Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Cloud Resource Integrated Prediction Model Based on Variational Modal Decomposition-Permutation Entropy and LSTM

Predicting the usage of container cloud resources has always been an important and challenging problem in improving the performance of cloud resource clusters.We proposed an integrated prediction method of stacking container cloud resources based on variational modal decomposition(VMD)-Permutation entropy(PE)and long short-term memory(LSTM)neural network to solve the prediction difficulties caused by the non-stationarity and volatility of resource data.The variational modal decomposition algorithm decomposes the time series data of cloud resources to obtain intrinsic mode function and residual components,which solves the signal decomposition algorithm’s end-effect and modal confusion problems.The permutation entropy is used to evaluate the complexity of the intrinsic mode function,and the reconstruction based on similar entropy and low complexity is used to reduce the difficulty of modeling.Finally,we use the LSTM and stacking fusion models to predict and superimpose;the stacking integration model integrates Gradient boosting regression(GBR),Kernel ridge regression(KRR),and Elastic net regression(ENet)as primary learners,and the secondary learner adopts the kernel ridge regression method with solid generalization ability.The Amazon public data set experiment shows that compared with Holt-winters,LSTM,and Neuralprophet models,we can see that the optimization range of multiple evaluation indicators is 0.338∼1.913,0.057∼0.940,0.000∼0.017 and 1.038∼8.481 in root means square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE)and variance(VAR),showing its stability and better prediction accuracy.

Short-Term Prediction of Photovoltaic Power Generation Based on LMD Permutation Entropy and Singular Spectrum Analysis

The power output state of photovoltaic power generation is affected by the earth’s rotation and solar radiation intensity.On the one hand,its output sequence has daily periodicity;on the other hand,it has discrete randomness.With the development of new energy economy,the proportion of photovoltaic energy increased accordingly.In order to solve the problem of improving the energy conversion efficiency in the grid-connected optical network and ensure the stability of photovoltaic power generation,this paper proposes the short-termprediction of photovoltaic power generation based on the improvedmulti-scale permutation entropy,localmean decomposition and singular spectrum analysis algorithm.Firstly,taking the power output per unit day as the research object,the multi-scale permutation entropy is used to calculate the eigenvectors under different weather conditions,and the cluster analysis is used to reconstruct the historical power generation under typical weather rainy and snowy,sunny,abrupt,cloudy.Then,local mean decomposition(LMD)is used to decompose the output sequence,so as to extract more detail components of the reconstructed output sequence.Finally,combined with the weather forecast of the Meteorological Bureau for the next day,the singular spectrumanalysis algorithm is used to predict the photovoltaic classification of the recombination decomposition sequence under typical weather.Through the verification and analysis of examples,the hierarchical prediction experiments of reconstructed and non-reconstructed output sequences are compared.The results show that the algorithm proposed in this paper is effective in realizing the short-term prediction of photovoltaic generator,and has the advantages of simple structure and high prediction accuracy.

Microseismic signal denoising by combining variational mode decomposition with permutation entropy

Remarkable progress has been achieved on microseismic signal denoising in recent years,which is the basic component for rock-burst detection.However,its denoising effectiveness remains unsatisfactory.To extract the effective microseismic signal from polluted noisy signals,a novel microseismic signal denoising method that combines the variational mode decomposition(VMD)and permutation entropy(PE),which we denote as VMD–PE,is proposed in this paper.VMD is a recently introduced technique for adaptive signal decomposition,where K is an important decomposing parameter that determines the number of modes.VMD provides a predictable eff ect on the nature of detected modes.In this work,we present a method that addresses the problem of selecting an appropriate K value by constructing a simulation signal whose spectrum is similar to that of a mine microseismic signal and apply this value to the VMD–PE method.In addition,PE is developed to identify the relevant effective microseismic signal modes,which are reconstructed to realize signal filtering.The experimental results show that the VMD–PE method remarkably outperforms the empirical mode decomposition(EMD)–VMD filtering and detrended fl uctuation analysis(DFA)–VMD denoising methods of the simulated and real microseismic signals.We expect that this novel method can inspire and help evaluate new ideas in this field.

Morphology Similarity Distance for Bearing Fault Diagnosis Based on Multi-Scale Permutation Entropy

Bearings are crucial components in rotating machines,which have direct effects on industrial productivity and safety.To fast and accurately identify the operating condition of bearings,a novel method based on multi⁃scale permutation entropy(MPE)and morphology similarity distance(MSD)is proposed in this paper.Firstly,the MPE values of the original signals were calculated to characterize the complexity in different scales and they constructed feature vectors after normalization.Then,the MSD was employed to measure the distance among test samples from different fault types and the reference samples,and achieved classification with the minimum MSD.Finally,the proposed method was verified with two experiments concerning artificially seeded damage bearings and run⁃to⁃failure bearings,respectively.Different categories were considered for the two experiments and high classification accuracies were obtained.The experimental results indicate that the proposed method is effective and feasible in bearing fault diagnosis.

