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Journal Article

Synchroextracting Transform

TL;DR: The main idea of SET is to only retain the TF information of STFT results most related to time-varying features of the signal and to remove most smeared TF energy, such that the energy concentration of the novel TF representation can be enhanced greatly.
Abstract: In this paper, we introduce a new time-frequency (TF) analysis (TFA) method to study the trend and instantaneous frequency (IF) of nonlinear and nonstationary data. Our proposed method is termed the synchroextracting transform (SET), which belongs to a postprocessing procedure of the short-time Fourier transform (STFT). Compared with classical TFA methods, the proposed method can generate a more energy concentrated TF representation and allow for signal reconstruction. The proposed SET method is inspired by the recently proposed synchrosqueezing transform (SST) and the theory of the ideal TFA. To analyze a signal, it is important to obtain the time-varying information, such as the IF and instantaneous amplitude. The SST is to squeeze all TF coefficients into the IF trajectory. Differ from the squeezing manner of SST, the main idea of SET is to only retain the TF information of STFT results most related to time-varying features of the signal and to remove most smeared TF energy, such that the energy concentration of the novel TF representation can be enhanced greatly. Numerical and real-world signals are employed to validate the effectiveness of the SET method.
Citations
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Journal Article
TL;DR: The proposed TFA method is based on synchrosqueezing transform and employs an iterative reassignment procedure to concentrate the blurry TF energy in a stepwise manner, meanwhile retaining the signal reconstruction ability.
Abstract: Time-frequency (TF) analysis (TFA) method is an important tool in industrial engineering fields. However, restricted to Heisenberg uncertainty principle or unexpected cross terms, the classical TFA methods often generate blurry TF representation, which heavily hinder its engineering applications. How to generate the concentrated TF representation for a strongly time-varying signal is a challenging task. In this paper, we propose a new TFA method to study the nonstationary features of strongly time-varying signals. The proposed method is based on synchrosqueezing transform and employs an iterative reassignment procedure to concentrate the blurry TF energy in a stepwise manner, meanwhile retaining the signal reconstruction ability. Two implementations of the discrete algorithm are provided, which show that the proposed method has limited computational burden and has potential in real-time application. Moreover, we introduce an effective algorithm to detect the instantaneous frequency trajectory, which can be used to decompose monocomponent modes. Numerical and real-world signals are employed to validate the effectiveness of the proposed method by comparing with some advanced methods. By comparisons, it is shown that the proposed method has the better performance in addressing strongly time-varying signals and noisy signals.

202 citations


Cites background or methods from "Synchroextracting Transform"

  • ...We substitute Ts[1](t, η) into Ts[2](t, η), and then the MSST (N = 2) can be expressed as...

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  • ...In this section, we focus on an abnormal vibration of a heavy oil catalytic machine set [2], [25]....

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  • ...T IME-FREQUENCY (TF) analysis (TFA) is an effective tool to analyze time-varying signals and has drawn considerable attention in the past few decades [1], [2]....

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  • ...If we substitute Ts[2](t, η) into Ts[3](t, η), the MSST (N = 3) can be derived as follows:...

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  • ...This is because the rub-impact fault makes the rotor running at an unstable speed [2], [25]....

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Journal ArticleDOI
TL;DR: A three-stage SSL approach using data augmentation (DA) and metric learning is proposed for an intelligent bearing fault diagnosis under limited labeled data to demonstrate that the proposed method can perform better in bearing fault diagnosed under limited labeling samples than existing diagnostic methods.

141 citations

Journal ArticleDOI
Gang Yu1
TL;DR: Comparisons show that the proposed transient-extracting transform method can provide a much more energy-concentrated time–frequency representation, and the transient components can be extracted with a significantly larger kurtosis.
Abstract: In industrial rotating machinery, the transient signal usually corresponds to the failure of a primary element, such as a bearing or gear. However, faced with the complexity and diversity of practical engineering, extracting the transient signal is a highly challenging task. In this paper, we propose a novel time–frequency analysis method termed the transient-extracting transform, which can effectively characterize and extract the transient components in the fault signals. This method is based on the short-time Fourier transform and does not require extended parameters or a priori information. Quantized indicators, such as Renyi entropy and kurtosis, are employed to compare the performance of the proposed method with other classical and advanced methods. The comparisons show that the proposed method can provide a much more energy-concentrated time–frequency representation, and the transient components can be extracted with a significantly larger kurtosis. The numerical and experimental signals are used to show the effectiveness of our method.

