Fault Recognition of Rolling Bearings Based on Parameter Optimized Multi-Scale Permutation Entropy and Gath-Geva

To extract fault features of rolling bearing vibration signals precisely, a fault diagnosis method based on parameter optimized multi-scale permutation entropy (MPE) and Gath-Geva (GG) clustering is proposed. The method can select the important parameters of MPE method adaptively, overcome the disadvantages of fixed MPE parameters and greatly improve the accuracy of fault identification. Firstly, aiming at the problem of parameter determination and considering the interaction among parameters comprehensively of MPE, taking skewness of MPE as fitness function, the time series length and embedding dimension were optimized respectively by particle swarm optimization (PSO) algorithm. Then the fault features of rolling bearing were extracted by parameter optimized MPE and the standard clustering centers is obtained with GG clustering. Finally, the samples are clustered with the Euclid nearness degree to obtain recognition rate. The validity of the parameter optimization is proved by calculating the partition coefficient and average fuzzy entropy. Compared with unoptimized MPE, the propose method has a higher fault recognition rate.     

Composite Multivariate Multi-Scale Permutation Entropy and Laplacian Score Based Fault Diagnosis of Rolling Bearing

As a powerful tool for measuring complexity and randomness, multivariate multi-scale permutation entropy (MMPE) has been widely applied to the feature representation and extraction of multi-channel signals. However, MMPE still has some intrinsic shortcomings that exist in the coarse-grained procedure, and it lacks the precise estimation of entropy value. To address these issues, in this paper a novel non-linear dynamic method named composite multivariate multi-scale permutation entropy (CMMPE) is proposed, for optimizing insufficient coarse-grained process in MMPE, and thus to avoid the loss of information. The simulated signals are used to verify the validity of CMMPE by comparing it with the often-used MMPE method. An intelligent fault diagnosis method is then put forward on the basis of CMMPE, Laplacian score (LS), and bat optimization algorithm-based support vector machine (BA-SVM). Finally, the proposed fault diagnosis method is utilized to analyze the test data of rolling bearings and is then compared with the MMPE, multivariate multi-scale multiscale entropy (MMFE), and multi-scale permutation entropy (MPE) based fault diagnosis methods. The results indicate that the proposed fault diagnosis method of rolling bearing can achieve effective identification of fault categories and is superior to comparative methods.     

Application of Parameter Optimized Variational Mode Decomposition Method in Fault Feature Extraction of Rolling Bearing

The decomposition effect of variational mode decomposition (VMD) mainly depends on the choice of decomposition number K and penalty factor α. For the selection of two parameters, the empirical method and single objective optimization method are usually used, but the aforementioned methods often have limitations and cannot achieve the optimal effects. Therefore, a multi-objective multi-island genetic algorithm (MIGA) is proposed to optimize the parameters of VMD and apply it to feature extraction of bearing fault. First, the envelope entropy (Ee) can reflect the sparsity of the signal, and Renyi entropy (Re) can reflect the energy aggregation degree of the time-frequency distribution of the signal. Therefore, Ee and Re are selected as fitness functions, and the optimal solution of VMD parameters is obtained by the MIGA algorithm. Second, the improved VMD algorithm is used to decompose the bearing fault signal, and then two intrinsic mode functions (IMF) with the most fault information are selected by improved kurtosis and Holder coefficient for reconstruction. Finally, the envelope spectrum of the reconstructed signal is analyzed. The analysis of comparative experiments shows that the feature extraction method can extract bearing fault features more accurately, and the fault diagnosis model based on this method has higher accuracy.     

