Hidden parameter tracking using delay coordinate embedding

Authors D. Chelidze, Joseph Paul Cusumano, N. K. Hecht

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

A model based experimental method of tracking the 'hidden' parameter drift in nonlinear dynamical systems is described. Local linear models constructed using delay coordinate embedding are used to analyze data collected from systems with parameters that are drifting on a slow time scale according to some hidden rate law. Data is sampled over a fast time scale. The method is applied to a numerical study of a forced nonlinear duffing oscillator. A forcing amplitude and a first natural frequency of a corresponding linear system served as the drifting parameters. The mean-square model single step prediction error, tracking parameter, is shown to follow closely the assigned variations in drifting parameters. Ramped and sinusoidal parameter variations were used. It is concluded that, at least in the cases studied, the tracking model based on delay coordinate embedding provides one to one correspondence between the drifting and tracking parameters.

Original languageEnglish (US)
Pages (from-to)525-530
Number of pages6
JournalProceedings - National Conference on Noise Control Engineering
Volume1
StatePublished - Dec 1 1997
EventProceedings of the 1997 National Conference on Noise Control Engineering , NOISE-CON. Part 2 (of 2) - University Park, PA, USA
Duration: Jun 15 1997Jun 17 1997

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embedding
linear systems
dynamical systems
resonant frequencies
oscillators
predictions

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics

Cite this

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title = "Hidden parameter tracking using delay coordinate embedding",
abstract = "A model based experimental method of tracking the 'hidden' parameter drift in nonlinear dynamical systems is described. Local linear models constructed using delay coordinate embedding are used to analyze data collected from systems with parameters that are drifting on a slow time scale according to some hidden rate law. Data is sampled over a fast time scale. The method is applied to a numerical study of a forced nonlinear duffing oscillator. A forcing amplitude and a first natural frequency of a corresponding linear system served as the drifting parameters. The mean-square model single step prediction error, tracking parameter, is shown to follow closely the assigned variations in drifting parameters. Ramped and sinusoidal parameter variations were used. It is concluded that, at least in the cases studied, the tracking model based on delay coordinate embedding provides one to one correspondence between the drifting and tracking parameters.",
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year = "1997",
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Hidden parameter tracking using delay coordinate embedding. / Chelidze, Authors D.; Cusumano, Joseph Paul; Hecht, N. K.

In: Proceedings - National Conference on Noise Control Engineering, Vol. 1, 01.12.1997, p. 525-530.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Hidden parameter tracking using delay coordinate embedding

AU - Chelidze, Authors D.

AU - Cusumano, Joseph Paul

AU - Hecht, N. K.

PY - 1997/12/1

Y1 - 1997/12/1

N2 - A model based experimental method of tracking the 'hidden' parameter drift in nonlinear dynamical systems is described. Local linear models constructed using delay coordinate embedding are used to analyze data collected from systems with parameters that are drifting on a slow time scale according to some hidden rate law. Data is sampled over a fast time scale. The method is applied to a numerical study of a forced nonlinear duffing oscillator. A forcing amplitude and a first natural frequency of a corresponding linear system served as the drifting parameters. The mean-square model single step prediction error, tracking parameter, is shown to follow closely the assigned variations in drifting parameters. Ramped and sinusoidal parameter variations were used. It is concluded that, at least in the cases studied, the tracking model based on delay coordinate embedding provides one to one correspondence between the drifting and tracking parameters.

AB - A model based experimental method of tracking the 'hidden' parameter drift in nonlinear dynamical systems is described. Local linear models constructed using delay coordinate embedding are used to analyze data collected from systems with parameters that are drifting on a slow time scale according to some hidden rate law. Data is sampled over a fast time scale. The method is applied to a numerical study of a forced nonlinear duffing oscillator. A forcing amplitude and a first natural frequency of a corresponding linear system served as the drifting parameters. The mean-square model single step prediction error, tracking parameter, is shown to follow closely the assigned variations in drifting parameters. Ramped and sinusoidal parameter variations were used. It is concluded that, at least in the cases studied, the tracking model based on delay coordinate embedding provides one to one correspondence between the drifting and tracking parameters.

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