Multiscale Permutation Entropy Based Rolling Bearing Fault Diagnosis

Fault diagnosis of rotating machinery is vital to identify incipient failures and avoid unexpected downtime in industrial systems. This paper proposes a new rolling bearing fault diagnosis method by integrating the fine-to-coarse multiscale permutation entropy (F2CMPE), Laplacian score (LS) and support vector machine (SVM). A novel entropy measure, named F2CMPE, was proposed by calculating permutation entropy via multiple-scale fine-grained and coarse-grained signals based on the wavelet packet decomposition. The entropy measure estimates the complexity of time series from both low- and high-frequency components. Moreover, the F2CMPE mitigates the drawback of producing time series with sharply reduced data length via the coarse-grained procedure in the conventional composite multiscale permutation entropy (CMPE). The comparative performance of the F2CMPE and CMPE is investigated by analyzing the synthetic and experimental signals for entropy-based feature extraction. In the proposed bearing fault diagnosis method, the F2CMPE is first used to extract the entropy-based features from bearing vibration signals. Then, LS and SVM are used for selection of features and fault classification, respectively. Finally, the effectiveness of the proposed method is verified for rolling bearing fault diagnosis using experimental vibration data sets, and the results have demonstrated the capability of the proposed method to recognize and identify the bearing fault patterns under different fault states and severity levels.

A method based on compound multiscale permutation entropy, support vector machine, and particle swarm optimization for roller bearings fault diagnosis was presented in this study. Firstly, the roller bearings vibration signals under different conditions were decomposed into permutation entropy values by the multiscale permutation entropy and compound multiscale permutation entropy methods. The compound multiscale permutation entropy model combined the different graining sequence information under each scale factor. The average value of each scale factor was regarded as the final entropy value in the compound multiscale permutation entropy model. The compound multiscale permutation entropy model suppressed the shortcomings of poor stability caused by the length of the original signals in the multiscale permutation entropy model. Validity and accuracy are considered in the numerical experiments, and then compared with the computational efficiency of the multiscale permutation entropy method. Secondly, the entropy values of the multiscale permutation entropy/compound multiscale permutation entropy under different scales are regarded as the input of the particle swarm optimization–support vector machine models for fulfilling the fault identification, the classification accuracy is used to verify the effectiveness of the multiscale permutation entropy/compound multiscale permutation entropy with particle swarm optimization–support vector machine. Finally, the experimental results show that the classification accuracy of the compound multiscale permutation entropy model is higher than that of the multiscale permutation entropy.

Aiming to address the nonlinear and non-stationary characteristics of rolling bearing fault vibration signals, traditional diagnostic methods face challenges such as mode mixing, insufficient feature discrimination, and sensitivity to classifier parameters, which limit further improvements in diagnostic accuracy. This paper proposes a comprehensive optimization framework for fault diagnosis, covering signal decomposition and fault feature classification. First, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is applied to decompose the signal into intrinsic mode functions (IMF), effectively suppressing mode mixing. Next, the correlation coefficient and multiscale permutation entropy (MPE) are employed to quantify the dynamic complexity of each IMF across multiple scales, enabling the extraction of highly discriminative multidimensional feature vectors. Finally, the black-winged kite algorithm (BKA) is used to optimize the penalty factor and kernel parameters of the least squares support vector machine (LSSVM). BKA achieves a dynamic balance between local exploitation and global exploration, and its integration with Cauchy mutation improves robustness to noise, thereby enhancing convergence speed and stability. Experimental results from publicly available datasets and a custom experimental platform show that the proposed approach effectively distinguishes among various fault types, offering superior performance, improved interpretability, and enhanced robustness.

To enhance the precision of rolling bearing fault diagnosis, an intelligent hybrid approach is proposed in this paper for signal processing and fault diagnosis in small samples. This approach is based on advanced techniques, combining parameter optimization variational mode decomposition weighted by multiscale permutation entropy (MPE) with maximal information coefficient and multi-target attention convolutional neural networks (MTACNN). First, an improved variational mode decomposition (VMD) is developed to denoise the raw signal. The whale optimization algorithm was used to optimize the penalty factor and mode component number in the VMD algorithm to obtain several intrinsic mode functions (IMFs). Second, separate MPE calculations are performed for both the raw signal and each of the IMF components obtained from the VMD decomposition; the results are used to calculate the maximum information coefficient (MIC). Subsequently, each MIC is normalized and converted to a weight coefficient for signal reconstruction. Ultimately, the reconstructed signals serve as input to the MTACNN for diagnosing rolling bearing faults. Results demonstrate that the signal processing approach exhibits superior noise reduction capability through simple processing. Furthermore, compared to several similar approaches, The method proposed for fault diagnosis achieves superior performance levels in the fault pattern recognition target and the fault severity recognition target.

