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

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