Modal Identification of damped vibrating systems by iterative smooth orthogonal decomposition method

Hu, Zhixaing; Li, Jun; Zhi, Lunhai; Huang, Xiao

doi:10.1177/1369433220968442

Cited by 3 publications

(3 citation statements)

References 30 publications

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“…However, it should be noted that the HAVOC framework is also applicable to linear structures since the HAVOC discovers a sparse Fourier basis made of sinusoids that match well with the Fourier spectrum (Dylewsky et al, 2020a; Kamb et al, 2020). According to the author’s previous study (Peng et al, 2021b), the eigenvalue and eigenvector of a linear steel frame approximated by HAVOC framework agree well with the natural frequency and mode shape obtained from frequency domain decomposition (FDD) and complex mode indication function (CMIF) methods (Hu et al, 2021; Li et al, 2015; Wen et al, 2017). In literature, the HAVOC framework has been applied to construct a linear control model to reconstruct and forecast the real-world power grid load (Dylewsky et al, 2020b).…”

Section: Introductionsupporting

confidence: 68%

Phase space reconstruction and Koopman operator based linearization of nonlinear model for damage detection of nonlinear structures

Peng

2022

Advances in Structural Engineering

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Vibration responses of structures with inherent nonlinear behaviors can degrade the performance of linear theory based damage detection methods. This paper integrates the phase space reconstruction and Koopman operator to provide a linear representation of strongly nonlinear systems. Similar to the modal analysis of linear systems, the linearized model allows for handling nonlinear vibration responses as a superposition of the discovered nonlinear coordinate basis. This property provides opportunities to identify the structural condition change of structures with initial nonlinearity. The eigen-frequencies extracted from the Koopman operator are served as damage features. The performance of using the eigen-frequencies from dynamic mode decomposition for nonlinear structural damage detection is compared with the natural frequencies obtained from fast Fourier transformation and the time-frequency analysis method to emphasize the superiority of the proposed approach. Two experimental structures exhibiting inherent nonlinearity, namely, a magneto-elastic system and a precast segment beam, are employed to demonstrate the feasibility and effectiveness of using the proposed method for identifying condition change of nonlinear structures. Results demonstrate that the presented nonlinearity linearization framework and the damage feature defined in this study are suitable for reliably identifying the occurrence of structural damage and condition change in structures with inherent nonlinearities.

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Section: Introductionsupporting

confidence: 68%

Phase space reconstruction and Koopman operator based linearization of nonlinear model for damage detection of nonlinear structures

Peng

2022

Advances in Structural Engineering

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“…In order to verify the accuracy of the improved SSI method, a spring oscillator system with three-degrees-of-freedom (DOF) was considered [30] (Figure 6). The parameters of the 3-DOF system were The difference between the conventional SSI method and the improved SSI method with reconstructed displacements was numerically simulated by the 3-DOF system.…”

Section: -Dof Mass-damping-spring Systemmentioning

confidence: 99%

“…In order to verify the accuracy of the improved SSI method, a spring oscillator system with three-degrees-of-freedom (DOF) was considered [30] (Figure 6). The parameters of the 3-DOF system were m 1 = 7 kg, m 2 = 10 kg, m 3 = 10 kg, k 1 = 1000 N/m, k 2 = 2000 N/m, and k 3 = 100 N/m.…”

Section: -Dof Mass-damping-spring Systemmentioning

confidence: 99%

Modal Parameter Identification of Structures Using Reconstructed Displacements and Stochastic Subspace Identification

Guo

Zhang

et al. 2021

Applied Sciences

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A method of modal parameter identification of structures using reconstructed displacements was proposed in the present research. The proposed method was developed based on the stochastic subspace identification (SSI) approach and used reconstructed displacements of measured accelerations as inputs. These reconstructed displacements suppressed the high-frequency component of measured acceleration data. Therefore, in comparison to the acceleration-based modal analysis, the operational modal analysis obtained more reliable and stable identification parameters from displacements regardless of the model order. However, due to the difficulty of displacement measurement, different types of noise interferences occurred when an acceleration sensor was used, causing a trend term drift error in the integral displacement. A moving average low-frequency attenuation frequency-domain integral was used to reconstruct displacements, and the moving time window was used in combination with the SSI method to identify the structural modal parameters. First, measured accelerations were used to estimate displacements. Due to the interference of noise and the influence of initial conditions, the integral displacement inevitably had a drift term. The moving average method was then used in combination with a filter to effectively eliminate the random fluctuation interference in measurement data and reduce the influence of random errors. Real displacement results of a structure were obtained through multiple smoothing, filtering, and integration. Finally, using reconstructed displacements as inputs, the improved SSI method was employed to identify the modal parameters of the structure.

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Damage Identification Method and Uncertainty Analysis of Beam Structures Based on SVM and Swarm Intelligence Algorithm

Hu¹,

Zhu²,

Huang³

et al. 2022

Buildings

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A two-stage damage identification method for beam structures based on support vector machine and swarm intelligence optimization algorithms is proposed. First, the frequencies and mode shapes of the beam structure are obtained using the smooth orthogonal decomposition method, and the normalized modal curvature is calculated as the input of a pre-trained support vector machine to determine the damage location. Then, the stiffness loss at the damaged location of the structure is calculated using swarm intelligence algorithms. The fitness function is the sum of the residual squares of the frequencies of the damaged structure identified by the smooth orthogonal decomposition method and the frequencies calculated for each iteration of the intelligent optimization algorithm. Numerical examples of a damaged simply supported beam structure are used to verify the damage identification performance of the two-stage method. The accuracy of the support vector machine model under different damage degrees and noise levels is studied using the Monte-Carlo method, and an uncertainty of the damage degree prediction value is studied by comparing the particle swarm optimization algorithm, moth-fire algorithm, and mayfly algorithm.

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Modal Identification of damped vibrating systems by iterative smooth orthogonal decomposition method

Cited by 3 publications

References 30 publications

Phase space reconstruction and Koopman operator based linearization of nonlinear model for damage detection of nonlinear structures

Phase space reconstruction and Koopman operator based linearization of nonlinear model for damage detection of nonlinear structures

Modal Parameter Identification of Structures Using Reconstructed Displacements and Stochastic Subspace Identification

Damage Identification Method and Uncertainty Analysis of Beam Structures Based on SVM and Swarm Intelligence Algorithm

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