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Rolling bearing fault diagnosis based on variational mode decomposition and fuzzy C means clustering

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Abstract

In order to extract fault features of rolling bearing precisely and steadily, a method which is based on variational mode decomposition (VMD) and singular value decomposition was proposed for fault diagnosis using standard fuzzy C means clustering (FCM). First of all, the known fault signals measured in the same load but with different faults were decomposed by VMD, and the modes' characteristics were further extracted using singular value decomposition technique, forming the standard clustering centers by FCM, and then the test samples were clustered by a Hamming nearness approach, and the classification performance was evaluated by calculating classification coefficient and average fuzzy entropy. At last, the method was applied in rolling bearing fault diagnosis under variable loads. By comparing with a method based on EMD, this approach is not sensitive to the initialization of standard FCM, and exhibits better classification performance in the same load fault diagnosis; For the variable loads, the fault characteristic lines of test samples are still around the former clustering centers except that the ones of outer race fault sample have migrated obviously. However, the overall classification accuracy is still maintained 100%, therefore, the method proposed can extract the fault features accurately and stably, providing a good reference for the actual rolling bearing intelligent fault diagnosis.

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... In reference [28], the combination of Complementary Ensemble Empirical Mode Decomposition and Extreme Gradient Boosting has significantly improved classification performance in terms of sensitivity, specificity, and accuracy. LightGBM is an improvement based on Gradient Boosting Decision Tree (GBDT) and XGBoost to ensure high efficiency and accuracy and prevent overfitting [29,30]. ...
... For example, suppose that two features are in a feature bundle, the range of feature A is [0, 10], and the range of feature B is [0,20]. Add an offset 10 to feature B, change it into [10,30], and then merge it. Replace features A and B with a feature bundle [0, 30]. ...
... an offset constant is added to the feature value so that the value of different features can be divided into different buckets in the binding set.For example, suppose that two features are in a feature bundle, the range of feature A is [0, 10], and the range of feature B is[0,20]. Add an offset 10 to feature B, change it into[10,30], and then merge it. Replace features A and B with a feature bundle[0,30]. ...
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... (1) e first type of method for K value determination is to observe the center frequency or the IMF spectrum distribution. Liu [6] proposed maximum central frequency observation (MCFO) method for determining the value of K. When there are two center frequency sets similar to each other, the value of K is the best. ...
... Mutual information (MI) value of the IMF and the original signal is calculated by (6). Decomposition will be stopped when the minimum value of NMI is less than the given threshold, and thus the value of K can be determined: ...
... x n (t) � A n · η, 6 are the amplitude of the corresponding components, respectively. f 1 , f 2 , f 3 , f 4 , f 5 , f 6 are the frequencies of the components, respectively. ...
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... e algorithm can be divided into the construction and seeking solution of the variational problem. It mainly involves three important concepts: classical Wiener filtering, Hilbert transform, and frequency mixing [29]. ...
... In general, the features can be searched using the incremental search method [29]. Assuming that the 푛 − 1 features that have been selected from the feature set together constitute the feature set 푛−1 , the selection of the n-th feature formula from the set 퐹 푚 − 퐽 푛−1 according to the incremental search method, the formula is as follows: ...
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... Additionally, if the frequency band falls within the higher order IMF component, some important PD characteristics may be lost because of the narrow frequency band of the IMF. Variational mode decomposition (VMD) based de-noising methods [23,24] orthogonally decompose the signal into independent frequency bands without redundancy. They can decompose narrowband noise and PD signal into corresponding frequency bands by adjusting its penalty factor and achieve outstanding effect of suppressing the periodic narrowband interference. ...
... This middle result is shown in Figure 6a. Secondly, adaptive wavelet packet decomposition proposed in Section2.3 is employed to remove the component containing white noise according to the threshold method [24], and the remaining components are synthesized as the denoising PD signal, which is shown in Figure 6b. As shown in Figure 6c,d, the de-noising PD signal extracted by the proposed method combined adaptive VMD and adaptive wavelet packet decomposition maintains a high degree of similarity with the original signal in amplitude and phase. ...
