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态系统的系统识别方法。 这是由于工程系统变得越来越复杂，反映多物理效应，并拥有不同的时间和频率尺度的响应，可能存在的，他们将表现出强烈的非线性和非平稳行为，敏感的初始和强制条件和参数的不确定性。 例如，具有松散机械接头的结构经受振动冲击，以及具有强几何非线性的超柔性结构部件。该方法完全依赖于直接的时间序列测量和后处理，导致双重全球/本地识别的动态和数据驱动的降阶模型（ROM）。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，可以识别控制动力学的维度，并导出具有许多应用的精确ROM，包括面向控制的设计，状态监测和损伤检测。如果成功，这项研究可以立即产生影响，并在系统识别和结构健康监测领域产生变革。 实际上，所提出的方法在测量的时间序列中将平滑效应与非平滑效应分离的能力允许快速检测通常与损坏相关联的非平滑动态（即，裂缝、轴承失效等）。 研究结果将予公布，以鼓励申请。 将开展外联活动，特别是在新墨西哥州州立大学附近，因为该大学有大量代表性不足的少数民族学生，将通过辅导方案、高中学生的实验室参观和动力系统领域的教师培训开展这些活动。PI计划与西班牙裔工程师协会和新墨西哥州少数民族参与联盟以及NMSU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。

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.