134 citations


Cites background from "Synchroextracting Transform"

  • ...Considering that the different fault signals occupy distinct frequency bands, the joined time–frequency (TF) analysis (TFA) is an effective tool for characterizing transient faults that have nonstationary TF features [4]....

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  • ...For more comparisons, we utilize the high-order SST (e.g., second-SST, third-SST, and fourth-SST) and SET methods to address this signal, and the TF results are shown in Fig....

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  • ..., demodulated SST [17], matching SST [18], high-order SST [19], and synchroextracting transform (SET) [4]....

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  • ...It can be observed that the SST and SET methods seem to TABLE III...

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  • ...To further improve the performance of the SST, some advanced methods are proposed, e.g., demodulated SST [17], matching SST [18], high-order SST [19], and synchroextracting transform (SET) [4]....

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Journal ArticleDOI
TL;DR: This paper presents a new decomposition approach called adaptive chirp mode pursuit (ACMP), similar to the matching pursuit method, the ACMP captures signal modes one by one in a recursive framework.

116 citations

Journal ArticleDOI
TL;DR: It is shown that the energy concentration of the time–frequency representation (TFR) of a strong frequency-modulated signal from a PCT transform can be further enhanced by an SET transform, and the TFR calculated from the proposed technique matches well with the ideal TFR, which demonstrates the superiority of the current technique in dealing with nonstationary signals having rapidly changing dynamics.
Abstract: Time–frequency analysis (TFA) technique is an effective approach to capture the changing dynamic in a nonstationary signal. However, the commonly adopted TFA techniques are inadequate in dealing with signals having a strong nonstationary characteristic or multicomponent signals having close frequency components. To overcome this shortcoming, a new TFA technique applying a polynomial chirplet transform (PCT) in association with a synchroextracting transform (SET) is proposed in this paper. It is shown that the energy concentration of the time–frequency representation (TFR) of a strong frequency-modulated signal from a PCT transform can be further enhanced by an SET transform. The technique can also be employed to accurately extract the signal components of a multicomponent nonstationary signal with close frequency components by adopting an iterative process. It is found that the TFR calculated from the proposed technique matches well with the ideal TFR, which demonstrates the superiority of the current technique in dealing with nonstationary signals having rapidly changing dynamics. Results from the analysis of the experimental data under varying speed conditions confirm the validity of the proposed technique in dealing with nonstationary signals from practical sources.

111 citations


Cites background or methods from "Synchroextracting Transform"

  • ...Nonstationary signals from practical sources are often manifested as multicomponent signals that can be modeled as [35]–[38]...

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  • ...Several preprocessing and postprocessing techniques were developed to improve the readability of the TFR results calculated using the above-mentioned TFA techniques [26]–[38]....

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  • ...Postprocessing techniques can be employed to improve the readability of TFR results by reallocating the TF coefficients of an original TFR into the correct IF trajectory positions [34]–[38]....

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  • ...The goal of a TFA algorithm is to achieve an ITFA as [27], [30], [38]...

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  • ...Several novel TFA techniques have been developed in recent years [22]–[38]....

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References
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Journal ArticleDOI
TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

18,956 citations


"Synchroextracting Transform" refers background in this paper

  • ...According to (4), the ITFA of a multicomponent signal is the superposition of ITFA of each monocomponent, and it is suggested to be decomposed first [15], [16]....

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Journal ArticleDOI
TL;DR: This paper introduces a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and proves that the method does indeed succeed in decomposing arbitrary functions in this class.

