双线性时频分布交叉项提取及损伤识别应用

响矩阵R=－K－1tt Kts。定性揭示了R的数学和物理意义，定量论证R的固有特征，并给予图解说明和算例论证，证明由R计算得到的拟静力响应在数学意义层面独立于结构的动力反应，而在物理意义层面二者并非相互独立而存在。

Cross-Term Extraction from Bilinear Time-Frequency Distributions and Application in Structural Damage Detection

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 characteristics 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 that combines the short-time flourier spectrum and Wigner-Ville distribution. Then a two-dimensional time-frequency transformation matrix is constructed, and the complete cross-term is extracted. The distribution character is in favor of the structural damage identification. Through theoretical analysis, model experiments and numerical simulation of the girder structure, the change rate of the cross-term amplitude is validated to identify the damage location and degree. The effectiveness of the cross-term of the bilinear time-frequency distribution for damage detection is confirmed, and the analytical method of damage identification used in structural engineering is available.