Multiscale Weighted Permutation Entropy Research Articles

Refined composite multivariate multiscale weighted permutation entropy and multicluster feature selection-based fault detection of gearbox

Refined composite multivariate multiscale weighted permutation entropy and multicluster feature selection-based fault detection of gearbox

Bearing fault diagnosis of induction machines using VMD-DWT and composite multiscale weighted permutation entropy

PurposeBearings play a critical role in the reliable operation of induction machines, and their failure can lead to significant operational challenges and downtime. Detecting and diagnosing these defects is imperative to ensure the longevity of induction machines and preventing costly downtime. The purpose of this paper is to develop a novel approach for diagnosis of bearing faults in induction machine.Design/methodology/approachTo identify the different fault states of the bearing with accurately and efficiently in this paper, the original bearing vibration signal is first decomposed into several intrinsic mode functions (IMFs) using variational mode decomposition (VMD). The IMFs that contain more noise information are selected using the Pearson correlation coefficient. Subsequently, discrete wavelet transform (DWT) is used to filter the noisy IMFs. Second, the composite multiscale weighted permutation entropy (CMWPE) of each component is calculated to form the features vector. Finally, the features vector is reduced using the locality-sensitive discriminant analysis algorithm, to be fed into the support vector machine model for training and classification.FindingsThe obtained results showed the ability of the VMD_DWT algorithm to reduce the noise of raw vibration signals. It also demonstrated that the proposed method can effectively extract different fault features from vibration signals.Originality/valueThis study suggested a new VMD_DWT method to reduce the noise of the bearing vibration signal. The proposed approach for bearing fault diagnosis of induction machine based on VMD-DWT and CMWPE is highly effective. Its effectiveness has been verified using experimental data.

Denatured recognition of biological tissue based on multi-scale phase weighted-permutation entropy during HIFU treatment

In the course of high-intensity focused ultrasound (HIFU) treatment, the capacity to precisely recognize biological tissue that has been denatured is crucial to ensuring the security and availability of HIFU treatment. Multi-scale permutation entropy (MPE) and its variant multi-scale weighted-permutation entropy (MWPE), as common methods to measure the complexity of nonlinear time series, are often used to recognize denatured biological tissue during HIFU treatment. In order to improve the inevitable disadvantages of MPE and MWPE in some cases, a new complexity method called multi-scale phase weighted-permutation entropy (MPWPE) is put forward. The proposed MPWPE improves MPE and MWPE by adding phase information through the Hilbert transform. The simulated analysis result indicates that the MPWPE can detect more dynamic changes in the synthetic signal compared with MPE and MWPE. Finally, based on the key MPWPE feature extraction algorithm, a novel intelligent biological tissue denatured recognition technology combined with the classifier is proposed. The actual HIFU echo signals of biological tissues are employed to verify the effectiveness of the proposed method. The results show that compared with MPE and MWPE, the MPWPE features can distinguish non-denatured and denatured tissues at multi scales with better performance and achieve higher recognition accuracy.

A mechanical part fault diagnosis method based on improved multiscale weighted permutation entropy and multiclass LSTSVM

Multi-scale permutation entropy (MPE) has poor stability, accuracy and noise immunity, recognition accuracy of twin SVM is low, so a diagnosis method based on improved multi-scale weighted permutation entropy (IMWPE) and least squares TSVM (LSTSVM) is proposed. The innovations include that the improved variational mode decomposition (IVMD) based on energy and mutual information is used to suppress noise, and novel composite coarse-grained and permutation pattern weighting methods are introduced to construct IMWPE, after which the noise immunity, stability and accuracy of features have been improved. LSTSVM is extended to a multi-class LSTSVM through one vs one (OVO) and binary tree (BT) strategies, the performance of the proposed methodology is significantly improved. The results show that signal-to-noise ratio of signal is enhanced, the stability of IMWPE is improved, the diagnosis accuracies for bearing and check valve are increased by 17.084 % and 12.498 %, which provides a reference for fault diagnosis under noise.

