Structural Modal Parameter Identification Based On Quadratic Time-Frequency Analysis

Structural modal parameter identification is the basic task of structural damage identification,and it is also of vital importance in the structural health monitoring system.The operational modal identification methods which only use the structural vibration responses have been widely concerned.Its advantage of no excitation information is of great value in the health monitoring of operational structures.In recent years,the time-frequency analysis based on blind source separation has become a popular method for operational modal identification.However,most of the existing time-frequency methods can only tackle the issue of determined blind modal identification,and cannot deal with the problem of underdetermined blind source separation in practical engineering.To avoid this issue,the structural modal parameter identification based on quadratic time-frequency analysis is proposed in this paper.The application range of time-frequency distribution matrix is extended from the problem of determined blind modal identification to the problem of underdetermined blind modal identification.Meanwhile,the problems of removing multi-source points in the time-frequency plane,determining the number of active modes and selecting window function parameters are studied in this paper.The detailed contents and achievements are as follows:(1)The underdetermined blind modal identification method based on quadratic time-frequency analysis is proposed by using smoothed pseudo Wigner-Ville distribution(SPWVD)to form the time-frequency distribution matrix.Firstly,the SPWVD of the structural vibration response signal is calculated.Then,a threshold criterion with the singular value decomposition is proposed to remove multi-source time-frequency points and noise points in the time-frequency plane,and then select the time-frequency points containing modal information about only one mode.After that,the clustering algorithm is used to identify the mode shapes of the structure.Finally,the modal frequencies and modal damping ratios are directly extracted from the reconstructed time-frequency domains of modes.Numerical tests show that the proposed method can accurately identify the mode shapes,frequencies and damping ratios.At the same time,the measured data analysis of the steel frame vibration test verifies the availability of the proposed method.The comparison of the results for different identification methods proves the superiority of the proposed method.(2)To tackle the issue that it is difficult to identify the number of active modes in the structural modal parameter identification method,a method to accurately determine the number of active modes involved in the structure is proposed in this paper.With this method,it is unnecessary to assume the number of active modes in the structure in advance.Firstly,the time-frequency distribution matrices of single-source points are selected by using the criterion of removing multi-source points proposed in this paper.Then the principal eigenvectors of all single source points are extracted by eigenvalue decomposition.After that,the density peaks clustering algorithm is introduced,and the principal eigenvector is taken as the data set to be clustered.Finally,the analysis results are drawn into a decision graph,from which the number of active modes in the structure can be automatically identified.Numerical tests prove that the method can accurately identify the number of active modes involved in the structure even in the case of the low signal-to-noise ratio.(3)We study the variation of SPWVD for the vibration response signal when the width of window function is different.Firstly,the effect of time-frequency smoothing window is discussed.Then,the time-frequency resolution changes as well as the variation of the single-source point distribution under different window width combinations are explored for the stationary vibration response signal and the time-varying signal.Finally,a method based on entropy measure is used to determine the optimal window width combination of time-frequency distribution for the different vibration response signals.An example of blind source separation of time-varying signals shows that the optimized time domain smoothing window can enhance the time resolution in time-frequency plane and improve the accuracy of instantaneous frequency identification.