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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.
... 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]. ...
The fault samples of high voltage circuit breakers are few, the vibration signals are complex, the existing research methods cannot extract the effective information in the features, and it is easy to overfit, slow training, and other problems. To improve the efficiency of feature extraction of a circuit breaker vibration signal and the accuracy of circuit breaker state recognition, a Light Gradient Boosting Machine (LightGBM) method based on time-domain feature extraction with multi-type entropy features for mechanical fault diagnosis of the high voltage circuit breaker is proposed. First, the original vibration signal of the high voltage circuit breaker is segmented in the time domain; then, 16 features including 5 kinds of entropy features are extracted directly from each part of the original signal after time-domain segmentation, and the original feature set is constructed. Second, the Split importance value of each feature is calculated, and the optimal feature subset is determined by the forward feature selection, taking the classification accuracy of LightGBM as the decision variable. After that, the LightGBM classifier is constructed based on the feature vector of the optimal feature subset, which can accurately distinguish the mechanical fault state of the high voltage circuit breaker. The experimental results show that the new method has the advantages of high efficiency of feature extraction and high accuracy of fault identification.
... (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. ...
Variational mode decomposition (VMD) method has been widely used in the field of signal processing with significant advantages over other decomposition methods in eliminating modal aliasing and noise robustness. The number (usually denoted by K) of intrinsic mode function (IMF) has a great influence on decomposition results. When dealing with signals including complex components, it is usually impossible for the existing methods to obtain correct results and also effective methods for determining K value are lacking. A method called center frequency statistical analysis (CFSA) is proposed in this paper to determine K value. CFSA method can obtain K value accurately based on center frequency histogram. To shed further light on its performance, we analyze the behavior of CFSA method with simulation signal in the presence of variable components amplitude, components frequency, and components number as well as noise amplitude. The normal and fault vibration signals obtained from a bearing experimental setup are used to verify the method. Compared with maximum center frequency observation (MCFO), correlation coefficient (CC), and normalized mutual information (NMI) methods, CFSA is more robust and accurate, and the center frequencies results are consistent with the main frequencies in FFT spectrum.
... 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: ...
Power system load forecasting is an important part of power system scheduling. Since the power system load is easily affected by environmental factors such as weather and time, it has high volatility and multi-frequency. In order to improve the prediction accuracy, this paper proposes a load forecasting method based on variational mode decomposition (VMD) and feature correlation analysis. Firstly, the original load sequence is decomposed using VMD to obtain a series of intrinsic mode function (IMF), it is referred to below as a modal component, and they are divided into high frequency, intermediate frequency, and low frequency signals according to their fluctuation characteristics. Then, the feature information related to the power system load change is collected, and the correlation between each IMF and each feature information is analyzed using the maximum relevance minimum redundancy (mRMR) based on the mutual information to obtain the best feature set of each IMF. Finally, each component is input into the prediction model together with its feature set, in which back propagation neural network (BPNN) is used to predict high-frequency components, least square-support vector machine (LS-SVM) is used to predict intermediate and low frequency components, and BPNN is also used to integrate the prediction results to obtain the final load prediction value, and compare the prediction results of method in this paper with that of the prediction models such as autoregressive moving average model (ARMA), LS-SVM, BPNN, empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and VMD. This paper carries out an example analysis based on the data of Xi’an Power Grid Corporation, and the results show that the prediction accuracy of method in this paper is higher.
... 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. ...
Periodic narrowband signals and white noise are the main interferences in online detection and localization of cable partial discharge (PD), however, existing research has always focused on the white noise suppression only, which is not in line with the actual scene. A novel de-noising method for effectively extracting random PD pulse from complex and strong interferences is proposed in this paper and applied to PD localization. Firstly, an improved adaptive variational mode decomposition (AVMD) is used to decompose periodic narrowband interference, white noise, and PD signal into different intrinsic mode. According to the characteristic that the power of intrinsic mode component of periodic narrowband interference in the discrete Fourier transformation (DFT) power spectrum is much larger than that of PD and white noise, the periodic narrowband is removed out. In order to effectively filter out white noise, a scale adaptive wavelet packet decomposition method based on correlation coefficient is proposed, which decomposes the signal into high, middle, and low-frequency components. The components with low frequency, small amplitude are removed out as the white noise interference according to the threshold method, and the residual is the de-noising PD signal. Experimental results show that the proposed method can robustly suppress the interference of periodic narrowband signal and white noise, and effectively preserve the essential characteristics of the real PD signal. In the multi-sensor travelling wave based localization system of cable PD source using time-varying kurtosis, accurate estimation of first arrival time of PD pulse can be achieved by the de-noising results.
... e value of the number of decomposition layers K directly affects the decomposition results. At the present, the research on the variable K in the VMD decomposition is still in its infancy, and there is no unified solution method [23][24][25][26][27][28]. In view of Shock and Vibration this problem, the value of K in the VMD method will be studied in the following section. ...
