An optimized variational mode decomposition method and its application in vibration signal analysis of bearings

The performance of the rolling bearing of a spindle device is directly related to the safety and reliability of the operation of a mine hoist. To extract bearing vibration signal features effectively for fault diagnosis, a feature extraction method based on the parameter optimization of a variational mode decomposition (VMD) method and permutation entropy (PE) is proposed. In addition, a support vector machine (SVM) classifier is used to identify bearing fault types. An analogue signal is used to test the effect of noise and sampling frequency on VMD performance. Focused on the problem of the VMD method needing to determine the number of mode components K and a penalty factor α during the signal decomposition process, a genetic algorithm is used to optimize the parameter combination [K,α] with the minimum sample entropy as the indicator. By using mean squared error (MSE) and correlation coefficient, an evaluation indicator is constructed to determine the decomposition effects of the optimized VMD, centre frequency, empirical mode decomposition (EMD) and ensemble EMD (EEMD) methods. The normalized PE of the five mode components is used as an eigenvalue, which is used as the input parameter of the SVM. Two different experimental datasets are used to verify the effectiveness of the proposed method. The results show that the proposed method has better diagnostic accuracy than EMD, EEMD and a BP neural network in the case of limited samples and unknown sample inputs. It can provide a good reference for the diagnosis of a rolling bearing and has practical application value.

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Application of Variational Mode Decomposition and Permutation Entropy for Rolling Bearing Fault Diagnosis

10.20855/ijav.2019.24.21325 ◽

2019 ◽

Vol 24 (2) ◽

pp. 303-311 ◽

Cited By ~ 5

Author(s):

Xiaoxia Zheng ◽

Guowang Zhou ◽

Dongdong Li ◽

Haohan Ren

Keyword(s):

Vibration Signal ◽

Rolling Bearing ◽

Permutation Entropy ◽

Support Vector ◽

Variational Mode Decomposition ◽

Intrinsic Mode Functions ◽

Bearing Fault Diagnosis ◽

Multi Scale ◽

Mode Decomposition ◽

Bearing Vibration

Rolling bearings are the key components of rotating machinery. However, the incipient fault characteristics of a rolling bearing vibration signal are weak and difficult to extract. To solve this problem, this paper presents a novel rolling bearing vibration signal fault feature extraction and fault pattern recognition method based on variational mode decomposition (VMD), permutation entropy (PE) and support vector machines (SVM). In the proposed method, the bearing vibration signal is decomposed by VMD, and the intrinsic mode functions (IMFs) are obtained in different scales. Then, the PE values of each IMF are calculated to uncover the multi-scale intrinsic characteristics of the vibration signal. Finally, PE values of IMFs are fed into SVM to automatically accomplish the bearing condition identifications. The proposed method is evaluated by rolling bearing vibration signals. The results indicate that the proposed method is superior and can diagnose rolling bearing faults accurately.

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Rolling Bearing Fault Diagnosis Based on VMD-MPE and PSO-SVM

Entropy ◽

10.3390/e23060762 ◽

2021 ◽

Vol 23 (6) ◽

pp. 762

Author(s):

Maoyou Ye ◽

Xiaoan Yan ◽

Minping Jia

Keyword(s):

