Collaborative Research: Global/Local System Identification of Strongly Nonlinear Dynamical Systems

合作研究：强非线性动力系统的全局/局部系统辨识

• 批准号: 0927995
• 负责人: Alexander Vakakis
• 金额: $ 26.91万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0927995&HistoricalAwards=false
• 关键词: Collaborative; Research; Global; Local; System

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The research objective of this award is to develop a method for system identification that is applicable to a general class of dynamical systems with nonlinear, time-varying and non-smooth effects. This is dictated by the realization that as engineering systems become more complex reflecting multi-physical effects and possessing responses across different time and frequency scales, the likelihood exists that they will exhibit strongly nonlinear and nonstationary behavior, sensitive to initial and forcing conditions and parameter uncertainty. Examples include structures with loose mechanical joints undergoing vibro-impacts, and ultra-flexible structural components with strong geometric nonlinearities. The approach relies solely upon direct time series measurement and post-processing, leading to dual global / local identification of the dynamics and data-driven reduced order models (ROMs). Key to this approach are slow/fast partitions of the measured time series, which when combined with powerful post-processing algorithms lead to identification of the dimensionality of the governing dynamics and derivation of accurate ROMs with many applications, including control-oriented design, condition monitoring, and damage detection.If successful, this research can have immediate impact and be transformative in the fields of system identification and structural health monitoring. Indeed, the capacity of the proposed method to separate smooth from non-smooth effects in measured time series allows for rapid detection of non-smooth dynamics often associated with damage (i.e., cracks, failed bearing, etc.). Results will be disseminated to encourage application. Outreach activities will be undertaken, particularly in the vicinity of New Mexico State University (NMSU) which has a large population of underrepresented minority students, through mentoring programs, laboratory visits by high school students, and teacher training in the area of dynamical systems. The PIs plan to work with the Society of Hispanic Engineers and the New Mexico Alliance for Minority Participation, and other organizations at NMSU to increase the enrollment and graduation rate of underrepresented groups in engineering.

该奖项根据 2009 年美国复苏和再投资法案（公法 111-5）提供资助。该奖项的研究目标是开发一种系统识别方法，该方法适用于一般类型的非线性、时间动态系统。变化的和不平滑的效果。 这是由于认识到，随着工程系统变得更加复杂，反映多物理效应并在不同时间和频率尺度上拥有响应，它们可能会表现出强烈的非线性和非平稳行为，对初始和强迫条件以及参数不确定性敏感。 例子包括承受振动冲击的松散机械接头的结构，以及具有强几何非线性的超柔性结构部件。该方法仅依赖于直接时间序列测量和后处理，从而实现动态和数据驱动的降阶模型（ROM）的双重全局/局部识别。这种方法的关键是测量时间序列的慢/快划分，当与强大的后处理算法相结合时，可以识别控制动态的维度，并导出具有许多应用的精确 ROM，包括面向控制的设计、条件如果成功，这项研究可以在系统识别和结构健康监测领域产生立竿见影的影响和变革。 事实上，所提出的方法能够在测量的时间序列中区分平滑效应和非平滑效应，从而可以快速检测通常与损坏（即裂纹、失效轴承等）相关的非平滑动力学。 结果将被传播以鼓励申请。 将通过辅导计划、高中生参观实验室以及动力系统领域的教师培训等方式开展外展活动，特别是在新墨西哥州立大学 (NMSU) 附近，该大学拥有大量代表性不足的少数族裔学生。 PI 计划与西班牙裔工程师协会、新墨西哥州少数族裔参与联盟以及新墨西哥州立大学的其他组织合作，提高工程领域代表性不足群体的入学率和毕业率。