1,704 citations


"Synchroextracting Transform" refers background or methods in this paper

  • ...However, considering the calculation error and that the SEO’s real part needs to be utilized in practical applications [6], [17], it is suggested that (25) be rewritten as the following equation:...

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  • ...As a benefit of the reconstruction ability, the monocomponent modes can be recovered from the SST result to a highly precise degree [6]....

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  • ...For a well-separated multicomponent signal, the expression (16) can also work for estimating the IF of each mode effectively [6], [17], which is calculated by...

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  • ...2696503 [6]–[8], parametric TFA (PTFA) method [9]–[12], and demodulated TFA (DTFA) method [7], [13]....

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  • ...RS [4] and SST [6], [8] were developed as postprocessing tools and have the ability to reassign or squeeze the TF coefficients by classical TFA methods into the IF trajectory, which are approximated to the ITFA representation....

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Journal ArticleDOI
TL;DR: The reassignment method, first applied by Kodera, Gendrin, and de Villedary (1976) to the spectrogram, is generalized to any bilinear time-frequency or time-scale distribution.
Abstract: In this paper, the use of the reassignment method, first applied by Kodera, Gendrin, and de Villedary (1976) to the spectrogram, is generalized to any bilinear time-frequency or time-scale distribution. This method creates a modified version of a representation by moving its values away from where they are computed, so as to produce a better localization of the signal components. We first propose a new formulation of this method, followed by a thorough theoretical study of its characteristics. Its practical use for a large variety of known time-frequency and time-scale distributions is then addressed. Finally, some experimental results are reported to demonstrate the performance of this method. >

1,268 citations


"Synchroextracting Transform" refers methods in this paper

  • ...Recently, some advanced postprocessing methods have been proposed, such as the reassignment method (RS) [4], [5], synchrosqueezing transform (SST)...

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  • ...RS [4] and SST [6], [8] were developed as postprocessing tools and have the ability to reassign or squeeze the TF coefficients by classical TFA methods into the IF trajectory, which are approximated to the ITFA representation....

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Journal ArticleDOI
TL;DR: This article introduces the so-called model-based (or parametric) time-frequency analysis method, and introduces the basic concepts and well-tested algorithms for joint time- frequencies analysis.
Abstract: It has been well understood that a given signal can be represented in an infinite number of different ways. Different signal representations can be used for different applications. For example, signals obtained from most engineering applications are usually functions of time. But when studying or designing the system, we often like to study signals and systems in the frequency domain. Although the frequency content of the majority of signals in the real world evolves over time, the classical power spectrum does not reveal such important information. In order to overcome this problem, many alternatives, such as the Gabor (1946) expansion, wavelets, and time-dependent spectra, have been developed and widely studied. In contrast to the classical time and frequency analysis, we name these new techniques joint time-frequency analysis. We introduce the basic concepts and well-tested algorithms for joint time-frequency analysis. Analogous to the classical Fourier analysis, we roughly partition this article into two parts: the linear (e.g., short-time Fourier transform, Gabor expansion) and the quadratic transforms (e.g., Wigner-Ville (1932, 1948) distribution). Finally, we introduce the so-called model-based (or parametric) time-frequency analysis method.

699 citations


"Synchroextracting Transform" refers methods in this paper

  • ...The TFA method has been developed over many years, and classical TFA methods include the short-time Fourier transform (STFT), wavelet transform, and Wigner–Ville distribution [3]....

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Journal ArticleDOI
TL;DR: This article provides a general overview of time-frequency (T-F) reassignment and synchrosqueezing techniques applied to multicomponent signals, covering the theoretical background and applications.
Abstract: This article provides a general overview of time-frequency (T-F) reassignment and synchrosqueezing techniques applied to multicomponent signals, covering the theoretical background and applications. We explain how synchrosqueezing can be viewed as a special case of reassignment enabling mode reconstruction and place emphasis on the interest of using such T-F distributions throughout with illustrative examples.

458 citations


"Synchroextracting Transform" refers methods in this paper

  • ...Recently, some advanced postprocessing methods have been proposed, such as the reassignment method (RS) [4], [5], synchrosqueezing transform (SST)...

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