A dynamical systems approach to damage evolution tracking, part 2: Model-based validation and physical interpretation

Joseph P. Cusumano, David Chelidze, Anindya Chatterjee

Research output: Contribution to journalArticle

67 Citations (Scopus)

Abstract

In this paper, the hidden variable damage tracking method developed in Part 1 is analyzed using a physics-based mathematical model of the experimental system: a mechanical oscillator with a nonstationary two-well potential. Numerical experiments conducted using the model are in good agreement with the experimental study presented in Part 1, and explicitly show how the tracking metric is related to the slow hidden variable evolution responsible for drift in the fast system parameters. Using the idea of averaging, the slow flow equation governing the hidden variable evolution is obtained. It is shown that the solution to the slow flow equation corresponds to the hidden variable trajectory obtained with the experimental tracking method. Thus we establish in principle the relationship of our algorithm to any underlying physical process. Based on this result, we discuss the application of the tracking method to systems with evolving material damage using the results of some preliminary experiments.

Original languageEnglish (US)
Pages (from-to)258-264
Number of pages7
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume124
Issue number2
DOIs
StatePublished - Apr 2002

Fingerprint

dynamical systems
Dynamical systems
Oscillators (mechanical)
damage
flow equations
Physics
Experiments
Trajectories
Mathematical models
mechanical oscillators
mathematical models
trajectories
physics

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

@article{eaaf33f4e5b04d9b82d112b5297ce7dd,
title = "A dynamical systems approach to damage evolution tracking, part 2: Model-based validation and physical interpretation",
abstract = "In this paper, the hidden variable damage tracking method developed in Part 1 is analyzed using a physics-based mathematical model of the experimental system: a mechanical oscillator with a nonstationary two-well potential. Numerical experiments conducted using the model are in good agreement with the experimental study presented in Part 1, and explicitly show how the tracking metric is related to the slow hidden variable evolution responsible for drift in the fast system parameters. Using the idea of averaging, the slow flow equation governing the hidden variable evolution is obtained. It is shown that the solution to the slow flow equation corresponds to the hidden variable trajectory obtained with the experimental tracking method. Thus we establish in principle the relationship of our algorithm to any underlying physical process. Based on this result, we discuss the application of the tracking method to systems with evolving material damage using the results of some preliminary experiments.",
author = "Cusumano, {Joseph P.} and David Chelidze and Anindya Chatterjee",
year = "2002",
month = "4",
doi = "10.1115/1.1456907",
language = "English (US)",
volume = "124",
pages = "258--264",
journal = "Journal of Vibration and Acoustics, Transactions of the ASME",
issn = "1048-9002",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "2",

}

A dynamical systems approach to damage evolution tracking, part 2 : Model-based validation and physical interpretation. / Cusumano, Joseph P.; Chelidze, David; Chatterjee, Anindya.

In: Journal of Vibration and Acoustics, Transactions of the ASME, Vol. 124, No. 2, 04.2002, p. 258-264.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A dynamical systems approach to damage evolution tracking, part 2

T2 - Model-based validation and physical interpretation

AU - Cusumano, Joseph P.

AU - Chelidze, David

AU - Chatterjee, Anindya

PY - 2002/4

Y1 - 2002/4

N2 - In this paper, the hidden variable damage tracking method developed in Part 1 is analyzed using a physics-based mathematical model of the experimental system: a mechanical oscillator with a nonstationary two-well potential. Numerical experiments conducted using the model are in good agreement with the experimental study presented in Part 1, and explicitly show how the tracking metric is related to the slow hidden variable evolution responsible for drift in the fast system parameters. Using the idea of averaging, the slow flow equation governing the hidden variable evolution is obtained. It is shown that the solution to the slow flow equation corresponds to the hidden variable trajectory obtained with the experimental tracking method. Thus we establish in principle the relationship of our algorithm to any underlying physical process. Based on this result, we discuss the application of the tracking method to systems with evolving material damage using the results of some preliminary experiments.

AB - In this paper, the hidden variable damage tracking method developed in Part 1 is analyzed using a physics-based mathematical model of the experimental system: a mechanical oscillator with a nonstationary two-well potential. Numerical experiments conducted using the model are in good agreement with the experimental study presented in Part 1, and explicitly show how the tracking metric is related to the slow hidden variable evolution responsible for drift in the fast system parameters. Using the idea of averaging, the slow flow equation governing the hidden variable evolution is obtained. It is shown that the solution to the slow flow equation corresponds to the hidden variable trajectory obtained with the experimental tracking method. Thus we establish in principle the relationship of our algorithm to any underlying physical process. Based on this result, we discuss the application of the tracking method to systems with evolving material damage using the results of some preliminary experiments.

UR - http://www.scopus.com/inward/record.url?scp=0036554994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036554994&partnerID=8YFLogxK

U2 - 10.1115/1.1456907

DO - 10.1115/1.1456907

M3 - Article

AN - SCOPUS:0036554994

VL - 124

SP - 258

EP - 264

JO - Journal of Vibration and Acoustics, Transactions of the ASME

JF - Journal of Vibration and Acoustics, Transactions of the ASME

SN - 1048-9002

IS - 2

ER -