In the field of blasting vibration signal analysis, accurate removal of low-frequency noise in the signal has important practical significance. In view of the shortcomings of the existing methods, such as cumbersome calculation and limited scope of application, a method based on variational mode decomposition (VMD) to remove low-frequency noise was proposed. In this paper, the parameter selection of VMD algorithm to identify low-frequency noise of blasting signal is optimized by simulation experiment. The results show that frequency has little influence on the decomposition effect. When the frequency of low-frequency noise is between 0 and 5 Hz, the influence of frequency on the decomposition effect remains basically unchanged. The amplitude has a significant effect on the decomposition effect. The smaller the amplitude, the worse the decomposition effect of the VMD method. Taking the excavation of the Badaling Great Wall Station as the background, the LSM method, EMD method, and VMD method are used to remove the low-frequency noise of the randomly selected test signals in order. Compared with the LSM method and the EMD method, the signal processed by the VMD method does not have modal mixing and does not have much low-frequency noise residue. It has more extensive applicability in removing low-frequency noise of blasting signal.
... Data-driven fault diagnosis generally includes two steps: fault feature extraction and fault classification. e common methods of feature extraction include Fast Fourier Transformation (FFT) [5], Wavelet Transform (WT) [6], Empirical Mode Decomposition (EMD) [7], Local Mean Decomposition (LMD) [8], and Variational Mode Decomposition (VMD) [9]. e common fault classification algorithms include support vector machine (SVM) [10], BP neural networks [11], Bayesian classifier [12], K-Nearest Neighbor (KNN) [13], Random Forest (RF) [14], and Classification and Regression Tree (CART) [15]. ...
Intelligent mechanical fault diagnosis has developed very fast in recent years due to the advancement and application of deep learning technologies. Thus, there are many deep learning network models that have been explored in fault classification and diagnosis. However, there are still limitations in research on the relationship between fault location, fault type, and fault severity. In this paper, a novel method for diagnosis of bearing fault using hierarchical multitask convolution neural networks (HMCNNs) is proposed, taking into account the mentioned relationships. The HMCNN model includes a main task and multiple subtasks. In the HMCNN model, a weighted probability is used to reduce the classification error propagation among multitasks to improve the fault diagnosis accuracy. The validity of the proposed method is verified on bearing datasets. Experimental results show that the proposed method is very effective and superior to the existing methods.
... 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. ...
In order to extract the vibration signal feature of rolling bearing with non-steady feature and improve the fault diagnosis rate accurately and stably, a variational mode decomposition (VMD) feature extraction method is proposed. Particle swarm optimization (PSO) is used to optimize the parameters of support vector machine to construct a fault diagnosis model to achieve fault diagnosis of rolling bearings. Firstly, change the modal decomposition of the known fault signal under the same load to get the modal function, and the modal function is further extracted by the singular value decomposition. The time domain, frequency domain feature and modal feature of the original signal are extracted. Constructing hybrid features to achieve efficient fault feature extraction. Optimizing SVM parameters through PSO algorithm to construct fault diagnosis models to achieve efficient fault diagnosis. Finally, by comparing with EMD-based feature extraction methods in the same load, the method shows better classification performance and the overall fault recognition rate remains above 99.17%, which verifies the reliability and effectiveness of the method.
... 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. ...
Precipitation is an important parameter of water resource management, flood warning and hydrological analysis, so it is important to predict rainfall accurately. However, many previous studies did not extract the information of error series and only used a single model to predict rainfall data, ignoring the importance of model stability. Therefore, based on the idea of combination prediction and error correction strategy, this paper proposes a novel combined prediction model for monthly mean precipitation. It combines the variational mode decomposition (VMD), the improved butterfly optimization algorithm (IBOA), the least squares support vector machine model (LSSVM), the adaptive Volterra and autoregressive moving average (ARMA) model. Firstly, in order to find the best parameters of LSSVM, an improved butterfly optimization algorithm is proposed. The simulation results show the performance of IBOA is better than that of other algorithms, such as PSO, DE and BOA. Then the IBOA-LSSVM model and Volterra model are established for the mode components of the VMD, named VMD-IBOA-LSSVM and VMD-Volterra. Secondly, to solve the problem that the uncertainty of the hydrological prediction model, a combined precipitation prediction method based on the induced ordered weighted average (IOWA) operator of VMD-IBOA-LSSVM and VMD-Volterra is proposed. Finally, the ARMA model is established to correct the error sequence of the combined forecasting model. The precipitation data of two stations in Shaanxi Province are predicted. Experiment 1 is taken as an example, the maximum error of the proposed prediction model for rainfall is less than 9 mm, and the performance of the proposed model is improved by at least 43%. It shows that the proposed model can effectively reduce the prediction error of precipitation, and provide a new idea for precipitation prediction.
... 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. ...
The prediction of underwater acoustic signal is the basis of underwater acoustic signal processing, which can be applied to underwater target signal noise reduction, detection, and feature extraction. Therefore, it is of great significance to improve the prediction accuracy of underwater acoustic signal. Aiming at the difficulty in underwater acoustic signal sequence prediction, a new hybrid prediction model for underwater acoustic signal is proposed in this paper, which combines the advantages of variational mode decomposition (VMD), artificial intelligence method, and optimization algorithm. In order to reduce the complexity of underwater acoustic signal sequence and improve operation efficiency, the original signal is decomposed by VMD into intrinsic mode components (IMFs) according to the characteristics of the signal, and dispersion entropy (DE) is used to analyze the complexity of IMF. The subsequences (VMD-DE) are obtained by adding the IMF with similar complexity. Then, extreme learning machine (ELM) is used to predict the low-frequency subsequence obtained by VMD-DE. Support vector regression (SVR) is used to predict the high-frequency subsequence. In addition, an artificial bee colony (ABC) algorithm is used to optimize model performance by adjusting the parameters of SVR. The experimental results show that the proposed new hybrid model can provide enhanced accuracy with the reduction of prediction error compared with other existing prediction methods.