Online Chatter Identification for Thin-Walled Parts Machining Based on Improved Multisensor Signal Fusion and Multiscale Entropy

Thin-walled workpieces frequently appear to chatter during milling, causing the creation of vibration patterns on the surface of the workpiece, which affects the machining quality and workpiece performance. Identification of online chatter is important for thin-walled parts. The vibration signal associated with chatter changes dynamically throughout the milling process due to changes in tool position, removal of workpiece material, and transmission-related vibration signal attenuation characteristics, making reliable chatter identification difficult. This research proposes a unique online chatter identification approach for the machining of thin-walled parts based on improved multi-sensor signal fusion and multi-scale entropy. In order to acquire the fused vibration signals, the vibration signals produced during the machining of thin-walled parts are first acquired by sensors at various test sites and adaptively given weight coefficients by the improved Hausdorff distance and distance factor. Second, using the multi-scale sample entropy (MSSE) and multi-scale weighted permutation entropy (MSWPE), the eigenvalues of the fused vibration signals are obtained. Finally, the trained Logistic regression (LR) classification model is used to determine the vibration status of thin-walled parts. The analysis’s results demonstrated that the technique can properly identify the vibration state of thin-walled parts, and that the fusion signal can reflect the vibration state at the tool contact site more accurately.

SVMWPE-HLLE Based Fault Diagnosis Approach for Rolling Bearing

Multi-scale permutation entropy (MPE) is an analytical method describing the complexity of time series, which has been applied to the fault diagnosis of rolling bearings. To solve the problems of MPE in coarse-grained process and permutation entropy calculation, multi-scale weighted permutation entropy based on sliding variance (SVMWPE) was proposed in this paper. By analyzing WGN signal and 1/f noise signal, the parameter selections for SVMWPE were studied, and the stability and superiority were investigated by comparing SVMWPE with MPE, MWPE, and SVMPE. The high-dimensional matrix obtained by MPE feature extraction to pattern recognition was solved by introducing Hessian local linear embedding (HLLE) dimension reduction method, and the feature extraction method based on SVMWPE-HLLE was proposed. The clustering effect was studied by comparing SVMWPE-HLLE with SVMWPE-LLE through the analysis of three simulation signals. Fault diagnosis method for rolling bearing was proposed by combining SVMWPE-HLLE with extreme learning machine (ELM), which was applied to two experimental cases of rolling bearings for analysis. The experimental results showed that the proposed method can realize intelligent diagnosis of different fault types and degrees of rolling bearing, and the fault recognition rate of the proposed method was higher than other methods.

Distribution Network Fault-Line Selection Method Based on MICEEMDAN–Recurrence Plot–Yolov5

Distribution system fault signals contain severe noise components. In order to solve the problem of distribution network fault-line selection, a fault-line selection method based on modifying the Improved Complete Ensemble Empirical Mode Decomposition Adaptive Noise (MICEEMDAN) algorithm, Recurrence Plot, and Yolov5 network is proposed. First, ICEEMDAN is optimized using multi-scale weighted permutation entropy (MWPE). MICEEMDAN can decompose an electrical signal into a series of intrinsic mode functions (IMFs). Recurrence Plot transformation of all IMFs, obtained from decomposition and stitching from top to bottom, realizes the conversion of 1D time series to 2D images. Then, the recurrence maps obtained from all lines in the distribution network are stitched to obtain the distribution network recurrence map, realizing the mining of the fault-signal features of the whole distribution network. Finally, the Yolov5 network is used to mine the fault features of the recurrence map of the distribution network autonomously to realize the fault-line selection. The experiments show that the method has a good noise immunity and 99.98% fault-selection accuracy, which can effectively complete the distribution network fault selection.

Exploring the impact of flow values on multiscale complexity quantification of airport flight flow fluctuations

