The term "system identification" can address various levels of the modeling stage. At one extreme, the goal might be to find the number of active states in a system. In one viewpoint, a dimensionality study on nonlinear-system data often starts with the reconstruction of the phase space from a single observable. We have studied the application of delay phase-space reconstructions to chaotic stick-slip systems. Another viewpoint might involve the usage of proper orthogonal decompostion (POD), which can be helpful in determining the number of active modes in an oscillatory system, and also an optimal representation of the form of the modes, which may help in the reduced-order modeling. Our activity in POD is on a separate page.

At the other extreme is parametric identification, in which the actual form of a dynamical system model is known, but unknown parameters need to be identified. We have extended the harmonic-balance identification method to chaotic systems by extracting the unstable periodic orbits from a chaotic set, treating them as periodic solutions to a differential equation with unknown parameters, and balancing harmonics of these unstable solutions to estimate parameters.  We are also investigating ways of extracting damping parameters in free and forced vibration systems--see the friction page.

Support:  NASA Langley Research Center, 4/01-11/02

Publications

• G. Lin, B. F. Feeny, and T. Das, 2008, "Fractional Derivative Reconstruction of Forced Oscillators," Nonlinear Dynamics, to appear.
• Y. Liang and B. F. Feeny, 2008,  “Parametric identification of a chaotic base-excited double pendulum experiment,”  Nonlinear Dynamics, accepted.   Conference version.
  
• Y. Liang and B. F. Feeny, 2006, "Parametric identification of a base-excited single pendulum," Nonlinear Dynamics 46 (1-2) 17-29.  Preprint.
  
• B. F. Feeny and G. Lin, 2004, "Fractional derivatives applied to phase-space reconstructions," Nonlinear Dynamics 38 (1-4) 85-99, special issue on fractional calculus. Preprint.
  
• B. F. Feeny, C.-M. Yuan, and J. Cusumano, 2001, "Parametric Identification of a Magneto-Elastic Oscillator," Journal of Sound and Vibration 247(5) 785-806. (preprint)
• B. F. Feeny, 2000, "Fast multifractal analysis by recursive box covering," International Journal of Bifurcation and Chaos 10(9) 2277-2287. (preprint, figures)
• R. Kappagantu and B. F. Feeny, 2000, "Part 1: Dynamical characterization of a frictionally excited beam," Nonlinear Dynamics 22(4) 317-333. (Preprint).
• R. Kappagantu and B. F. Feeny, 2000, "Part 2: Proper orthogonal modeling of a frictionally excited beam," Nonlinear Dynamics 23(1) 1-11. (Preprint).
• B. F. Feeny and J.-W. Liang, 2000, "Stick-slip and the phase-space reconstruction," in Applied Nonlinear Dynamcis and Chaos of Mechanical Systems with Discontinuities, M. Wiercigroch and B. de Kraker (eds.), pp. 261-291, World Scientific, Singapore. (preprint)
  
• C.-M. Yuan and B. F. Feeny, 1998, "Parametric identification of chaotic systems," Journal of Vibration and Control 4 (4) 405-426. (preprint)
• J. W. Liang and B. F. Feeny, 1998, "Identification of Coulomb and viscous friction from free-vibration decrements," Nonlinear Dynamics 16 (4) 337-347.
• B. F. Feeny, 1997, "Interpreting proper orthogonal modes in vibrations," Mode Localization and Nonlinear Normal Modes, proceedings of the 1997 Design Engineering Technical Conferences, Sacramento, CA, September 14-17, CD-ROM. (similar preprint)
• B. F. Feeny and J. W. Liang, 1997, "Phase-space reconstructions and stick-slip," Nonlinear Dynamics 13 (1), 39-57. (preprint)
• B. F. Feeny and J. W. Liang, 1996, "A decrement method for the simultaneous estimation of viscous and Coulomb friction," Journal of Sound and Vibration 195 (1) 149-154. (preprint)
• G. Lin, 2001, Alternative Methods of Phase Space Reconstruction
• Z. Al-Zamel, 1999, Unstable Periodic Orbit Extraction Error and its Effect on Nonlinear System Parametric Identification, PhD thesis, Michigan State University, East Lansing.
• C. M. Yuan, 1995, A Method of Parametric Identification of Chaotic Systems, PhD thesis, Michigan State University, East Lansing.
• R. Kappagantu, 1997, An Optimal Modal Reduction for Frictionally Excited Systems, PhD thesis, Michigan State University.