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

[+] 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
Copyright © 2002 by ASME
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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 NR, the number of consecutive records used for the moving average ē5: (left) NR=20; (right) NR=40. Plot details are the same as in Fig. 4. As can be seen by comparison with Fig. 4, the different values of NR affect only the local fluctuations of the tracking, not the general trend.
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The correlation dimension (dc) and largest short time Lyapunov exponent (λ1) vs. the battery voltage. See the discussion in text.




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