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... VMD needs to predetermine the modal number K. The difference of each mode is mainly the difference of the center frequency. The literature [12] uses the method of observing the center frequency to obtain the center frequency corresponding to different K values, and finds that starting from K is 5, a mode with a similar center frequency appears, and it's considered that over decomposition occurs, so the modal number is selected as 4. ...
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... At the same time, too many mode numbers will increase the complexity of operation. It is the most common and intuitive method to determine K [49] by observing the center frequency. The mode center frequency corresponding to each K value is checked. ...
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... erefore, the selection of appropriate mode number K is very important for the result of decomposition. Because the center frequency of each mode number is different, the method of observing the center frequency is usually used to determine K [49] and check the mode center frequency corresponding to each K value. If the center frequency value is close, it is regarded as overdecomposition, and the optimal decomposition layer is K − 1. ...
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... Ren Weijian et al. used particle swarm algorithm to optimize back-propagation(BP) neural network to realize fault diagnosis [4]. Liu Changliang et al. performed fault diagnosis of rolling bearing based on the variational mode decomposition and fuzzy c-mean clustering [5]. Zheng Hanbo et al. conducted fault diagnosis of power transformer by using a support vector machine and improved particle swarm optimization algorithm [6]. ...
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... This paper makes use of the Case Western Reserve University Laboratory's bearing fault data to conduct a test simulation [19]. ...
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... Since Dragomiretskiy and Zosso [16] proposed the variational mode decomposition algorithm in 2014, it has been applied in diverse areas of signal processing, especially in mechanical fault diagnosis [17,18]. VMD was introduced as an alternative to EMD to decompose signals. ...
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... As the research on the VMD method is still in its infancy, only few methods are available for determining the mode number K. Dragomiretskiy and Zosso (2014) determined the K value by judging the spectral overlap or orthogonality between modes, but the method is difficult to implement. Liu et al. (2015) suggested that too many or too few modes K can be checked by observing whether the center frequency of each mode is close to each other. However, there is no definite measure standard for this method, which cannot select the K value adaptively. ...
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... According to the characteristics of the fault vibration signal of rolling bearing, a simulation signal y(u) is constructed. The expression of the simulated signal is given in Formula (9). ...
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Aiming at the problem that it is difficult to extract fault features from the nonlinear and non-stationary vibration signals of wind turbine rolling bearings, which leads to the low diagnosis and recognition rate, a feature extraction method based on multi-island genetic algorithm (MIGA) improved variational mode decomposition (VMD) and multi-features is proposed. The decomposition effect of the VMD method is limited by the number of decompositions and the selection of penalty factors. This paper uses MIGA to optimize the parameters. The improved VMD method is used to decompose the vibration signal into a number of intrinsic mode functions (IMF), and a group of components containing the most information is selected through the Holder coefficient. For these components, multi-features based on Renyi entropy feature, singular value feature, and Hjorth parameter feature are extracted as the final feature vector, which is input to the classifier to realize the fault diagnosis of rolling bearing. The experimental results prove that the proposed method can more effectively extract the fault characteristics of rolling bearings. The fault diagnosis model based on this method can accurately identify bearing signals of 16 different fault types, severity, and damage points.
... When using VMD for signal decomposition, the parameter K needs to be determined in advance. Termination of the number of modes according to the approach degree of the center frequency [49]. When the center frequency between the two modal functions is close to each other, it is considered that there is over-decomposition. ...
