CAREER: Model Reduction for Control of Fluids

职业：流体控制的模型简化

• 批准号: 0347239
• 负责人: Clarence Rowley
• 金额: $ 40万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-03-01 至 2010-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0347239&HistoricalAwards=false
• 关键词: CAREER; Model; Reduction; Control; Fluids

Model reduction for control of fluidsC. W. RowleyAbstractMany powerful techniques are available for analyzing and controlling dynamical systems, if one has a tractable mathematical model, for instance in the form of a differential equation. For fluids, and many other systems of interest, models are well known, but are too complex for traditional techniques from dynamical systems and control theory to be practical. This program develops techniques for obtaining simpler models of complex systems, in order to provide a bridge between interesting multiscale applications, and the mathematical tools useful for their analysis and control. The techniques will then be used to address problems in fluid mechanics, focusing on controlling transition to turbulence in a plane channel.Specific model reduction techniques addressed will include balanced truncation and Proper Orthogonal Decomposition (POD), and symmetry reduction methods from geometric mechanics. Each of these techniques has severe limitations when applied to fluids problems. POD often produces highly unreliable models, and often the accuracy of the models does not improve as the number of modes increases. Balanced truncation applies to stable linear systems, and has good error bounds that improve as the number of modes increases, but the method is not tractable for very large systems such as fluids. A central component of the research involves a new method for performing "balanced POD," which may be viewed as form of weighted POD that more heavily weights states of large dynamical importance. In addition, ideas from symmetry reduction, and heirarchical finite-element modeling combine to guide the development of local versions of POD and balanced truncation, which will capture traveling structures better than the global basis functions produced by standard POD and balanced truncation.The educational components of the program include developing an exchange program with Brazil, in order to promote engineering education in an international setting. In addition, a new outreach program will help local elementary school teachers introduce engineering into K-6 classrooms, by organizing undergraduates to volunteer their time to assist with the technical aspects of engineering projects.

流体控制的模型降阶。如果一个人有一个易于处理的数学模型，例如以微分方程的形式，就可以使用许多强大的技术来分析和控制动态系统。对于流体和许多其他感兴趣的系统，模型是众所周知的，但对于动力系统和控制理论的传统技术来说，模型太复杂了，无法实用。这个项目开发了获得复杂系统的更简单模型的技术，以便在有趣的多尺度应用程序和对其分析和控制有用的数学工具之间建立桥梁。这些技术将被用来解决流体力学中的问题，重点是控制平面通道中的湍流过渡。具体的模型降阶技术将包括平衡截断和适当的正交分解(POD)，以及几何力学中的对称性降阶方法。当应用于流体问题时，这些技术每一种都有严重的局限性。Pod经常产生非常不可靠的模型，并且模型的精度通常不会随着模式数量的增加而提高。平衡截断适用于稳定的线性系统，具有良好的误差界，随着模式数的增加而改善，但该方法对于流体等非常大的系统并不容易处理。这项研究的一个核心部分涉及一种执行“平衡POD”的新方法，该方法可以被视为加权POD的形式，该加权POD对具有较大动力学重要性的状态进行更重的加权。此外，对称性约化和层次化有限元建模的思想相结合，以指导POD和平衡截断的本地版本的开发，该版本将比标准POD和平衡截断产生的全局基函数更好地捕捉旅行结构。该计划的教育组成部分包括与巴西发展交流计划，以促进国际环境下的工程教育。此外，一项新的外展计划将帮助当地小学教师将工程学引入K-6课堂，方法是组织本科生自愿抽出时间协助工程项目的技术方面。