A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM

This paper proposes a novel fault diagnosis method for rolling bearing based on hierarchical refined composite multiscale fluctuation-based dispersion entropy (HRCMFDE) and particle swarm optimization-based extreme learning machine (PSO-ELM). First, HRCMFDE is used to extract fault features in the vibration signal at different time scales. By introducing the hierarchical theory algorithm into the vibration signal decomposition process, the problem of missing high-frequency signals in the coarse-grained process is solved. Fluctuation-based dispersion entropy (FDE) has the characteristics of insensitivity to noise interference and high computational efficiency based on the consideration of nonlinear time series fluctuations, which makes the extracted feature vectors more effective in describing the fault information embedded in each frequency band of the vibration signal. Then, PSO is used to optimize the input weights and hidden layer neuron thresholds of the ELM model to improve the fault identification capability of the ELM classifier. Finally, the performance of the proposed rolling bearing fault diagnosis method is verified and analyzed by using the CWRU dataset and MFPT dataset as experimental cases, respectively. The results show that the proposed method has high identification accuracy for the fault diagnosis of rolling bearings with varying loads and has a good load migration effect.     

Double Feature Extraction Method of Ship-Radiated Noise Signal Based on Slope Entropy and Permutation Entropy

In order to accurately identify various types of ships and develop coastal defenses, a single feature extraction method based on slope entropy (SlEn) and a double feature extraction method based on SlEn combined with permutation entropy (SlEn&PE) are proposed. Firstly, SlEn is used for the feature extraction of ship-radiated noise signal (SNS) compared with permutation entropy (PE), dispersion entropy (DE), fluctuation dispersion entropy (FDE), and reverse dispersion entropy (RDE), so that the effectiveness of SlEn is verified, and SlEn has the highest recognition rate calculated by the k-Nearest Neighbor (KNN) algorithm. Secondly, SlEn is combined with PE, DE, FDE, and RDE, respectively, to extract the feature of SNS for a higher recognition rate, and SlEn&PE has the highest recognition rate after the calculation of the KNN algorithm. Lastly, the recognition rates of SlEn and SlEn&PE are compared, and the recognition rates of SlEn&PE are higher than SlEn by 4.22%. Therefore, the double feature extraction method proposed in this paper is more effective in the application of ship type recognition.     

Intelligent Fault Diagnosis of Rolling-Element Bearings Using a Self-Adaptive Hierarchical Multiscale Fuzzy Entropy

The fuzzy-entropy-based complexity metric approach has achieved fruitful results in bearing fault diagnosis. However, traditional hierarchical fuzzy entropy (HFE) and multiscale fuzzy entropy (MFE) only excavate bearing fault information on different levels or scales, but do not consider bearing fault information on both multiple layers and multiple scales at the same time, thus easily resulting in incomplete fault information extraction and low-rise identification accuracy. Besides, the key parameters of most existing entropy-based complexity metric methods are selected based on specialist experience, which indicates that they lack self-adaptation. To address these problems, this paper proposes a new intelligent bearing fault diagnosis method based on self-adaptive hierarchical multiscale fuzzy entropy. On the one hand, by integrating the merits of HFE and MFE, a novel complexity metric method, named hierarchical multiscale fuzzy entropy (HMFE), is presented to extract a multidimensional feature matrix of the original bearing vibration signal, where the important parameters of HMFE are automatically determined by using the bird swarm algorithm (BSA). On the other hand, a nonlinear feature matrix classifier with strong robustness, known as support matrix machine (SMM), is introduced for learning the discriminant fault information directly from the extracted multidimensional feature matrix and automatically identifying different bearing health conditions. Two experimental results on bearing fault diagnosis show that the proposed method can obtain average identification accuracies of 99.92% and 99.83%, respectively, which are higher those of several representative entropies reported by this paper. Moreover, in the two experiments, the standard deviations of identification accuracy of the proposed method were, respectively, 0.1687 and 0.2705, which are also greater than those of the comparison methods mentioned in this paper. The effectiveness and superiority of the proposed method are verified by the experimental results.     

