Symplectic transformation based Variational Bayesian Learning and its applications to gear fault diagnosis

Pan, Haiyang; Yu, Yang; Zheng, Jinde; Cheng, Junsheng

doi:10.1016/j.measurement.2019.07.055

Cited by 9 publications

(4 citation statements)

References 32 publications

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“…The analysis of eigenvalues are also called as the symplectic geometry spectrums analysis (SGSA) [6,18,19]. The corresponding components are also regarded as symplectic geometry mode decomposition (SGMD) [7,8,20,21]. According to the symplectic geometry spectrums above, if the number of the chosen symplectic principal components is k, the corresponding principal eigenvector matrix p can be constructed by using the first k eigenvectors of the matrix P in the matrix Q.…”

Section: Symplectic Principal Component Analysis (Spca) Of a Time Seriesmentioning

confidence: 99%

“…Besides, the symplectic geometry method also further integrate other approaches to better investigate the fault extraction and identification for rotating systems, such as symplectic geometry mode decomposition [19] with power spectral entropy [7] as well as Lagrange multiplier [20], symplectic transformation based variational Bayesian learning [21].…”

Section: Applicationsmentioning

confidence: 99%

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Symplectic Geometry and Its Applications on Time Series Analysis

Lei¹

2021

Structure Topology and Symplectic Geometry

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This chapter serves to introduce the symplectic geometry theory in time series analysis and its applications in various fields. The basic concepts and basic elements of mathematics relevant to the symplectic geometry are introduced in the second section. It includes the symplectic space, symplectic transformation, Hamiltonian matrix, symplectic principal component analysis (SPCA), symplectic geometry spectrum analysis (SGSA), symplectic geometry mode decomposition (SGMD), and symplectic entropy (SymEn), etc. In addition, it also briefly reviews the applications of symplectic geometry on time series analysis, such as the embedding dimension estimation, nonlinear testing, noise reduction, as well as fault diagnosis. Readers who are familiar with the mathematical preliminaries may omit the second section, i.e. the theory part, and go directly to the third section, i.e. the application part.

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Section: Symplectic Principal Component Analysis (Spca) Of a Time Seriesmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Symplectic Geometry and Its Applications on Time Series Analysis

Lei¹

2021

Structure Topology and Symplectic Geometry

View full text Add to dashboard Cite

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“…As a crucial component for industrial equipment, gears will impact the operation of the entire system in case of fault, which causes substantial economic loss and safety hazards [1,2]. Consequently, the gear fault warning is achieved through health assessment and condition monitoring of gears, * Author to whom any correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

An adaptive threshold-selected symplectic geometry mode decomposition for application to multi-modulation complex fault signals

Lv,

Li,

Xiong

et al. 2024

Meas. Sci. Technol.

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The signals obtained from complex mechanical systems are characterized by multilevel modulation and strong noise, which can lead to difficulties in fault feature extraction. Symplectic geometry mode decomposition (SGMD) proves to be a valid approach for decomposing signals. However, inaccurate threshold selection in the iterative decomposition process can compromise the quality of fault diagnosis results. To address the shortcomings of SGMD, this paper proposes adaptive symplectic geometry mode decomposition (A-SGMD) with adaptive threshold selection for fault diagnosis. Based on minimum dispersion entropy indicators, correlation coefficient and stopping thresholds are adaptively chosen using the proposed enhanced dung beetle optimizer (eDBO) algorithm. Then the optimal symplectic geometry component is filtered based on the value of the integrated indicators after decomposition. Finally, the optimal symplectic geometry component is analyzed by envelope demodulation to extract gear fault information. Through simulation and experimental analysis, this method surpasses SGMD and other signal decomposition methods in the aspect of fault feature extraction and noise robustness. Additionally, the results indicate an increase in feature energy ratio by 2.14% to 9.85% compared to SGMD. The paper demonstrates that the proposed method extracts the fault feature frequencies of gears more effectively in complex mechanical systems.

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“…However, since the sifting process involves the detection and interpolation of local extreme points of the signal, EMD is susceptible to noise interference and can cause mode mixing. In addition, the sifting algorithm is empirical, which makes the lack of mathematical theoretical foundations and endpoint effect [18,19]. To address the aforementioned issues, some EMD-based methods such as ensemble EMD (EEMD) [20], complete ensemble EMD (CEEMD) [7], local mean decomposition [21], local characteristic-scale decomposition [22] have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Adaptive spectrum segmentation Ramanujan decomposition and its application to gear fault diagnosis

Huang,

Yang,

Cheng

et al. 2023

Meas. Sci. Technol.

Self Cite

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Ramanujan Fourier mode decomposition (RFMD) is a novel non-stationary signal decomposition method, which can decompose a complex signal into several components and extract the periodic characteristics of the signal. However, the mode generation method adopted by RFMD does not consider the physical meaning of the component signal, which makes over-decomposition when dealing with real-life gear signals with complex modulation characteristics, thus destroying the integrity of the signal sideband, increasing the difficulty of subsequent analysis, and even losing key fault information. The iterative envelope-segmentation algorithm combines the modulation characteristics of the fault gear signal and divides the original signal into a limited number of dominant frequency bands containing the modulation region in the Fourier spectrum, thereby ensuring that the obtained frequency bands contain rich fault information. Based on the above algorithm, a new adaptive decomposition method is proposed in this paper, which is Adaptive Spectrum Segmentation Ramanujan Decomposition (ASSRD). ASSRD uses fault envelope harmonic noise ratio (FHNR) as theindex to evaluate the fault information content of component signals and uses it to assist theiterative envelopesegmentation algorithm to complete the adaptive segmentation of the Fourier spectrum. Finally, based on the segmentation result, the inverse RFT reconstruction of each frequency band is performed. Thus, the signal is decomposed into a finite number of component signals containing rich fault information. In addition, through the gear simulation signal and the measured gear signal experiment, the ASSRD method is compared with the original RFMD method and the existing ensemble empirical mode decomposition, variational mode decomposition, empirical wavelet transform, and singular spectrum decomposition method, verifying the feasibility and superiority of ASSRD in gear fault diagnosis. The results show that the proposed method can extract the fault information in the gear signal more effectively, and the performance is better than the comparison method.

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Symplectic transformation based Variational Bayesian Learning and its applications to gear fault diagnosis

Cited by 9 publications

References 32 publications

Symplectic Geometry and Its Applications on Time Series Analysis

Symplectic Geometry and Its Applications on Time Series Analysis

An adaptive threshold-selected symplectic geometry mode decomposition for application to multi-modulation complex fault signals

Adaptive spectrum segmentation Ramanujan decomposition and its application to gear fault diagnosis

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