### 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) |
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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 |
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Volume | 3 |

ISSN (Print) | 2191-5644 |

ISSN (Electronic) | 2191-5652 |

### Other

Other | 29th IMAC, a Conference on Structural Dynamics, 2011 |
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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

*Modal Analysis Topics - Proceedings of the 29th IMAC, a Conference on Structural Dynamics, 2011*(pp. 513-524). (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 3).

**A global-local approach to nonlinear system identification.** / Lee, Young S.; Vakakis, Alexander F; McFarland, D. Michael; Bergman, Lawrence.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Modal Analysis Topics - Proceedings of the 29th IMAC, a Conference on Structural Dynamics, 2011.*Conference Proceedings of the Society for Experimental Mechanics Series, vol. 3, pp. 513-524, 29th IMAC, a Conference on Structural Dynamics, 2011, Jacksonville, FL, United States, 1/31/11.

}

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.

UR - http://www.scopus.com/inward/record.url?scp=79958156672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958156672&partnerID=8YFLogxK

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 -