Orthogonal Wavelet Research Articles

Experimental study on transition of dynamic airfoil in pitching oscillation

The transition characteristics of dynamic airfoil have significant effects on the aerodynamic performance of wind turbines, helicopter rotor blades, jet engine compressor blades, etc. The time domain and time-frequency domain characteristics of transition on a NACA0012 airfoil during its pitching oscillation were experimentally studied using wall pressure measurement technology with high time accuracy in this paper. The variable slip window technology was used to detect the transition position, and the proper orthogonal decomposition (POD) method and wavelet analysis were combined to perform the time-frequency analysis. In the gradual forward movement of the transition, the low-frequency instability is gradually enhanced by the main flow and the inverse pressure gradient, and significantly submerges the high-frequency fluctuated feature. The higher order moments of the wall pressure during dynamic airfoil transition deviate significantly from the Gaussian characteristics, which is caused by the low-frequency instability and high-frequency burst. The POD method is able to distinguish low-frequency instability from the high-frequency feature. The reduced frequency had significant effects on the transition. With the increase of the reduced frequency, the hysteresis effect of the transition became more and more significant, and the frequency component of transition was more concentrated and the energy was stronger.

A novel Block Bi‐diagonalization based pre‐coding scheme for bit error reduction in mutiple input multiple output‐orthogonal frequency division multiplexing

SummaryThe MIMO‐OFDM increases spectral efficiency without the use of channel state information (CSI). However, the bit error rate (BER) in the MIMO‐OFDM model increases dramatically due to the increase in nonlinear distortion in the power amplifier (PA). In this research, a novel pre‐coder integrated MIMO‐OFDM technology is designed for effective BER reduction, and its performance is analyzed. The discrete wavelet‐based OFDM system is one of the key ideas to present good orthogonal by emphasizing orthogonal wavelets. It helps to mitigate inter‐symbol interference (ISI) and noise within the channel by extending the bandwidth (BW) compared to conventional OFDM systems. But, DWT‐OFDM highly suffered due to downsampling, which degrades system efficiency. To overcome this, a redundant discrete wavelet transform (RDWT) is proposed in this article to enhance spectral efficiency. For modulation, 16‐bit quadrature amplitude modulation (QAM) is introduced in this work. In addition to this, a block bi‐diagonalization (BBD) pre‐coder technique is proposed to mitigate unwanted noise and interference in the MIMO‐OFDM system. The performance measures such as ergodic sum capacity, BER, throughput, average jitter noise power, mean square error (MSE), and power consumption are analyzed using the MATLAB platform. The proposed method obtains the ergodic sum capacity of 6.25 bps/Hz, a BER of 0.021, a throughput of 95.2%, MSE of −0.47, and a power consumption of 1.15 μW. The simulative results prove the efficacy of the proposed method.

Multi-scale analysis on particle dynamics in horizontal pneumatic conveying with oscillating air flow

This study focuses on multi-scale particle dynamics of horizontal pneumatic conveying equipped with two types of soft fins at the air velocity of the minimum pressure drop. The particle velocity fields of non-fin and using soft fin's cases are measured by high-speed particle image velocimetry. Then the particle fluctuation velocities are decomposed into various scales based on one-dimensional orthogonal wavelet decomposition. It is found that the non-uniform case of Fin260 yields the highest axial- and vertical- particle velocities and fluctuation energies, giving rise to the lowest pressure drop and conveying air velocity. The overall relative energy distributions of wavelet components suggest that the particle fluctuation energies become more concentrated at wavelet levels 3 and 4 by using fins, especially for the case of non-uniform Fin260. The energy concentration on specific wavelet levels indicates a more organized particle motions under the effect of air turbulence induced by non-uniform soft fins. The correlation analysis suggests that the spatial correlation of wavelet component is associated with the contribution of wavelet component to the measured particle fluctuation energy. The oscillating soft fins modulate the air turbulence and promote the particle motions to be spatially correlated in a range of specific frequency.