Vibration Signal ◽

Rolling Bearing ◽

Classification Model ◽

Permutation Entropy ◽

Support Vector ◽

Detection Accuracy ◽

Variational Mode Decomposition ◽

Mode Decomposition ◽

Reconstructed Signal ◽

Bearing Vibration

The goal of the paper is to present a solution to improve the fault detection accuracy of rolling bearings. The method is based on variational mode decomposition (VMD), multiscale permutation entropy (MPE) and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, the original bearing vibration signal is decomposed into several intrinsic mode functions (IMF) by using the VMD method, and the feature energy ratio (FER) criterion is introduced to reconstruct the bearing vibration signal. Secondly, the multiscale permutation entropy of the reconstructed signal is calculated to construct multidimensional feature vectors. Finally, the constructed multidimensional feature vector is fed into the PSO-SVM classification model for automatic identification of different fault patterns of the rolling bearing. Two experimental cases are adopted to validate the effectiveness of the proposed method. Experimental results show that the proposed method can achieve a higher identification accuracy compared with some similar available methods (e.g., variational mode decomposition-based multiscale sample entropy (VMD-MSE), variational mode decomposition-based multiscale fuzzy entropy (VMD-MFE), empirical mode decomposition-based multiscale permutation entropy (EMD-MPE) and wavelet transform-based multiscale permutation entropy (WT-MPE)).

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A Rolling Bearing Fault Diagnosis Method Based on EMD and Quantile Permutation Entropy

Mathematical Problems in Engineering ◽

10.1155/2019/3089417 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 4

Author(s):

Qiang-qiang Chen ◽

Shao-wu Dai ◽

Hong-de Dai

Keyword(s):

Fault Diagnosis ◽

Vibration Signal ◽

Rolling Bearing ◽

Permutation Entropy ◽

Support Vector ◽

Intrinsic Mode Functions ◽

Rolling Bearings ◽

Bearing Fault Diagnosis ◽

Mode Decomposition ◽

Main Fault

The vibration signals resulting from rolling bearings are nonlinear and nonstationary, and an approach for the fault diagnosis of rolling bearings using the quantile permutation entropy and EMD (empirical mode decomposition) is proposed. Firstly, the EMD is used to decompose the rolling bearings vibration signal, and several IMFs (intrinsic mode functions) spanning different scales are obtained. Secondly, aiming at the shortcomings of the permutation entropy algorithm, a new permutation entropy algorithm based on sample quantile is proposed, and the quantile permutation entropy of the first few IMFs, which contain the main fault information, is calculated. The quantile permutation entropies are accordingly seen as the characteristic vector and then input to the particle swarm optimization and support vector machine. Finally, the proposed method is applied to the experimental data. The analysis results show that the proposed approach can effectively achieve fault diagnosis of rolling bearings.

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Research on gearbox impact feature extraction method based on improved ESMD

Insight - Non-Destructive Testing and Condition Monitoring ◽

10.1784/insi.2022.64.1.20 ◽

2022 ◽

Vol 64 (1) ◽

pp. 20-27

Author(s):

Fengfeng Bie ◽

Sheng Gu ◽

Yue Guo ◽

Gang Yang ◽

Jian Peng

Keyword(s):

Feature Vector ◽

Vibration Signal ◽

Permutation Entropy ◽

Significant Feature ◽

Support Vector ◽

Feature Extraction Method ◽

Mode Decomposition ◽

Envelope Spectrum ◽

Impact Characteristics ◽

The Impact

A gearbox vibration signal contains non-linear impact characteristics and the significant feature information tends to be overwhelmed by other interference components, which make it difficult to extract the typical fault features fully and effectively. Aiming at the key issue of how to effectively extract the impact characteristics, a fault diagnosis method based on improved extreme symmetric mode decomposition (ESMD) and a support vector machine (SVM) is proposed in this paper. The vibration signal is adaptively decomposed into multiple intrinsic mode function (IMF) components by the improved ESMD and then a certain number of components are selected with the maximum kurtosis-envelope spectrum index. The singular spectral entropy, energy entropy and permutation entropy of each component are applied to construct the feature vector set, in which the dimensionality of the set is reduced with the distance separability criterion. Finally, the dimension-reduced feature vector set is input into the SVM for pattern recognition. Dynamic simulation and experimental gearbox research show that the improved ESMD method can extract and identify gearbox fault information effectively.

