Flight Flutter Modal Parameters Identification with Atmospheric Turbulence Excitation Based on Wavelet Transformation

In view of the feature of flight flutter test data with atmospheric turbulence excitation, a method which combines wavelet transformation with random decrement technique for identifying flight flutter modal parameters is presented. This approach firstly uses random decrement technique to gain free decays corresponding to the acceleration response of the structure to some non-zero initial conditions. Then the continuous Morlet wavelet transformation of the free decays is performed; and the Parseval formula and residue theorem are used to simplify the transformation. The maximal wavelet transformation coefficients in different scales are searched out by means of band-filtering characteristic of Morlet wavelet, and then the modal parameters are identified according to the relationships with maximal modulus and angle of the wavelet transform. In addition, the condition of modal uncoupling is discussed according to variation trend of flight flutter modal parameters in the flight flutter state. The analysis results of simulation and flight flutter test data show that this approach is not only simple, effective and feasible, but also having good noise immunity.

Application of fast wavelet transformation in signal processing of MEMS gyroscope

Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-time, is analyzed. The algorithm will no longer have the processing of decimation and interpolation of usual WT. The formulae of the decomposition and the reconstruction are given. Simulation results of the MEMS （micro-electro mechanical systems） gyroscope drift signal show that the algorithm spends much less processing time to finish the de-noising process than the usual WT. And the de-noising effect is the same. The fast algorithm has been implemented in a TMS320C6713 digital signal processor. The standard variance of the gyroscope static drift signal decreases from 78. 435 5 （°）/h to 36. 763 5 （°）/h. It takes 0. 014 ms to process all input data and can meet the real-time analysis of signal.

Measurement of interstation phase velocity by wavelet transformation

In this paper, we present wavelet transformation method to measure interstation phase velocity. We use Morlet wavelet function as mother wavelet to filter two seismograms at various period of interest, and correlate the wavelet filtered seismograms to form cross-correlogram. If both wavelet filtered signals are in phase at that period, the phase of the cross-correlogram is a minimum. Using 3-spline interpolation to transform cross-correlation matrix to a phase velocity verse period image, it is convenient for us to measure interstation phase velocity.

Multi-Focus Image Fusion Based on Wavelet Transformation

In the fusion of image,how to measure the local character and clarity is called activity measurement. According to the problem,the traditional measurement is decided only by the high-frequency detail coefficients, which will make the energy expression insufficient to reflect the local clarity. Therefore,in this paper,a novel construction method for activity measurement is proposed. Firstly,it uses the wavelet decomposition for the fusion resource image, and then utilizes the high and low frequency wavelet coefficients synthetically. Meantime,it takes the normalized variance as the weight of high-frequency energy. Secondly,it calculates the measurement by the weighted energy,which can be used to measure the local character. Finally,the fusion coefficients can be got. In order to illustrate the superiority of this new method,three kinds of assessing indicators are provided. The experiment results show that,comparing with the traditional methods,this new method weakens the fuzzy and promotes the indicator value. Therefore,it has much more advantages for practical application.

Fourier and wavelet transformations application to fault detection of induction motor with stator current

Fault detection of an induction motor was carried out using the information of the stator current. After synchronizing the actual data, Fourier and wavelet transformations were adopted in order to obtain the sideband or detail value characteristics under healthy and various faulty operating conditions. The most reliable phase current among the three phase currents was selected using an approach that employs the fuzzy entropy measure. Data were trained with a neural network system, and the fault detection algorithm was verified using the unknown data. Results of the proposed approach based on Fourier and wavelet transformations indicate that the faults can be properly classified into six categories. The training error is 5.3×10-7, and the average test error is 0.103.

Analysis of penetration acceleration signal based on wavelet transformation

In order to analyze the composition and frequency distribution of acceleration signal in the process of projectile penetrating,this paper uses wavelet transform to decompose penetration acceleration signal to get the distribution of penetration acceleration signal in different frequency bands.Compared with the ideal acceleration signal curve and its characteristics,it can be concluded that the frequency range of the acceleration signal in the axis of the projectile and the vibration frequency range of the projectile are 31.25-62.5kHz and 62.5-125 kHz,respectively.Finally,the penetration acceleration signal curve is obtained by Simulink.

Olive Leaf Disease Detection via Wavelet Transform and Feature Fusion of Pre-Trained Deep Learning Models

Olive trees are susceptible to a variety of diseases that can cause significant crop damage and economic losses.Early detection of these diseases is essential for effective management.We propose a novel transformed wavelet,feature-fused,pre-trained deep learning model for detecting olive leaf diseases.The proposed model combines wavelet transforms with pre-trained deep-learning models to extract discriminative features from olive leaf images.The model has four main phases:preprocessing using data augmentation,three-level wavelet transformation,learning using pre-trained deep learning models,and a fused deep learning model.In the preprocessing phase,the image dataset is augmented using techniques such as resizing,rescaling,flipping,rotation,zooming,and contrasting.In wavelet transformation,the augmented images are decomposed into three frequency levels.Three pre-trained deep learning models,EfficientNet-B7,DenseNet-201,and ResNet-152-V2,are used in the learning phase.The models were trained using the approximate images of the third-level sub-band of the wavelet transform.In the fused phase,the fused model consists of a merge layer,three dense layers,and two dropout layers.The proposed model was evaluated using a dataset of images of healthy and infected olive leaves.It achieved an accuracy of 99.72%in the diagnosis of olive leaf diseases,which exceeds the accuracy of other methods reported in the literature.This finding suggests that our proposed method is a promising tool for the early detection of olive leaf diseases.