Being able to characterize the dynamic characteristics of the air traffic system and embody the dynamic evolution thereof, the complexity of air traffic flows has attracted the broad attention of scholars and researchers. To fully consider amplitude information, we adopt the improved multiscale weighted permutation entropy (IMWPE) and propose an improved multivariate multiscale weighted permutation entropy (IMMWPE) to explore the complexity of flight flows of the top ten busy airports in China from a univariate and a multivariate perspective, respectively. In addition, we propose an improved multiscale weight contingency to investigate the inhomogeneity between fluctuation pattern distributions in departure and arrival flight flows. At the advantages of the multiple coarse-graining procedures, we obtain more reliable and stable entropy and contingency results, considering amplitude information. Comparisons between the weighted and unweighted results show that the weighted methods are as capable as the unweighted in exactly characterizing the dynamic characteristics of flight flow fluctuations, i.e., temporal scale dependency, spike distributions, differences between univariate and multivariate perspectives. Results also show that the weight has a stronger impact on the complexity of univariate time series than the multivariate. From the univariate perspective, the complexity of departure and arrival flight flows of ZLXY and ZGGG is more sensitive to the amplitude information. From the multivariate perspective, ZUCK could be a typical representative of the complexity of the total flight flows of the ten airports.

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.

The discriminant statistic based on MPE-MWPE relationship and non-uniform embedding

The slope fitting line between MPE (multi-scale permutation entropy) and MWPE (multi-scale weighted permutation entropy) is recently proposed as a discriminant statistic for testing the nonlinearity of a time series. The main objective of this paper is to demonstrate that the selection of the optimal parameters of the non-uniform embedding is essential for the proposed discriminant statistic. In particular, the presented case studies indicate that the modified discriminant statistic based on non-uniform embedding can detect differences between such time series which remain indistinguishable if the original approach is used.

Research on Twin Extreme Learning Fault Diagnosis Method Based on Multi-Scale Weighted Permutation Entropy.

Due to the complicated engineering operation of the check valve in a high−pressure diaphragm pump, its vibration signal tends to show non−stationary and non−linear characteristics. These leads to difficulty extracting fault features and, hence, a low accuracy for fault diagnosis. It is difficult to extract fault features accurately and reliably using the traditional MPE method, and the ELM model has a low accuracy rate in fault classification. Multi−scale weighted permutation entropy (MWPE) is based on extracting multi−scale fault features and arrangement pattern features, and due to the combination of extracting a sequence of amplitude features, fault features are significantly enhanced, which overcomes the deficiency of the single−scale permutation entropy characterizing the complexity of vibration signals. It establishes the check valve fault diagnosis model from the twin extreme learning machine (TELM). The TELM fault diagnosis model established, based on MWPE, aims to find a pair of non−parallel classification hyperplanes in the equipment state space to improve the model’s applicability. Experiments show that the proposed method effectively extracts the characteristics of the vibration signal, and the fault diagnosis model effectively identifies the fault state of the check valve with an accuracy rate of 97.222%.

Analysis of axial fretting mode and mechanical model for a four-row tapered roller bearing

Studies show that relative sliding of small amplitude may result in fretting wear or fatigue of the contact surface between the roller and the raceway. Generally, fretting mode in a ball-on-flat contact include tangential, radial, torsional and rotational modes. In the present study, the new concept of axial fretting mode and the corresponding mechanical model are proposed for the study of a four-row tapered roller bearing (FTRB) in the roughing mill. The mechanical models of axial thrust and radial load causing axial fretting phenomenon are established and the coupled load distributions are calculated by considering the pre-displacement principle and the elastic contact theory. Moreover, an engineering test rig is built to collect the vibration signals caused by axial fretting phenomenon. The improved multivariate variational mode decomposition (IMVMD) combined with multivariate composite multiscale weighted permutation entropy (MCMWPE) are applied to process the vibration signals in order to provide better maintenance strategy about the FTRBs. The analysis results indicate that the axial fretting regime and slip region of contact surface are affected by axial thrust, friction coefficient, and roller position angle. The axial thrust under different cross angles varies nonlinearly and the radial load of the contact surface varies with the row number and position angle of the roller. The MCMWPE of fretting bearing is significantly lower than that of healthy bearing, and there is a regular impact phenomenon.