... The decomposition quantity K needs to be preset. In this paper, central frequency method [36] is used to select the parameter K. In order to avoid the influence of irrelevant force signals generated at the beginning and end of cutting, 50000 data points in total from 40001 to 90000 in each time are selected. ...
Tool states affect the surface quality and equipment stop time. It is essential to seek a method with high accuracy and efficiency to model and predict tool states. Cutting process signal is usually used to in industry monitoring, which contains lots of fault information. In this paper, the spectrum analysis of milling force is carried out to obtain the signal frequency that can reflect tool wear degree. A force signal decomposition model based on whitening variational mode decomposition (WVMD) is established to screen out sensitive signals, which effectively avoids mode mixing. Joint information entropy (JIE) is adopted to select the force signal features. Compared with other dimensionality reduction algorithms, the optimal feature subset obtained by JIE method can reflect strong relativity between features and the wear state. The classification is realized by the optimal-path forest (OPF) algorithm. According to the experimental results, compared with other recognition models, WVMD-JIE-OPF method has a classification accuracy as high as 98.41%. The training speed of OPF is increased by 58.43% compared with LSSVM, which shows excellent tool condition monitoring performance.
... 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]. ...
A fault diagnosis method based on deep belief network (DBN) is to solve the high fault rate of a submersible reciprocating pumping unit, and to address the difficulties in measurement of downhole operation parameters. The running current of the submersible motor is obtained directly through the ground equipment. The running current is used as the characteristic parameter of the operation status of the submersible reciprocating pumping unit. The vector that is extracted from the running current is used as the input data for the fault diagnosis model. The DBN is firstly trained by the original currents, and then the fault feature’s gradual extraction is realized through the multi-layered structure, thereby allowing the fault diagnosis of the submersible reciprocating pumping unit. In the experiment, the fault diagnosis model is tested by simulation samples. Results show that the model can extract the fault feature from the running currents of the submersible motor and implement the fault diagnosis effectively.
... Moreover, the network coverage and the overlap coverage index are used as optimization parameters to optimize. The model is compared with the fuzzy C-means clustering algorithm [44] to obtain the optimal MR candidate deployment plan. ...
This study aims to propose a deployment optimization method based on IEEE 802.11 heterogeneous wireless mesh networks (WMNs) for the condition monitoring system (CMS) of wind turbines. This method can provide a flexible, low-cost, and easy-to-implement network framework for wind farms in harsh environments, thereby avoiding interference of the newly installed CMS on the communication network of the SCADA system. The K-medoids clustering algorithm transforms the continuous space location problem into the discrete space location problem. Moreover, the mesh client (MC) coverage and backbone network connectivity issues are considered to ensure that the generated candidate point set can meet the coverage and connectivity requirements without generating numerous redundant nodes. Firstly, according to the characteristics of the model, the K-medoids clustering algorithm is used to obtain a set of candidate points of mesh routers (MRs) that meet the coverage rate. Secondly, a reasonable connection algorithm is proposed according to the constraints, and the optimal deployment is selected from the candidate points. Thirdly, taking the number of hops from MR to MG and the priority of MC as the weight. The path planning with the least number of MRs and load balancing is obtained by constructing a minimum spanning tree (MST) based on the improved Kruskal algorithm. Finally, Multi-channel inter-frequency networking technology is adopted to reduce interference between co-channels and between adjacent channels. The result shows that the method proposed can minimize network operating costs, meet the capacity requirements of MC, and reduce link losses.
... This paper makes use of the Case Western Reserve University Laboratory's bearing fault data to conduct a test simulation [19]. ...
A feature cognitive model combined with an improved variational mode and singular value decomposition is presented to recognise the characteristics of the fault signals from vibration signals of mechanical equipment in this study. Specifically, the variational mode model is constructed firstly to decompose the known fault signals for mechanical equipment with the same load. Singular value decomposition approach is applied to recognise further the inherent modal features of the fault signals and construct the feature set. The supervised learning-support vector machine and the unsupervised learning-fuzzy c-means clustering are used to verify the effectiveness of the presented method. Finally, the provided feature cognitive model is used to recognise the bearing faults to verify its effectiveness. From simulation results, it can be seen that compared to the complete integration empirical mode decomposition method, the feature cognitive model combined by an improved variational mode and singular value decomposition can obtain more higher accuracy and larger evaluation coefficients. It is worth mentioning that the presented method can also be applied to recognise the key characteristics of the other signals.
... Because the central frequency of each mode number is different, the central frequency method is used to determine the mode number K in this paper, and the corresponding mode central frequency of each K value is tested. If the central frequency value approaches the mode value, it will be regarded as overdecomposition [45]. After repeated experiments, the subsequent tend to approximate when K > 6, so K � 6 is chosen in this paper. ...
