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TECHNICAL PAPERS

Experimental Enhanced Nonlinear Dynamics and Identification of Attractor Morphing Modes for Damage Detection

[+] Author and Article Information
Shih-Hsun Yin

Department of Civil Engineering, National Taipei University of Technology, Taipei 106 Taiwan, R.O.C.shihhsun@ntut.edu.tw

Bogdan I. Epureanu1

Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109epureanu@umich.edu

1

Corresponding author.2 An earlier version of this work has has been presented at the 2006 ASME IMECE, Chicago IL.

J. Vib. Acoust 129(6), 763-770 (Jul 09, 2007) (8 pages) doi:10.1115/1.2775507 History: Received July 30, 2006; Revised July 09, 2007

This paper demonstrates two novel methods for identifying small parametric variations in an experimental system based on the analysis of sensitivity vector fields (SVFs) and probability density functions (PDFs). The experimental system includes a smart sensing beam excited by a nonlinear feedback excitation through two lead zirconate titanate patches symmetrically bonded on both sides at the root of the beam. The nonlinear feedback excitation requires the measurement of the dynamics (e.g., velocity of one point at the tip of the beam) and a nonlinear feedback loop, and is designed such that the beam vibrates in a chaotic regime. Changes in the state space attractor of the dynamics due to small parametric variations can be captured by SVFs, which, in turn, are collected by applying point cloud averaging to points distributed in the attractors for nominal and changed parameters. Also, the PDFs characterize statistically the distribution of points in the attractors. The differences between the PDFs of the attractors for different changed parameters and the base line attractor can provide different attractor morphing modes for identifying variations in distinct parameters. Experimental results based on the proposed approaches show that very small amounts of added mass at different locations along the beam can be accurately identified.2

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic plot and photos of the experimental setup of the smart sensing beam excited by a nonlinear feedback excitation including a laser vibrometer, an enhanced real-time processor connected to a laptop, and a voltage amplifier

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Figure 2

Estimating the maximal Lyapunov exponent of the dynamics of the smart sensing beam based on the experimental time series. S(ε,m,t) exhibits an approximately linear increase with a positive slope for all embedding dimensions (m⩾3) for a reasonable length scale ε.

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Figure 3

The correlation dimension D2(ε,m) of the dynamics of the smart sensing beam based on the experimental time series is estimated between 2 and 3 for all embedding dimensions (m⩾3) for a reasonable length scale ε

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Figure 4

The reconstructed base line attractor of the dynamics of the smart sensing beam excited by the designed nonlinear feedback excitation in the state space spanned by the velocity, the acceleration, and the acceleration derivative of one point at the tip of the beam

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Figure 5

A sensitivity vector estimated for one neighborhood around a chosen center that passes all checks required for a qualified sensitivity vector for all considered cases with different amounts of added mass at different locations

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Figure 6

The mean values and the standard deviations of the angle between two vectors of SVFs in the same neighborhood from all cases where mass is added at the tip (i=1), from all cases where mass is added at the middle (i=2), and, respectively, from the previous two groups (i=3)

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Figure 7

Eigenvalues of the correlation matrix based on the snapshots of sensitivity vector fields for all cases where different amounts of mass are added at different locations

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Figure 8

The difference between the PDFs of the attractors for the cases where different amounts of mass are added at different locations and the PDF of the base line attractor (without added mass)

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Figure 9

Eigenvalues of the correlation matrix based on the snapshots of probability density difference for all cases where different amounts of mass are added at different locations

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