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.

持续而令人信服的需求，需要准确有效地模拟由多种应用引起的物理系统的动力学行为，这导致了越来越大且复杂的模型。还原阶建模（ROM），也称为模型降低，技术在提供有效的计算原型制作工具中起着必不可少的作用，以通过近似较小的模型替换此类大型模型。这样的减少阶模型必须能够捕获关键的动态行为，并忠实地保留其近似模型的基本特性。可以应用准确有效的降低阶模型，以进行大规模模型及其模拟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大大减少设计时间，并追求更具侵略性的设计策略。设计师可以在数小时而不是几天内尝试``什么if-if''实验。在这项建议中，我们提出了与ROM有关的广泛的协同研究活动，与三个相互联系的链接相关：计算理论，可靠的算法和高表演软件工具，我们还将在ROM技术中进行启动和新的方法，并在ROM技术中进行构建，并将其与新的方法相关联，并将其与新的方法进行模拟，并将其与新的方法相关联，并将新的方法与新的方法进行指示，并将新方法与新的方法相关联，并将新的方法与新的方法相关联，并将新的方法与新的方法相关联，并将新的方法与新的方法相关联，并将新的方法与新的方法相关联，并将新的方法与新的方法相关联，并将新的方法与新的方法相关联，并将新的方法与新的方法相关联，那么系统和微机械系统（MEMS）。对于某些类型的大规模非线性技术的技术重要性。