Hidden variable tracking: Formulation and analysis of a mathematical model

David Chelidze; Joseph P. Cusumano; Anindya Chatterjee

doi:10.1115/detc99-vib-8358

Hidden variable tracking: Formulation and analysis of a mathematical model

David Chelidze, Joseph P. Cusumano, Anindya Chatterjee

Engineering Science and Mechanics

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

1 Scopus citations

Abstract

The hidden variable tracking method developed by Cusumano et al, (1998) is analyzed using a simple model of the mechanical oscillator with nonstationary two-well potential previously studied experimentally. Numerical experiments conducted using the model are in good agreement with the experimental study, and explicitly show how the tracking metric (or drift observer) is related to drift in system parameters caused by the slow evolution of a hidden variable. Using the idea of averaging, the slow flow equation governing hidden variable evolution is obtained. It is shown that solutions to the slow flow equation correspond to the drift trajectory obtained with the experimental tracking method.

Original language	English (US)
Title of host publication	17th Biennial Conference on Mechanical Vibration and Noise
Publisher	American Society of Mechanical Engineers (ASME)
Pages	2769-2779
Number of pages	11
ISBN (Electronic)	9780791880395
DOIs	https://doi.org/10.1115/detc99-vib-8358
State	Published - 1999
Event	ASME 1999 Design Engineering Technical Conferences, DETC 1999 - Las Vegas, United States Duration: Sep 12 1999 → Sep 16 1999

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	7B-1999

Conference

Conference	ASME 1999 Design Engineering Technical Conferences, DETC 1999
Country/Territory	United States
City	Las Vegas
Period	9/12/99 → 9/16/99

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/detc99-vib-8358

Cite this

Chelidze, D., Cusumano, J. P., & Chatterjee, A. (1999). Hidden variable tracking: Formulation and analysis of a mathematical model. In 17th Biennial Conference on Mechanical Vibration and Noise (pp. 2769-2779). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 7B-1999). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/detc99-vib-8358

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title = "Hidden variable tracking: Formulation and analysis of a mathematical model",

abstract = "The hidden variable tracking method developed by Cusumano et al, (1998) is analyzed using a simple model of the mechanical oscillator with nonstationary two-well potential previously studied experimentally. Numerical experiments conducted using the model are in good agreement with the experimental study, and explicitly show how the tracking metric (or drift observer) is related to drift in system parameters caused by the slow evolution of a hidden variable. Using the idea of averaging, the slow flow equation governing hidden variable evolution is obtained. It is shown that solutions to the slow flow equation correspond to the drift trajectory obtained with the experimental tracking method.",

author = "David Chelidze and Cusumano, {Joseph P.} and Anindya Chatterjee",

note = "Publisher Copyright: {\textcopyright} 1999 American Society of Mechanical Engineers (ASME). All rights reserved.; ASME 1999 Design Engineering Technical Conferences, DETC 1999 ; Conference date: 12-09-1999 Through 16-09-1999",

year = "1999",

doi = "10.1115/detc99-vib-8358",

language = "English (US)",

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

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

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booktitle = "17th Biennial Conference on Mechanical Vibration and Noise",

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Chelidze, D, Cusumano, JP & Chatterjee, A 1999, Hidden variable tracking: Formulation and analysis of a mathematical model. in 17th Biennial Conference on Mechanical Vibration and Noise. Proceedings of the ASME Design Engineering Technical Conference, vol. 7B-1999, American Society of Mechanical Engineers (ASME), pp. 2769-2779, ASME 1999 Design Engineering Technical Conferences, DETC 1999, Las Vegas, United States, 9/12/99. https://doi.org/10.1115/detc99-vib-8358

Hidden variable tracking: Formulation and analysis of a mathematical model. / Chelidze, David; Cusumano, Joseph P.; Chatterjee, Anindya.
17th Biennial Conference on Mechanical Vibration and Noise. American Society of Mechanical Engineers (ASME), 1999. p. 2769-2779 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 7B-1999).

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

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T1 - Hidden variable tracking

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AU - Cusumano, Joseph P.

AU - Chatterjee, Anindya

PY - 1999

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N2 - The hidden variable tracking method developed by Cusumano et al, (1998) is analyzed using a simple model of the mechanical oscillator with nonstationary two-well potential previously studied experimentally. Numerical experiments conducted using the model are in good agreement with the experimental study, and explicitly show how the tracking metric (or drift observer) is related to drift in system parameters caused by the slow evolution of a hidden variable. Using the idea of averaging, the slow flow equation governing hidden variable evolution is obtained. It is shown that solutions to the slow flow equation correspond to the drift trajectory obtained with the experimental tracking method.

AB - The hidden variable tracking method developed by Cusumano et al, (1998) is analyzed using a simple model of the mechanical oscillator with nonstationary two-well potential previously studied experimentally. Numerical experiments conducted using the model are in good agreement with the experimental study, and explicitly show how the tracking metric (or drift observer) is related to drift in system parameters caused by the slow evolution of a hidden variable. Using the idea of averaging, the slow flow equation governing hidden variable evolution is obtained. It is shown that solutions to the slow flow equation correspond to the drift trajectory obtained with the experimental tracking method.

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BT - 17th Biennial Conference on Mechanical Vibration and Noise

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Hidden variable tracking: Formulation and analysis of a mathematical model

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