Time-varying modal identification using multi-channel measurements based on multivariate variational mode decomposition

Structural modal parameters are essential to provide dynamic information for data analysis of structural health monitoring (SHM) system. Because of the variation of the physical properties or the influence of the environment, the structural modal parameters may change with time during the operation, showing time-varying characteristics. Therefore, accurate identification of time-varying modal parameters shows to be an important issue for SHM. In this paper, a time-varying modal identification method is proposed by improving the multivariate variational mode decomposition (MVMD) method with autoregressive power spectrum and windowed principal component analysis (PCA). Firstly, the method for determination of initial center frequency is proposed by autoregressive power spectrum to improve the efficiency of MVMD. Secondly, intrinsic mode function for each mode is extracted using multi-channel responses by MVMD. Subsequently, instantaneous frequencies are identified through detecting the ridgeline of the synchro-squeezed short-time Fourier transform (SSTFT). Moreover, identification method for time-varying mode shapes is proposed by using the windowed PCA of the multi-channel intrinsic modes. Finally, the proposed method is verified by the numerical and practical studies. The results of the numerical study show that the method is effective for continuously varying modal parameters under impulse and random excitations. Through the data analysis of practical bridge, the capability for practical application is demonstrated.