Climate is a complex and chaotic system, and temperature prediction is a challenging problem. Accurate temperature prediction is also concerned in the fields of energy, environment, industry, and agriculture. In order to improve the accuracy of monthly mean temperature prediction and reduce the calculation scale of hybrid prediction process, a combined prediction model based on variational mode decomposition-differential symbolic entropy (VMD-DSE) and Volterra is proposed. Firstly, the original monthly mean meteorological temperature sequence is decomposed into finite mode components by VMD. The DSE is used to analyze the complexity and reconstruct the sequences. Then, the new sequence is reconstructed in phase space. The delay time and embedding dimension are determined by the mutual information method and G-P method, respectively. On this basis, the Volterra adaptive prediction model is established to modeling and predicting each component. Finally, the final predicted values are obtained by superimposing the predicted results. The monthly mean temperature data of Xianyang and Yan’an are used to verify the prediction performance of the proposed model. The experimental results show that the VMD-DSE-Volterra model shows better performance in the prediction of monthly mean temperature compared with other benchmark models in this paper. In addition, the combined forecasting model proposed in this paper can reduce the modeling time and improve the forecasting accuracy, so it is an effective forecasting model.
... 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. ...
Accurate and timely fault diagnosis for the diesel engine is crucial to guarantee it works safely and reliably, and reduces the maintenance costs. A novel diagnosis method based on variational mode decomposition (VMD) and kernel-based fuzzy c-means clustering (KFCM) is proposed in this paper. Firstly, the VMD algorithm is optimized to select the most suitable K value adaptively. Then KFCM is employed to classify the feature parameters of intrinsic mode functions (IMFs). Through the comparison of many different parameters, the singular value is selected finally because of the good classification effect. In this paper, the diesel engine fault simulation experiment was carried out to simulate various faults including valve clearance fault, fuel supply fault and common rail pressure fault. Each kind of machine fault varies in different degrees. To prove the effectiveness of VMD-KFCM, the proposed method is compared with empirical mode decomposition (EMD)-KFCM, ensemble empirical mode decomposition (EEMD)-KFCM, VMD-back propagation neural network (BPNN), and VMD-deep belief network (DBN). Results show that VMD-KFCM has advantages in accuracy, simplicity, and efficiency. Therefore, the method proposed in this paper can be used for diesel engine fault diagnosis, and has good application prospects.
... 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. ...
Operation feature extraction of flood discharge structures under ambient excitation has attracted increasing attention in recent years. However, the vibration signal of flood discharge structures is a nonstationary random signal with low signal-to-noise ratio, which is mixed with lots of low-frequency water flow noise and high-frequency white noise. It is difficult to excavate the hidden vibration characteristic information accurately. To solve the problem, we propose a novel denoising method called improved variational mode decomposition. As an improved method of variational mode decomposition, improved variational mode decomposition can effectively determine the decomposition mode number of variational mode decomposition by using the mutual information method. Furthermore, improved variational mode decomposition is combined with a variance dedication rate to extract the overall operation characteristic information of the structure. In order to evaluate the applicability and effectiveness of the proposed improved variational mode decomposition–variance dedication rate method, we compare the denoising results of simulation signals produced by an improved variational mode decomposition–variance dedication rate with those produced by digital filter, wavelet threshold, empirical mode decomposition, empirical wavelet transform, complete ensemble empirical mode decomposition with adaptive noise, and improved variational mode decomposition methods and find a better performance of the improved variational mode decomposition–variance dedication rate method. In addition, the proposed method is applied to the Three Gorges Dam, and the results show that the improved variational mode decomposition–variance dedication rate method can effectively remove heavy background noises and extract the operation characteristic information of the flood discharge structure, which contributes to health monitoring and damage identification of the flood discharge structure.
... 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). ...
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. ...
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]. ...
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. ...
This paper studies the dynamics of a two-stage gear transmission system in both the normal state and the fault state with tooth breakage. The torsional vibration model of the two-stage parallel shaft gear was developed by using the lumped parameter method. The time-varying meshing stiffness of the gear transmission system is described by Fourier series which is determined by the periodical meshing characteristics of the gears with both the single-tooth and the double-tooth contacts. By introducing the pulse into the regular time-varying meshing stiffness, the tooth breakage existing in the gear transmission system is mimicked. Based on the numerical simulation of the developed dynamic model, both the time domain analysis and the frequency domain analysis of the gear transmission system under both the normal condition and the tooth breakage are compared accordingly. The influence of the tooth breakage on the dynamic characteristics of the gear transmission system is analyzed comprehensively. Furthermore, based on the developed test bench of a two-stage gear transmission system, the experimental research was carried out, and the experimental results show great agreements with the results of numerical simulation, and thus the validity of the developed mathematical model is demonstrated. By comparing the periodic motion with the chaotic motion, the fault identification for the gear transmission system is verified to be tightly related to its vibration condition, and the control of the vibration condition of the gear transmission system as periodic motion is of great significance to the fault diagnosis.
... 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. ...