Adaptive Bearing Fault Diagnosis based on Wavelet Packet Decomposition and LMD Permutation Entropy

Bearing fault signal is nonlinear and non-stationary, therefore proposed a fault feature extraction method based on wavelet packet decomposition （WPD） and local mean decomposition （LMD） permutation entropy, which is based on the support vector machine （SVM） as the feature vector pattern recognition device Firstly, the wavelet packet analysis method is used to denoise the original vibration signal, and the frequency band division and signal reconstruction are carried out according to the characteristic frequency. Then the decomposition of the reconstructed signal is decomposed into a number of product functions （PE） by the local mean decomposition （LMD） , and the permutation entropy of the PF component which contains the main fault information is calculated to realize the feature quantization of the PF component. Finally, the entropy feature vector input multi-classification SVM, which is used to determine the type of fault and fault degree of bearing The experimental results show that the recognition rate of rolling bearing fault diagnosis is 95%. Comparing with other methods, the present this method can effectively extract the features of bearing fault and has a higher recognition accuracy

A New Methodology for Early Detection of Thermoacoustic Combustion Oscillations Based on Permutation Entropy

We carry out a series of experimental investigations in a model combustor to detect a precursor of thermoacoustic combustion oscillations based on permutation entropy,which can amplify the subtle changes effected in the time sequence to identify the anomaly.By changing the flame’s location or the fuel flow to a value,an abrupt switch from aperiodic small-amplitude oscillations to periodic large-amplitude oscillations would occur in pressure fluctuations.The characteristic frequency of combustion oscillation is obtained by spectral analysis,with which a modified algorithm of the permutation entropy is proposed.The impact evaluation on key parameters such as moving step sizes and window sizes reveals that the moving data permutation entropy has strong robustness,and can accurately detect the onset of thermoacoustic oscillations.Further nonlinear analysis exhibits peculiar dynamics of the combustion system,which result in specific patterns in the time series and provide a theoretical basis for anomaly detection.Our results suggest that the permutation entropy has a certain potential in early warning and detection of combustion oscillations.

Wind power forecasting based on improved variational mode decomposition and permutation entropy

Due to the significant intermittent,stochastic and non-stationary nature of wind power generation,it is difficult to achieve the desired prediction accuracy.Therefore,a wind power prediction method based on improved variational modal decomposition with permutation entropy is proposed.First,based on the meteorological data of wind farms,the Spearman correlation coefficient method is used to filter the meteorological data that are strongly correlated with the wind power to establish the wind power prediction model data set;then the original wind power is decomposed using the improved variational modal decomposition technique to eliminate the noise in the data,and the decomposed wind power is reconstructed into a new subsequence by using the permutation entropy;with the meteorological data and the new subsequence as input variables,a stacking deeply integrated prediction model is developed;and finally the prediction results are obtained by optimizing the hyperparameters of the model algorithm through a genetic algorithm.The validity of the model is verified using a real data set from a wind farm in north-west China.The results show that the mean absolute error,root mean square error and mean absolute percentage error are improved by at least 33.1%,56.1%and 54.2%compared with the autoregressive integrated moving average model,the support vector machine,long short-term memory,extreme gradient enhancement and convolutional neural networks and long short-term memory models,indicating that the method has higher prediction accuracy.

基于EEMD、相关系数、排列熵和小波阈值去噪的新型水下声学信号去噪方法

The complexities of the marine environment and the unique characteristics of underwater channels pose challenges in obtaining reliable signals underwater,necessitating the filtration of underwater acoustic noise.Herein,an underwater acoustic signal denoising method based on ensemble empirical mode decomposition(EEMD),correlation coefficient(CC),permutation entropy(PE),and wavelet threshold denoising(WTD)is proposed.Furthermore,simulation experiments are conducted using simulated and real underwater acoustic data.The experimental results reveal that the proposed denoising method outperforms other previous methods in terms of signal-to-noise ratio,root mean square error,and CC.The proposed method eliminates noise and retains valuable information in the signal.

A novel signal feature extraction technology based on empirical wavelet transform and reverse dispersion entropy

Feature extraction is an important part of signal processing,which is significant for signal detection,classification,and recognition.The nonlinear dynamic analysis method can extract the nonlinear characteristics of signals and is widely used in different fields.Reverse dispersion entropy(RDE)proposed by us recently,as a nonlinear dynamic analysis method,has the advantages of fast computing speed and strong anti-noise ability,which is more suitable for measuring the complexity of signal than traditional permutation entropy(PE)and dispersion entropy(DE).Empirical wavelet transform(EWT),based on the theory of wavelet analysis,can decompose a complex non-stationary signal into a number of empirical wavelet functions(EWFs)with compact support set spectrum,which has better decomposition performance than empirical mode decomposition(EMD)and its improved algorithms.Considering the advantages of RDE and EWT,on the one hand,we introduce EWT into the field of underwater acoustic signal processing and fault diagnosis to improve the signal decomposition accuracy;on the other hand,we use RDE as the features of EWFs to improve the signal separability and stability.Finally,we propose a novel signal feature extraction technology based on EWT and RDE in this paper.Experimental results show that the proposed feature extraction technology can effectively extract the complexity features of actual signals.Moreover,it also has higher distinguishing ability for different types of signals than five latest feature extraction technologies.

