Analysis of non-linear systems using wavelets

Abstract Analysis of non-linear systems is an essential part of engineering structural dynamics. A number of methods have been developed in recent years. Classical Fourier-based methods have been extended to the use of phase plane, combined time-frequency, time-scale approaches and multidimensional spectra. This paper is an attempt to collate in one place some of the recent advances in wavelet analysis for the study of non-linear systems. This includes methods related to system identification based on wavelet ridges and skeletons, damping estimation procedures, wavelet-based frequency response functions, cross-wavelet analysis, self-similar signals, coherent structures and chaos.

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