Advanced research studies on industrial Internet of things require effective feature extraction and accurate machinery health state evaluation. For roller bearing, a well-known mechanical component most extensively used in the industry, its running status directly affects the operation of the entire machinery and equipment. For intelligent fault diagnosis of roller bearing, the selection of the intrinsic mode function (IMF) modes in approaches of ensemble empirical mode decomposition (EEMD)/variational mode decomposition (VMD) becomes a tricky problem. To solve this problem, this study proposed an efficient scheme on roller bearing fault diagnosis that combines the refined composite multivariate multiscale sample entropy (RCMMSE) with different classifiers. Firstly, the synthetic noise signals are introduced to compare the effectiveness of the multiscale sample entropy (MSE) and the RCMMSE models. Secondly, the random noise signals are used to compare the performance of EEMD and VMD methods, where the envelope spectrum characteristics of fault signals are well described. Moreover, EEMD/VMD methods are utilized to decompose the roller bearing vibration signals into various modes to get the entropy values. Finally, the obtained RCMMSE is adopted as a feature vector and subsequently employed as an input of support vector machine, random forest, and probabilistic neural network models to conduct roller bearing fault identification. The extensive experimental results prove that this proposed scheme performs well and the classification accuracy of VMD-RCMMSE is higher than EEMD-RCMMSE.
... 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. ...
With the booming development of intelligent manufacturing in modern industry, intelligent fault diagnosis systems have become a necessity to equipment and machine, which have attracted many researchers’ attention. However, due to the requirements of enough labeled data for most of the current approaches, it is difficult to implement them in real industrial scenarios. In this paper, an unsupervised intelligent fault diagnosis system based on feature transfer is constructed to extract the historical labeled data of the source domain, using feature transfer to facilitate the fault diagnosis of the target domain. The original feature set is acquired by EEMD time-frequency analysis. Then, the transfer component analysis algorithm is adopted to minimize the distance between the marginal distributions of the source and target domains which reduces the discrepancy of features between the different domains. Finally, SVM is used in multiclassification to identify different categories of faults. The performance of the fault diagnosis system under different loads is tested on the CWRU bearing data set, and the experiments show that the proposed system could effectively improve the recognition ability of unsupervised fault diagnosis.
... 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. ...
The internal detector in a pipeline needs to use the ground marker to record the elapsed time for accurate positioning. Most existing ground markers use the magnetic flux leakage testing principle to detect whether the internal detector passes. However, this paper uses the method of detecting vibration signals to track and locate the internal detector. The Variational Mode Decomposition (VMD) algorithm is used to extract features, which solves the defect of large noise and many disturbances of vibration signals. In this way, the detection range is expanded, and some non-magnetic flux leakage internal detectors can also be located. Firstly, the extracted vibration signals are denoised by the VMD algorithm, then kurtosis value and power value are extracted from the intrinsic mode functions (IMFs) to form feature vectors, and finally the feature vectors are input into random forest and Multilayer Perceptron (MLP) for classification. Experimental research shows that the method designed in this paper, which combines VMD with a machine learning classifier, can effectively use vibration signals to locate the internal detector and has the characteristics of high accuracy and good adaptability.
... In essence, it is used to construct and solve variational problems, to replace the recursive decomposition mode, which has greatly improved the mode mixing problem and the robustness to noise. It has good denoising effect and strong ability to extract key feature information from vibration signal [14]. ...
Abstract In order to make accurate judgements of rolling bearing main fault types using the small sample size fault data set, a novel approach is put forward that combines particle swarm optimisation kernel fuzzy C‐means (PSO‐KFCM) and variational mode decomposition (VMD). Firstly, by calculating the centre frequency and Pearson correlation coefficient of each mode function of VMD, the decomposition level K of VMD is determined, and the optimal decomposition result is obtained. The singular value decomposition method was used to extract a characteristic value corresponding to the main fault types of bearings from the optimal decomposition results, and faulty feature sample space was established. Then, the kernel function parameters and the initial clustering centre were used as optimisation variables. The PSO algorithm was used to solve the clustering model. The clustering centre of each fault type under the optimal classification result was obtained, and the fault diagnosis model was established. Finally, different fault classification methods are compared, and the conclusions drawn from the experiment show that the method can achieve good results in bearing fault diagnosis. The accuracy of fault classification was improved obviously.
Variational mode decomposition (VMD) is widely used in rotating machinery fault diagnosis. However, the choice of its main parameters is often based on experience, affecting the decomposition results. Aiming to mitigate this drawback, an adaptive VMD method using the Archimedes optimization algorithm (AOA) is presented. Firstly, the computational domain of the objective function is set to the amplitude spectrum of the signal envelope spectrum. Secondly, a correlation waveform index (Cwi) is proposed to evaluate the complexity of the signal. The minimum average value of the Cwi of all intrinsic modal functions (IMFs) is taken as the objective function. Finally, the AOA is used to search for the optimal mode number and penalty factor to find IMFs which are sensitive to fault features. Compared to the other improved VMD methods, the proposed method has a better performance in extracting the fault characteristics from the simulated and actual cases.
The rolling bearing is the most basic key component of rotating machinery, and has high failure rates. In this paper, a fault diagnosis method based on segment-tensor rank-(Lr, Lr, 1) decomposition for rolling bearings is proposed. First, the IMF-SVD (intrinsic mode function, IMF; singular value decomposition, SVD) method is utilized to estimate the source number of the vibration observation signals. Then, each observation signal is reshaped into a segment matrix by a segmentation method, and then stacked into a third order segment tensor. Using the segment tensor rank-(Lr, Lr, 1) decomposition, a set of sub tensors that correspond to the source signals can be obtained. Next, the source signal can be reconstructed using mode-1 and mode-2 of the corresponding sub tensor. Finally, through the envelope demodulation of the source signals, the fault characteristic frequency (FCF) is extracted to achieve the purpose of fault diagnosis. The results of simulation and actual data analysis verified the effectiveness of the proposed method in rolling bearing fault diagnosis.
