Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

A novel internet traffic identification approach using wavelet packet decomposition and neural network

Internet traffic classification plays an important role in network management, and many approaches have been proposed to classify different kinds of internet traffics. A novel approach was proposed to classify network applications by optimized back-propagation (BP) neural network. Particle swarm optimization (PSO) algorithm was used to optimize the BP neural network. And in order to increase the identification performance, wavelet packet decomposition (WPD) was used to extract several hidden features from the time-frequency information of network traffic. The experimental results show that the average classification accuracy of various network applications can reach 97%. Moreover, this approach optimized by BP neural network takes 50% of the training time compared with the traditional neural network.

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition （EMD） method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrin- sic mode functions （IMFs） through the filtering algorithm based on the wavelet packet decomposition （GIFWPD）. In this paper, it is demonstrated that the CIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis （CEDA） and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.

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

Wavelet packet decomposition entropy threshold method for discrete spectrum interferences rejection of on-line partial discharge monitoring

The frequency domain division theory of dyadic wavelet decomposition and wavelet packet decomposition (WPD) with orthogonal wavelet base frame are presented. The WPD coefficients of signals are treated as the outputs of equivalent bandwidth filters with different center frequency. The corresponding WPD entropy values of coefficients increase sharply when the discrete spectrum interferences (DSIs), frequency spectrum of which is centered at several frequency points existing in some frequency region. Based on WPD, an entropy threshold method (ETM) is put forward, in which entropy is used to determine whether partial discharge (PD) signals are interfered by DSIs. Simulation and real data processing demonstrate that ETM works with good efficiency, without pre-knowing DSI information. ETM extracts the phase of PD pulses accurately and can calibrate the quantity of single type discharge.

Enhancing photovoltaic energy forecasting:a progressive approach using wavelet packet decomposition

Accurate photovoltaic(PV)energy forecasting plays a crucial role in the efficient operation of PV power stations.This study presents a novel hybrid machine-learning(ML)model that combines Gaussian process regression with wavelet packet decomposition to forecast PV power half an hour ahead.The proposed technique was applied to the PV energy database of a station located in Algeria and its performance was compared to that of traditional forecasting models.Performance evaluations demonstrate the superiority of the proposed approach over conventional ML methods,including Gaussian process regression,extreme learning machines,artificial neural networks and support vector machines,across all seasons.The proposed model exhibits lower normalized root mean square error(nRMSE)(2.116%)and root mean square error(RMSE)(208.233 kW)values,along with a higher coefficient of determination(R^(2))of 99.881%.Furthermore,the exceptional performance of the model is maintained even when tested with various prediction horizons.However,as the forecast horizon extends from 1.5 to 5.5 hours,the prediction accuracy decreases,evident by the increase in the RMSE(710.839 kW)and nRMSE(7.276%),and a decrease in R2(98.462%).Comparative analysis with recent studies reveals that our approach consistently delivers competitive or superior results.This study provides empirical evidence supporting the effectiveness of the proposed hybrid ML model,suggesting its potential as a reliable tool for enhancing PV power forecasting accuracy,thereby contributing to more efficient grid management.

Fault diagnosis of spur gearbox based on random forest and wavelet packet decomposition

This paper addresses the development of a random forest classifier for the muki-class fault diagnosis in spur gearboxes. The vibration signal＇s condition parameters are first extracted by applying the wavelet packet decomposition with multiple mother wavelets, and the coefficients＇ energy content for terminal nodes is used as the input feature for the classification problem. Then, a study through the parameters＇ space to find the best values for the number of trees and the number of random features is performed. In this way, the best set of mother wavelets for the application is identified and the best features are selected through the internal ranking of the random forest classifier. The results show that the proposed method reached 98.68% in classification accuracy, and high efficiency and robustness in the models.