Spherical-Orthogonal-Symmetric Haar Wavelet for Driver's Visual Detection

This work proposes a spherical-orthogonal-symmetric Haar wavelet to decompose and reconstruct spherical iris signals to obtain stronger geometric features of iris surface. It compares its feature extraction abilities of spherical harmonics, semi-orthogonal and nearly orthogonal spherical Haar wavelet. The developed spherical-orthogonal-symmetric Haar wavelet with a convolutional neural network is also proposed for drivers’ iris recognition. It can effectively capture the local fine features of iris spherical surface, and has stronger ability of iris recognition than semi-orthogonal or nearly orthogonal spherical Haar wavelet bases.

Study on the Localization of Defects in Typical Steel Butt Welds Considering the Effect of Residual Stress

When using magnetic memory detection technology to locate weld cracks and porous defects, the traditional zero-point polarity theory leads to misjudgments in defect location and difficulty in distinguishing between the residual stress and the magnetic signals generated by defects due to the influence of external noise and residual stress. Therefore, this paper considers the different mechanisms of magnetic signal generation in areas where crack- and porosity-type defects and residual stresses are located and discusses research focused on the detection of weld defect localization considering the influence of residual stresses. Using the mechanism of magnetic signal generation as a starting point, the three-dimensional magnetic modulus gradient polarity determination method is proposed to distinguish residual stress and defects’ magnetic signals. Through the COMSOL simulation of a welding defect’s finite element magnetic signal, the resulting magnetic signal is converted into a characteristic determination formula for characterization. To verify the accuracy of the simulated characterization, the 3D magnetic signal is extracted and verified manually. Finally, a double orthogonal wavelet transform is introduced to eliminate the random noise in the gradient of the three-dimensional magnetic modulus. The results show that the theoretical analysis, numerical simulation, and experimental results agree with each other. The three-dimensional magnetic modulus gradient values of cracks and pores are much higher than that of the defect-free residual stress area. The three-dimensional magnetic gradient modulus can locate defects and characterize the lengths of defects. The dual orthogonal wavelet eliminates noise interference while improving the accuracy of locating three-dimensional magnetic modulus gradient defects.

Multi-Scale Wake Characteristics of the Flow over a Cylinder with Different V-Groove Numbers

The near-wake structure resulting from the interaction between the water and the cylinder is researched. The wake characteristics for the smooth cylinder and the cylinder with different numbers of grooves are measured by high-speed particle image velocimetry (PIV) at a Reynolds number of 7400. From the measured data, it is observed that the v-groove increases the Reynolds shear stress and the turbulent kinetic energy; thus, the formation of the Karman-like vortices is prevented and the recirculation region is reduced. The number of grooves has a limited effect on the wake characteristics. In addition, a one-dimensional orthogonal wavelet decomposes the fluctuation velocities in the cylindrical wake region to study the multi-scale wake characteristics behind the v-groove cylinders. The large-scale structures show that the Karman-like vortices of the grooved cylinder are closer to the trailing edge of the cylinder. The intermediate-scale structures show more vortices behind the 32-groove cylinder. The small-scale structures show that the phase difference between the upper and lower oscillation positions has become smaller. Meanwhile, the large-, intermediate- and small-scale Reynolds shear stress distributions suggest that the shear layer instability in the near-wake region creates vortices, which increase the turbulent kinetic energy and narrow the wake region.

Prestack seismic random noise attenuation using the wavelet-inspired invertible network with atrous convolutions spatial pyramid

Convolutional Neural Network (CNN) is widely used in seismic data denoising due to its simplicity and effectiveness. However, traditional seismic denoising methods based on CNN ignore multi-scale features of seismic data in the wavelet domain. The lack of these features will decrease the accuracy of denoising results. To address this barrier, a seismic denoise method based on the wavelet-inspired invertible network with atrous convolutions spatial pyramid (WINNet_ACSP) is proposed. WINNet_ACSP follows the principle of lifting wavelet transform. The proposed method utilizes the redundant orthogonal wavelet transform to obtain frequency multi-scale information from noisy seismic data. Then predict update network (PUNet) extracts spatial multi-scale features of approximate and detailed parts. The sparse driven network (SDN) learns the complex multi-scale information and obtains sparse features. These sparse features are processed to eliminate random noise. Compared to standard convolution, the atrous convolutions spatial pyramid (ACSP) can extract more features. The redundant features are the key to ensure the precision of multi-scale information. Therefore, the introduction of ACSP in PUNet can guarantee the denoising effect of the network. WINNet_ASCP combines the characteristics of wavelet transform and neural network and has a high generalization. Besides, transfer learning is used to overcome the difficulty caused by the training sample size of seismic data. The training process includes pre-training and post-training. The former is trained to obtain the initial denoising network by natural image samples. The latter is trained with a small sample of seismic data to enhance stratigraphic continuity. Finally, the proposed method is tested with synthetic and field data. The experimental results show that the proposed method can effectively remove random noise and reduce the loss of detailed information in prestack seismic data. In the future, we will make further improvements on this basis and conduct experiments on 3D prestack data.

