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.

Tool State Detection by Harmonic Wavelet and Sample Entropy

It is a fact that acoustic emission(AE) signals contain potentially valuable information for tool wear and breakage monitoring and detection.However,AE stress waves produced in the cutting zone are distorted by the transmission path and the measurement systems,it is difficult to obtain a reliable result by these raw AE data.It is generally known that the process of tool wear belongs to detect weak singularity signals in strong noise.The objective of this paper is to combine Newland Harmonic wavelet and Richman-Moorman(2000) sample entropy for detecting weak singularity signals embedded in strong signals.First,the raw AE signal is decomposed by harmonic wavelet and transformed into the three-dimensional time-frequency mesh map of the harmonic wavelet,at the same time,the contours of the mesh map with log space is induced.Second,the profile map of the three-dimensional time-frequency mesh map is offered,which corresponds to decomposed level on harmonic wavelets.Final,by computing sample entropy in each level,the weak singularity signal can be easily extracted from strong noise.Machining test was carried out on HL-32 NC turning center.This lathe does not have a tailstock.Tungsten carbide finishing tool was used to turn free machining mild steel.The work material was chosen for ease of machining,allowing for generation of surfaces of varying quality without the use of cutting fluids.In turning experiments,the feasibility for tool condition monitoring is demonstrated by 27 kinds of cutting conditions with the sharp tool and the worn tool,54 group data are sampled by AE.The sample entropy of each level of wavelet decomposed for each one of 54 AE datum is computed,wear tool and shaper tool can be distinguished obviously by the sample entropy value at the 12th level,this is a criterion.The proposed research provides a new theoretical basis and a new engineering application on the tool condition monitoring.

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 wavelet-approximate entropy method for epileptic activity detection from EEG and its sub-bands

Epilepsy is a common brain disorder that about 1% of world's population suffers from this disorder. EEG signal is summation of brain electrical activities and has a lot of information about brain states and also used in several epilepsy detection methods. In this study, a wavelet-approximate entropy method is ap-plied for epilepsy detection from EEG signal. First wavelet analysis is applied for decomposing the EEG signal to delta, theta, alpha, beta and gamma sub- ands. Then approximate entropy that is a chaotic measure and can be used in estimation complexity of time series applied to EEG and its sub-bands. We used this method for separating 5 group EEG signals (healthy with opened eye, healthy with closed eye, interictal in none focal zone, interictal in focal zone and seizure onset signals). For evaluating separation ability of this method we used t-student statistical analysis. For all pair of groups we have 99.99% separation probability in at least 2 bands of these 6 bands (EEG and its 5 sub-bands). In comparing some groups we have over 99.98% for EEG and all its sub-bands.

Wavelet Entropy Based Algorithm for Fault Detection and Classification in FACTS Compensated Transmission Line

Distance protection of transmission lines including advanced flexible AC transmission system (FACTS) de-vices has been a very challenging task. FACTS devices of interest in this paper are static synchronous series compensators (SSSC) and unified power flow controller (UPFC). In this paper, a new algorithm is proposed to detect and classify the fault and identify the fault position in a transmission line with respect to a FACTS device placed in the midpoint of the transmission line. Discrete wavelet transformation and wavelet entropy calculations are used to analyze during fault current and voltage signals of the compensated transmission line. The proposed algorithm is very simple and accurate in fault detection and classification. A variety of fault cases and simulation results are introduced to show the effectiveness of such algorithm.

Pattern recognition of surface electromyography signal based on wavelet coefficient entropy

This paper introduced a novel, simple and ef-fective method to extract the general feature of two surface EMG (electromyography) signal patterns: forearm supination (FS) surface EMG signal and forearm pronation (FP) surface EMG signal. After surface EMG (SEMG) signal was decomposed to the fourth resolution level with wavelet packet transform (WPT), its whole scaling space (with frequencies in the interval (0Hz, 500Hz]) was divided into16 frequency bands (FB). Then wavelet coefficient entropy (WCE) of every FB was calculated and corre-spondingly marked with WCE(n) (from the nth FB, n=1,2,…16). Lastly, some WCE(n) were chosen to form WCE feature vector, which was used to distinguish FS surface EMG signals from FP surface EMG signals. The result showed that the WCE feather vector consisted of WCE(7) (187.25Hz, 218.75Hz) and WCE(8) (218.75Hz, 250Hz) can more effectively recog-nize FS and FP patterns than other WCE feature vector or the WPT feature vector which was gained by the combination of WPT and principal components analysis.

Radar emitter signal recognition based on multi-scale wavelet entropy and feature weighting

In modern electromagnetic environment, radar emitter signal recognition is an important research topic. On the basis of multi-resolution wavelet analysis, an adaptive radar emitter signal recognition method based on multi-scale wavelet entropy feature extraction and feature weighting was proposed. With the only priori knowledge of signal to noise ratio(SNR), the method of extracting multi-scale wavelet entropy features of wavelet coefficients from different received signals were combined with calculating uneven weight factor and stability weight factor of the extracted multi-dimensional characteristics. Radar emitter signals of different modulation types and different parameters modulated were recognized through feature weighting and feature fusion. Theoretical analysis and simulation results show that the presented algorithm has a high recognition rate. Additionally, when the SNR is greater than-4 d B, the correct recognition rate is higher than 93%. Hence, the proposed algorithm has great application value.