A comparative study of four nonlinear dynamic methods and their applications in classification of ship-radiated noise

Refined composite multi-scale dispersion entropy(RCMDE),as a new and effective nonlinear dynamic method,has been applied in the field of medical diagnosis and fault diagnosis.In this paper,we first introduce RCMDE into the field of underwater acoustic signal processing for complexity feature extraction of ship radiated noise,and then propose a novel classification method for ship-radiated noise based on RCMDE and k-nearest neighbor(KNN),termed RCMDE-KNN.The results of a comparative experiment show that the proposed RCMDE-KNN classification method can effectively extract the complexity features of ship-radiated noise,and has better classification performance under one and two scales than the other three classification methods based on multi-scale permutation entropy(MPE)and KNN,multi-scale weighted-permutation entropy(MW-PE)and KNN,and multi-scale dispersion entropy(MDE)and KNN,termed MPE-KNN,MW-PE-KNN,and MDE-KNN.It is proved that the RCMDE-KNN classification method for ship-radiated noise is feasible and effective,and can obtain a very high recognition rate.

Non-Linear EEG Measures in Meditation

In this study, the performance of Sevcik’s algorithm that calculates the fractal dimension and permutation entropy as discriminants to detect calming and insight meditation in electroencephalo-graphic (EEG) signals was assessed. The proposed methods were applied to EEG recordings from meditators practicing insight meditation and calming meditation before as well as during both types of meditation. Analysis was conducted using statistical hypothesis testing to determine the validity of the proposed meditation-identifying techniques. For both types of meditation, there was a statistically significant reduction in the permutation entropy. This result can be explained by the increased EEG synchronization, which is repeatedly observed in the course of meditation. In contrast, the fractal dimension (FD) was significantly increased during calming meditation, but during insight meditation, no statistically significant change was detected. Increased FD during meditation can be interpreted as an increase in self-similarity of EEG signals during self-organisation of hierarchical structure oscillators in the brain. Our results indicate that fractal dimension and permutation entropy could be used as parameters to detect both types of meditation. The permutation entropy is advantageous compared with the fractal dimension because it does not require a stationary signal.

Spatial-temporal variability of the fluctuation of soil temperature in the Babao River Basin, Northwest China

The Babao River Basin is the "water tower" of the Heihe River Basin.The combination of vulnerable ecosystems and inhospitable natural environments substantially restricts the existence of humans and the sustainable development of society and environment in the Heihe River Basin.Soil temperature(ST) is a critical soil variable that could affect a series of physical,chemical and biological soil processes,which is the guarantee of water conservation and vegetation growth in this region.To measure the temporal variation and spatial pattern of ST fluctuation in the Babao River Basin,fluctuation of ST at various depths were analyzed with ST data at depths of 4,10 and 20 cm using classical statistical methods and permutation entropy.The study results show the following: 1) There are variations of ST at different depths,although ST followed an obvious seasonal law.ST at shallower depths is higher than at deeper depths in summer,and vice versa in winter.The difference of ST between different depths is close to zero when ST is near 5℃ in March or –5℃ in September.2) In spring,ST at the shallower depths becomes higher than at deeper depths as soon as ST is above –5℃;this is reversed in autumn when ST is below 5℃.ST at a soil depth of 4 cm is the first to change,followed by ST at 10 and 20 cm,and the time that ST reaches the same level is delayed for 10–15 days.In chilling and warming seasons,September and February are,respectively,the months when ST at various depths are similar.3) The average PE values of ST for 17 sites at 4 cm are 0.765 in spring > 0.764 in summer > 0.735 in autumn > 0.723 in winter,which implies the complicated degree of fluctuations of ST.4) For the variation of ST at different depths,it appears that Max,Ranges,Average and the Standard Deviation of ST decrease by depth increments in soil.Surface soil is more complicated because ST fluctuation at shallower depths is more pronounced and random.The average PE value of ST for 17sites are 0.863 at a depth of 4 cm > 0.818 at 10 cm > 0.744 at 20 cm.5) For the variation of ST at different elevations,it appears that Max,Ranges,Average,Standard Deviation and ST fluctuation decrease with increasing elevation at the same soil depth.And with the increase of elevation,the decrease rates of Max,Range,Average,Standard Deviation at 4 cm are –0.89℃/100 m,–0.94℃/100 m,–0.43℃/100 m,and –0.25℃/100 m,respectively.In addition,this correlation decreased with the increase of soil depth.6) Significant correlation between PE values of ST at depths of 4,10 and 20 cm can easily be found.This finding implies that temperature can easily be transmitted within soil at depths between 4 and 20 cm.7) For the variation of ST on shady slope and sunny slope sides,it appears that the PE values of ST at 4,10 and 20 cm for 8 sites located on shady slope side are 0.868,0.824 and 0.776,respectively,whereas they are 0.858,0.810 and 0.716 for 9 sites located on sunny slope side.