Identification of Grinding Wheel Wear Signature by a Wavelet Packet Decomposition Method

Grinding is known as the most complicated material removal process and the method for monitoring the grinding wheel wear has its own characteristics comparing with the approaches for detecting the wear on regular cutting tools.Research efforts were made to develop the wheel wear monitoring system due to its significance in grinding process.This paper presents a novel method for identification of grinding wheel wear signature by combination of wavelet packet decomposition(WPD) based energies.The distinctive feature of the method is that it takes advantage of the combinational information of the decomposed frequency components based on the WPD so the extracted features can be customized according to the specific monitored object to get better diagnosis effects.Experiments are researched on monitoring of grinding wheel wear states under different machining conditions.The results show that the energy ratio extracted from the measured vibration signals is consistent with the grinding wheel wear condition evaluated by experiment and the further extracted feature ratio can be used in prediction of wheel wear condition.

Appropriate Sub-band Selection in Wavelet Packet Decomposition for Automated Glaucoma Diagnoses

The most common reason for blindness among human beings is Glaucoma.The increase of fluid pressure damages the optic nerve which gradually leads to irreversible loss of vision.A technique for automated screening of Glaucoma from the fundal retinal images is presented in this paper.This paper intends to explore the significance of both the approximate and detail coefficients through wavelet packet decomposition(WPD).Decomposition is done with "db3" wavelet function and the images are decomposed up to level-3producing 84 sub-bands.Two features,the energy and the entropy are calculated for each sub-band producing two feature matrices(158 images × 84 features).The above step is purely a statistical measure based on WPD.To enhance the diagnostic accuracy,the second phase considers the structural(biological) region of interest(ROI) in the image and then extracts the same features.It is worthy to note that direct biological features are not extracted to eliminate the drawbacks of segmentation whereas the biologically significant region is taken as biological-ROI.Interestingly,the detailed coefficient sub-bands(prominent edges) show more significance in the biological-ROI phase.Apart from enhancing the diagnostic accuracy by feature reduction,the paper intends to mark the significance indices,uniqueness and discrimination capability of the significant features(sub-bands) in both the phases.Then,the crisp inputs are fed to the classifier ANN.Finally,from the significant features of the biological-ROI feature matrices,the accuracy is raised to 85%which is notable than the accuracy of 79%achieved without considering the ROI.

Distance Measuring Equipment Pulse Interference Suppression Based on Wavelet Packet Analysis

As an indispensable part of global satellite navigation system, the frequency band of DME will overlap with that of the navigation signal, which will cause the signal from the DME platform to be accepted by the Global Navigation Satellite System receiver and form interference. Therefore, it is of great significance to study an effective algorithm to suppress DME pulse interference. This paper has the following research on this problem. In this paper, wavelet packet transform is used to solve for the suppression of DME pulse interference method, wavelet packet analysis belongs to the linear time-frequency analysis method, it has good time-frequency localization characteristics and the signal adaptive ability, due to the function of wavelet packet and parameter selection of DME will affect the ability of interference suppression, combining with the theory of wavelet threshold, function type and decomposition series are discussed to prove the validity of the selected parameters on the pulse interference suppression.

Wear State Recognition of Drills Based on K-means Cluster and Radial Basis Function Neural Network

Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps： first, decomposing cutting torque components from the original signals by wavelet packet decomposition （WPD）; second, extracting wavelet coefficients of different wear states （i.e., slight, normal, or severe wear） with signal features adapting to Welch spectrum. Finally, monitoring and recognition of the feature vectors of cutting torque signal are performed by using the K-means cluster and radial basis function neural network （RBFNN）. The experiments on different tool wears of the multivariable features reveal that the results of monitoring and recognition are significant and effective.

Denoising of SAR Images Based on Lifting Scheme Wavelet Packet Transform

According to the different characteristics that signal and noise exhibit during wavelet decomposition, a new denoising method based on the lifting scheme wavelet packet decomposition is presented. In this method, the SAR images are decom- posed by using the best wavelet packet and the norm of each sub-band are calculated; signals and noise can be discriminated based on the norm and soft-threshold method, and the images can be denoised. Experiments show that the proposed algorithm has excellent performance in denoising SAR images, and can remove most noise of images with well-kept texture detail informa- tion. The calculating speed of the method is twice the speed of the general wavelet packet transform algorithm.

