Parameters identification of closely spaced modes with the covariance-drivern stochastic subspace and damping ratio dispersion method

Electromechanical equipment with quasi-symmetric and partially symmetrical structures is widespread in the industry, which not only makes the dynamic characteristics of the system more complex but also leads to severe closely spaced modes. The existence of closely spaced modes can lead to more confusion, because severe closely spaced modes have similar frequency eigenvalues and some singular eigenvalues are prone to generate spurious modes in matrix computations. In this paper, the covariance-drivern stochastic subspace and damping ratio dispersion (SSI-COV-DRD) method is proposed, which in comparison with previous methods, identification process directly is performed in the stochastic subspace by solving the system matrix of the time domain signal to overcome modal aliasing of the frequency-based method. Firstly, a Toeplitz matrix is constructed with a time series signal and then the system modal parameters are gained from the system matrix after performing singular value decomposition (SVD) to the Toeplitz matrix. Subsequently, the poles of the continuous model order are classified by a hierarchical clustering algorithm to obtain stabilization diagram and the real physical modes are automatically extracted from the stabilization diagram according to the choice criteria. Finally, the damping ratio dispersion index is calculated to express the nonlinear distribution characteristic of the damping ratio. Numerical examples for the five-order free vibration simulation signals with noise-free and noise indicate that the proposed method can simultaneously identify the modal frequency and damping ratio with high accuracy in severe closely spaced modes, especially for the repeated frequency modes. Since the bolt connection rotor of the aero-engine usually produces severe closely spaced modes in vibration due to the structural symmetry, the frequency and damping ratio are extracted and the damping ratio dispersion index is calculated from different bolt loosening states, which is helpful for the bolt loosening detection of aviation safety assurance and maintenance.