Fault Diagnosis of Rolling Bearings Based on WPE by Wavelet Decomposition and ELM

The fault diagnosis classification method based on wavelet decomposition and weighted permutation entropy (WPE) by the extreme learning machine (ELM) is proposed to address the complexity and non-smoothness of rolling bearing vibration signals. The wavelet decomposition based on ‘db3’ is used to decompose the signal into four layers and extract the approximate and detailed components, respectively. Then, the WPE values of the approximate (CA) and detailed (CD) components of each layer are calculated and composed to be the feature vectors, which are finally fed into the extreme learning machine with optimal parameters for classification. The comparative study of the simulations based on WPE and permutation entropy (PE) shows that the classification method of seven kinds of signals of normal bearing signals and six types of fault states (7 mils and 14 mils) based on WPE (CA, CD) with the number of nodes in the hidden layers of ELM determined by the five-fold cross-validation has the best performances, the training accuracy can reach 100%, and the testing accuracy can reach 98.57% with 37 nodes of the hidden layer by ELM. The proposed method using WPE (CA, CD) by ELM provides guidance for the multi-classification of normal bearing signals.     

An Improved Incipient Fault Diagnosis Method of Bearing Damage Based on Hierarchical Multi-Scale Reverse Dispersion Entropy

The amplitudes of incipient fault signals are similar to health state signals, which increases the difficulty of incipient fault diagnosis. Multi-scale reverse dispersion entropy (MRDE) only considers difference information with low frequency range, which omits relatively obvious fault features with a higher frequency band. It decreases recognition accuracy. To defeat the shortcoming with MRDE and extract the obvious fault features of incipient faults simultaneously, an improved entropy named hierarchical multi-scale reverse dispersion entropy (HMRDE) is proposed to treat incipient fault data. Firstly, the signal is decomposed hierarchically by using the filter smoothing operator and average backward difference operator to obtain hierarchical nodes. The smoothing operator calculates the mean sample value and the average backward difference operator calculates the average deviation of sample values. The more layers, the higher the utilization rate of filter smoothing operator and average backward difference operator. Hierarchical nodes are obtained by these operators, and they can reflect the difference features in different frequency domains. Then, this difference feature is reflected with MRDE values of some hierarchical nodes more obviously. Finally, a variety of classifiers are selected to test the separability of incipient fault signals treated with HMRDE. Furthermore, the recognition accuracy of these classifiers illustrates that HMRDE can effectively deal with the problem that incipient fault signals cannot be easily recognized due to a similar amplitude dynamic.     

Feature Enhancement Method of Rolling Bearing Based on K-Adaptive VMD and RBF-Fuzzy Entropy

The complex and harsh working environment of rolling bearings cause the fault characteristics in vibration signal contaminated by the noise, which make fault diagnosis difficult. In this paper, a feature enhancement method of rolling bearing signal based on variational mode decomposition with K determined adaptively (K-adaptive VMD), and radial based function fuzzy entropy (RBF-FuzzyEn), is proposed. Firstly, a phenomenon called abnormal decline of center frequency (ADCF) is defined in order to determine the parameter K of VMD adaptively. Then, the raw signal is separated into K intrinsic mode functions (IMFs). A coefficient En for selecting optimal IMFs is calculated based on the center frequency bands (CFBs) of all IMFs and frequency spectrum for original signal autocorrelation operation. After that, the optimal IMFs of which En are bigger than the threshold are selected to reconstruct signal. Secondly, RBF is introduced as an innovative fuzzy function to enhance the feature discrimination of fuzzy entropy between bearings in different states. A specific way for determination of parameter r in fuzzy function is also presented. Finally, RBF-FuzzyEn is used to extract features of reconstructed signal. Simulation and experiment results show that K-adaptive VMD can effectively reduce the noise and enhance the fault characteristics; RBF-FuzzyEn has strong feature differentiation, superior noise robustness, and low dependence on data length.     

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

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)).     

