Data Decomposition Techniques with Multi-Scale Permutation Entropy Calculations for Bearing Fault Diagnosis

Entropy-Based Methods for Motor Fault Detection: A Review

In the signal analysis context, the entropy concept can characterize signal properties for detecting anomalies or non-representative behaviors in fiscal systems. In motor fault detection theory, entropy can measure disorder or uncertainty, aiding in detecting and classifying faults or abnormal operation conditions. This is especially relevant in industrial processes, where early motor fault detection can prevent progressive damage, operational interruptions, or potentially dangerous situations. The study of motor fault detection based on entropy theory holds significant academic relevance too, effectively bridging theoretical frameworks with industrial exigencies. As industrial sectors progress, applying entropy-based methodologies becomes indispensable for ensuring machinery integrity based on control and monitoring systems. This academic endeavor enhances the understanding of signal processing methodologies and accelerates progress in artificial intelligence and other modern knowledge areas. A wide variety of entropy-based methods have been employed for motor fault detection. This process involves assessing the complexity of measured signals from electrical motors, such as vibrations or stator currents, to form feature vectors. These vectors are then fed into artificial-intelligence-based classifiers to distinguish between healthy and faulty motor signals. This paper discusses some recent references to entropy methods and a summary of the most relevant results reported for fault detection over the last 10 years.

Intelligent Compound Fault Diagnosis of Roller Bearings Based on Deep Graph Convolutional Network

The high correlation between rolling bearing composite faults and single fault samples is prone to misclassification. Therefore, this paper proposes a rolling bearing composite fault diagnosis method based on a deep graph convolutional network. First, the acquired raw vibration signals are pre-processed and divided into sub-samples. Secondly, a number of sub-samples in different health states are constructed as graph-structured data, divided into a training set and a test set. Finally, the training set is used as input to a deep graph convolutional neural network (DGCN) model, which is trained to determine the optimal structure and parameters of the network. A test set verifies the feasibility and effectiveness of the network. The experimental result shows that the DGCN can effectively identify compound faults in rolling bearings, which provides a new approach for the identification of compound faults in bearings.

An improved Autogram and MOMEDA method to detect weak compound fault in rolling bearings

When weak compound fault occurs in rolling bearing, the faint fault features suffer from serious noise interference, and different type faults are coupled together, making it a great challenge to separate the fault features. To solve the problems, a novel weak compound fault diagnosis method for rolling bearing based on improved Autogram and multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) is proposed. Firstly, the kurtosis index in Autogram is modified with multi-scale permutation entropy, and improved Autogram finds the optimal resonance frequency band to preliminarily denoise the weak compound fault signal. Then, MOMEDA is performed to deconvolute the denoised signal to decouple the features of compound fault. Finally, square envelope analysis is applied on the separated deconvoluted signals to identify different type faults according to the fault characteristic frequencies in the spectrums. The proposed method is performed to analyze the simulated signal and experimental datasets of different types of rolling bearing weak compound faults. The results indicate that the proposed method can accurately diagnose the weak compound faults, and comparison with the analysis results of parameter-adaptive variational mode decomposition algorithm verifies its effectiveness and superiority.

Rolling Bearing Fault Diagnosis Based on Successive Variational Mode Decomposition and the EP Index

Rolling bearing is an important part guaranteeing the normal operation of rotating machinery, which is also prone to various damages due to severe running conditions. However, it is usually difficult to extract the weak fault characteristic information from rolling bearing vibration signals and to realize a rolling bearing fault diagnosis. Hence, this paper offers a rolling bearing fault diagnosis method based on successive variational mode decomposition (SVMD) and the energy concentration and position accuracy (EP) index. Since SVMD decomposes a vibration signal of a rolling bearing into a number of modes, it is difficult to select the target mode with the ideal fault characteristic information. Comprehensively considering the energy concentration degree and frequency position accuracy of the fault characteristic component, the EP index is proposed to indicate the target mode. As the balancing parameter is crucial to the performance of SVMD and must be set properly, the line search method guided by the EP index is introduced to determine an optimal value for the balancing parameter of SVMD. The simulation and experiment results demonstrate that the proposed SVMD method is effective for rolling bearing fault diagnosis and superior to the variational mode decomposition (VMD) method.