Rolling mill bearings fault diagnosis based on improved multivariate variational mode decomposition and multivariate composite multiscale weighted permutation entropy

The multi-row bearings of rolling mills are subject to axial and radial loads. Due to the complex working conditions, it is difficult to achieve better results in fault diagnosis by analyzing signal directional vibration signals. In order to realize the fault diagnosis of bearings subjected to multiple directional loads, this paper introduces the idea of cooperative processing of multi-sensing signals and proposes a fault feature extraction method of improved multivariate variational mode decomposition (IMVMD) combined with multivariate composite multiscale weighted permutation entropy (MCMWPE). First, reconstruct the signal by variational modal decomposition (VMD). Upgrade VMD to multi-channel decomposition mode by considering the correlation of the multi-channel signal and optimizing its parameters. Secondly, propose the method to calculate multi-channel signal entropy. Represent bearing fault features by calculating the MCMWPE of multi-channel reconstructed signals. The method proposed in this paper is validated on experiment rolling mill datasets and actual rolling mill datasets from a factory. Entropy curves and PSO-SVM classification results show that IMVMD-MCMWPE can extract fault features better than other methods.

Multiscale Weighted Permutation Entropy Analysis of Schizophrenia Magnetoencephalograms.

Schizophrenia is a neuropsychiatric disease that affects the nonlinear dynamics of brain activity. The primary objective of this study was to explore the complexity of magnetoencephalograms (MEG) in patients with schizophrenia. We combined a multiscale method and weighted permutation entropy to characterize MEG signals from 19 schizophrenia patients and 16 healthy controls. When the scale was larger than 42, the MEG signals of schizophrenia patients were significantly more complex than those of healthy controls (). The difference in complexity between patients with schizophrenia and the controls was strongest in the frontal and occipital areas (), and there was almost no difference in the central area. In addition, the results showed that the dynamic range of MEG complexity is wider in healthy individuals than in people with schizophrenia. Overall, the multiscale weighted permutation entropy method reliably quantified the complexity of MEG from schizophrenia patients, contributing to the development of potential magnetoencephalographic biomarkers for schizophrenia.

Recognition study of denatured biological tissues based on multi-scale rescaled range permutation entropy.

The recognition of denatured biological tissue is an indispensable part in the process of high intensity focused ultrasound treatment. As a nonlinear method, multi-scale permutation entropy (MPE) is widely used in the recognition of denatured biological tissue. However, the traditional MPE method neglects the amplitude information when calculating the time series complexity. The disadvantage will affect the recognition effect of denatured tissues. In order to solve the above problems, the method of multi-scale rescaled range permutation entropy (MRRPE) is proposed in this paper. The simulation results show that the MRRPE not only includes the amplitude information of the signal when calculating the signal complexity, but also extracts the extreme volatility characteristics of the signal effectively. The proposed method is applied to the HIFU echo signals during HIFU treatment, and the support vector machine (SVM) is used for recognition. The results show that compared with MPE and the multi-scale weighted permutation entropy (MWPE), the recognition rate of denatured biological tissue based on the MRRPE is higher, up to 96.57%, which can better recognize the non-denatured biological tissues and the denatured biological tissues.

State degradation evaluation and early fault identification of wind turbine bearings

To solve the shortage of state degradation characteristic and evaluation parameters in the monitoring of the running state of wind turbine bearings, and the low accuracy of early fault identification, a state degradation characteristic index, which combines multi-scale weighted permutation entropy (MWPE) and local linear embedding algorithm (LLE), is proposed for performance degradation monitoring and early fault identification of wind turbine bearings. The degradation index is quantitatively evaluated by four evaluation parameters: the initial time of state degradation, the sensitivity of initial degradation, the failure mutability and the consistency of degradation trend. Through the full cycle acceleration life monitoring data of the bearings, the result show that the proposed MWPE LLE degradation index can effectively characterize the whole process of bearing life cycle from stable operation to degradation to failure. Compared with the quantitative evaluation result of the kernel principal component analysis (KPCA), weighted permutation entropy (WPE), the root mean square (RMS) and kurtosis index, the comprehensive expression ability of MWPE-LLE degradation index is better. It can not only accurately capture the mutation time of state degradation, but also detect the initial degradation time in advance of the four kinds of characteristic indexes, and accurately judge the failure type of the early failure of the test bearing, and the judgment result is consistent with the inspection result after the experiment.