Reduced information transmission in the internal segment of the globus pallidus of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine-induced rhesus monkey models of Parkinson's disease

Rhesus monkey models of Parkinson＇s disease were induced by injection of N-methyl-4-phenyl- 1,2,3,6-tetrahydropyridine. Neural firings were recorded using microelectrodes placed in the interna segment of the globus pallidus. The wavelets and power spectra show gradual power reduction during the disease process along with increased firing rates in the Parkinson＇s disease state. Singular values of coefficients decreased considerably during tremor-related activity as well as in the Parkinson＇s disease state compared with normal signals, revealing that higher-frequency components weaken when Parkinson＇s disease occurs. We speculate that the death of neurons could be reflected by irregular frequency spike trains, and that wavelet packet decomposition can effectively detect the degradation of neurons and the loss of information transmission in the neural circuitry.

Condition Monitoring of an Industrial Oil Pump Using a Learning Based Technique

This paper proposes an efficient learning based approach to detect the faults of an industrial oil pump.The proposed method uses the wavelet transform and genetic algorithm(GA)ensemble for an optimal feature extraction procedure.Optimal features,which are dominated through this method,can remarkably represent the mechanical faults in the damaged machine.For the aim of condition monitoring,we considered five common types of malfunctions such as casing distortion,cavitation,looseness,misalignment,and unbalanced mass that occur during the machine operation.The proposed technique can determine optimal wavelet parameters and suitable statistical functions to exploit excellent features via an appropriate distance criterion function.Moreover,our optimization algorithm chooses the most appropriate feature submatrix to improve the final accuracy in an iterative method.As a case study,the proposed algorithms are applied to experimental data gathered from an industrial heavy-duty oil pump installed in Arak Oil Refinery Company.The experimental results are very promising.

Hybrid Deep Learning Model for Short-Term Wind Speed Forecasting Based on Time Series Decomposition and Gated Recurrent Unit

Accurate wind speed prediction has been becoming an indispensable technology in system security,wind energy utilization,and power grid dispatching in recent years.However,it is an arduous task to predict wind speed due to its variable and random characteristics.For the objective to enhance the performance of forecasting short-term wind speed,this work puts forward a hybrid deep learning model mixing time series decomposition algorithm and gated recurrent unit(GRU).The time series decomposition algorithm combines the following two parts:(1)the complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),and(2)wavelet packet decomposition(WPD).Firstly,the normalized wind speed time series(WSTS)are handled by CEEMDAN to gain pure fixed-frequency components and a residual signal.The WPD algorithm conducts the second-order decomposition to the first component that contains complex and high frequency signal of raw WSTS.Finally,GRU networks are established for all the relevant components of the signals,and the predicted wind speeds are obtained by superimposing the prediction of each component.Results from two case studies,adopting wind data from laboratory and wind farm,respectively,suggest that the related trend of the WSTS can be separated effectively by the proposed time series decomposition algorithm,and the accuracy of short-time wind speed prediction can be heightened significantly mixing the time series decomposition algorithm and GRU networks.

A hybrid ensemble deep reinforcement learning model for locomotive axle temperature using the deterministic and probabilistic strategy

This paper proposes a hybrid deep reinforcement learning framework for locomotive axle temperature by combining the wavelet packet decomposition(WPD),long short-term memory(LSTM),gated recurrent unit(GRU)reinforcement learning and generalized autoregressive conditional heteroskedasticity(GARCH)algorithms.The WPD is utilized to decompose the raw nonlinear series into subseries.Then the deep learning predictors LSTM and GRU are established to predict the future axle temperatures in each subseries.The Q-learning could generate optimal ensembleweights to integrate the predictors to finish the deterministic forecasting and GARCH is used to conduct the deterministic forecasting based on the deterministic forecasting residual.These parts of the hybrid ensemble structure contributed to optimal modelling accuracy and provided effective support in the real-time monitoring and fault diagnosis of transportation.

