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography. Regularized Gauß-Newton schemes have been proposed for their solution. [...] Read more.
The reconstruction of the spatial complex conductivity σ+jωε0εr from complex valued impedance measurements forms the inverse problem of complex electrical impedance tomography or complex electrical capacitance tomography. Regularized Gauß-Newton schemes have been proposed for their solution. However, the necessary computation of the Jacobian is known to be computationally expensive, as standard techniques such as adjoint field methods require additional simulations. In this work, we show a more efficient way to computationally access the Jacobian matrix. In particular, the presented techniques do not require additional simulations, making the use of the Jacobian, free of additional computational costs. Full article
(This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems)
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14 pages, 2989 KiB  
Article
A Source Identification Problem in Magnetics Solved by Means of Deep Learning Methods
by Sami Barmada, Paolo Di Barba, Nunzia Fontana, Maria Evelina Mognaschi and Mauro Tucci
Mathematics 2024, 12(6), 859; https://doi.org/10.3390/math12060859 - 15 Mar 2024
Viewed by 779
Abstract
In this study, a deep learning-based approach is used to address inverse problems involving the inversion of a magnetic field and the identification of the relevant source, given the field data within a specific subdomain. Three different techniques are proposed: the first one [...] Read more.
In this study, a deep learning-based approach is used to address inverse problems involving the inversion of a magnetic field and the identification of the relevant source, given the field data within a specific subdomain. Three different techniques are proposed: the first one is characterized by the use of a conditional variational autoencoder (CVAE) and a convolutional neural network (CNN); the second one employs the CVAE (its decoder, more specifically) and a fully connected deep artificial neural network; while the third one (mainly used as a comparison) uses a CNN directly operating on the available data without the use of the CVAE. These methods are applied to the magnetostatic problem outlined in the TEAM 35 benchmark problem, and a comparative analysis between them is conducted. Full article
(This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems)
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26 pages, 5521 KiB  
Article
Innovative Approach for the Determination of a DC Motor’s and Drive’s Parameters Using Evolutionary Methods and Different Measured Current and Angular Speed Responses
by Marko Jesenik, Miha Ravber and Mislav Trbušić
Mathematics 2024, 12(1), 42; https://doi.org/10.3390/math12010042 - 22 Dec 2023
Viewed by 596
Abstract
The determination is presented of seven parameters of a DC motor’s drive. The determination was based on a comparison between the measured and simulated current and speed responses. For the parameters’ determination, different evolutionary methods were used and compared to each other. The [...] Read more.
The determination is presented of seven parameters of a DC motor’s drive. The determination was based on a comparison between the measured and simulated current and speed responses. For the parameters’ determination, different evolutionary methods were used and compared to each other. The mathematical model presenting the DC drives model was written using two coupled differential equations, which were solved using the Runge–Kutta first-, second-, third- and fourth-order methods. The approach allows determining the parameters of controlled drives in such a way that the controller is taken into account with the measured voltage. Between the tested evolutionary methods, which were Differential Evolution with three strategies, Teaching-Learning Based Optimization and Artificial Bee Colony, the Differential Evolution (DE/rand/1/exp) can be suggested as the most appropriate for the presented problem. Measurements with different sampling times were used, and it was found out that at least some measuring points should be at the speed-up interval. Different lengths of the measured signal were tested, and it is sufficient to use a signal consisting of the drive’s acceleration and a short part of the stationary operation. The analysis showed that the procedure has good repeatability. The biggest deviation of calculated parameters considering 10 repeated measurements was 6% in case of the La calculation. The deviations of all the other parameters’ calculations were less than 2%. Full article
(This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems)
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