Abstract
We present the basic components of a time-domain nonlinear system identification (NSI) method with promise of applicability to a broad class of smooth and non-smooth dynamical systems. The proposed NSI method is based on the close correspondence between analytical and empirical slow-flow dynamics, and relies on direct analysis of measured time series without any a priori assumptions on the system dynamics. The central assumption is that the measured time series can be decomposed in terms of a finite number of oscillating components that are in the form of fast monochromatic oscillations modulated by slow amplitudes. The empirical slow-flow model of the dynamics is obtained from empirical mode decomposition, and its correspondence to the analytical slow-flow model establishes a local nonlinear interaction model (NIM). A NIM consists of a set of intrinsic modal oscillators (IMOs) that can reproduce the measured time series over different time scales and can account for (even strongly) nonlinear modal interactions. Hence, it represents a local model of the dynamics, identifying specific nonlinear transitions. By collecting energy-dependent frequency behaviors from all identified IMOs, a frequency-energy plot (in the modal space) can be constructed, which depicts global features of the dynamical system.
| Original language | English (US) |
|---|---|
| Title of host publication | Modal Analysis Topics - Proceedings of the 29th IMAC, a Conference on Structural Dynamics, 2011 |
| Pages | 513-524 |
| Number of pages | 12 |
| State | Published - Jun 13 2011 |
| Event | 29th IMAC, a Conference on Structural Dynamics, 2011 - Jacksonville, FL, United States Duration: Jan 31 2011 → Feb 3 2011 |
Publication series
| Name | Conference Proceedings of the Society for Experimental Mechanics Series |
|---|---|
| Volume | 3 |
| ISSN (Print) | 2191-5644 |
| ISSN (Electronic) | 2191-5652 |
Other
| Other | 29th IMAC, a Conference on Structural Dynamics, 2011 |
|---|---|
| Country | United States |
| City | Jacksonville, FL |
| Period | 1/31/11 → 2/3/11 |
Fingerprint
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Mechanical Engineering
Cite this
A global-local approach to nonlinear system identification. / Lee, Young S.; Vakakis, Alexander F; McFarland, D. Michael; Bergman, Lawrence.
Modal Analysis Topics - Proceedings of the 29th IMAC, a Conference on Structural Dynamics, 2011. 2011. p. 513-524 (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 3).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - A global-local approach to nonlinear system identification
AU - Lee, Young S.
AU - Vakakis, Alexander F
AU - McFarland, D. Michael
AU - Bergman, Lawrence
PY - 2011/6/13
Y1 - 2011/6/13
N2 - We present the basic components of a time-domain nonlinear system identification (NSI) method with promise of applicability to a broad class of smooth and non-smooth dynamical systems. The proposed NSI method is based on the close correspondence between analytical and empirical slow-flow dynamics, and relies on direct analysis of measured time series without any a priori assumptions on the system dynamics. The central assumption is that the measured time series can be decomposed in terms of a finite number of oscillating components that are in the form of fast monochromatic oscillations modulated by slow amplitudes. The empirical slow-flow model of the dynamics is obtained from empirical mode decomposition, and its correspondence to the analytical slow-flow model establishes a local nonlinear interaction model (NIM). A NIM consists of a set of intrinsic modal oscillators (IMOs) that can reproduce the measured time series over different time scales and can account for (even strongly) nonlinear modal interactions. Hence, it represents a local model of the dynamics, identifying specific nonlinear transitions. By collecting energy-dependent frequency behaviors from all identified IMOs, a frequency-energy plot (in the modal space) can be constructed, which depicts global features of the dynamical system.
AB - We present the basic components of a time-domain nonlinear system identification (NSI) method with promise of applicability to a broad class of smooth and non-smooth dynamical systems. The proposed NSI method is based on the close correspondence between analytical and empirical slow-flow dynamics, and relies on direct analysis of measured time series without any a priori assumptions on the system dynamics. The central assumption is that the measured time series can be decomposed in terms of a finite number of oscillating components that are in the form of fast monochromatic oscillations modulated by slow amplitudes. The empirical slow-flow model of the dynamics is obtained from empirical mode decomposition, and its correspondence to the analytical slow-flow model establishes a local nonlinear interaction model (NIM). A NIM consists of a set of intrinsic modal oscillators (IMOs) that can reproduce the measured time series over different time scales and can account for (even strongly) nonlinear modal interactions. Hence, it represents a local model of the dynamics, identifying specific nonlinear transitions. By collecting energy-dependent frequency behaviors from all identified IMOs, a frequency-energy plot (in the modal space) can be constructed, which depicts global features of the dynamical system.
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M3 - Conference contribution
AN - SCOPUS:79958156672
SN - 9781441992987
T3 - Conference Proceedings of the Society for Experimental Mechanics Series
SP - 513
EP - 524
BT - Modal Analysis Topics - Proceedings of the 29th IMAC, a Conference on Structural Dynamics, 2011
ER -