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Gearbox Fault Diagnosis Using Complementary Ensemble Empirical Mode Decomposition and Permutation Entropy

Shock and Vibration ◽

10.1155/2016/3891429 ◽

2016 ◽

Vol 2016 ◽

pp. 1-8 ◽

Cited By ~ 14

Author(s):

Liye Zhao ◽

Wei Yu ◽

Ruqiang Yan

Keyword(s):

Fault Diagnosis ◽

Empirical Mode Decomposition ◽

Correlation Coefficients ◽

Ensemble Empirical Mode Decomposition ◽

Permutation Entropy ◽

Support Vector ◽

Svm Classifier ◽

Intrinsic Mode Functions ◽

Vibration Signals ◽

Mode Decomposition

This paper presents an improved gearbox fault diagnosis approach by integrating complementary ensemble empirical mode decomposition (CEEMD) with permutation entropy (PE). The presented approach identifies faults appearing in a gearbox system based on PE values calculated from selected intrinsic mode functions (IMFs) of vibration signals decomposed by CEEMD. Specifically, CEEMD is first used to decompose vibration signals characterizing various defect severities into a series of IMFs. Then, filtered vibration signals are obtained from appropriate selection of IMFs, and correlation coefficients between the filtered signal and each IMF are used as the basis for useful IMFs selection. Subsequently, PE values of those selected IMFs are utilized as input features to a support vector machine (SVM) classifier for characterizing the defect severity of a gearbox. Case study conducted on a gearbox system indicates the effectiveness of the proposed approach for identifying the gearbox faults.

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Fault Diagnosis for Rolling Element Bearings Based on Feature Space Reconstruction and Multiscale Permutation Entropy

Entropy ◽

10.3390/e21050519 ◽

2019 ◽

Vol 21 (5) ◽

pp. 519 ◽

Cited By ~ 6

Author(s):

Weibo Zhang ◽

Jianzhong Zhou

Keyword(s):

Diagnostic Algorithm ◽

Feature Space ◽

Vibration Signal ◽

Rolling Bearing ◽

Ensemble Empirical Mode Decomposition ◽

Classification Performance ◽

Fault Classification ◽

Permutation Entropy ◽

Support Vector ◽

Intrinsic Mode Functions

Aimed at distinguishing different fault categories of severity of rolling bearings, a novel method based on feature space reconstruction and multiscale permutation entropy is proposed in the study. Firstly, the ensemble empirical mode decomposition algorithm (EEMD) was employed to adaptively decompose the vibration signal into multiple intrinsic mode functions (IMFs), and the representative IMFs which contained rich fault information were selected to reconstruct a feature vector space. Secondly, the multiscale permutation entropy (MPE) was used to calculate the complexity of reconstructed feature space. Finally, the value of multiscale permutation entropy was presented to a support vector machine for fault classification. The proposed diagnostic algorithm was applied to three groups of rolling bearing experiments. The experimental results indicate that the proposed method has better classification performance and robustness than other traditional methods.

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Identification of Cutting Chatter through Deep Learning and Classification

International Journal of Simulation Modelling ◽

10.2507/ijsimm19-4-co16 ◽

2020 ◽

Vol 19 (4) ◽

pp. 667-677

Author(s):

H. N. Gao ◽

D. H. Shen ◽

L. Yu ◽

W. C. Zhang

Keyword(s):

Vibration Signal ◽

Identification Accuracy ◽

Support Vector ◽

Identification Algorithm ◽

Variational Mode Decomposition ◽

Time Frequency ◽

Chatter Identification ◽

Mode Decomposition ◽

Cutting Chatter ◽

Cutting Vibration

The traditional analytical method has difficulty in accurately modelling cutting chatter. This paper constructs the vibration datasets of different chatter states and establishes a machine learning (ML) model for chatter identification, treating physical vibration signal as the input. Specifically, the cutting vibration signal was converted into the time-frequency spectrum, which was then classified by a self-designed deep residual convolutional neural network (DR-CNN). After that, the cutting vibration signal was broken down into chatter bands through variational mode decomposition (VMD). The information entropies of the chatter bands were calculated as cutting chatter features. Next, support vector machine (SVM) was introduced to classify the extracted features and used to create an online cutting chatter identification algorithm. The proposed method achieved a much higher mean identification accuracy (92.57 %) than the traditional identification method.