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In mechanical fault diagnosis of the high voltage circuit breakers (HVCBs), it is often expected that the fault type should be confirmed in time to avoid delaying the best time for mechanical fault diagnosis. The traditional diagnosis method of HVBC is not so profound for the identification of slight faults and does not consider the impact of the recall rate of fault samples on the fault diagnosis results. In this paper, we propose a method for HVCBs mechanical fault diagnosis utilizing variational mode decomposition (VMD) based on improved time segment energy entropy (ITSEE) and a new hybrid classifier. Firstly, the signal is decomposed into $K$ intrinsic mode functions (IMFs) via VMD to establish a component matrix. Secondly, the ITSEE method is used to calculate the energy entropy of the matrix in time domain and frequency domain, so as to better extract the features of slight fault types. Finally, an optimal hybrid classifier model combined of one-class support vector machine (OCSVM) and probabilistic neural network (PNN) is used to identify four types of vibration signals of HVCBs. The experimental results show that the accuracy of unknown samples is 98.75%, and the recall of fault type is 100%. The experimental results show the effectiveness of the method and have important application value for the diagnosis of HVBCs.
... A rolling bearing is one of the core components of rotating machinery. Its normal operation is of great significance to the whole mechanical system [1][2][3]. Status monitoring and fault diagnosis have always been an important part of maintaining health [4][5][6]. ...
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A rolling element signal has a long transmission path in the acquisition process. The fault feature of the rolling element signal is more difficult to be extracted. Therefore, a novel weak fault feature extraction method using optimized variational mode decomposition with kurtosis mean (KMVMD) and maximum correlated kurtosis deconvolution based on power spectrum entropy and grid search (PGMCKD), namely KMVMD-PGMCKD, is proposed. In the proposed KMVMD-PGMCKD method, a VMD with kurtosis mean (KMVMD) is proposed. Then an adaptive parameter selection method based on power spectrum entropy and grid search for MCKD, namely PGMCKD, is proposed to determine the deconvolution period T and filter order L. The complementary advantages of the KMVMD and PGMCKD are integrated to construct a novel weak fault feature extraction model (KMVMD-PGMCKD). Finally, the power spectrum is employed to deal with the obtained signal by KMVMD-PGMCKD to effectively implement feature extraction. Bearing rolling element signals of Case Western Reserve University and actual rolling element data are selected to prove the validity of the KMVMD-PGMCKD. The experiment results show that the KMVMD-PGMCKD can effectively extract the fault features of bearing rolling elements and accurately diagnose weak faults under variable working conditions.
... To highlight the weak difference information of the spectrum, the original spectra were first subjected to first-order differential calculations and then to VMD processing. According to the principle of similarity of center frequencies [26], the value of K was set to 4 in this experiment. Taking Cu(4 0 0)-1 as an example, the modal components u 1~u4 were obtained, as shown in Fig. 3. ...
... Gao et al. [32] found that the gear system's transmission error, vibration shock state and vibration severity varied with the degree of wear on tooth surface. For the feature extraction of rolling bearing faults, based on variational modal decomposition and singular value decomposition, Liu et al. [33] proposed a method to accurately extract fault features from vibration signals. Li et al. [34] used empirical wavelet transform to extract the modulation components in the frequency spectrum of rubbing fault signal. ...
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... e multivariate multiscale sample entropy (MMSE) was a scheme that gets different time series and conducts various embedding aspects, delay time, and amplitude ranges of data channels in a strict way. Hence, it can directly analyse multichannel data [26]. erefore, a scheme that relied on VMD and RCMMSE was proposed in this study to get the vibration feature of roller bearings. ...
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... In order to exactly identify the various categories of rotating machinery faults, many researchers try to propose approaches to improve the performance of intelligent fault diagnosis systems. Liu et al. [22] proposed an intelligent fault diagnosis model which is based on variational mode decomposition (VMD) and singular value decomposition. Yu et al. [23] proposed a deep inception net with atrous convolution (ACDIN) to realize bearing fault diagnosis. ...
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... More feature values extracted by VMD will better reflect the attributes of the sample. The authors of [14] proposed a method based on VMD and singular value decomposition of rolling bearing fault feature extraction. Compared with the EMD feature extraction method, it has better classification performance for the same fault diagnosis. ...
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