An automatic sleep-scoring system in elderly women with osteoporosis fractures using frequency localized finite orthogonal quadrature Fejer Korovkin kernels.

Healthy sleep signifies a good physical and mental state of the body. However, factors such as inappropriate work schedules, medical complications, and others can make it difficult to get enough sleep, leading to various sleep disorders. The identification of these disorders requires sleep stage classification. Visual evaluation of sleep stages is time intensive, placing a significant strain on sleep experts and prone to human errors. As a result, it is crucial to develop machine learning algorithms to score sleep stages to acquire an accurate diagnosis. Hence, a new methodology for automated sleep stage classification is suggested using machine learning and filtering electroencephalogram (EEG) signals. The national sleep research resource's (NSRR) study of osteoporotic fractures (SOF) dataset comprising 453 subjects' polysomnograph (PSG) data is used in this study. Only two unipolar EEG derivations C4-A1 and C3-A2 are employed individually and jointly in this work. The EEG signals are decomposed into sub-bands using a frequency-localized finite orthogonal quadrature Fejer Korovkin wavelet filter bank. The wavelet-based entropy features are extracted from sub-bands. Subsequently, extracted features are classified using machine learning techniques. Our developed model obtained the highest classification accuracy of 81.3%, using an ensembled bagged trees classifier with a 10-fold cross-validation method and Cohen's Kappa coefficient of 0.72. The proposed model is accurate, dependable, and easy to implement and can be employed as an alternative to a PSG-based system at home with minimal resources. It is also ready to be tested on other EEG data to evaluate the sleep stages of healthy and unhealthy subjects.

Trend and spatial-temporal variation of drought characteristics over equatorial East Africa during the last 120 years

Centennial drought characteristics in Equatorial East Africa (EEA) is investigated using the Standardized Precipitation Evapotranspiration Index (SPEI) derived from the Climatic Research Unit (CRU) dataset. The spatial pattern of drought distribution, as well as drought duration, intensity and frequency, are analyzed for SPEI at a 3-month timescale for March-April-May (MAM) season. Rotated Empirical Orthogonal Function (REOF), Mann-Kendall method (MK), and wavelet analyses are used to study drought’s spatial pattern, trend, and periodicity. The result of the principal component analysis returned six homogenous drought sub-regions. A low drought frequency characterizes EEA (<20%). The drought in the MAM season lasts between 2.2 and 2.8 months. Overall, the result showed a weak long-term drying trend for most parts of EEA that were significant in some sub-regions and insignificant in others. An increase in drought areal extent after the 1980s could be ascribed to the increase in potential evapotranspiration (PET) and is consistent with the negative trend in SPEI value over the six sub-regions. The apparent increase is mainly attributed to the increase in moderate and severe droughts area rather than extreme drought areas. The spectral analysis further reveals that inter-annual drought variability with periodicities less than 8 years dominates in all sub-regions of Equatorial East Africa, which is associated with the critical role of El-Niño in driving the drought variations in EEA.

Large-scale orthogonal integer wavelet transform features-based active support vector machine for multi-class face recognition

Large-scale orthogonal integer wavelet transform features-based active support vector machine for multi-class face recognition

Large-scale orthogonal integer wavelet transform features-based active support vector machine for multi-class face recognition

Large-scale orthogonal integer wavelet transform features-based active support vector machine for multi-class face recognition

Retracted: Brain Tumor Detection and Classification by MRI Using Biologically Inspired Orthogonal Wavelet Transform and Deep Learning Techniques.

[This retracts the article DOI: 10.1155/2022/2693621.].

