Blind modal identification using generalized multivariate autoregressive model and extended joint eigenvalue decomposition

This study introduces the concept of blind source separation (BSS) based on a multivariate autoregressive (AR) model in the field of operational modal analysis (OMA), with improvements and extensions. A novel blind modal identification method is proposed, which combines a non-adjacent widely linear generalized multivariate AR (GMAR) model with an extended joint eigenvalue decomposition (EJEVD) approach. First, a non-adjacent widely linear GMAR model is constructed for the analytical form of vibration response signals. Then, the GMAR coefficients are subjected to joint approximate diagonalization using EJEVD to obtain the mode shape matrix. This process converts the multi-degree-of-freedom vibration responses in the physical space into single-degree-of-freedom modal coordinates in the modal space. Finally, a simple single-modal identification method is employed to extract modal frequencies and damping parameters. The proposed method is applicable to both real and complex modal analysis, combining the practical engineering advantages of OMA with the benefit of BSS, which does not require parametric estimation of the system model. Comparative results from numerical simulations show that the proposed method outperforms methods based on second-order blind identification and complexity pursuit BSS methods in separating closely spaced modes. Experimental validation further demonstrates the effectiveness and engineering value of this method.