Abstract
Abundant damage information is implicated in the bilinear time-frequency distribution of structural dynamic signals, which could provide effective support for structural damage identification. Signal time-frequency analysis methods are reviewed, and the characters of linear time-frequency distribution and bilinear time-frequency distribution typically represented by the Wigner-Ville distribution are compared. The existence of the cross-term and its application in structural damage detection are demonstrated. A method of extracting the dominant term is proposed, which combines the short-time Fourier spectrum and Wigner-Ville distribution; then two-dimensional time-frequency transformation matrix is constructed and the complete cross-term is extracted finally. The distribution character of which could be applied to the structural damage identification. Through theoretical analysis, model experiment and numerical simulation of the girder structure, the change rate of cross-term amplitude is validated to identify the damage location and degree. The effectiveness of the cross-term of bilinear time-frequency distribution for damage detection is confirmed and the analytical method of damage identification used in structural engineering is available.
Highlights
In the whole life cycle, the components in the engineering structure will damage inevitably under the influence of the performance changes in materials, loads, and other uncertain factors
This paper proposed that the inner product is built up between the short-time Fourier transform and the bilinear time-frequency distribution represented by Wigner-Ville distribution (WVD)
Through the inner product between the shorttime Fourier transform spectrogram and WVD, the crossterm of bilinear time-frequency distribution that is the Wigner-Ville distribution as the basis method of damage identification explores the purification of damaged signal
Summary
In the whole life cycle, the components in the engineering structure will damage inevitably under the influence of the performance changes in materials, loads, and other uncertain factors. Study on damage detection in engineering frequently focuses on linear time-frequency analysis such as short-time Fourier transform and wavelet transform; the bilinear time-frequency distribution is rarely discussed in this field. Mathematical Problems in Engineering function is selected, the time-frequency resolution will not be changed This property makes the short-time Fourier transform to be limited in the analysis of mutation signals and nonstationary signals, especially for the mutation signal in damaged structures. The wavelet transform can effectively obtain favorable localized characteristics with multiresolution analysis in the timefrequency domain from the signal It is widely used in the damage detection. WVD can be regarded as the distribution of signal energy in two-dimensional time-frequency space with many excellent properties such as symmetry, time shift, combinations, and complex conjugation relationship. The advantages and disadvantages of the linear timefrequency analysis method should be discussed dialectically, and as the typical method in bilinear time-frequency analysis, the improvement on WVD is a crucial problem and a breakthrough for damage detection
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