The invention discloses a mode identification method based on an unsupervised optimization
covariance random subspace method. The method comprises the following steps: arranging a
vibration sensor on a to-be-detected structure with
noise interference or a weak excitation mode to obtain a structure dynamic response; constructing a
Hankel matrix, calculating a
covariance matrix Ri, and constructing a
Toeplitz matrix based on the Ri; calculating an extended
observable matrix Oi and an extended controllable matrix Gamma i based on the weighted
Toeplitz matrix; defining the range of the row
block number i and the
model order N of the
Toeplitz matrix; analyzing the sensitivity of the row
block number i of the Toeplitz matrix and the
model order N based on a parameter optimization index kP (i, N); the singular entropy increment of the weighted Toeplitz matrix T1i is calculated; calculating the singular entropy increment curvature of the weighted Toeplitz matrix T1i, and determining a critical
model order Nc (i); calculating an accumulated parameter optimization index kappa P value from a minimum model order Nmin to a critical model order Nc (i) under the condition of different Toeplitz matrix row block numbers i; selecting a parameter combination {iopt, Nopt} corresponding to the minimum parameter as an optimal parameter; identifying a
system matrix and determining
modal parameters, and drawing an original
stability diagram; and on the basis of
DBSCAN clustering, automatically identifying each order of physical modality from candidate modalities containing
noise interference. A corresponding
system is also disclosed.