On using the Hilbert transform for blind identification of complex modes: A practical approach

Antunes, José; Debut, Vincent; Piteau, Pilippe; Delaune, Xavier; Borsoi, Laurent

doi:10.1016/j.jsv.2017.09.017

Cited by 7 publications

(9 citation statements)

References 23 publications

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“…The details have been investigated by the authors’ previous paper (Yao et al., 2018). The real modal shapes can be also obtained by the related works (Antunes et al., 2018; Reju et al., 2009).…”

Section: Complex Frequency Identificationmentioning

confidence: 99%

“…Motivated from Antunes et al. (2018), according to Equations () and (), the following equation is satisfied:

[\begin{matrix} y_{d} ((), k) \\ {\hat{boldy}}_{d} ((), k) \end{matrix}] = [\begin{matrix} {normalΦ}^{R} & - Φ^{I} \\ {normalΦ}^{I} & {normalΦ}^{R} \end{matrix}] [\begin{matrix} q^{R} ((), k) \\ q^{I} ((), k) \end{matrix}]

…”

Section: Complex Frequency Identificationmentioning

confidence: 99%

“…Antunes et al. (2018) identified the complex modes using the blind identification method through analytic signals. Variational mode decomposition separates the response into modal responses according to center frequency and frequency bandwidth, and calculates the modal parameters through Hilbert transform (Dragomiretskiy & Zosso, 2014).…”

Section: Introductionmentioning

confidence: 99%

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Complex frequency identification using real modal shapes for a structure with proportional damping

Yao

et al. 2021

Computer aided Civil Eng

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Modal identification is based on modal superposition theory. For structures with proportional damping, the structural responses are recognized as real modal shapes multiplied by real modal coordinates. However, it is not true because the actual modal shapes should be complex even though they can be normalized to real ones. If the modal shapes are recognized as real ones, the modal superposition theory cannot reflect the actual modal parameters. This paper proposes an innovative method to identify complex frequencies for a structure with proportional damping using the identified real modal shapes, where the complex modal shapes are considered. The proportional damping is ideal but always assumed in practical engineering. The characteristic of the proposed method is that the complex property of frequencies is considered along with modal identification process. First, the reason why the complex modal shapes are hidden is revealed. When the real modal shapes are obtained, the Hilbert transform of analytical responses is used to estimate complex coordinates. Then, formulas to identify the complex frequencies are derived. The k‐means clustering method is employed. Finally, the proposed method is used in a numerical example and a practical bridge example. The results show that the proposed method can estimate the complex frequencies effectively, and can be used in practical engineering.

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Section: Complex Frequency Identificationmentioning

confidence: 99%

“…Motivated from Antunes et al. (2018), according to Equations () and (), the following equation is satisfied:

[\begin{matrix} y_{d} ((), k) \\ {\hat{boldy}}_{d} ((), k) \end{matrix}] = [\begin{matrix} {normalΦ}^{R} & - Φ^{I} \\ {normalΦ}^{I} & {normalΦ}^{R} \end{matrix}] [\begin{matrix} q^{R} ((), k) \\ q^{I} ((), k) \end{matrix}]

…”

Section: Complex Frequency Identificationmentioning

confidence: 99%

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Complex frequency identification using real modal shapes for a structure with proportional damping

Yao

et al. 2021

Computer aided Civil Eng

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“…More and more nonlinear analysis techniques can be applied to signal processing and recognition [4]. Examples are combining high-order spectrum [5], wavelet packet transform [6], Hilbert transforms [7], extracting eigenfrequencies from signals, empirical mode decomposition, and other advanced signal processing techniques. EMD has become a popular method due to its inherent properties and adaptability to nonstationary signals [8].…”

Section: Introductionmentioning

confidence: 99%

A Method for Extracting Fingerprint Feature of Communication Satellite Signal

Huang

Guo

et al. 2022

Wireless Communications and Mobile Computing

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Satellite communications have historically played a vital role in a variety of industries, including maritime communications. The marine communication environment is exceedingly complicated, and extracting the characteristics of communication equipment signals is difficult. This research proposes a method for extracting satellite signal fingerprint characteristics based on the maritime complex communication environment. To create the signal fingerprint feature vector, the marginal spectral entropy is determined using the HHT (Hilbert-Huang transform) time-frequency analysis approach. Furthermore, by merging the Mahalanobis distance approach with the EEMD (ensemble empirical mode decomposition) algorithm, this study enhances it. The improved EEMD algorithm decomposes the original signal using EEMD, calculates the Mahalanobis distance between each IMF (intrinsic mode function) component and the raw data, optimizes the adaptive threshold using MPA (marine predators algorithm), and then analyzes the IMF components and redundant IMF components. It was decided to eliminate superfluous IMF components. Finally, this article mimics the Iridium satellite signal. The results of the experiments suggest that using this strategy minimizes the computational cost of the next step in fingerprint feature extraction while ensuring the accuracy of signal fingerprint feature recognition.

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“…With the development of nonlinear dynamics, many nonlinear analytical techniques have been applied to identifying and predicting the complex dynamic nonlinearity of the radiation source signal [ 3 ]. Among them, the most typical technique is to extract the characteristic frequency from the radiation source signal through the combined usage of some advanced signal processing techniques (higher order spectra [ 4 ], wavelet package transform [ 5 ], the Hilbert transform [ 6 ], empirical mode decomposition, etc.) and further evaluating the radiation source signal by comparing it with the theoretical characteristic frequency value with the aid of expert judgement.…”

Section: Introductionmentioning

confidence: 99%

Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

Chen¹,

Han³

et al. 2018

R. Soc. open sci.

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Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.

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On using the Hilbert transform for blind identification of complex modes: A practical approach

Cited by 7 publications

References 23 publications

Complex frequency identification using real modal shapes for a structure with proportional damping

Complex frequency identification using real modal shapes for a structure with proportional damping

A Method for Extracting Fingerprint Feature of Communication Satellite Signal

Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

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