Multiscale Permutation Entropy (MPE) analysis is a powerful ordinal tool in the measurement of information content of time series. MPE refinements, such as Composite MPE (cMPE) and Refined Composite MPE (rcMPE), greatly increase the precision of the entropy estimation by modifying the original method. Nonetheless, these techniques have only been proposed as algorithms, and are yet to be described from the theoretical perspective. Therefore, the purpose of this article is two-fold. First, we develop the statistical theory behind cMPE and rcMPE. Second, we propose an alternative method, Refined Composite Downsampling Permutation Entropy (rcDPE) to further increase the entropy estimation’s precision. Although cMPE and rcMPE outperform MPE when applied on uncorrelated noise, the results are higher than our predictions due to inherent redundancies found in the composite algorithms. The rcDPE method, on the other hand, not only conforms to our theoretical predictions, but also greatly improves over the other methods, showing the smallest bias and variance. By using MPE, rcMPE and rcDPE to classify faults in bearing vibration signals, rcDPE outperforms the multiscaling methods, enhancing the difference between faulty and non-faulty signals, provided we apply a proper anti-aliasing low-pass filter at each time scale.

Due to the plenty of redundant information contained in the fault feature sets of the original vibration signals of rolling bearings, the diagnostic accuracy is reduced and computational complexity is increased, making it very difficult to achieve accurate and fast fault recognition. So as to address the hard issue, this article develops an Enhanced Hessian Locally Linear Embedding (EHLLE) method for rolling bearing fault diagnosis based upon Novel Variational Mode Decomposition (NVMD). Firstly, NVMD method is utilized to denoise sample vibration signals and the sensitive modes containing main fault information are obtained. Secondly, some time-domain and frequency-domain statistical features are used to construct sample high-dimensional features, the dimensionality of which is reduced by EHLLE. Ultimately, K-Means algorithm is employed to cluster the low-dimensional features, which are utilized to train Support Vector Machine (SVM), and then the trained SVM is applied to the recognition of testing sample low-dimensional features. Two experiments of rolling bearing fault diagnosis demonstrate the effectiveness of NVMD-EHLLE method. Additionally, the superiority of the developed method is verified by comparing with other three typical methods.

Support Vector Machine (SVM) is a machine learning algorithm based on the Statistical Learning Theory (SLT), which can get good classification effects with a few learning samples. SVM represents a new approach to pattern classification and has been shown to be particularly successful in many fields such as image identification and face recognition. It also provides us with a new method to develop intelligent fault diagnosis. This paper presents a SVM based approach for fault diagnosis of rolling bearings. Experimentation with vibration signals of bearing was conducted. The vibration signals acquired from the bearings were directly used in the calculating without the preprocessing of extracting its features. Compared with the Artificial Neural Network (ANN) based method, the SVM based method has desirable advantages. Also a multi-faults SVM classifier based on binary classifiers is constructed for gear faults in this paper. Other experiments with gear fault samples showed that the multi-fault SVM classifier has good classification ability and high efficiency, and suitable for on line diagnosis for mechanical system.

Financial time series analysis using the relation between MPE and MWPE

Support Vector Machine (SVM) is a machine learning algorithm based on the Statistical Learning Theory (SLT), which can get good classification effects with a few learning samples. SVM represents a new approach to pattern classification and has been shown to be particularly successful in many fields such as image identification and face recognition. It also provides us with a new method to develop intelligent fault diagnosis. This paper presents an SVM based approach for fault diagnosis of rolling bearings. Experimentation with vibration signals of bearing was conducted. The vibration signals acquired from the bearings were directly used in the calculating without the preprocessing of extracting its features. Compared with the Artificial Neural Network (ANN) based method, the SVM based method has desirable advantages. Also a multi-fault SVM classifier based on binary clas- sifier is constructed for gear faults in this paper. Other experiments with gear fault samples showed that the multi-fault SVM classifier has good classification ability and high efficiency in mechanical system. It is suitable for on line diagnosis for mechanical system.

Based on pattern spectrum entropy and proximal support vector machine (PSVM), a motor rolling bearing fault diagnosis method is proposed in this paper. It is very difficult to filter the fault vibration signals from the strong noise background because the roller bearing fault diagnosis is a problem of multi-class classification of inner ring fault, outer ring fault and ball fault. Firstly, vibration signals are processed by the pattern spectrum. Secondly, the morphological pattern spectrum entropy, and pattern spectrum values are utilized to identify the fault features of input parameters of PSVM classifiers. The experiment results demonstrate that the pattern spectrum quantifies various aspects of the shape-size content of a signal, and PSVM costs a little time and has better efficiency than the standard SVM.