Total soluble solids (TSS) are one of the most essential attributes determining the quality and price of fruit. This study aimed to use hyperspectral imaging (HSI) and wavelength selection for nondestructive detection of TSS in grape. A novel method involving variational mode decomposition and regression coefficients (VMD-RC) was proposed to select feature wavelengths. VMD was introduced to decompose the hyperspectral images data of samples with bands of (400.68-1001.61 nm) to get a series of feature components. Afterward, these components were processed separately using regression analysis to obtain the stability values of RC of each component. Finally, a filter-based selection strategy was used to screen key wavelengths. The least squares support vector machine (LSSVM) and partial least squares (PLS) were constructed under full and feature wavelengths for predicting TSS. The VMD-RC-LSSVM model obtained the best prediction accuracy for TSS, with R p 2 of 0.93, with R M S E P of 0.6 %, with R E R of 18.14 and R P D p of 3.69. The overall results indicated that the VMD-RC algorithm can be used as an alternative to handle high-dimensional hyperspectral images data, and HSI has great potential for nondestructive and rapid evaluation of quality attributes in fruit. PRACTICAL APPLICATION: Traditional methods of evaluating grape quality attributes are destructive, time-consuming and laborious. Therefore, HSI was used to achieve rapid and nondestructive determination of TSS in grape. The results indicated that it was feasible to use HSI and variable selection for predicting TSS. It is of great significance to improve grape quality, guide postharvest handling and provide a valuable reference for noninvasively evaluating other internal attributes of fruit.
Aiming at the characteristics of time-frequency analysis of unsteady vibration signals, this paper proposes a method based on time-frequency image feature extraction, which combines non-downsampling contour wave transform and local binary mode LBP (Local Binary Pattern) to extract the features of time-frequency image faults. SVM is used for classification and recognition. Finally, the method is verified by simulation data. The results show that the classification accuracy of the method reaches 98.33%, and the extracted texture features are relatively stable. Also, the method is compared with the other 3 feature extraction methods. The results also show that the classification effect of the method is better than that of the traditional feature extraction method.
A novel fractal dimension estimation method based on VMD is proposed in this paper. VMD is utilized to decompose the multi-component signal into several components. Multi-dimensional super-body volume is defined and calculated based on the decomposed components. Fractal dimension is then estimated by the least square method. Simulation results verify that fractal dimension estimation accuracy of the proposed method outperform box counting method and detrended fluctuation analysis. Furthermore, with this novel method, fractal characteristics of vibration signals form rolling bearing are studied. Achievements indicate that vibration signals are characterized by double-scale fractal features. Thus, two fractal dimensions corresponding to the small and large time scales respectively are extracted as feature parameters of vibration signals. Finally, double-scale fractal dimensions are employed for rolling bearing fault diagnosis. Classification results indicate that double-scale fractal dimensions extracted by VMD are capable of expressing fractal characteristics of vibration signals and diagnosing the rolling bearing faults.
The vibration signals of rolling bearings are unstable and nonlinear, with weak information on failure features and extremely low signal-to-noise ratio (SNR). To solve these problems, this paper presents a failure diagnosis method based on variational mode decomposition (VMD) optimized by the improved whale optimization algorithm (IWOA) is proposed, and verifies the effectiveness of the method through a failure experiment on a test stand. Specifically, the whale optimization algorithm (WOA) was improved by replacing the linear parameter a1 with a nonlinear rule. The replacement effectively improves the solution accuracy, and convergence speed. Next, the VMD parameters were optimized with IWOA. Experimental results show that the VMD optimized with IWOA can effectively and easily extract the early failure features of rolling bearings by enhancing the weak information on failure features.
The DFT studies of the 1-Amino-5-chloro-anthraquinone (ACAQ) molecule have been carried out with extensive and accurate investigations of detailed vibrational and spectroscopic investigations and validated by experimentally. The optimized molecular structure and harmonic resonance frequencies were computed based on DFT/B3LYP method with 6-311G++(d,p) basis set using the Gaussian 09 program. The experimental and calculated vibrational wavenumbers were assigned on the basis of PED calculations using VEDA 4.0 program. The ¹³C NMR isotropic chemical shifts of the molecule were calculated using Gauge-Invariant-Atomic Orbital (GIAO) method in DMSO solution and compared with the experimental data. The absorption spectrum of the molecule was computed in liquid phase (ethanol), which exhibits л to л* electronic transition and compared with observed UV-Vis spectrum. Frontier molecular orbitals analysis shows the molecular reactivity and kinetic stability of the molecule. The Mulliken atomic charge distribution and molecular electrostatic potential surface analysis of the molecule validate the reactive site of the molecule. The natural bond orbital analysis proves the bioactivity of the molecule. Molecular docking analysis indicate that ACAQ molecule inhibits the action of c-Met Kinase protein, which is associated with the thyroid cancer. Hence, the present study pave the way for the development of novel drugs in the treatment of thyroid cancer.