A pre-generated matrix-based method for real-time robotic drilling chatter monitoring

Currently, due to the detrimental effects on surface finish and machining system, chatter has been one crucial factor restricting robotic drilling operations, which improve both quality and efficiency of aviation manufacturing. Based on the matrix notch filter and fast wavelet packet decomposition, this paper presents a novel pre-generated matrix-based real-time chatter monitoring method for robotic drilling. Taking vibration characteristics of robotic drilling into account, the matrix notch filter is designed to eliminate the interference of spindle-related components on the measured vibration signal. Then, the fast wavelet packet decomposition is presented to decompose the filtered signal into several equidistant frequency bands, and the energy of each sub-band is obtained. Finally, the energy entropy which characterizes inhomogeneity of energy distribution is utilized as the feature to recognize chatter on-line, and the effectiveness of the presented algorithm is validated by extensive experimental data. The results show that the proposed algorithm can effectively detect chatter before it is fully developed. Moreover, since both filtering and decomposition of signal are implemented by the pre-generated matrices, calculation for an energy entropy of vibration signal with 512 samples takes only about 0.690 ms. Consequently, the proposed method achieves real-time chatter monitoring for robotic drilling, which is essential for subsequent chatter suppression.

Energy Management and Optimization of Vehicle-to-grid Systems for Wind Power Integration

An approach to smoothing the fluctuations of largescale wind power is investigated using vehicle-to-grid(V2G)systems.First,an energy management and optimization system is designed and modeled.By using the wavelet packet decomposition method,the target grid-connected wind power,the required electric vehicle(EV)power,and supercapacitor power are determined.The energy management model for EVs is then developed by introducing a knapsack problem that can evaluate the needs of an EV fleet.Furthermore,an optimized dispatch strategy for EVs and wind power is developed by using a dynamic programming method.A case study demonstrates that the energy management and optimization method for V2G systems achieves noticeable performance improvements over benchmark techniques.

Impact Localization of CFRP Structure Based on FBG Sensor Network

Low energy impact can induce invisible damage of carbon fiber reinforced polymer(CFRP).The damage can seriously affect the safety of the CFRP structure.Therefore,damage detection is crucial to the CFRP structure.Impact location information is the premise of damage detection.Hence,impact localization is the primary issue.In this paper,an impact localization system,based on the fiber Bragg grating(FBG)sensor network,is proposed for impact detection and localization.For the completed impact signal,the FBG sensor and narrow-band laser demodulation technology are applied.Wavelet packet decomposition is introduced to extract available frequency band signals and attenuate noise.According to the energy of the available frequency band signal,an impact localization model,based on the extreme learning machine(ELM),is established with the faster training speed and less parameters.The above system is verified on the 500 mm×500 mm×2 mm CFRP plate.The maximum localization error and the minimum localization error are 30.4 mm and 6.7 mm,respectively.The average localization error is 14.7 mm,and training time is 0.7 s.Compared with the other machine learning methods,the localization system,proposed in this paper,has higher accuracy and faster training speed.This paper provides a practical system for impact localization of the CFRP structure.

Chatter identification of thin-walled parts for intelligent manufacturing based on multi-signal processing

Machine chatter is still an unresolved and challenging issue in the milling process,and developing an online chatter identification and process monitoring system towards smart manufacturing is an urgent requirement.In this paper,two indicators of chatter detection are investigated.One is the real-time variance of milling force signals in the time domain,and the other one is the wavelet energy ratio of acceleration signals based on wavelet packet decomposition in the frequency domain.Then,a novel classification concept for vibration condition,called slight chatter,is proposed and integrated successfully into the designed multi-classification support vector machine(SVM)model.Finally,a mapping model between image and chatter indicators is established via a distance threshold on the image.The multi-SVM model is trained by the results of three signals as an input.Experiment data and detection accuracy of the SVM model are verified in actual machining.The identification accuracy of 96.66%has proved that the proposed solution is feasible and effective.The presented method can be used to select optimized milling parameters to improve machining process stability and strengthen manufacturing system monitoring.