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. 2018 Aug 13;376(2126):20170245.
doi: 10.1098/rsta.2017.0245.

Wavelet-based analysis of time-variant adaptive structures

Kajetan Dziedziech  1 , Alexander Nowak  2 , Alexander Hasse  2 , Tadeusz Uhl  1 , Wiesław J Staszewski  3
Affiliations

Wavelet-based analysis of time-variant adaptive structures

Kajetan Dziedziech et al. Philos Trans A Math Phys Eng Sci. .

Abstract

Wavelet analysis is applied to identify the time-variant dynamics of adaptive structures. The wavelet-based power spectrum of the structural response, wavelet-based frequency response function (FRF) and wavelet-based coherence are used to identify continuously and abruptly varying natural frequencies. A cantilever plate with surface-bonded macro fibre composite-which alters the structural stiffness-is used to demonstrate the application of the methods. The results show that the wavelet-based input-output characteristics-i.e. the FRF and coherence-can identify correctly the dynamics of the analysed time-variant system and reveal the varying natural frequency. The wavelet-based coherence can be used not only for the assessment of the quality of the wavelet-based FRF but also for the identification.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Keywords: adaptive structures; time-variant systems; wavelet-based coherence; wavelet-based frequency response function; wavelets.

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Conflict of interest statement

We declare we have no competing interests.

Figures

Figure 1.
Figure 1.
Adaptive structure—experimental test set-up. (Online version in colour.)
Figure 2.
Figure 2.
Linear time-invariant (LTI) system—auto-power spectra: (a) excitation signal and (b) response signal. (Online version in colour.)
Figure 3.
Figure 3.
Linear time-invariant (LTI) system—the classical analysis: (a) frequency–response function and (b) coherence function. (Online version in colour.)
Figure 4.
Figure 4.
Linear time-variant (LTV) system—MFC actuation signal leading to the continuously varying stiffness change. (Online version in colour.)
Figure 5.
Figure 5.
Linear time-variant system (LTV) for the continuously varying stiffness. Wavelet output-only analysis—wavelet-based auto-power spectra for (a) excitation signal and (b) response signal. (Online version in colour.)
Figure 6.
Figure 6.
Linear time-variant (LTV) system for the continuously varying stiffness. Wavelet-based input–output analysis: (a) time-variant frequency response function (TV-FRF) and (b) time-variant coherence (TV-COH). (Online version in colour.)
Figure 7.
Figure 7.
Linear time-variant (LTV) system—MFC actuation signal leading to the abruptly varying stiffness change. (Online version in colour.)
Figure 8.
Figure 8.
Linear time-variant system (LTV) for the abruptly varying stiffness. Wavelet output-only analysis—wavelet-based auto-power spectra for: (a) excitation signal and (b) response signal. (Online version in colour.)
Figure 9.
Figure 9.
Linear time-variant (LTV) system for the abruptly varying stiffness. Wavelet-based input–output analysis: (a) time-variant frequency response function (TV-FRF) and (b) time-variant coherence (TV-COH). (Online version in colour.)
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