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Multivariate Interpolation Methods for Parametric Model Reduction (MIM4PMOR)

用于参数模型缩减的多元插值方法 (MIM4PMOR)

基本信息

批准号：
201063239
负责人：
Professor Dr. Athanasios C. Antoulas
金额：
--
依托单位：
Fachgruppe Computational Methods in Systems and Control Theory
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2011
资助国家：
德国
起止时间：
2010-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/201063239?language=en
关键词：
Multivariate Interpolation Methods Parametric Model

项目摘要

Dynamical systems are a principal tool in modeling and control of physical processes in engineering, economics, the natural and social sciences. In many areas, direct numerical simulation (DNS) has become essential for studying the rich complexity of these phenomena and for the design process. Due to the increasing complexity of the underlying mathematical models, unmatched by the increase in computing power, model reduction has become an indispensable tool in order to facilitate or even enable simulation (in particular parameter studies and uncertainty analysis), control, and optimization of dynamical systems. Here, we will focus on parametrized models where the preservation of parameters as symbolic quantities in the reduced-order model is essential. We will pursue two complementary approaches. The first one starts from empirical data and employs advanced interpolation techniques, overcoming limitations of standard projection methods. The empirical data may be provided by physical experimentation or by DNS. The second approach is model-based and employs a connection between bilinear and linear parameter-varying control systems to derive optimal interpolation conditions. Our common theme is to construct reduced-order models satisfying interpolation and certain optimality conditions. We are proposing to put these techniques on firm mathematical foundations in order to assure accuracy and to derive computationally efficient model reduction algorithms.

动力系统是工程、经济、自然和社会科学中物理过程建模和控制的主要工具。在许多领域，直接数值模拟（DNS）已成为研究这些现象的丰富复杂性和设计过程中必不可少的。由于基础数学模型的复杂性不断增加，计算能力的增加无法与之相比，模型简化已经成为一种不可或缺的工具，以促进甚至实现动态系统的仿真（特别是参数研究和不确定性分析），控制和优化。在这里，我们将集中在参数化模型中的参数作为符号量的降阶模型中的保存是必不可少的。我们将采取两种相辅相成的办法。第一种方法从经验数据出发，采用先进的插值技术，克服了标准投影方法的局限性。经验数据可以通过物理实验或DNS提供。第二种方法是基于模型的，并采用双线性和线性参数变化控制系统之间的连接，以获得最佳插值条件。我们的共同主题是构建降阶模型满足插值和一定的最优性条件。我们建议把这些技术的坚实的数学基础，以确保准确性和计算效率的模型简化算法。