Aiming at the problem of insufficient comprehensive feature extraction in the fault diagnosis of rolling bearings, this paper proposes a fault diagnosis model of convolutional neural network (CNN) based on Convolutional Block Attention Module (CBAM). The model uses CBAM instead of pooling layer to join the CNN, and then exports to the full connected layer to realize the fault type identification and complete the fault diagnosis of rolling bearing. Experiments show that the accuracy of this method is 99.94%, and comparison with some other methods proves the effectiveness of this method.
During the late 1990s, Huang introduced the algorithm called Empirical Mode Decomposition, which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands. EMD is known for limitations like sensitivity to noise and sampling. These limitations could only partially be addressed by more mathematical attempts to this decomposition problem, like synchrosqueezing, empirical wavelets or recursive variational decomposition. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the input signal, while each being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. We show important relations to Wiener filter denoising. Indeed, the proposed method is a generalization of the classic Wiener filter into multiple, adaptive bands. Our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand. The variational model is efficiently optimized using an alternating direction method of multipliers approach. Preliminary results show attractive performance with respect to existing mode decomposition models. In particular, our proposed model is much more robust to sampling and noise. Finally, we show promising practical decomposition results on a series of artificial and real data.
Aiming at the non-stationary characteristics of roller bearing fault vibration signals, roller bearing fault diagnosis method based on Empirical Mode Decomposition (EMD) and neural networks is put forward. First of all, original signals are decomposed into a finite number of stationary Intrinsic Mode functions (IMFs), then a number of IMFs containing main fault information is selected for further analysis. The energy of acceleration vibration signal would vary in different frequency bands when bearing fault occurs, therefore energy feature parameter extracted from IMFs could be served as input parameter of neural networks to identify fault patterns of roller bearing. The analysis results from roller bearing signals with inner-race and out-race faults show that the approach of neural network diagnosis based on EMD-extracting energy parameter of different frequency bands as feature is superior to that based on wavelet packet decomposition and reconstruction and can identify roller bearing fault patterns accurately and effectively.
For the non-stationary characteristics of diesel vibration signal and fuzzy characteristics of feature parameters, a method of fault diagnosis based on EEMD and Fuzzy C Mean clustering arithmetic is proposed. By decomposing the known-fault samples with EEMD, an initial characteristic vector matrix is obtained. Using a SVD method to the initial vector matrix, these singular values compose the fault feature vector, which is used as the input of FCM after standardization. The optimized classified matrix and clustering centers are obtained. Calculating the nearness degree between the unknown-fault samples and the known-fault ones, the fault pattern is identified. Experimental results indicate that this method can effectively diagnose the faults of diesel crankshaft bearing.
In order to realize the precise fault diagnosis of rolling bearing, an envelope demodulation method was proposed based on ensemble empirical mode decomposition (EEMD) and kurtosis criterion. EEMD was used to decompose the vibration signal into several Intrinsic Mode Functions (IMFs) first, and then an envelope demodulation was adopted with the IMF which selected by the maximal kurtosis criterion to extract the fault information. This method can not only restrain the mode mixing phenomenon caused by empirical mode decomposition (EMD), but also avoid the selection of center frequency and filter band in resonance demodulation method, so it has good adaptability. On the basis of discussing inner and outer vibration fault mechanism of rolling bearing, the proposed method was used to analyze the vibration signal of the actual fault rolling bearings. The result shows that this method can efficiently extract the fault information and realize the precise fault diagnosis of rolling bearing.
A new approach for mechanical fault diagnosis based on local mean decomposition (LMD) approximate entropy and fuzzy C-means clustering (FCM) is proposed. Firstly, fault mechanical vibration signal is decomposed with LMD to obtain a certain number of product function (PF) components that have physical meaning. With correlation analysis, three PF components that have largest correlation coefficients with the original signal are sifted out and used as the data source. The approximate entropies of these three PF components are calculated and used as the eigenvectors. At last, the constructed eigenvectors are put into FCM classifier to recognize different fault types. The results of experiment and engineering analysis demonstrate that the method based on local mean decomposition (LMD) approximate entropy and fuzzy c-means clustering is able to diagnose mechanical faults accurately and effectively. In addition, compared with the method based on empirical mode decomposition(EMD)approximate entropy and FCM, the proposed approach could obtain better fault identification result.
Most roller bearing fault vibration signals are always multi-component amplitude-modulated and frequency-modulated (AM-FM) signals, however, the selection of central frequency of band-pass filter needs to be determined with experience in conventional envelope analysis method, which would bring demodulation error. To target this problem, a roller bearing fault diagnosis approach based on LMD (local mean decomposition) and envelope spectrum characteristics was proposed. Firstly, by using LMD method, the vibration signal of roller bearing can be decomposed into a set of product functions (PF) whose instantaneous frequencies owned physical sense and each of which was a product of an envelope signal and a purely frequency modulated signal. Secondly, spectrum analysis can be used directly to envelope signal and then the envelope spectrum can be obtained. Finally, the amplitudes ratios in different characteristic frequencies of envelope spectrum were defined as the envelope spectrum characteristics, which served as input parameters of support sector machine classifier to classify working condition and fault patterns of roller bearings. The analysis results demonstrate the effectiveness of the proposed method.
