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Research Papers

Damage Detection in Nonlinear Systems Using Optimal Feedback Auxiliary Signals and System Augmentations

[+] Author and Article Information
Kiran D’Souza

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109

Bogdan I. Epureanu1

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

1

Corresponding author.

J. Vib. Acoust 132(2), 021002 (Mar 15, 2010) (9 pages) doi:10.1115/1.4000839 History: Received December 07, 2007; Revised June 24, 2008; Published March 15, 2010; Online March 15, 2010

An optimal sensitivity enhancing feedback control has been proposed recently. This method differs from previous sensitivity enhancing approaches because in addition to placing the closed-loop eigenvalues of the interrogated system, the eigenvectors are also optimally placed. This technique addresses two major limitations of frequency-based damage detection methods: the low sensitivity of the frequencies to damages and the limited range of damage scenarios identifiable from frequency-only measurement data. An unresolved challenge is enhancing sensitivity for nonlinear systems. This paper addresses this challenge by using optimal feedback auxiliary signals to enhance sensitivity for damage detection in nonlinear systems. The nonlinearity is accounted for by creating augmented linear models of higher order (in a higher dimensional state space). The methodology for constructing augmented linear systems with this property has been previously proposed by the authors (2008, “Multiple Augmentations of Nonlinear Systems and Generalized Minimum Rank Perturbations for Damage Detection  ,” J. Sound Vib., 316(1-5), pp. 101–121). Herein, the focus is on generalizing the previous work on sensitivity enhancing feedback and on system augmentation for enhancing sensitivity of damage detection in nonlinear systems. Results obtained by applying the optimal feedback auxiliary signals and optimal augmentation to a nonlinear mass-spring system are presented.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

A two degrees of freedom nonlinear system containing cubic springs

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Figure 2

A nonlinear mass-spring system that contains two cubic spring nonlinearities denoted by the cubic stiffness kn1 and kn2 (mi=1, i=1,…,5, k1g=k34=10,000, k12=k23=15,000, k45=20,000, and kn1=kn2=10,000)

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Figure 8

Comparison of the frequency shift due to a 0.5% loss of stiffness in each parameter for the open-loop (OL) system and four physically stable, optimally augmented, closed-loop systems (CL1−4) for the first (top), second (middle), and third (bottom) frequencies

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Figure 9

Damage detection results for frequencies contaminated with 0.5% random noise for the fully stable and physically stable augmented systems. Left: the first (top), second (center), and third (bottom) elements. Right: the fifth (top), sixth (center), and seventh (bottom) elements.

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Figure 3

Sensitivity of the first resonant frequency to a change in a linear spring (left) and a cubic spring (right) for the open-loop (OL) system and four fully stable, closed-loop systems (CL1−4)

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Figure 4

Comparison of the frequency shift due to a 3% loss of stiffness in each parameter for the open-loop (OL) system and four fully stable, optimally augmented, closed-loop systems (CL1−4) for the first (top), second (middle), and third (bottom) frequencies

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Figure 5

Damage detection results for natural frequencies contaminated with 1% random noise for the optimal and ad hoc augmented systems. Left: the first (top), second (center), and third (bottom) elements. Right: the fifth (top), sixth (center), and seventh (bottom) elements.

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Figure 6

Change in function cost (left), sensitivity enhancement (center), and control effort (right) with increase in ε

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Figure 7

Sensitivity of the first resonant frequency to a change in a linear spring (left) and a cubic spring (right) for the open-loop (OL) system and four physically stable, closed-loop systems (CL1−4)

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