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 Scopus citations


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
Issue number2
StatePublished - Apr 2002


All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

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