Alcoholism Detection by Wavelet Energy Entropy and Linear Regression Classifier

Alcoholism is an unhealthy lifestyle associated with alcohol dependence.Not only does drinking for a long time leads to poor mental health and loss of self-control,but alcohol seeps into the bloodstream and shortens the lifespan of the body’s internal organs.Alcoholics often think of alcohol as an everyday drink and see it as a way to reduce stress in their lives because they cannot see the damage in their bodies and they believe it does not affect their physical health.As their drinking increases,they become dependent on alcohol and it affects their daily lives.Therefore,it is important to recognize the dangers of alcohol abuse and to stop drinking as soon as possible.To assist physicians in the diagnosis of patients with alcoholism,we provide a novel alcohol detection system by extracting image features of wavelet energy entropy from magnetic resonance imaging(MRI)combined with a linear regression classifier.Compared with the latest method,the 10-fold cross-validation experiment showed excellent results,including sensitivity 91.54±1.47%,specificity 93.66±1.34%,Precision 93.45±1.27%,accuracy 92.61±0.81%,F1 score 92.48±0.83%and MCC 85.26±1.62%.

Adaptive control of machining process based on extended entropy square error and wavelet neural network

Combining information entropy and wavelet analysis with neural network,an adaptive control system and an adaptive control algorithm are presented for machining process based on extended entropy square error(EESE)and wavelet neural network(WNN).Extended entropy square error function is defined and its availability is proved theoretically.Replacing the mean square error criterion of BP algorithm with the EESE criterion,the proposed system is then applied to the on-line control of the cutting force with variable cutting parameters by searching adaptively wavelet base function and self adjusting scaling parameter,translating parameter of the wavelet and neural network weights.Simulation results show that the designed system is of fast response,non-overshoot and it is more effective than the conventional adaptive control of machining process based on the neural network.The suggested algorithm can adaptively adjust the feed rate on-line till achieving a constant cutting force approaching the reference force in varied cutting conditions,thus improving the machining efficiency and protecting the tool.

Wavelets and Entropy for Power Quality Assessment

In this paper, wavelet transform and entropy are evaluated using the mathematical analysis concepts of reflexibility, regularity and series obtention, these concepts remark the reason to make a selective reference framework for power quality applications. With this idea the paper used the same treatment for the two algorithms (Multiresolution and Multiscale Entropy). The wavelet is denoted to have the most power full consistence to the light off the reflexibility, regularity and series obtention. The paper proposes a power quality technique namely MpqAT.

Brain Tumour Detection by Gamma DeNoised Wavelet Segmented Entropy Classifier

Magnetic resonance imaging(MRI)is an essential tool for detecting brain tumours.However,identification of brain tumours in the early stages is a very complex task since MRI images are susceptible to noise and other environmental obstructions.In order to overcome these problems,a Gamma MAP denoised Strömberg wavelet segmentation based on a maximum entropy classifier(GMDSWS-MEC)model is developed for efficient tumour detection with high accuracy and low time consumption.The GMDSWS-MEC model performs three steps,namely pre-processing,segmentation,and classification.Within the GMDSWS-MEC model,the Gamma MAP filter performs the pre-processing task and achieves a significant increase in the peak signal-tonoise ratio by removing noisy artefacts from the input brain image.After pre-processing,Strömberg wavelet transform segmentation is carried out to partition the pre-processed image into a number of blocks based on the features extracted from the image.Finally,the maximum entropy classifier identifies and locates the tumour from the input image based on extracted features with high accuracy and minimal error rate.Using a number of MRI images,experimental evaluation and comparison of the proposed model and existing methods is carried out on the basis of four metrics:peak signalto-noise ratio,tumour detection accuracy,error rate,and tumour detection time with respect to MRI image size.The proposed model offers superior performance in terms of all four metrics.

P-Wave Detection Combining Entropic Criterion and Wavelet Transform

The objective of this paper is to develop an efficient P wave detection method in electrocardiogram (ECG) using the local entropy criterion (EC) and wavelet transform (WT) modulus maxima. The detection of P wave relates to the diagnosis of many heart diseases and it is also a difficult point during the ECG signal detection. Determining the position of a P-wave is complicated due to the low amplitude, the ambiguous and changing form of the complex. In a first step, QRS complexes are detected using the pan-Tompkins method. Then, we look for the best position of the analysis window and the value of the most appropriate width to the P wave. Finally, the determination of P wave peaks, as well as their onsets and offsets. The method has been validated using ECG-recordings with a wide variety of P-wave morphologies from MIT-BIH Arrhythmia and QT database. The P-wave method obtains a sensitivity of 99.87% and a positive predictivity of 98.04% over the MIT-BIH Arrhythmia, while for the QT, sensitivity and predictivity over 99.8% are attained.