Rolling Bearing Fault Monitoring for Sparse Time-Frequency Representation and Feature Detection Strategy

Data-driven fault diagnosis methods for rotating machinery have developed rapidly with the help of deep learning methods. However, traditional intelligent fault diagnosis methods still have some limitations in fault feature extraction and the latest object detection theory has not been applied in fault diagnosis. To this end, a fault diagnosis method based on a sparse short-term Fourier transform (SSTFT) and object detection theory is developed in this paper. First, a sparse constraint is introduced in time-frequency analysis to improve the time-frequency resolution of the model without cross-term interference and proximal gradient descent (PGD) is adopted to quickly and effectively optimize the model to obtain a high-quality time-frequency representation (TFR). Second, a fault diagnosis model based on a region-based convolutional neural network (RCNN) is built; the model can extract multiple regions that can characterize fault features from the TFR. This process avoids the interference of irrelevant vibration components and improves the interpretability of the fault diagnosis model. Finally, multicategory rolling bearing fault identification is realized. The effectiveness of the proposed method is validated by simulation signals and bearing experiments. The results indicate that the proposed method is more effective than existing methods.     

Research on Fault Diagnosis of Rolling Bearings Based on Variational Mode Decomposition Improved by the Niche Genetic Algorithm

Due to the influence of signal-to-noise ratio in the early failure stage of rolling bearings in rotating machinery, it is difficult to effectively extract feature information. Variational Mode Decomposition (VMD) has been widely used to decompose vibration signals which can reflect more fault omens. In order to improve the efficiency and accuracy, a method to optimize VMD by using the Niche Genetic Algorithm (NGA) is proposed in this paper. In this method, the optimal Shannon entropy of modal components in a VMD algorithm is taken as the optimization objective, by using the NGA to constantly update and optimize the combination of influencing parameters composed of α and K so as to minimize the local minimum entropy. According to the obtained optimization results, the optimal input parameters of the VMD algorithm were set. The method mentioned is applied to the fault extraction of a simulated signal and a measured signal of a rolling bearing. The decomposition process of the rolling-bearing fault signal was transferred to the variational frame by the NGA-VMD algorithm, and several eigenmode function components were obtained. The energy feature extracted from the modal component containing the main fault information was used as the input vector of a particle swarm optimized support vector machine (PSO-SVM) and used to identify the fault type of the rolling bearing. The analysis results of the simulation signal and measured signal show that: the NGA-VMD algorithm can decompose the vibration signal of a rolling bearing accurately and has a better robust performance and correct recognition rate than the VMD algorithm. It can highlight the local characteristics of the original sample data and reduce the interference of the parameters selected artificially in the VMD algorithm on the processing results, improving the fault-diagnosis efficiency of rolling bearings.     

A Bearing Fault Diagnosis Method Based on PAVME and MEDE

When rolling bearings have a local fault, the real bearing vibration signal related to the local fault is characterized by the properties of nonlinear and nonstationary. To extract the useful fault features from the collected nonlinear and nonstationary bearing vibration signals and improve diagnostic accuracy, this paper proposes a new bearing fault diagnosis method based on parameter adaptive variational mode extraction (PAVME) and multiscale envelope dispersion entropy (MEDE). Firstly, a new method hailed as parameter adaptive variational mode extraction (PAVME) is presented to process the collected original bearing vibration signal and obtain the frequency components related to bearing faults, where its two important parameters (i.e., the penalty factor and mode center-frequency) are automatically determined by whale optimization algorithm. Subsequently, based on the processed bearing vibration signal, an effective complexity evaluation approach named multiscale envelope dispersion entropy (MEDE) is calculated for conducting bearing fault feature extraction. Finally, the extracted fault features are fed into the k-nearest neighbor (KNN) to automatically identify different health conditions of rolling bearing. Case studies and contrastive analysis are performed to validate the effectiveness and superiority of the proposed method. Experimental results show that the proposed method can not only effectively extract bearing fault features, but also obtain a high identification accuracy for bearing fault patterns under single or variable speed.     

