Abstract: The present disclosure provides a method for identifying modal parameters of engineering structures based on fast stochastic subspace identification, and relates to the field of structural modal parameters identification. The method includes the following steps: collecting responses; obtaining a unitary matrix by performing random projection on and QR decomposition of a matrix; obtaining a small matrix by projecting a Toeplitz matrix onto the unitary matrix; obtaining U, S, V matrices respectively by performing singular value decomposition of the small matrix; performing eigenvalue decomposition; and determining an order interval. According to the present disclosure, the small matrix is obtained through performing random projection on and QR decomposition of the traditional Toeplitz matrix, the dimensionality of the matrix by singular value decomposition is reduced and the computational efficiency of the matrix is improved.

Abstract: A damage identification method for a cantilever beam based on a multifractal spectrum of a multi-scale reconstructed attractor includes: acquiring an original acceleration signal of the cantilever beam by a dynamic measurement system, performing stationary wavelet decomposition on a pretreated acceleration signal to obtain multi-scale sub-signals, selecting the multi-scale sub-signal that can represent main vibration characteristics of the cantilever beam for phase space reconstruction and normalization to obtain a normalized multi-scale reconstructed attractor, constructing the multifractal spectrum of the multi-scale reconstructed attractor, establishing a damage index based on a singularity index of the multifractal spectrum, and identifying and locating damage of the cantilever beam according to a relative numerical value of the damage index.