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.

Fault Diagnosis of a Wind Turbine Gearbox Based on Improved Variational Mode Algorithm and Information Entropy

The working environment of wind turbine gearboxes is complex, complicating the effective monitoring of their running state. In this paper, a new gearbox fault diagnosis method based on improved variational mode decomposition (IVMD), combined with time-shift multi-scale sample entropy (TSMSE) and a sparrow search algorithm-based support vector machine (SSA-SVM), is proposed. Firstly, a novel algorithm, IVMD, is presented for solving the problem where VMD parameters (K and α) need to be selected in advance, which mainly contains two steps: the maximum kurtosis index is employed to preliminarily determine a series of local optimal decomposition parameters (K and α), then from the local parameters, the global optimum parameters are selected based on the minimum energy loss coefficient (ELC). After decomposition by IVMD, the raw signal is divided into K intrinsic mode functions (IMFs), the optimal IMF(s) with abundant fault information is (are) chosen based on the minimum envelopment entropy criterion. Secondly, the time-shift technique is introduced to information entropy, the time-shift multi-scale sample entropy algorithm is applied for the analysis of the complexity of the chosen optimal IMF and extract fault feature vectors. Finally, the sparrow search algorithm, which takes the classification error rate of SVM as the fitness function, is used to adaptively optimize the SVM parameters. Next, the extracted TSMSEs are input into the SSA-SVM model as the feature vector to identify the gear signal types under different conditions. The simulation and experimental results confirm that the proposed method is feasible and superior in gearbox fault diagnosis when compared with other methods.

Surface intrusion event identification for subway tunnels using ultra-weak FBG array based fiber sensing

A scheme is proposed for the identification of surface intrusion events, from signals detected by an ultra-weak fiber Bragg grating array in a subway tunnel. The spectral subtraction and the root mean square of the power spectral density are combined to extract event signals. The local characteristics-scale decomposition and the multi-scale permutation entropy are employed subsequently for feature extraction, which can improve the event recognition rate from the perspective of multi-scale analysis. Experimental demonstration verifies that the proposed scheme can identify four common events. Among the events, the discrete pulse construction and the continuous pulse construction on the ground surface are intrusion events, the subway train traveling in the tunnel and the lorry passing on the ground surface are non-intrusion events. The average recognition rate of 96.57% is achieved, which can satisfy actual application requirements.

Related Entropy Theories Application in Condition Monitoring of Rotating Machineries

Rotating machinery plays an important role in various kinds of industrial engineering. How to assess their conditions is a key problem for operating safety and condition-based maintenance. The potential anomaly, fault and failure information can be obtained by analyzing the collected condition monitoring data of the previously deployed sensors in rotating machinery. Among the available methods of analyzing sensors data, entropy and its variants can provide quantitative information contained in these sensing data. For implementing fault detection, diagnosis, and prognostics, this information can be utilized for feature extraction and selecting appropriate training data for machine learning methods. This article aims to review the related entropy theories which have been applied for condition monitoring of rotating machinery. This review consists of typical entropy theories presentation, application, summary, and discussion.

Time-Shift Multi-scale Weighted Permutation Entropy and GWO-SVM Based Fault Diagnosis Approach for Rolling Bearing

