Using phase space reconstruction to track parameter drift in a nonlinear system

J. P. Cusumano; D. Chelidze; N. K. Hecht

doi:10.1115/DETC97/VIB-4012

Using phase space reconstruction to track parameter drift in a nonlinear system

J. P. Cusumano, D. Chelidze, N. K. Hecht

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

4 Scopus citations

Abstract

A model-based experimental method for tracking parameter drift in nonlinear dynamical systems is described. Local linear tracking models are constructed using data sampled over a fast time scale. These models are used to analyze data from systems with parameters which evolve over a slow time scale according to a "hidden" rate law. The method is applied to a numerical study of a nonlinear electrical circuit with a variable resistance as the drifting parameter. The mean-square tracking model prediction error is shown to follow successfully both ramped and sinusoidal parameter variations, suggesting that, at least in the cases studied, the method provides an invertible mapping between the parameter space and the observable space. Thus it should be possible to extract rate information about hidden drift, a requirement for true prediction.

Original language	English (US)
Title of host publication	16th Biennial Conference on Mechanical Vibration and Noise
Publisher	American Society of Mechanical Engineers (ASME)
ISBN (Electronic)	9780791880425
DOIs	https://doi.org/10.1115/DETC97/VIB-4012
State	Published - 1997
Event	ASME 1997 Design Engineering Technical Conferences, DETC 1997 - Sacramento, United States Duration: Sep 14 1997 → Sep 17 1997

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	1C-1997

Conference

Conference	ASME 1997 Design Engineering Technical Conferences, DETC 1997
Country/Territory	United States
City	Sacramento
Period	9/14/97 → 9/17/97

All Science Journal Classification (ASJC) codes

Mechanical Engineering
Computer Graphics and Computer-Aided Design
Computer Science Applications
Modeling and Simulation

Access to Document

10.1115/DETC97/VIB-4012

Cite this

Cusumano, J. P., Chelidze, D., & Hecht, N. K. (1997). Using phase space reconstruction to track parameter drift in a nonlinear system. In 16th Biennial Conference on Mechanical Vibration and Noise Article V01CT12A017 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1C-1997). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC97/VIB-4012

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title = "Using phase space reconstruction to track parameter drift in a nonlinear system",

abstract = "A model-based experimental method for tracking parameter drift in nonlinear dynamical systems is described. Local linear tracking models are constructed using data sampled over a fast time scale. These models are used to analyze data from systems with parameters which evolve over a slow time scale according to a {"}hidden{"} rate law. The method is applied to a numerical study of a nonlinear electrical circuit with a variable resistance as the drifting parameter. The mean-square tracking model prediction error is shown to follow successfully both ramped and sinusoidal parameter variations, suggesting that, at least in the cases studied, the method provides an invertible mapping between the parameter space and the observable space. Thus it should be possible to extract rate information about hidden drift, a requirement for true prediction.",

author = "Cusumano, {J. P.} and D. Chelidze and Hecht, {N. K.}",

note = "Funding Information: This work was supported by the Office of Naval Research MURI on Integrated Predictive Diagnostics, Grant #N0014-95-0461. Publisher Copyright: {\textcopyright} 1997 American Society of Mechanical Engineers (ASME). All rights reserved.; ASME 1997 Design Engineering Technical Conferences, DETC 1997 ; Conference date: 14-09-1997 Through 17-09-1997",

year = "1997",

doi = "10.1115/DETC97/VIB-4012",

language = "English (US)",

series = "Proceedings of the ASME Design Engineering Technical Conference",

publisher = "American Society of Mechanical Engineers (ASME)",

booktitle = "16th Biennial Conference on Mechanical Vibration and Noise",

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Cusumano, JP, Chelidze, D & Hecht, NK 1997, Using phase space reconstruction to track parameter drift in a nonlinear system. in 16th Biennial Conference on Mechanical Vibration and Noise., V01CT12A017, Proceedings of the ASME Design Engineering Technical Conference, vol. 1C-1997, American Society of Mechanical Engineers (ASME), ASME 1997 Design Engineering Technical Conferences, DETC 1997, Sacramento, United States, 9/14/97. https://doi.org/10.1115/DETC97/VIB-4012

Using phase space reconstruction to track parameter drift in a nonlinear system. / Cusumano, J. P.; Chelidze, D.; Hecht, N. K.
16th Biennial Conference on Mechanical Vibration and Noise. American Society of Mechanical Engineers (ASME), 1997. V01CT12A017 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1C-1997).

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

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T1 - Using phase space reconstruction to track parameter drift in a nonlinear system

AU - Cusumano, J. P.

AU - Chelidze, D.

AU - Hecht, N. K.

N1 - Funding Information: This work was supported by the Office of Naval Research MURI on Integrated Predictive Diagnostics, Grant #N0014-95-0461. Publisher Copyright: © 1997 American Society of Mechanical Engineers (ASME). All rights reserved.

PY - 1997

Y1 - 1997

N2 - A model-based experimental method for tracking parameter drift in nonlinear dynamical systems is described. Local linear tracking models are constructed using data sampled over a fast time scale. These models are used to analyze data from systems with parameters which evolve over a slow time scale according to a "hidden" rate law. The method is applied to a numerical study of a nonlinear electrical circuit with a variable resistance as the drifting parameter. The mean-square tracking model prediction error is shown to follow successfully both ramped and sinusoidal parameter variations, suggesting that, at least in the cases studied, the method provides an invertible mapping between the parameter space and the observable space. Thus it should be possible to extract rate information about hidden drift, a requirement for true prediction.

AB - A model-based experimental method for tracking parameter drift in nonlinear dynamical systems is described. Local linear tracking models are constructed using data sampled over a fast time scale. These models are used to analyze data from systems with parameters which evolve over a slow time scale according to a "hidden" rate law. The method is applied to a numerical study of a nonlinear electrical circuit with a variable resistance as the drifting parameter. The mean-square tracking model prediction error is shown to follow successfully both ramped and sinusoidal parameter variations, suggesting that, at least in the cases studied, the method provides an invertible mapping between the parameter space and the observable space. Thus it should be possible to extract rate information about hidden drift, a requirement for true prediction.

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T3 - Proceedings of the ASME Design Engineering Technical Conference

BT - 16th Biennial Conference on Mechanical Vibration and Noise

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ER -

Using phase space reconstruction to track parameter drift in a nonlinear system

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