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

点击翻译按钮获取中文摘要

The goal of this research project is to develop methods based on time series analysis techniques (information theory, nonlinear dynamics, statistical methods) in order to manufacture improved reduced order models (ROM) for spatially discretized nonlinear transient electro-quasistatic and magneto-quasistatic field problems. Transient electro-quasistatic field simulations based on spatial discretization schemes as e.g. the finite element method (FEM) are used for the design of electric power transmission systems, especially when featuring electric field stress grading materials with nonlinear electrical conductivity characteristics. Transient magneto-quasistatic field problems, also dubbed as eddy current problems, are often numerically calculated using FEM simulations within the design process of electro-mechanical or electro-thermal energy conversion systems such as e.g. electric machines, magnetic actuators, inductive power transfer and heating devices. Here, ferromagnetic material behavior typically contributes to the nonlinearity of the models involved. Since, in general, phenomena that vary with time and are governed by nonlinear laws may exhibit a complex, unsystematic time evolution, the commonly employed reduced basis that is obtained using a singular value decomposition within the discrete empirical interpolation method (DEIM), i.e., a variant of the proper orthogonal decomposition (POD) method used for the model order reduction of nonlinear problems, may fail due to the the weak separability of some of the field signals. Hence, novel model order reduction methods need to be developed that are based on information geometrical and statistical notions of entropy and divergence, to be used as measures of (relative) information content. Such an approach will involve developing alternatives to the non-optimal greedy interpolation node selection that is commonly used as part of nonlinear model reduction methods such as DEIM and in many cases generates substandard, i.e., non-reliable reduced order models. Furthermore, this research project aims at exploiting the possibilities of the newly introduced strategies with their origin in nonlinear dynamic system theory within the transient signal analysis of time-discrete electro- and magneto-quasistatic field solutions of FEM simulations. The focus of this research aims at an effective snapshot selection, an automated domain decomposition of the spatially discretized field problem into subregions with only linear or weak or strongly non-linear solution behavior as well as possible mesh refinement techniques for adaptive spatial discretization schemes.