Novel Approach for Fault Detection and Diagnosis of Sensors in Air Handling Units Using Wavelet Energy Entropy

A novel fault diagnosis method for sensors in air handling unit（AHU） using wavelet energy entropy was presented. Instead of directly comparing the numerous data under noise conditiom, the wavelet energy entropy residual was compared in the proposed method. Three.level wavelet analysis was used to decompose the measurement data under both fault-free and faulty operation conditions. The concept of Shannon entropy was referred to define wavelet energy entropy of the wavelet coefficients. The sensor faults were diagnosed by comparing the deviation of the wavelet energy entropy of the measured signal and the estimated one with the preset threshold. Testing results showed that the wavelet energy entropy was sensitive to diagnose the biased faults. The wavelet energy entropy residuals exceed the threshold significantly when faults occur. In addition, the severer the faults were, the larger the residuals would be. The results prove that the proposed method is feasible and effective for the fault detection and diagnosis of the sensors.

The Study of Image Segmentation Based on the Combination of the Wavelet Multi-scale Edge Detection and the Entropy Iterative Threshold Selection

This paper proposes an image segmentation method based on the combination of the wavelet multi-scale edge detection and the entropy iterative threshold selection.Image for segmentation is divided into two parts by high- and low-frequency.In the high-frequency part the wavelet multiscale was used for the edge detection,and the low-frequency part conducted on segmentation using the entropy iterative threshold selection method.Through the consideration of the image edge and region,a CT image of the thorax was chosen to test the proposed method for the segmentation of the lungs.Experimental results show that the method is efficient to segment the interesting region of an image compared with conventional methods.

Image Coding Using Wavelet Transform and EntropyConstrained Vector Quantization with Quadtree Structure Vectors

This paper presents a new wavelet transform image coding method. On the basis of a hierarchical wavelet decomposition of images, entropy constrained vector quantization is employed to encode the wavelet coefficients at all the high frequency bands with

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

Classification of Power Quality Disturbances Using Wavelet Packet Energy Entropy and LS-SVM

The power quality (PQ) signals are traditionally analyzed in the time-domain by skilled engineers. However, PQ disturbances may not always be obvious in the original time-domain signal. Fourier analysis transforms signals into frequency domain, but has the disadvantage that time characteristics will become unobvious. Wavelet analysis, which provides both time and frequency information, can overcome this limitation. In this paper, there were two stages in analyzing PQ signals: feature extraction and disturbances classification. To extract features from PQ signals, wavelet packet transform (WPT) was first applied and feature vectors were constructed from wavelet packet log-energy entropy of different nodes. Least square support vector machines (LS-SVM) was applied to these feature vectors to classify PQ disturbances. Simulation results show that the proposed method possesses high recognition rate, so it is suitable to the monitoring and classifying system for PQ disturbances.

A STUDY OF WAVELET ENTROPY MEASURE DEFINITION AND ITS APPLICATION FOR FAULT FEATURE PICK-UP AND CLASSIFICATION

Shannon entropy in time domain is a measure of signal or system uncertainty.When based on spectrum entropy,Shannon entropy can be taken as a measure of signal or system complexity. Therefore,wavelet analysis based on wavelet entropy measure can signify the complexity of non-steady signal or system in both time and frequency domain.In this paper,in order to meet the requirements of post-analysis on abundant wavelet transform result data and the need of information mergence,the basic definition of wavelet entropy measure is proposed,corresponding algorithms of several wavelet entropies,such as wavelet average entropy,wavelet time-frequency entropy,wavelet distance entropy, etc.are put forward,and the physical meanings of these entropies are analyzed as well.The application principle of wavelet entropy measure in ElectroEncephaloGraphy (EEG) signal analysis,mechanical fault diagnosis,fault detection and classification in power system are analyzed.Finally,take the transmission line fault detection in power system for example,simulations in two different systems,a 10kV automatic blocking and continuous power transmission line and a 500kV Extra High Voltage (EHV) transmission line,are carried out,and the two methods,wavelet entropy and wavelet modulus maxima,are compared,the results show feasibility and application prospect of the six wavelet entro- pies.

Entropy of images after wavelet transform

We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous experiments were done on typical images to calculate (using Matlab) the entropy before and after wavelet transform. It was verified that, to obtain minimal entropy, a three-layer decomposition should be adopted rather than higher orders. The result achieved by using biorthogonal wavelet decomposition is better than that of the orthogonal wavelet decomposition. The results are not directly proportional to the vanishing moment, however.

Research on the detecting methods of singularity in deformation signal based on two kinds of wavelet entropy

There are various influencing factors that affect the deformation observation, and deformation signals show differ- ent characteristics under different scales. Wavelet analysis possesses multi-scale property, and the information entropy has great representational capability to the complexity of information. By hamming window to the wavelet coefficients and windowed wavelet energy obtained by multi-resolution analysis （MRA）, it can be achieved to measure the wavelet time entropy （WTE） and wavelet energy entropy （WEE）. The paper established deformation signals, selected the parameters, and compared the sin- gularity detection ability and anti-noise ability of two kinds of wavelet entropy and applied them to the singularity detection at the GPS continuously operating reference stations. It is shown that the WTE performs well in weak singularity information de- tection in finite frequency components signals and the WEE is more suitable for detecting the singularity in the signals with complex, strong background noise.