Use of the Morlet mother wavelet in the frequency-scale domain decomposition technique for the modal identification of ambient vibration responses

•Frequency-scale domain decomposition method based on the Morlet mother wavelet.•Identification of modal parameters from local maxima in frequency-scale plane.•Validation using numerical examples and a laboratory test. The frequency-scale domain decomposition technique has recently been proposed for...

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Published inMechanical systems and signal processing Vol. 95; pp. 488 - 505
Main Author Le, Thien-Phu
Format Journal Article
LanguageEnglish
Published Berlin Elsevier Ltd 01.10.2017
Elsevier BV
Elsevier
Subjects
Ambient vibration
Cauchy problems
Continuous wavelet transform
Domain decomposition methods
Frequency-scale domain
Maxima
Mechanics
Modal identification
Morlet mother wavelet
Physics
Power spectral density
Regression analysis
Regressive mother wavelet
Signal processing
Singular value decomposition
Vibration response
Wavelet analysis
Wavelet transform
Wavelet transforms
Wavelet transform
Morlet mother wavelet
Regressive mother wavelet
Power spectral density
Modal identification
Ambient vibration
Frequency-scale domain
Singular value decomposition
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Abstract •Frequency-scale domain decomposition method based on the Morlet mother wavelet.•Identification of modal parameters from local maxima in frequency-scale plane.•Validation using numerical examples and a laboratory test. The frequency-scale domain decomposition technique has recently been proposed for operational modal analysis. The technique is based on the Cauchy mother wavelet. In this paper, the approach is extended to the Morlet mother wavelet, which is very popular in signal processing due to its superior time-frequency localization. Based on the regressive form and an appropriate norm of the Morlet mother wavelet, the continuous wavelet transform of the power spectral density of ambient responses enables modes in the frequency-scale domain to be highlighted. Analytical developments first demonstrate the link between modal parameters and the local maxima of the continuous wavelet transform modulus. The link formula is then used as the foundation of the proposed modal identification method. Its practical procedure, combined with the singular value decomposition algorithm, is presented step by step. The proposition is finally verified using numerical examples and a laboratory test.
AbstractList The frequency-scale domain decomposition technique has recently been proposed for operational modal analysis. The technique is based on the Cauchy mother wavelet. In this paper, the approach is extended to the Morlet mother wavelet, which is very popular in signal processing due to its superior time-frequency localization. Based on the regressive form and an appropriate norm of the Morlet mother wavelet, the continuous wavelet transform of the power spectral density of ambient responses enables modes in the frequency-scale domain to be highlighted. Analytical developments first demonstrate the link between modal parameters and the local maxima of the continuous wavelet transform modulus. The link formula is then used as the foundation of the proposed modal identification method. Its practical procedure, combined with the singular value decomposition algorithm, is presented step by step. The proposition is finally verified using numerical examples and a laboratory test.
•Frequency-scale domain decomposition method based on the Morlet mother wavelet.•Identification of modal parameters from local maxima in frequency-scale plane.•Validation using numerical examples and a laboratory test. The frequency-scale domain decomposition technique has recently been proposed for operational modal analysis. The technique is based on the Cauchy mother wavelet. In this paper, the approach is extended to the Morlet mother wavelet, which is very popular in signal processing due to its superior time-frequency localization. Based on the regressive form and an appropriate norm of the Morlet mother wavelet, the continuous wavelet transform of the power spectral density of ambient responses enables modes in the frequency-scale domain to be highlighted. Analytical developments first demonstrate the link between modal parameters and the local maxima of the continuous wavelet transform modulus. The link formula is then used as the foundation of the proposed modal identification method. Its practical procedure, combined with the singular value decomposition algorithm, is presented step by step. The proposition is finally verified using numerical examples and a laboratory test.
Author Le, Thien-Phu
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Keywords Wavelet transform
Morlet mother wavelet
Regressive mother wavelet
Power spectral density
Modal identification
Ambient vibration
Frequency-scale domain
Singular value decomposition
Language English
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Snippet •Frequency-scale domain decomposition method based on the Morlet mother wavelet.•Identification of modal parameters from local maxima in frequency-scale...
The frequency-scale domain decomposition technique has recently been proposed for operational modal analysis. The technique is based on the Cauchy mother...
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SubjectTerms Ambient vibration
Cauchy problems
Continuous wavelet transform
Domain decomposition methods
Frequency-scale domain
Maxima
Mechanics
Modal identification
Morlet mother wavelet
Physics
Power spectral density
Regression analysis
Regressive mother wavelet
Signal processing
Singular value decomposition
Vibration response
Wavelet analysis
Wavelet transform
Wavelet transforms
Title Use of the Morlet mother wavelet in the frequency-scale domain decomposition technique for the modal identification of ambient vibration responses
URI https://dx.doi.org/10.1016/j.ymssp.2017.03.045
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https://univ-evry.hal.science/hal-02398158
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