Variational mode decomposition is a new signal decomposition method, which can process non-linear and non-stationary signals. It can overcome the problems of mode mixing and compensate for the shortcomings in empirical mode decomposition. Permutation entropy is a method which can detect the randomness and kinetic mutation behavior of a time series. It can be considered for use in fault diagnosis. The complexity of wind power generation systems means that the randomness and kinetic mutation behavior of their vibration signals are displayed at different scales. Multi-scale permutation entropy analysis is therefore needed for such vibration signals. This research investigated a method based on variational mode decomposition and permutation entropy for the fault diagnosis of a wind turbine roller bearing. Variational mode decomposition was adopted to decompose the bearing vibration signal into its constituent components. The components containing key fault information were selected for the extraction of their permutation entropy. This entropy was used as a bearing fault characteristic value. The nearest neighbor algorithm was employed as a classifier to identify faults in a roller bearing. The experimental data showed that the proposed method can be applied to wind turbine roller bearing fault diagnosis.

To achieve the goal of automated rolling bearing fault diagnosis, a variational mode decomposition (VMD) based diagnosis scheme was proposed. VMD was firstly used to decompose the vibration signals into a series of band-limited intrinsic mode functions (BLIMFs). Subsequently, the multiscale fractal dimension (MSFD) and multiscale energy (MSEN) of each BLIMF were calculated and combined together as features of the original vibration signals. In an attempt to accelerate the classification speed, one-way analysis of variance (ANOVA) test was adopted to extract significant features from the redundant features. Finally, those significant features were fed into the optimized support vector machine (SVM), which was optimized by the genetic algorithm (GA), for classification. Experimental results on the international public Case Western Reserve University bearing data indicate the effectiveness of the proposed method with a classification accuracy of 99.75 % for seven classes. Moreover, our approach also shows good anti-noise performance in different signal-to-noise ratios (SNRs).

It is an important practical problem to accurately recognize whether biological tissue is denatured during high intensity focused ultrasound (HIFU) treatment. Ultrasonic scattering echo signals are related to some physical properties of biological tissues. According to the characteristics of ultrasonic scattering echo signals, the recognition of denatured biological tissues is studied based on the variational mode decomposition (VMD) and multi-scale permutation entropy (MPE) in this paper. The ultrasonic echo signals are decomposed into various modal components by the VMD. The noise components and the useful components are separated according to the power spectrum information entropy of various modal components. The separated useful signals are reconstructed and the MPE are extracted. Furthermore, Gustafson-Kessel (GK) fuzzy clustering analysis is employed to obtain the standard clustering center, and the recognition of denatured biological tissues is carried out by Euclid approach degree and principle of proximity. The proposed method is applied to ultrasonic scattering echo signal during HIFU treatment. In order to determine the parameters of MPE algorithm for ultrasonic scattering echo signals, the embedding dimension of the MPE is discussed, and the scale factor of the MPE algorithm is optimized by genetic algorithm. When the delay time and the embedding dimension are 2 and 7 respectively, the MPE values decrease with scale factor increasing. Assuming that the scale factor is 12 from optimization results, the 293 ultrasonic scattering echo signals from normal tissues and denatured tissues are analyzed by the MPE. It is found that the MPE values of the denatured tissues are higher than those of the normal tissues. The MPE can be used to distinguish normal tissues and denatured tissues. Comparing with the recognition methods of the EMD-MPE-GK fuzzy clustering method and the VMD-WE-GK fuzzy clustering, the proposed method has good clustering performance and separability. Its partition coefficient (PC) is close to 1 and the Xie-Beni (XB) index is smaller. There are fewer feature points in the overlap region between MPE features of denatured tissues and normal tissues. The recognition results of denatured biological tissues in this experimental environment show that the recognition rate based on this method is higher, reaching up to 93.81%.

Quantifying the complexity of the EEG signal during prolonged wakefulness and during sleep is gaining interest as an additional mean to characterize the mechanisms associated with sleep and wakefulness regulation. Here, we characterized how EEG complexity, as indexed by Multiscale Permutation Entropy (MSPE), changed progressively in the evening prior to light off and during the transition from wakefulness to sleep. We further explored whether MSPE was able to discriminate between wakefulness and sleep around sleep onset and whether MSPE changes were correlated with spectral measures of the EEG related to sleep need during concomitant wakefulness (theta power-Ptheta: 4-8 Hz). To address these questions, we took advantage of large datasets of several hundred of ambulatory EEG recordings of individual of both sexes aged 25-101 years. Results show that MSPE significantly decreases before light off (i.e. before sleep time) and in the transition from wakefulness to sleep onset. Furthermore, MSPE allows for an excellent discrimination between pre-sleep wakefulness and early sleep. Finally, we show that MSPE is correlated with concomitant Ptheta. Yet, the direction of the latter correlation changed from before light-off to the transition to sleep. Given the association between EEG complexity and consciousness, MSPE may track efficiently putative changes in consciousness preceding sleep onset. An MSPE stands as a comprehensive measure that is not limited to a given frequency band and reflects a progressive change brain state associated with sleep and wakefulness regulation. It may be an effective mean to detect when the brain is in a state close to sleep onset.

A comparative study of four multi-scale entropies combined with grey relational degree in classification of ship-radiated noise