Although conventional methods such as the short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) have been effectively used for the analysis of dispersive elastic waves, rapidly varying wave signals may not be accurately analyzed by these methods. Because the time-frequency tiling of conventional methods do not take into account dispersion phenomena, it is often difficult to trace accurately the time-frequency varying feature of the signals. The objective of this work is to develop advanced adaptive time-frequency analysis methods whose time-frequency tiling is varying to the dispersion characteristics of the signal to be analyzed. More specifically, a method called, "the dispersion-based short-time Fourier transform (D-STFT) and the dispersion-based continuous wavelet transform (DCWT)" are newly developed. In these methods, each time-frequency tiling is adaptively rotated in the time-frequency plane depending on the estimated local dispersion rate of a wave signal. In the proposed approach, the dispersion
relationship is estimated iteratively from the ridge analysis of the result by the proposed adaptive methods where the initial estimation is based on the result by the standard methods. To verify the validity of the present approach, the Lamb waves measured in an aluminum plate were considered.
The continuous wavelet transform (CWT) has been utilized as an effective and powerful time-frequency analysis tool for identifying the rapidly-varying characteristics of some dispersive wave signals. Particularly, in the applications of continuous Gabor wavelet transform, its effectiveness is strongly influenced by the shape of the applied Gabor wavelet so the determination of an optimal shape tracing well the time-frequency evolution of a given signal. Since the characteristics of signals are rarely known in advance, the determination of the optimal shape is usually difficult. The main objective of this work is to propose a method to determine the signal-dependent optimal shape of the Gabor wavelet for the best time-frequency localization. To find the optimal Gabor wavelet shape, the notion of the Shannon entropy which measures the extent of signal energy concentration in the time-frequency plane, is employed. To verify the validity of the present approach, a set of elastic bending wave signals generated by an impact in a solid cylinder are analyzed.
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