A New Fault Diagnosis of Rolling Bearing Based on Markov Transition Field and CNN

The rolling bearing is a crucial component of the rotating machine, and it is particularly vital to ensure its normal operation. In addition, the selection of different category features will add uncertainty and bias to the classification results. In order to decrease the interference of these factors to fault diagnosis, a new method that automatically learns the features of the data combined with Markov transition field (MTF) and convolutional neural network (CNN) is proposed in this paper, namely MTF-CNN. The MTF contributes to convert the original time series into corresponding figures, and the CNN is used to extract the deep feature information in the figure to complete the fault diagnosis. The effectiveness of the proposed method is verified by two public data sets. The experimental results show that MTF-CNN can classify different types of faults, and the highest accuracy rate can reach 100%. Likewise, the classification accuracy of this method is higher than some existing methods.     

A Rolling Bearing Fault Classification Scheme Based on k-Optimized Adaptive Local Iterative Filtering and Improved Multiscale Permutation Entropy

The health condition of the rolling bearing seriously affects the operation of the whole mechanical system. When the rolling bearing parts fail, the time series collected in the field generally shows strong nonlinearity and non-stationarity. To obtain the faulty characteristics of mechanical equipment accurately, a rolling bearing fault detection technique based on k-optimized adaptive local iterative filtering (ALIF), improved multiscale permutation entropy (improved MPE), and BP neural network was proposed. In the ALIF algorithm, a k-optimized ALIF method based on permutation entropy (PE) is presented to select the number of ALIF decomposition layers adaptively. The completely average coarse-graining method was proposed to excavate more hidden information. The performance analysis of the simulation signal shows that the improved MPE can more accurately dig out the depth information of the time series, and the entropy value obtained is more consistent and stable. In the research application, rolling bearing time series are decomposed by k-optimized ALIF to obtain a certain number of intrinsic mode functions (IMFs). Then the improved MPE value of effective IMF is calculated and input into backpropagation (BP) neural network as the feature vector for automatic fault identification. The comparative analysis of simulation signals shows that this method can extract fault information effectively. At the same time, the experimental part shows that this scheme not only effectively extracts the fault features, but also realizes the classification and identification of different fault modes and faults of different degrees, which has a certain application prospect in the research and application direction of rolling bearing fault identification.     

Remaining Useful Life Prediction Model for Rolling Bearings Based on MFPE–MACNN

Aiming to resolve the problem of redundant information concerning rolling bearing degradation characteristics and to tackle the difficulty faced by convolutional deep learning models in learning feature information in complex time series, a prediction model for remaining useful life based on multiscale fusion permutation entropy (MFPE) and a multiscale convolutional attention neural network (MACNN) is proposed. The original signal of the rolling bearing was extracted and decomposed by resonance sparse decomposition to obtain the high-resonance and low-resonance components. The multiscale permutation entropy of the low-resonance component was calculated. Moreover, the locally linear-embedding algorithm was used for dimensionality reduction to remove redundant information. The multiscale convolution module was constructed to learn the feature information at different time scales. The attention module was used to fuse the feature information and input it into the remaining useful life prediction module for evaluation. The appropriate network structure and parameter configuration were determined, and a multiscale convolutional attention neural network was designed to determine the remaining useful life prediction model. The results show that the method demonstrates effectiveness and superiority in degrading the feature information representation and improving the remaining useful life prediction accuracy compared with other models.     

A Fault Detection Method for Electrohydraulic Switch Machine Based on Oil-Pressure-Signal-Sectionalized Feature Extraction

A turnout switch machine is key equipment in a railway, and its fault condition has an enormous impact on the safety of train operation. Electrohydraulic switch machines are increasingly used in high-speed railways, and how to extract effective fault features from their working condition monitoring signal is a difficult problem. This paper focuses on the sectionalized feature extraction method of the oil pressure signal of the electrohydraulic switch machine and realizes the fault detection of the switch machine based on this method. First, the oil pressure signal is divided into three stages according to the working principle and action process of the switch machine, and multiple features of each stage are extracted. Then the max-relevance and min-redundancy (mRMR) algorithm is applied to select the effective features. Finally, the mini batch k-means method is used to achieve unsupervised fault diagnosis. Through experimental verification, this method can not only derive the best sectionalization mode and feature types of the oil pressure signal, but also achieve the fault diagnosis and the prediction of the status of the electrohydraulic switch machine.     