Biological Tissue Damage Monitoring Method Based on IMWPE and PNN during HIFU Treatment

Biological tissue damage monitoring is an indispensable part of high-intensity focused ultrasound (HIFU) treatment. As a nonlinear method, multi-scale permutation entropy (MPE) is widely used in the monitoring of biological tissue. However, the traditional MPE method neglects the amplitude information when calculating the time series complexity, and the stability of MPE is poor due to the defects in the coarse-grained process. In order to solve the above problems, the method of improved coarse-grained multi-scale weighted permutation entropy (IMWPE) is proposed in this paper. Compared with the MPE, the IMWPE method not only includes the amplitude of signal when calculating the signal complexity, but also improves the stability of entropy value. The IMWPE method is applied to the HIFU echo signals during HIFU treatment, and the probabilistic neural network (PNN) is used for monitoring the biological tissue damage. The results show that compared with multi-scale sample entropy (MSE)-PNN and MPE-PNN methods, the proposed IMWPE-PNN method can correctly identify all the normal tissues, and can more effectively identify damaged tissues and denatured tissues. The recognition rate for the three kinds of biological tissues is higher, up to 96.7%. This means that the IMWPE-PNN method can better monitor the status of biological tissue damage during HIFU treatment.

Intelligent fault diagnosis method for common rail injectors based on hierarchical weighted permutation entropy and pair-wise feature proximity feature selection

It is of great significance for intelligent manufacturing to study diagnosis methods to realize the diagnosis of mechanical equipment faults. Multiscale weighted permutation entropy is an effective method recently proposed to measure the complexity and dynamic changes of dynamic systems. To solve the shortcoming of multiscale weighted permutation entropy that does not consider high-frequency components, this article proposes hierarchical weighted permutation entropy, which can comprehensively and accurately reflect the low-frequency and high-frequency information of the time series. The simulation signal verifies the effectiveness and superiority of hierarchical weighted permutation entropy. Then, a novel intelligent fault diagnosis method for common rail injectors based on hierarchical weighted permutation entropy and pair-wise feature proximity is proposed. Finally, the proposed method is applied to the common rail injector fault data, and the results verify the effectiveness of the proposed method. Compared with other methods, this method has a higher fault recognition rate and stronger robustness.

Fault diagnosis of rolling bearing using a refined composite multiscale weighted permutation entropy

The health status information of rolling bearings is often contained in vibration signals, but it is difficult to detect bearing defects directly through vibration signals. To effectively extract the key feature information hidden in the original signal, this paper proposes the refined composite multiscale weighted permutation entropy (RCMWPE) method to efficiently characterize the operating state of the bearing. The proposed method focuses on two aspects: the improved version reduces the dependence of entropy on the length of the original time series, and the error caused by considering the amplitude information is suppressed. The performance of the proposed method is evaluated by synthetic signals and real bearing data, and compared with other traditional methods. By analyzing bearing signals of different fault types and different degrees of damage, it is verified that the proposed method can obtain more stable and reliable results and achieve higher fault diagnosis accuracy.

Refined Composite Multi-Scale Reverse Weighted Permutation Entropy and Its Applications in Ship-Radiated Noise.

Ship-radiated noise is one of the important signal types under the complex ocean background, which can well reflect physical properties of ships. As one of the valid measures to characterize the complexity of ship-radiated noise, permutation entropy (PE) has the advantages of high efficiency and simple calculation. However, PE has the problems of missing amplitude information and single scale. To address the two drawbacks, refined composite multi-scale reverse weighted PE (RCMRWPE), as a novel measurement technology of describing the signal complexity, is put forward based on refined composite multi-scale processing (RCMP) and reverse weighted PE (RWPE). RCMP is an improved method of coarse-graining, which not only solves the problem of single scale, but also improves the stability of traditional coarse-graining; RWPE has been proposed more recently, and has better inter-class separability and robustness performance to noise than PE, weighted PE (WPE), and reverse PE (RPE). Additionally, a feature extraction scheme of ship-radiated noise is proposed based on RCMRWPE, furthermore, RCMRWPE is combined with discriminant analysis classifier (DAC) to form a new classification method. After that, a large number of comparative experiments of feature extraction schemes and classification methods with two artificial random signals and six ship-radiated noise are carried out, which show that the proposed feature extraction scheme has better performance in distinguishing ability and stability than the other three similar feature extraction schemes based on multi-scale PE (MPE), multi-scale WPE (MWPE), and multi-scale RPE (MRPE), and the proposed classification method also has the highest recognition rate.