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Research on Fault Extraction Method of Variational Mode Decomposition Based on Immunized Fruit Fly Optimization Algorithm

Entropy ◽

10.3390/e21040400 ◽

2019 ◽

Vol 21 (4) ◽

pp. 400 ◽

Cited By ~ 7

Author(s):

Zhou ◽

Guo ◽

Wang ◽

Du ◽

Wang ◽

...

Keyword(s):

Optimization Algorithm ◽

Fruit Fly ◽

Permutation Entropy ◽

Measured Signal ◽

Fruit Fly Optimization Algorithm ◽

Variational Mode Decomposition ◽

Fruit Fly Optimization ◽

Mode Decomposition ◽

Penalty Factor ◽

Combined Parameters

In recent years, a new method of fault diagnosis, named variational mode decomposition (VMD), has been widely used in industrial production, but the decomposition accuracy of VMD is determined by two parameters, which are respectively the decomposition layer number k and the penalty factor α, if the parameters are not properly selected, there will be over-decomposition or under-decomposition. In order to find an approach to determine the parameters adaptively, a method to optimize VMD by using the immune fruit fly optimization algorithm (IFOA) is proposed in this paper. In this method, permutation entropy is used as the fitness function, firstly, the immune fruit fly optimization algorithm is used to search the combined parameters of k and α in VMD, searching for the best combination parameters of k and α by iteration, and then uses the combined parameters to perform VMD, finally, the center frequency is determined through frequency spectrum analysis. The method mentioned is applied to the fault extraction of a simulated signal and a measured signal of a wind turbine gearbox, and the fault frequency is successfully extracted. Using ensemble empirical mode decomposition (EEMD) and singular spectrum decomposition (SSD) to compare with the proposed method, which validated feasibility of the proposed method.

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A Denoising Method for Fiber Optic Gyroscope Based on Variational Mode Decomposition and Beetle Swarm Antenna Search Algorithm

Entropy ◽

10.3390/e22070765 ◽

2020 ◽

Vol 22 (7) ◽

pp. 765

Author(s):

Pengfei Wang ◽

Yanbin Gao ◽

Menghao Wu ◽

Fan Zhang ◽

Guangchun Li ◽

...

Keyword(s):

Noise Reduction ◽

Fiber Optic ◽

Search Algorithm ◽

Permutation Entropy ◽

Navigation Systems ◽

Variational Mode Decomposition ◽

Fiber Optic Gyroscope ◽

Denoising Method ◽

Mode Decomposition ◽

Penalty Factor

Fiber optic gyroscope (FOG) is one of the important components of Inertial Navigation Systems (INS). In order to improve the accuracy of the INS, it is necessary to suppress the random error of the FOG signal. In this paper, a variational mode decomposition (VMD) denoising method based on beetle swarm antenna search (BSAS) algorithm is proposed to reduce the noise in FOG signal. Firstly, the BSAS algorithm is introduced in detail. Then, the permutation entropy of the band-limited intrinsic mode functions (BLIMFs) is taken as the optimization index, and two key parameters of VMD algorithm, including decomposition mode number K and quadratic penalty factor α , are optimized by using the BSAS algorithm. Next, a new method based on Hausdorff distance (HD) between the probability density function (PDF) of all BLIMFs and that of the original signal is proposed in this paper to determine the relevant modes. Finally, the selected BLIMF components are reconstructed to get the denoised signal. In addition, the simulation results show that the proposed scheme is better than the existing schemes in terms of noise reduction performance. Two experiments further demonstrate the priority of the proposed scheme in the FOG noise reduction compared with other schemes.

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