Multi-scale phase average waveform of electroencephalogram signals in childhood absence epilepsy using wavelet transformation

BACKGROUND： Recent studies have focused on various methods of wavelet transformation for electroencephalogram （EEG） signals. However, there are very few studies reporting characteristics of multi-scale phase waves during epileptic discharge.OBJECTIVE： To extract multi-scale phase average waveforms from childhood absence epilepsy EEG signals between time and frequency domains using wavelet transformation, and to compare EEG signals of absence seizure with pre-epileptic seizure and normal children, and to quantify multi-scale phase average waveforms from childhood absence epilepsy EEG signals. DESIGN, TIME AND SETTING： The case-comparative experiment was performed at the Department of Neuroelectrophysiology, Tianjin Medical University from August 2002 to May 2005. PARTICIPANTS： A total of 15 patients with childhood absence epilepsy from the General Hospital of Tianjin Medical University were enrolled in the study. The patients were not administered anti-epileptic drugs or sedatives prior to EEG testing. In addition, 12 healthy, age- and gender-matched children were also enrolled.METHODS： EEG signals were tested on 15 patients with childhood absence epilepsy and 12 normal children. Epileptic discharge signals during clinical and subclinical seizures were collected 10 and 20 times, respectively. The collected EEG signals were treated with wavelet transformation to extract multi-scale characteristics during absence epilepsy seizure using a conditional sampling method. Multi-scale phase average waveforms were collected using a conditional phase averaging technique. Amplitude of phase average waveform from EEG signals of epilepsy seizure, subclinical epileptic discharge, and EEG signals of normal children were compared and statistically analyzed in the first half-cycle.MAIN OUTCOME MEASURES： Multi-scale wavelet coefficient and the evolution of EEG signals were observed during childhood absence epilepsy seizures using wavelet transformation. Multi-scale phase average waveforms from EEG signals were observed using a conditional sampling method and phase averaging technique.RESULTS： Multi-scale characteristics of EEG signals demonstrated that 12-scale （3 Hz） rhythmical activity was significantly enhanced during childhood absence epilepsy seizure and co-existed with background structure （〈1 Hz, low frequency discharge）. The phase average wave exhibited opposed phase abnormal rhythm at 3 Hz. Prior to childhood absence epilepsy seizure, EEG detected opposed abnormal a rhythm and 3 Hz composition, which were not detected with traditional EEG. Compared to EEG signals from normal children, epileptic discharges from clinical and subclinical childhood absence epilepsy seizures were positive and amplitude was significantly greater （P〈0.05）.CONCLUSION： Wavelet transformation was used to analyze EEG signals from childhood absence epilepsy to obtain multi-scale quantitative characteristics and phase average waveforms. Multi-scale wavelet coefficients of EEG signals correlated with childhood absence epilepsy seizure, and multi-scale waveforms prior to epilepsy seizure were similar to characteristics during the onset period. Compared to normal children, EEG signals during epilepsy seizure exhibited an opposed phase model.

Suppression of seismic random noise by deep learning combined with stationary wavelet packet transform

Many traditional denoising methods,such as Gaussian fi ltering,tend to blur and lose details or edge information while reducing noise.The stationary wavelet packet transform is a multi-scale and multi-band analysis tool.Compared with the stationary wavelet transform,it can suppress high-frequency noise while preserving more edge details.Deep learning has signifi cantly progressed in denoising applications.DnCNN,a residual network;FFDNet,an effi cient,fl exible network;U-NET,a codec network;and GAN,a generative adversative network,have better denoising effects than BM3D,the most popular conventional denoising method.Therefore,SWP_hFFDNet,a random noise attenuation network based on the stationary wavelet packet transform(SWPT)and modified FFDNet,is proposed.This network combines the advantages of SWPT,Huber norm,and FFDNet.In addition,it has three characteristics:First,SWPT is an eff ective featureextraction tool that can obtain low-and high-frequency features of different scales and frequency bands.Second,because the noise level map is the input of the network,the noise removal performance of diff erent noise levels can be improved.Third,the Huber norm can reduce the sensitivity of the network to abnormal data and enhance its robustness.The network is trained using the Adam algorithm and the BSD500 dataset,which is augmented,noised,and decomposed by SWPT.Experimental and actual data processing results show that the denoising eff ect of the proposed method is almost the same as those of BM3D,DnCNN,and FFDNet networks for low noise.However,for high noise,the proposed method is superior to the aforementioned networks.

