Abstract
An instantaneous frequency identification method of vibration signal based on linear chirplet transform and Wigner-Ville distribution is presented. This method has an obvious advantage in identifying closely spaced and time-varying frequencies. The matching pursuit algorithm is employed to select optimal chirplets, and a modified version of chirplet transform is presented to estimate nonlinear varying frequencies. Because of the high time resolution, the modified chirplet transform is superior to the original method. The proposed method is applied to time-varying systems with both linear and nonlinear varying stiffness and systems with closely spaced modes. A wavelet-based identification method is simulated to compare with the proposed method, with the comparison results showing that the chirplet-based method is effective and accurate in identifying both time-varying and closely spaced frequencies. A bat echolocation signal is used to verify the effectiveness of the modified chirplet transform. The result shows that it will significantly increase the accuracy of nonlinear frequency trajectory identification.
Highlights
Natural frequency is a crucial parameter in dynamic systems, and most of the frequency identification methods are based on the Fourier transform
Linear time-varying (LTV) systems are often used in engineering, such as large flexible structures for outer space exploration, spacecraft, launch vehicles, and vehicle-bridge systems [1, 2]
Similar to the previous case, the results show that continuous wavelet transform (CWT) is more sensitive to noise than chirplet transform (CT)
Summary
Natural frequency is a crucial parameter in dynamic systems, and most of the frequency identification methods are based on the Fourier transform. These methods are effective only when the frequency contents of the vibration signals are time-invariant. Parameter identification methods for LTV systems have been widely studied in the last two decades, but most of them are based on inaccurate and computationally sectional time invariance [3, 4]. According to the Heisenberg uncertainty principle, wavelet transform is incapable of simultaneously providing high resolutions in both time and frequency domains For this reason, great difficulties are encountered in using wavelet-based methods for identification of dynamical systems having close and/or fastvarying modal frequencies.
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