Time Series Analysis Techniques for Transient Electro- and Magneto-Quasistatic Field Simulations

• Applicant: Professor Dr. Markus Clemens
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering ; Electrical Energy Systems, Power Management, Power Electronics, Electrical Machines and Drives ; Mathematics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 425887141

• Final Report Year: 2024

Final Report Abstract

The project explores advanced methodologies for linear/nonlinear subdomain identification, focusing on temporal sensitivities and on the frequency composition of local time-series. Two primary approaches are discussed. The first one utilizes the maximum derivative of time signals associated with each degree of freedom characterizing overall sensitivity, while the second one employs the entropy of the power spectra associated with the frequency distributions of the degrees of freedom. The results demonstrate the effectiveness of global quantifiers in automatically identifying nodes high in information content. These methods prove computationally efficient, robust, and suitable for black-box model order reduction (MOR) implementations. Comparative studies against standard MOR methods like DEIM and gappy-POD highlight their competitive accuracy. The research establishes a therithm, proving its ε-accuracy for future states under certain conditions. Fidelity regions, oretical foundation for the minimum entropy snapshot/state sampling (MESS) algogoverned by a fidelity inequality, are presented, and the dynamical fidelity index (DFI) is introduced to estimate an upper bound for the future index. MESS is then positioned as a noise removal filter in constructing nonlinear principal curves for noisy datasets. Another focus of this project is on recurrence studies in dynamical systems, introducing a scaling-analysis framework to automate the selection of a suitable recurrence threshold. The CREST (critical recurrence scale threshold) set and scale spectrum are defined to quantify attractor complexity and persistency, aiding in tasks like reduction and surrogate modeling. The research concludes with a comprehensive approach to understanding and analyzing complex dynamical systems through innovative algorithms and theoretical foundations.

Publications

• Kernel-Based Regression in Transient Nonlinear Electro-Quasistatic Field Simulations. 2020 IEEE 19th Biennial Conference on Electromagnetic Field Computation (CEFC), 1-4. IEEE.
  Zhang, Dudu; Kasolis, Fotios; Jorgens, Christoph & Clemens, Markus
  
• Energy-Variation Analysis and Orbit-Complexity Quantification. Journal of Physics: Conference Series, 2090(1), 012086.
  Kasolis, Fotios & Clemens, Markus
  
• Maximum entropy snapshot sampling for reduced basis modelling. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 41(3), 954-966.
  Bannenberg, Marcus W.F.M.; Kasolis, Fotios; Günther, Michael & Clemens, Markus
  
• A comparative study on electromagnetic quasistatic time‐domain field calculations. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 36(3).
  Henkel, Marvin‐Lucas; Kasolis, Fotios; Schöps, Sebastian & Clemens, Markus
  
• Critical recurrence scale thresholds. Institute of Electrical and Electronics Engineers (IEEE).
  Kasolis, Fotios & Clemens, Markus
  
• Low-Frequency Stable Electro-Quasistatic Field Formulations Based on Penalty Approximations of Continuous Extensions, CEM 2023, Cannes, France, 11.-14.04.2023. Abstract accepted, 2022.
  F. Kasolis, M. Henkel & M. Clemens
  
• A GPU Accelerated Semi-Implicit Method for Large-Scale Nonlinear Eddy-Current Problems Using Adaptive Time Step Control. 2024 IEEE 21st Biennial Conference on Electromagnetic Field Computation (CEFC), 1-2. IEEE.
  Kähne, Bernhard & Clemens, Markus
  
• A Gradient-Divergence Operator-Regularized Electromagneto-Quasistatic Field Formulation. IEEE Transactions on Magnetics, 60(3), 1-4.
  Henkel, Marvin-Lucas; Kasolis, Fotios & Clemens, Markus
  
• Efficient Low-Frequency Human Exposure Assessment with the Maximum Entropy Snapshot Sampling. 2024 IEEE 21st Biennial Conference on Electromagnetic Field Computation (CEFC), 1-2. IEEE.
  Stroka, Steven; Kasolis, Fotios; Haußmann, Norman & Clemens, Markus
  
• Iterative Charge-Update Schemes for Electro-quasistatic Problems. Mathematics in Industry, 94-101. Springer Nature Switzerland.
  Kasolis, Fotios; Henkel, Marvin-Lucas & Clemens, Markus