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

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该奖项的研究目标是开发一种适用于具有非线性、时变和非光滑效应的一般动力系统的系统识别方法。这是由于人们认识到，随着工程系统变得越来越复杂，反映了多物理效应，并具有跨不同时间和频率尺度的响应，它们可能会表现出强烈的非线性和非平稳行为，对初始条件和强迫条件以及参数不确定性敏感。例如，具有受振动冲击的松散机械关节的结构，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的时间序列测量和后处理，导致动态和数据驱动的降阶模型（rom）的双重全局/局部识别。该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，可以识别控制动力学的维度，并在许多应用中派生精确的rom，包括面向控制的设计，状态监测和损伤检测。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直接影响和变革。事实上，所提出的方法在测量时间序列中分离光滑和非光滑效应的能力允许快速检测通常与损伤（即裂纹，轴承失效等）相关的非光滑动力学。结果将被传播以鼓励应用。通过指导项目、高中生实验室访问和动力系统领域的教师培训，将开展外展活动，特别是在新墨西哥州立大学（NMSU）附近，该大学有大量未被充分代表的少数民族学生。pi计划与西班牙裔工程师协会、新墨西哥少数民族参与联盟以及新密歇根州立大学的其他组织合作，以提高工程领域未被充分代表的群体的入学率和毕业率。

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.