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Research Papers

Derivation of a Damage Sensitive Feature Using the Haar Wavelet Transform

[+] Author and Article Information
K. Krishnan Nair

Department of Civil and Environmental Engineering, John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CA 94305kknair@stanford.edu

Anne S. Kiremidjian1

Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305ask@stanford.edu

1

Corresponding author.

J. Appl. Mech 76(6), 061015 (Jul 27, 2009) (9 pages) doi:10.1115/1.3130821 History: Received March 04, 2008; Revised February 04, 2009; Published July 27, 2009

In this paper, a damage sensitive feature based on the wavelet transform of the vibration signal is derived. The theoretical aspects of wavelet decomposition of vibration signals are presented. It is shown that the energies of the wavelet coefficients at appropriate scales can be used as damage sensitive features. Expressions for the energies of wavelet coefficients using the Haar wavelet basis function are derived for a single degree and a multidegree of freedom system. It is shown that the energies of the wavelet coefficients extracted at higher scales are functions of the physical parameters of the system and the loading function. Finally, the migration of damage sensitive feature vectors with damage is illustrated for the ASCE Benchmark Structure.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Haar wavelet: (a) Haar basis function and (b) its Fourier transform

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Figure 2

ASCE Benchmark Structure (18)

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Figure 3

Placement of sensors and directions of acceleration measurements on the ASCE Benchmark Structure (18)

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Figure 4

Migration of the Haar wavelet based damage sensitive feature E6 for sensor 2 with damage for minor patterns: (a) damage pattern 6 and (b) damage pattern 3

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Figure 5

Migration of the Haar wavelet based damage sensitive feature E6 for sensor 2 with damage for major patterns: (a) damage pattern 1 and (b) damage pattern 2

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Figure 6

Migration of the Haar wavelet based damage sensitive feature E6 for sensor 3 with damage for (a) damage pattern 4 and (b) damage pattern 5 (undamaged (○); damaged (+))

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Figure 7

Migration of the Haar wavelet based damage sensitive feature E6 for sensor 9 with damage for (a) damage pattern 3 and (b) damage pattern 4 (undamaged (○); damaged (+))

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Figure 8

Illustration of the proof of the contour integration formula

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