In order to reduce the training time and improve the classification accuracy of fault intelligent classification of the rolling bearing, a multi-condition classification method for normal, inner raceway fault, outer raceway fault and different fault degrees of the rolling bearing is proposed. At first, the intrinsic mode function (IMF) components are obtained by ensemble empirical mode decomposition (EEMD), and the IMFs that containing main condition information are determined by using kurtosis combined with correlation coefficient method. Then, the feature matrix is constructed with the selected IMFs, the singular values obtained by using singular value decomposition (SVD) are regarded as the feature vector. At last, when hypersphere multiclass support vector machine with optimized classification rules is used for classifying, the maximum values of each condition hypersphere spherical center distance are proposed to determine kernel parameter selection range of the multiclass classifier, narrow the selection range, and achieve multi-condition classification of the rolling bearing. The experimental results show that the training time of the classifier can be reduced and the classification accuracy can be improved by the proposed multi-condition classification method of the rolling bearing.
Vibration signals of distribution switches that contain mechanical information are characterized by nonlinearity and nonstationarity. Therefore, based on the singular value decomposition of time-frequency matrix, a vibration signal feature extraction method for distribution switches was proposed. Hilbert-Huang transform (HHT) band-pass filter was used to construct the time-frequency matrix for the vibration signal. After the singular value decomposition (SVD) of the time-frequency matrix, the characteristic information of the vibration signal would be decomposed into different time-frequency subspaces, so we can get time-frequency matrix singular values as the feature quantities, the feature quantities would represent the mechanical state of distribution switches. Fuzzy c-mean (FCM) clustering was applied to these time-frequency matrix singular values of vibration signals which was monitored in normal states and three kinds of typical malfunctions including relieved insulated pull rod of phase A contacts, mechanical structure clamping stagnation states and screw loosing states. The result shows that the feature quantity can represent the mechanical state of distribution switches accurately and effectively.
In view of the presence of a variety of interference and multi partial discharge (PD) around the electrical equipment, the paper proposed multi PD online monitoring and identification method for partial discharge based on a single defect. It was pointed out that one of the key technologies of developing multi PD online monitoring and identification system was the rapid classification pulse groups using pulse waveform feature extraction and clustering analysis algorithm. With respect to 108 times/s ultra-wideband partial discharge pulse waveform-time series, the paper focused on the pulse waveform feature extraction and classification techniques. The improvements on equivalent frequency algorithm and fuzzy C-means clustering algorithm was proposed. Gas insulated switchgear (GIS) partial discharge test results show, that using the improved algorithm the computer can realize accurate partial discharge pulse automatic classification, and through introducing clustering threshold the low similarity subclass pulse pulse can be filtered out. This provides the experimental and theoretical basis for the development of multi-Bureau online monitoring and modelling system.
Targeting the shock characteristics of the vibration signal of a rotor system with local rub-impact fault, a local rub-impact fault diagnosis method of rotor system based on ELMD (ensemble local means decomposition) is proposed in this paper. The local mean decomposition (LMD) is a newly self-adaptive time–frequency analysis method, by which any complicated multi-component signal could be decomposed into a set of product functions (PFs) whose instantaneous frequencies in theory have physical significance. Unfortunately, mode mixing phenomenon which makes the decomposition results devoid of physical meaning is common when LMD is performed in practice. Targeting this shortcoming, the filter bank structure of white noise by LMD is obtained by numerical experiments, and then an improved method based upon noise-assisted analysis, ensemble local mean decomposition, is put forward. In ELMD, firstly, different white noise is added to the targeted signal; secondly, LMD is used to decompose the noise-added signal into product functions (PFs); finally, the ensemble means of corresponding PF components derived from LMD is regarded as the final decomposition result. The analytical results from simulation signal and experimental rotor local rub-impact signal demonstrate that the ELMD approach can be used to overcome the mode mixing of the original LMD method effectively.
For rolling bearing fault detection, it is expected that a desired time–frequency analysis method should have good computation efficiency, and have good resolution in both time domain and frequency domain. As the best available time–frequency method so far, the wavelet transform still cannot fulfill the rolling bearing fault detection task very well since it has some inevitable deficiencies. The recent popular time–frequency analysis method, Hilbert–Huang transform (HHT), has good computation efficiency and does not involve the concept of the frequency resolution and the time resolution. So the HHT seems to have potential to become a perfect tool for rolling bearing fault detection. However, in practical applications, the HHT also suffers from some unsolved deficiencies. To ameliorate these deficiencies, by seeking help from the wavelet packet transform (WPT) and a simple but effective method for intrinsic mode function (IMF) selection, an improved HHT is put forward in this studying. Several numerical study cases will be used to validate the capabilities of the improved HHT. Finally, the improved HHT's performance in rolling bearing fault detection is compared with that of the wavelet based scalogram through experimental case studies. The comparison results have shown that (1) the improved HHT has better resolution both in time domain and in frequency domain than the scalogram; (2) the improved HHT has better computing efficiency than scalogram; (3) the HHT spectrum also has one unresolved and maybe inevitable deficiency—ripple phenomenon in its estimated frequency, which would mislead our analysis.