Intelligent Fault Identification for Rolling Bearings Fusing Average Refined Composite Multiscale Dispersion Entropy-Assisted Feature Extraction and SVM with Multi-Strategy Enhanced Swarm Optimization

Rolling bearings act as key parts in many items of mechanical equipment and any abnormality will affect the normal operation of the entire apparatus. To diagnose the faults of rolling bearings effectively, a novel fault identification method is proposed by merging variational mode decomposition (VMD), average refined composite multiscale dispersion entropy (ARCMDE) and support vector machine (SVM) optimized by multistrategy enhanced swarm optimization in this paper. Firstly, the vibration signals are decomposed into different series of intrinsic mode functions (IMFs) based on VMD with the center frequency observation method. Subsequently, the proposed ARCMDE, fusing the superiorities of DE and average refined composite multiscale procedure, is employed to enhance the ability of the multiscale fault-feature extraction from the IMFs. Afterwards, grey wolf optimization (GWO), enhanced by multistrategy including levy flight, cosine factor and polynomial mutation strategies (LCPGWO), is proposed to optimize the penalty factor C and kernel parameter g of SVM. Then, the optimized SVM model is trained to identify the fault type of samples based on features extracted by ARCMDE. Finally, the application experiment and contrastive analysis verify the effectiveness of the proposed VMD-ARCMDE-LCPGWO-SVM method.     

Fault Diagnosis Method Based on AUPLMD and RTSMWPE for a Reciprocating Compressor Valve

In order to effectively extract the key feature information hidden in the original vibration signal, this paper proposes a fault feature extraction method combining adaptive uniform phase local mean decomposition (AUPLMD) and refined time-shift multiscale weighted permutation entropy (RTSMWPE). The proposed method focuses on two aspects: solving the serious modal aliasing problem of local mean decomposition (LMD) and the dependence of permutation entropy on the length of the original time series. First, by adding a sine wave with a uniform phase as a masking signal, adaptively selecting the amplitude of the added sine wave, the optimal decomposition result is screened by the orthogonality and the signal is reconstructed based on the kurtosis value to remove the signal noise. Secondly, in the RTSMWPE method, the fault feature extraction is realized by considering the signal amplitude information and replacing the traditional coarse-grained multi-scale method with a time-shifted multi-scale method. Finally, the proposed method is applied to the analysis of the experimental data of the reciprocating compressor valve; the analysis results demonstrate the effectiveness of the proposed method.     

A New Method Based on Time-Varying Filtering Intrinsic Time-Scale Decomposition and General Refined Composite Multiscale Sample Entropy for Rolling-Bearing Feature Extraction

The early fault diagnosis of rolling bearings has always been a difficult problem due to the interference of strong noise. This paper proposes a new method of early fault diagnosis for rolling bearings with entropy participation. First, a new signal decomposition method is proposed in this paper: intrinsic time-scale decomposition based on time-varying filtering. It is introduced into the framework of complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN). Compared with traditional intrinsic time-scale decomposition, intrinsic time-scale decomposition based on time-varying filtering can improve frequency-separation performance. It has strong robustness in the presence of noise interference. However, decomposition parameters (the bandwidth threshold and B-spline order) have significant impacts on the decomposition results of this method, and they need to be artificially set. Aiming to address this problem, this paper proposes rolling-bearing fault diagnosis optimization based on an improved coyote optimization algorithm (COA). First, the minimal generalized refined composite multiscale sample entropy parameter was used as the objective function. Through the improved COA algorithm, optimal intrinsic time-scale decomposition parameters based on time-varying filtering that match the input signal are obtained. By analyzing generalized refined composite multiscale sample entropy (GRCMSE), whether the mode component is dominated by the fault signal is determined. The signal is reconstructed and decomposed again. Finally, the mode component with the highest energy in the central frequency band is selected for envelope spectrum variation for fault diagnosis. Lastly, simulated and experimental signals were used to verify the effectiveness of the proposed method.