ITR: Computational Theory and Tools for Reduced-Order Modeling of Very Large Dynamical Systems and Applications

ITR：超大型动力系统和应用降阶建模的计算理论和工具

• 批准号: 0220104
• 负责人: Zhaojun Bai
• 金额: $ 31.75万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-09-15 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0220104&HistoricalAwards=false
• 关键词: ITR; Computational; Theory; Tools; Reduced

The continual and compelling need for accurately and efficiently simulating dynamical behavior of physical systems arising from a wide variety of applications has led to increasingly large and complex models. Reduced-order modeling (ROM), also called model reduction, techniques play an indispensable role in providing efficient computational prototyping tools to replace such large-scale models by approximate smaller models. Such reduced-order models must be capable of capturing critical dynamical behavior and faithfully preserving essential properties of the larger models they approximate. An accurate and effiective reduced-order model can be applied for steady-state analysis, transient analysis, or sensitivity analysis of large-scale models and the physical systems they emulate. Consequently, scientists and engineers can significantly reduce design time and pursue more aggressive design strategies. Designers can try ``what-if" experiments in hours instead of days.In this proposal, we propose a broad range of synergistic research activities on ROM relating to three interlinking strands: computational theory, reliable algorithms, and high-performance software tools. We will also be actively involved with promoting applications of ROM techniques and testing our methods through existing and new collaborations with researchers in circuit simulation, structural dynamics, control systems, and microelectromechanical systems (MEMS). Specifically, our proposed research activities on computational theory and algorithms include: Accuracy estimation in both time and frequency domains. Sensitivity analysis of linear systems using the techniques of ROM and statistical condition estimation. Development of ROM techniques that directly exploit so-called second-order model structures and generate a reduced-order model in second-order form. Exploration of a framework of ROM techniques for certain types of large-scale nonlinear systems of technological importance.

对准确有效地模拟各种应用所产生的物理系统的动态行为的持续和迫切的需求导致了模型越来越大和复杂。降阶建模（ROM），也称为模型缩减，技术在提供高效的计算原型工具以用近似较小的模型替代大规模模型方面发挥着不可或缺的作用。这种降阶模型必须能够捕获关键的动态行为并忠实地保留它们近似的较大模型的基本属性。准确有效的降阶模型可应用于大型模型及其模拟的物理系统的稳态分析、瞬态分析或灵敏度分析。因此，科学家和工程师可以显着减少设计时间并追求更积极的设计策略。设计人员可以在数小时而不是数天内尝试“假设”实验。在本提案中，我们提出了一系列与三个相互关联的链相关的 ROM 协同研究活动：计算理论、可靠算法和高性能软件工具。我们还将通过与电路仿真、结构动力学、控制系统和微机电系统 (MEMS) 领域的研究人员现有和新的合作，积极参与推广 ROM 技术的应用并测试我们的方法。算法包括：使用 ROM 和统计条件估计技术进行线性系统的精度估计，直接利用所谓的二阶模型结构并生成二阶降阶模型。探索用于某些类型的具有技术重要性的大规模非线性系统的 ROM 技术框架。