Analytical mode decomposition of time series with decaying amplitudes and overlapping instantaneous frequencies

Wang, Zuo‐Cai; Chen, Gen-Da

doi:10.1088/0964-1726/22/9/095003

Cited by 40 publications

(25 citation statements)

References 37 publications

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“…The analytical signal of

u_{r}^{f} ((), t)

can be written as follows:

A_{r} ((), t) e^{j θ_{r} ((), t)} = u_{r}^{f} ((), t) + italicjH ([], u_{r}^{f} ((), t))

in which A r ( t ) and θ r ( t ) are the instantaneous amplitude and phase angle of the r th free vibration response

u_{r}^{f} ((), t)

, respectively; H [] represents the Hilbert Transform. The phase and amplitude can be expressed as follows:

θ_{r} = {tan}^{- 1} ({}, \frac{u_{r}^{f} (t)}{H [u_{r}^{f} (t)]}), A_{r} ((), t) = \sqrt{{\{A_{r} (t)\}}^{2} + {\{H [u_{r}^{f} (t)]\}}^{2}} .

…”

Section: Operational Modal Identification Based On the Improved Ewt Amentioning

confidence: 99%

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Operational modal identification of structures based on improved empirical wavelet transform

Hao

2019

Struct Control Health Monit

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Summary This paper proposes an improved Empirical Wavelet Transform (EWT) approach for structural operational modal identification based on measured dynamic responses of structures under ambient vibrations. Two steps are involved in the improved EWT approach. In the first step, the standardized autoregressive power spectrum of the measured response is calculated to define the boundaries of frequency components for the subsequent EWT analysis. The second step is to decompose the measured response into a number of Intrinsic Mode Functions (IMFs) by using EWT. When the Intrinsic Mode Functions are obtained, structural modal information such as natural frequencies, mode shapes, and damping ratios can be identified by using Hilbert transform and Random Decrement Technique. In numerical studies, a simulated signal is used to investigate the effectiveness of the proposed approach. Operational modal identification based on the proposed approach and procedure is conducted to identify the modal parameters of a simulated spatial frame structure under the ambient excitations. The proposed approach is further used for operational modal identification of a seven‐storey shear type steel frame structure in the laboratory and a real footbridge under ambient vibrations to verify the accuracy and performance. The modal identification results from both numerical simulations and experimental validations demonstrate that the proposed approach can effectively and accurately decompose the vibration responses and identify the structural modal parameters under operational conditions.

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“…The analytical signal of

u_{r}^{f} ((), t)

can be written as follows:

A_{r} ((), t) e^{j θ_{r} ((), t)} = u_{r}^{f} ((), t) + italicjH ([], u_{r}^{f} ((), t))

in which A r ( t ) and θ r ( t ) are the instantaneous amplitude and phase angle of the r th free vibration response

u_{r}^{f} ((), t)

, respectively; H [] represents the Hilbert Transform. The phase and amplitude can be expressed as follows:

θ_{r} = {tan}^{- 1} ({}, \frac{u_{r}^{f} (t)}{H [u_{r}^{f} (t)]}), A_{r} ((), t) = \sqrt{{\{A_{r} (t)\}}^{2} + {\{H [u_{r}^{f} (t)]\}}^{2}} .

…”

Section: Operational Modal Identification Based On the Improved Ewt Amentioning

confidence: 99%

“…in which A r (t) and θ r (t) are the instantaneous amplitude and phase angle of the rth free vibration response u f r t ð Þ, respectively; H[] represents the Hilbert Transform. The phase and amplitude can be expressed as follows: 40,41…”

Section: Operational Modal Identification Based On the Improved Ewtmentioning

confidence: 99%

Operational modal identification of structures based on improved empirical wavelet transform

Hao

2019

Struct Control Health Monit

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“…Further, AMD-based Hilbert transform analysis was proposed to identify the instantaneous frequencies of time-varying and time-invariant systems. [28,29] Continuous wavelet transform was also employed to identify the time-varying frequency of civil structures. [30] A penalty function was used to reduce the effect of the measurement noise, and the time-varying frequencies of a cable system with the varying tension force were calculated from the wavelet ridges.…”

Section: Introductionmentioning

confidence: 99%

Time‐varying system identification using variational mode decomposition

Hao

et al. 2018

Struct Control Health Monit

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Summary A new time‐varying system identification approach is proposed in this paper by using variational mode decomposition. The newly developed variational mode decomposition technique can decompose the measured responses into a limited number of intrinsic mode functions, and the instantaneous frequencies of time‐varying systems are identified by the Hilbert transform of each intrinsic mode function. Numerical and experimental verifications are conducted to demonstrate the effectiveness and accuracy of using the proposed approach for time‐varying system identification, that is, to obtain the instantaneous frequency. Numerical studies on a structural system with time‐varying stiffness are conducted. Experimental validations on analyzing the measured vibration data in the laboratory from a steel frame structure and a time‐varying bridge–vehicle system are also conducted. The results from the presented technique are compared with those from empirical mode decomposition‐based methods, which verify that the developed approach can identify the instantaneous frequencies with a better accuracy.

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“…WT has become an important tool in MPI, because it can be used to analyze nonlinear and non-stationary signals, characteristics found in the measured signals [25,26]; however, a carefully selection of the mother wavelet and its parameters must be done in order to ensure a good time-frequency resolution. Moreover, it is sensitive to noisy signals [26]. On the other hand, the EMD method is an adaptive scheme, which is designed to process nonlinear and non-stationary signals according to the frequencies contented in the time-series signal.…”

Section: Introductionmentioning

confidence: 99%

A Two-Step Strategy for System Identification of Civil Structures for Structural Health Monitoring Using Wavelet Transform and Genetic Algorithms

et al. 2017

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Nowadays, the accurate identification of natural frequencies and damping ratios play an important role in smart civil engineering, since they can be used for seismic design, vibration control, and condition assessment, among others. To achieve it in practical way, it is required to instrument the structure and apply techniques which are able to deal with noise-corrupted and non-linear signals, as they are common features in real-life civil structures. In this article, a two-step strategy is proposed for performing accurate modal parameters identification in an automated manner. In the first step, it is obtained and decomposed the measured signals using the natural excitation technique and the synchrosqueezed wavelet transform, respectively. Then, the second step estimates the modal parameters by solving an optimization problem employing a genetic algorithm-based approach, where the micropopulation concept is used to improve the speed convergence as well as the accuracy of the estimated values. The accuracy and effectiveness of the proposal are tested using both the simulated response of a benchmark structure and the measurements of a real eight-story building. The obtained results show that the proposed strategy can estimate the modal parameters accurately, indicating than the proposal can be considered as an alternative to perform the abovementioned task.

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Analytical mode decomposition of time series with decaying amplitudes and overlapping instantaneous frequencies

Cited by 40 publications

References 37 publications

Operational modal identification of structures based on improved empirical wavelet transform

Operational modal identification of structures based on improved empirical wavelet transform

Time‐varying system identification using variational mode decomposition

A Two-Step Strategy for System Identification of Civil Structures for Structural Health Monitoring Using Wavelet Transform and Genetic Algorithms

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