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

瞬态电场和磁准静态场仿真的时间序列分析技术

• 批准号: 425887141
• 负责人: Professor Dr. Markus Clemens
• 金额: --
• 依托单位: Lehrstuhl für Theoretische Elektrotechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/425887141?language=en
• 关键词: Time; Series; Analysis; Techniques; Transient

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.

本研究项目的目标是开发基于时间序列分析技术（信息论，非线性动力学，统计方法）的方法，以制造改进的降阶模型（ROM）的空间离散非线性瞬态电准静态和磁准静态场问题。基于空间离散化方案（例如有限元法（FEM））的瞬态电-准静态场模拟用于电力传输系统的设计，特别是当以具有非线性电导率特性的电场应力分级材料为特征时。瞬态磁准静态场问题，也被称为涡流问题，通常在机电或电热能量转换系统的设计过程中使用FEM模拟进行数值计算，例如电机，磁致动器，感应功率传输和加热设备。在这里，铁磁材料的行为通常有助于所涉及的模型的非线性。一般来说，由于随时间变化并受非线性规律支配的现象可能表现出复杂的、非系统的时间演化，因此通常采用的简化基是使用离散经验插值法（DEIM）内的奇异值分解获得的，即，用于非线性问题的模型降阶的本征正交分解（POD）方法的变体可能由于某些场信号的弱可分离性而失败。因此，需要开发新的模型降阶方法，该方法基于熵和发散的信息几何和统计概念，以用作（相对）信息内容的度量。这种方法将涉及开发非最优贪婪插值节点选择的替代方案，该非最优贪婪插值节点选择通常用作非线性模型简化方法（例如DEIM）的一部分，并且在许多情况下生成不合格的，即，不可靠的降阶模型。此外，本研究项目的目的是利用新引入的战略，其起源在非线性动态系统理论的时间离散的电磁准静态场有限元模拟的解决方案的瞬态信号分析的可能性。本研究的重点是一个有效的快照选择，一个自动的区域分解的空间离散化领域的问题，只有线性或弱或强非线性的解决方案的行为，以及可能的网格细化技术的自适应空间离散化计划的子区域。