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

• Published in: Mechanical systems and signal processing Vol. 95; pp. 488 - 505
• Main Author: Le, Thien-Phu
• Format: Journal Article
• Language: English
• 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
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.03.045

•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.