Multi-scale permutation entropy (MPE) is an effective nonlinear dynamic approach for complexity measurement of time series and it has been widely applied to fault feature representation of rolling bearing. However, the coarse-grained time series in MPE becomes shorter and shorter with the increase of the scale factor, which causes an imprecise estimation of permutation entropy. In addition, the different amplitudes of the same patterns are not considered by the permutation entropy used in MPE. To solve these issues, the time-shift multi-scale weighted permutation entropy (TSMWPE) approach is proposed in this paper. The inadequate process of coarse-grained time series in MPE was optimized by using a time shift time series and the process of probability calculation that cannot fully consider the symbol mode is solved by introducing a weighting operation. The parameter selections of TSMWPE were studied by analyzing two different noise signals. The stability and robustness were also studied by comparing TSMWPE with TSMPE and MPE. Based on the advantages of TSMWPE, an intelligent fault diagnosis method for rolling bearing is proposed by combining it with gray wolf optimized support vector machine for fault classification. The proposed fault diagnostic method was applied to two cases of experimental data analysis of rolling bearing and the results show that it can diagnose the fault category and severity of rolling bearing accurately and the corresponding recognition rate is higher than the rate provided by the existing comparison methods.

Analysis of Weak Fault in Hydraulic System Based on Multi-scale Permutation Entropy of Fault-Sensitive Intrinsic Mode Function and Deep Belief Network

With the aim of automatic recognition of weak faults in hydraulic systems, this paper proposes an identification method based on multi-scale permutation entropy feature extraction of fault-sensitive intrinsic mode function (IMF) and deep belief network (DBN). In this method, the leakage fault signal is first decomposed by empirical mode decomposition (EMD), and fault-sensitive IMF components are screened by adopting the correlation analysis method. The multi-scale entropy feature of each screened IMF is then extracted and features closely related to the weak fault information are then obtained. Finally, DBN is used for identification of fault diagnosis. Experimental results prove that this identification method has an ideal recognition effect. It can accurately judge whether there is a leakage fault, determine the degree of severity of the fault, and can diagnose and analyze hydraulic weak faults in general.

Combining Multi-Scale Wavelet Entropy and Kernelized Classification for Bearing Multi-Fault Diagnosis

Discriminative feature extraction and rolling element bearing failure diagnostics are very important to ensure the reliability of rotating machines. Therefore, in this paper, we propose multi-scale wavelet Shannon entropy as a discriminative fault feature to improve the diagnosis accuracy of bearing fault under variable work conditions. To compute the multi-scale wavelet entropy, we consider integrating stationary wavelet packet transform with both dispersion (SWPDE) and permutation (SWPPE) entropies. The multi-scale entropy features extracted by our proposed methods are then passed on to the kernel extreme learning machine (KELM) classifier to diagnose bearing failure types with different severities. In the end, both the SWPDE–KELM and the SWPPE–KELM methods are evaluated on two bearing vibration signal databases. We compare these two feature extraction methods to a recently proposed method called stationary wavelet packet singular value entropy (SWPSVE). Based on our results, we can say that the diagnosis accuracy obtained by the SWPDE–KELM method is slightly better than the SWPPE–KELM method and they both significantly outperform the SWPSVE–KELM method.

Self-Adaptive Spectrum Analysis Based Bearing Fault Diagnosis

Bearings are critical parts of rotating machines, making bearing fault diagnosis based on signals a research hotspot through the ages. In real application scenarios, bearing signals are normally non-linear and unstable, and thus difficult to analyze in the time or frequency domain only. Meanwhile, fault feature vectors extracted conventionally with fixed dimensions may cause insufficiency or redundancy of diagnostic information and result in poor diagnostic performance. In this paper, Self-adaptive Spectrum Analysis (SSA) and a SSA-based diagnosis framework are proposed to solve these problems. Firstly, signals are decomposed into components with better analyzability. Then, SSA is developed to extract fault features adaptively and construct non-fixed dimension feature vectors. Finally, Support Vector Machine (SVM) is applied to classify different fault features. Data collected under different working conditions are selected for experiments. Results show that the diagnosis method based on the proposed diagnostic framework has better performance. In conclusion, combined with signal decomposition methods, the SSA method proposed in this paper achieves higher reliability and robustness than other tested feature extraction methods. Simultaneously, the diagnosis methods based on SSA achieve higher accuracy and stability under different working conditions with different sample division schemes.