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. 2022 Mar 28;22(7):2585.
doi: 10.3390/s22072585.

Singular Spectrum Analysis for Modal Estimation from Stationary Response Only

Chang-Sheng Lin  1 , Yi-Xiu Wu  1
Affiliations

Singular Spectrum Analysis for Modal Estimation from Stationary Response Only

Chang-Sheng Lin et al. Sensors (Basel). .

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.

Keywords: Hankel matrix; modal estimation; singular spectrum analysis; state space.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
A schematic diagram of the 6-DOF chain model.
Figure 2
Figure 2
Power spectrum associated with the simulated stationary white noise served as the excitation input acting on the 6-DOF chain model.
Figure 3
Figure 3
A stabilization diagram of 6-DOF chain model subjected to stationary white noise excitation (K = 50,000) (a) original SSA (b) modified SSA (MSSA).
Figure 4
Figure 4
A stabilization diagram with various K of 6-DOF chain model subjected to stationary white noise excitation.
Figure 5
Figure 5
Convergence trend curves with various K for damping ratios identification results of 6-DOF chain model subjected to stationary white noise excitation.
Figure 5
Figure 5
Convergence trend curves with various K for damping ratios identification results of 6-DOF chain model subjected to stationary white noise excitation.
Figure 6
Figure 6
A stabilization diagram with various L of 6-DOF chain model subjected to stationary white noise excitation.
Figure 7
Figure 7
Convergence trend curves with various L for damping ratios identification results of 6-DOF chain model subjected to stationary white noise excitation.
Figure 7
Figure 7
Convergence trend curves with various L for damping ratios identification results of 6-DOF chain model subjected to stationary white noise excitation.
Figure 8
Figure 8
Comparison between the identified and exact mode shapes of the 6-DOF chain model system subjected to stationary white-noise input.
Figure 9
Figure 9
A schematic diagram of 2-D truss structure.
Figure 10
Figure 10
Power spectra associated with the simulated stationary white noise served as the excitation input respectively acting on the eight mass points of 2-D truss structure.
Figure 10
Figure 10
Power spectra associated with the simulated stationary white noise served as the excitation input respectively acting on the eight mass points of 2-D truss structure.
Figure 11
Figure 11
A stabilization diagram of 2-D truss structure subjected to stationary white noise excitation.
Figure 12
Figure 12
Comparison between the identified and exact mode shapes of the 2-D truss structure subjected to stationary white-noise input.
Figure 12
Figure 12
Comparison between the identified and exact mode shapes of the 2-D truss structure subjected to stationary white-noise input.
Figure 13
Figure 13
A 7-DOF model of a sedan.
Figure 14
Figure 14
A stabilization diagram of 7-DOF model of a sedan subjected to stationary white noise excitation.
Figure 15
Figure 15
Comparison between the identified mode shapes and the exact mode shapes of the 7-DOF model of a sedan subjected to stationary white-noise input.
Figure 15
Figure 15
Comparison between the identified mode shapes and the exact mode shapes of the 7-DOF model of a sedan subjected to stationary white-noise input.
Figure 16
Figure 16
A model of 7-DOF highly coupled system.
Figure 17
Figure 17
Power spectra associated with the simulated stationary white noise served as the excitation input respectively acting on each mass point of a 7-DOF highly coupled system.
Figure 18
Figure 18
A stabilization diagram of 7-DOF highly coupled system subjected to stationary white noise excitation.
Figure 19
Figure 19
A model of 7-DOF highly coupled system.
Figure 19
Figure 19
A model of 7-DOF highly coupled system.
See this image and copyright information in PMC

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