Singular Spectrum Analysis for Modal Estimation from Stationary Response Only

Abstract

Conventional experimental modal analysis uses excitation and response information to estimate the frequency response function. However, many engineering structures face excitation signals that are difficult to measure, so output-only modal estimation is an important issue. In this paper, singular spectrum analysis is employed to construct a Hankel matrix of appropriate dimensions based on the measured response data, and the observability of the system state space model is used to treat the Hankel matrix as three components containing system characteristics, excitation and noise. Singular value decomposition is used to factorize the data matrix and use the characteristics of the left and right singular matrices to reduce the dimension of the data matrix to improve calculation efficiency. Furthermore, the singular spectrum is employed to estimate the minimum order to reconstruct the Hankel matrix; then, the excitation and noise components can be removed, and the system observability matrix can be obtained. By appropriately a factorizing system observability matrix, we obtain the system matrix to estimate the modal parameters. In addition, the fictitious modes produced by increasing the order of the matrix can be eliminated through the stabilization diagram.

SSANet: normal-mode interference spectrum extraction via SSA algorithm-unrolled neural network

“…V † ∈ R RÂK , its row vectors are orthogonal and normalized. S ∈ R RÂR is a singular value matrix consisting of zero off-diagonal entries and obvious non-zero singular values on the main diagonal entries (Lin and Wu, 2022). The symbol ' †' represents the conjugate transpose.…”

“…It is well known that, if the signal subspace has finite dimensions and is orthogonal to the noise subspace, SSA is a powerful tool for separating the signal subspace from the noise subspace through grouping (Vautard et al, 1992;Li et al, 2019). Generally, SSA consists of four steps: embedding, singular value decomposition (SVD), grouping, and diagonal averaging (Hassani, 2007;Kalantari et al, 2020;Lin and Wu, 2022). The received SIS consists of a finite number of dominant NMIS that satisfy the above SSA assumption.…”