A Dynamical Systems Approach to Damage Evolution Tracking, Part 1: Description and Experimental Application

David Chelidze; Joseph P. Cusumano; Anindya Chatterjee

doi:10.1115/1.1456908

Journal of Vibration and Acoustics | Volume 124 | Issue 2 | TECHNICAL PAPERS

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TECHNICAL PAPERS

A Dynamical Systems Approach to Damage Evolution Tracking, Part 1: Description and Experimental Application

David Chelidze, Joseph P. Cusumano and Anindya Chatterjee

[+] Author and Article Information

David Chelidze

Department of Mechanical Engineering & Applied Mechanics, University of Rhode Island, Kingston, RI 02881e-mail: chelidze@egr.uri.edu

Joseph P. Cusumano

Department of Engineering, Science & Mechanics, Pennsylvania State University, University Park, PA 16802e-mail: jpc@crash.esm.psu.edu

Anindya Chatterjee

Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560012, Indiae-mail: anindya@mecheng.iisc.ernet.in

J. Vib. Acoust 124(2), 250-257 (Mar 26, 2002) (8 pages) doi:10.1115/1.1456908 History: Received July 01, 2001; Revised December 01, 2001; Online March 26, 2002

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Schematic drawing illustrating the basic idea behind tracking function estimation. Trajectories of the reference system in phase space are shown in gray. The solid black line represents a measured trajectory of the perturbed system, passing through y(l) and the dashed gray line represents where a trajectory would have gone in the reference system, if starting from the same point y(l).

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Schematic diagram of the experiment with the two-well electromechanical oscillator

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Power spectra taken throughout the experiment (left). Passages through periodic windows occurring during the experimental run (right). See text for further discussion.

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Experimental tracking results: (left) plot of unscaled tracking metric ē₅ vs. the battery voltage; (right) scaled battery voltage vs. time. In both figures, black dots show the moving average of tracking metric over ten data records, and the gray background represents ±one standard deviation of the mean. In the right figure, the dark gray gives the outline of the actual (unaveraged) battery voltage, and the solid gray line is the corresponding local average in one data record.

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Additional tracking results showing the effect of changing N_R, the number of consecutive records used for the moving average ē₅: (left) N_R=20; (right) N_R=40. Plot details are the same as in Fig. 4. As can be seen by comparison with Fig. 4, the different values of N_R affect only the local fluctuations of the tracking, not the general trend.

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The correlation dimension (d_c) and largest short time Lyapunov exponent (λ₁) vs. the battery voltage. See the discussion in text.

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Chelidze D, Cusumano JP, Chatterjee A. A Dynamical Systems Approach to Damage Evolution Tracking, Part 1: Description and Experimental Application. ASME. J. Vib. Acoust. 2002;124(2):250-257. doi:10.1115/1.1456908.

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A Dynamical Systems Approach to Damage Evolution Tracking, Part 1: Description and Experimental Application

References

Figures

Schematic diagram of the experiment with the two-well electromechanical oscillator

Power spectra taken throughout the experiment (left). Passages through periodic windows occurring during the experimental run (right). See text for further discussion.

The correlation dimension (d_c) and largest short time Lyapunov exponent (λ₁) vs. the battery voltage. See the discussion in text.

Tables

Errata

Discussions

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A Dynamical Systems Approach to Damage Evolution Tracking, Part 1: Description and Experimental Application

References

Figures

Schematic diagram of the experiment with the two-well electromechanical oscillator

Power spectra taken throughout the experiment (left). Passages through periodic windows occurring during the experimental run (right). See text for further discussion.

The correlation dimension (dc) and largest short time Lyapunov exponent (λ1) vs. the battery voltage. See the discussion in text.

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

The correlation dimension (d_c) and largest short time Lyapunov exponent (λ₁) vs. the battery voltage. See the discussion in text.