Chair of Electromagnetic Theory

Time Series Analysis Techniques for Transient Electro- and Magneto-quasi-static field simulations

Project title (German)
Zeitreihenanalyse Techniken für transiente elektro- und magneto-quasistatische Feldsimulationen

Project manager
Prof. Dr. rer. nat. Markus Clemens

Project member
Dr. Fotios Kasolis

Project duration
01.04.2020 - 31.03.2023

Reduced-order method, Circuit analysis, Model order reduction, Numerical linear algebra, Electro-quasistatic fields, Transient analysis, Implicit time integration, Start value estimation, Kernel-based regression, Entropy, Recurrent states, Snapshot sampling

Deutsche Forschungsgemeinschaft (DFG) under grant no. CL143/18-1.

Project description

The aim of this research project is to develop and analyze improved model order reduction schemes for discretized models of nonlinear transient electro- and magneto-quasi-static field problems based on time series analyis techniques (information theory, nonlinear dynamics, and statistical methods). Transient electro-quasi-static field simulations based on discretization methods, such as the Finite Elements Methods (FEM), are commonly used for the design of electrical power transmission equipment, especially when using materials with nonlinear electrical conductivity properties to control the electric field distributions. FEM simulations are often used within the design process of electro-mechanical and electro-thermal energy conversion systems, e.g., electrical machines, magnetical actuators, or inductive heating and charging devices, to numerically compute transient magneto-quasi-static field problems, so-called eddy current problems. In this context, the behavior of ferromagnetic materials is responsible for the typical nonlinearity of the used FEM models. Considering that phenomena depending on varying time and existing nonlinearity generally exhibit complex and unsystematic time evolution, the usually used reduced basis obtianed with singular value decomposition via, e.g., Discrete Empirical Interpolation Method (DEIM) -- a variant of the Proper Orthogonal Decomposition (POD) method for model order reduction of nonlinear problems -- can fail due to the weak separability of some time domain signals. Within this research project, noval model order reduction methods shall be develoed based on informational and statistical concepts of entropy and divergence and used as measure for the "relative" information content of a time signal -- in the research context in the form of time discretized elctro- or magneto-quasi-static field solutions. This approach involves the development of alternatives to the non-optimal interpolation node selection with a Greedy approach, which is commonly applied in nonlinear model order reduction methods, such as DEIM, and in many cases leads to unreliable reduced models. In addition, this research project aims to utilize the capabilities of the recently introduced strategies originating in nonlinear dynamical systems theory in the transient signal analysis of time-discretized electro- and magento-quasi-static field solutions in FEM simulations. The focus is on effective snashot selection, an automated domain decomposition of the spatially discretized field problem into subspaces with only linear, weakly, or strongly nonlinear solution behavior as well as possible mesh refinement techniques for adaptive spatial discretizations.

Project-related publications

S. Stroka, F. Kasolis, N. Haussmann and M. Clemens, "Efficient Low-Frequency Human Exposure Assessment with the Maximum Entropy Snapshot Sampling", 21st Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2024), Jeju, Korea, 02.-05.06.2024, Nov. 2023.
F. Kasolis and M. Clemens, "Critical Recurrence-Scale Thresholds", 21th International Conference of Numerical Analysis and Applied Mathematics 2023 (ICNAAM 2023), Heraklion, Crete, Greece, 11.-17.09.2023, Four page extended abstract submitted, 02 2023.
M. W. F. M. Bannenberg, F. Kasolis, M. Günther and M. Clemens, "Maximum Entropy Snapshot Sampling for Reduced Basis Modelling", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 41, no. 3, pp. 954-966, 2022. Emerald Publishing Limited.
D. Zhang, F. Kasolis, C. Jörgens and M. Clemens, "Kernel-Based Regression in Transient Nonlinear Electro-Quasistatic Field Simulations", IEEE 19th Biennial Conference on Electromagnetic Field Computation (CEFC 2020), Pisa, Italy, 16-18 November 2020, IEEE, 06 2021, pp. 1-4.
F. Kasolis and M. Clemens, "Energy-Variation Analysis and Orbit Complexity Quantification", Journal of Physics: Conference Series, vol. 2090, no. 1, pp. 012086, 2021. IOP Publishing.
F. Kasolis and M. Clemens, "Entropy Snapshot Filtering for QR-based Model Reduction of Transient Nonlinear Electro-Quasistatic Simulations", IEEE Transactions on Magnetics (Early access) January 09, 2020, vol. 56, no. 2, Jan. 2020. IEEE.
F. Kasolis and M. Clemens, "Maximum Entropy Snapshot Sampling for Reduced Basis Generation", arXiv:2005.01280, 2020. arXiv,
M. W. F. M. Bannenberg, F. Kasolis, M. Günther and M. Clemens, "Maximum Entropy Snapshot Sampling Reduction of a Diode Chain Model", 17th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering (IGTE 2020), Graz, Austria, 20.-23.09.2020, 2020, pp. 1.
F. Kasolis and M. Clemens, "Information-Based Model Reduction for Nonlinear Electro-Quasistatic Problems", Journal on Computational Physics, November 2019. Early online publication, Nov. 2019.
F. Kasolis and M. Clemens, "An Entropy-Based Sampling Framework for Reducing Large-Scale Nonlinear Field Problems in the Electro-Quasistatic Limit", Nineteenth Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2020), 18.-22.04.2020, Pisa, Italy. One page digest, accepted, 2019.
F. Kasolis, D. Zhang and M. Clemens, "Recurrent Quantification Analysis for Model Order Reduction of Nonlinear Transient Electro-Quasistatic Field Problems", 21st Edition of the International Conference on Electromagnetics in Advanced Applications and 9th edition of the IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (ICEAA-IEEE APWC 2019), Granada, Spain, 09.-13.09.2019, IEEE, 2019.

ISBN: 978-1-7281-0563-5

F. Kasolis and M. Clemens, "Snapshot Selection Criteria for Model Order Reduction", Eighteenth Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2018), 28.-31.10.2018, Hangzhou, VRC. Full paper submitted to IEEE Transactions on Magnetics, Okt. 2018.

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