Research on the longitudinal protection of a through-type cophase traction direct power supply system based on the empirical wavelet transform

This paper proposes a longitudinal protection scheme utilizing empirical wavelet transform(EWT)for a through-type cophase traction direct power supply system,where both sides of a traction network line exhibit a distinctive boundary structure.This approach capitalizes on the boundary’s capacity to attenuate the high-frequency component of fault signals,resulting in a variation in the high-frequency transient energy ratio when faults occur inside or outside the line.During internal line faults,the high-frequency transient energy at the checkpoints located at both ends surpasses that of its neighboring lines.Conversely,for faults external to the line,the energy is lower compared to adjacent lines.EWT is employed to decompose the collected fault current signals,allowing access to the high-frequency transient energy.The longitudinal protection for the traction network line is established based on disparities between both ends of the traction network line and the high-frequency transient energy on either side of the boundary.Moreover,simulation verification through experimental results demonstrates the effectiveness of the proposed protection scheme across various initial fault angles,distances to faults,and fault transition resistances.

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.

Performance of Continuous Wavelet Transform over Fourier Transform in Features Resolutions

This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.

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.

Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

AN ALGORITHM FOR CODING VIDEO SIGNAL BASED ON 3-D WAVELET TRANSFORMATION

This paper presents an algorithm for coding video signal based on 3-D wavelet transformation. When the frame order t of a video signal is replaced by order 2, the video signal can be looked as a block in 3-D space. After splitting the block into smaller sub-blocks, imitate the method of 2-D wavelet transformation for images, we can transform the sub-blocks with 3-D wavelet. Most of video signal energy is in the decomposed low-frequency sub-bands. These sub-bands affect the visual quality of the video signal most. Quantizing different sub-bands with different precision and then entropy encoding each sub-band, we can eliminate inter- and intra-frame redundancy of the video signal and compress data. Our simulation experiments show that this algorithm can achieve very good result.

Arrival time measurements of first arrival phases P and PKIKP using the method of fixed scale wavelet transformation ratio

The arrival times of first teleseismic phases are difficult to be measured precisely because of slowly and gradually changed onsets and weak amplitudes. The arrival times measured manually are usually behind the real ones. In this paper, using the ratio method of fixed scale wavelet transformations improved by us, the arrival times for the first arrival phases (such as P and PKIKP) at the teleseismic and far-teleseismic distances were measured. The results are reasonable and reliable based on the analysis and discussion of the reliabilities and errors.

Recognition of vortex structures in turbulent refractive index field using wavelet transformation

When the light wave propagates through the hypersonic flow field, the aero-optic distortion happens. It is necessary to recognize the vortex structure for studying the light propagation model. A new vortex structure recognition method is proposed in this paper. Firstly, the refractive index field, which is transformed from the turbulent density field, is changed to gray scale images with a- bundant texture information equivalently. Then, wavelet transform is performed to decompose these images and the entropy values of the wavelet base coefficients are calculated. Comparing the entropy value to a given threshold, the modules with lower entropy are considered to be the large-scale vortex modules while those with higher entropy are small-scale vortex modules. The computer simulation results show that the proposed method is valid to recognize the vortex structures. This paper provides basis for investigation on the optics propagation model in terms of the turbulence vortex structures.

Inversion of receiver function by wavelet transformation

A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution.

Watermarking Scheme Based on Wavelet Transformation and Visual Cryptography

Based on the principles of the visual cryptography and the law of large numbers, the unexpanded shares are generated during the processes of embedding and verifying the hidden watermark. The watermark embedding is done in the frequency domain, which can be decoded by the human visual system （HVS） without the necessity of any complicated computation and the help of the original image. Experimental results indicated that our method had a good robustness on darkening, lightening, blurring, sharpening, noise, distorting, jitter, joint photographic experts group （JPEG） compression, and crop attacks.

Anomaly Detection Based on Discrete Wavelet Transformation for Insider Threat Classification

Unlike external attacks,insider threats arise from legitimate users who belong to the organization.These individuals may be a potential threat for hostile behavior depending on their motives.For insider detection,many intrusion detection systems learn and prevent known scenarios,but because malicious behavior has similar patterns to normal behavior,in reality,these systems can be evaded.Furthermore,because insider threats share a feature space similar to normal behavior,identifying them by detecting anomalies has limitations.This study proposes an improved anomaly detection methodology for insider threats that occur in cybersecurity in which a discrete wavelet transformation technique is applied to classify normal vs.malicious users.The discrete wavelet transformation technique easily discovers new patterns or decomposes synthesized data,making it possible to distinguish between shared characteristics.To verify the efficacy of the proposed methodology,experiments were conducted in which normal users and malicious users were classified based on insider threat scenarios provided in Carnegie Mellon University’s Computer Emergency Response Team(CERT)dataset.The experimental results indicate that the proposed methodology with discrete wavelet transformation reduced the false-positive rate by 82%to 98%compared to the case with no wavelet applied.Thus,the proposed methodology has high potential for application to similar feature spaces.