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

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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.