An Improved High-Resistance Fault Detection Method in DC Microgrid Based on Orthogonal Wavelet Decomposition

High-resistance faults in direct current (DC) microgrids are small and thus difficult to detect. Such faults may be “invisible” in that grid operation continues for a considerable time, which damages the grid. It is essential to detect and remove high-resistance faults; we present a detection method herein. First, the transient DC current during the fault is subjected to hierarchical wavelet decomposition to identify high-resistance faults accurately and sensitively; the wavelet coefficients are detected using the singular value decomposition (SVD) method. The SVD valve can denoise the dc microgrid fault current, which eliminates the influence of converter switching frequency and background noise effectively. Power system computer-aided design (PSCAD)/electromagnetic transients including direct current (EMTDC)-based simulations showed that our method successfully identified high-resistance faults.

Comparison of the representational ability in individual difference analysis using 2-D time-series image and time-series feature patterns

Physiological signals, as crucial indicators for measuring physical health, must be acquired by model learning, but the modeling and analysis performance is strongly affected by different representation patterns and feature extraction methods, even for the same data. This work investigated the capacity of the 2-D time-series image patterns on the weakening of individual differences and compared them with the time-series feature patterns. First, the time-series features of electrocardiograph (ECG) were extracted using the permutation conditional mutual information (PCMI), principal component analysis (PCA), power spectral density (PSD), and compactly supported sym-5 orthogonal wavelets with approximate symmetry (CSOWAS); the time-series coupling features of electroencephalogram (EEG) and SEED were extracted using PCMI. Then, the features of ECG, EEG, and SEED were reconstructed into 2-dimensional (2-D) time-series images using Gradient Angle Difference Field (GADF) algorithm. Finally, the classification performance of the 2-D time-series images and time-series features on the ECG, EEG, and SEED data sets are analyzed using the backpropagation (BP) neural network, LeNet 5, convolutional neural network (CNN), Deep Residual Shrinkage Networks (DRSN), ResNet 18, and VGG 16 models and compared to each other. The results show that 1) the representation ability of the 2-D time-series image pattern is better than that of the time-series feature pattern in physiological data (ECG, EEG, and SEED) analysis; 2) the Gamma band is a stabler in the classification task of individual differences (best accuracy: 100%), which can be used as the first choice for the analysis of similarity features between individuals; 3) the classification performance of the 2-D time-series images in Theta, Alpha 1, Beta 1, and Beta 2 bands on EEG datasets are greatly improved. This work shows that the 2-D time-series image patterns of the ECG, EEG, and SEED are an effective method for distinguishing individual differences.

Automatic detection of Alzheimer’s disease from EEG signals using low-complexity orthogonal wavelet filter banks

Background:Alzheimer’s disease (AD) is one of the most common neurodegenerative disorder. As the incidence of AD is rapidly increasing worldwide, detecting it at an early stage can prevent memory loss and cognitive dysfunctions in patients. Recently, Electroencephalogram (EEG) signals in AD cases show less synchronization and a slowing effect. The abrupt and transient behavior of EEG signals can be detected from specific frequency bands that are cortical rhythms of interest such as delta (0−4Hz), theta (4−8Hz), alpha (8−12Hz), beta1 (12−16Hz), beta2 (16−32Hz), and gamma (32−48Hz). Method:This paper proposes novel low-complexity orthogonal wavelet filter banks with vanishing moments (LCOWFBs-v) to decompose the AD and normal controlled (NC) EEG signals into subbands (SBs). A generalized design technique is suggested to reduce the computational complexity of original irrational wavelet filter banks (FBs). The two features, Higuchi’s fractal dimension (HFD) and Katz’s fractal dimension (KFD), were extracted from EEG SBs. The significance of these extracted features has been inspected using Kruskal–Wallis test. Results:The present study analyzed the EEG recordings of 23 subjects (AD-12 and NC-11) with the combination of LCOWFBs, HFD, and KFD. The proposed technique achieved a classification accuracy of 98.5% and 98.6% using the LCOWFBs-4 and LCOWFBs-6, respectively with a cubic-support vector machine classifier and 10-fold cross-validation technique. Conclusion:The proposed method with newly designed LCOWFBs is efficient compared with the well-known FBs and existing techniques for detecting AD.

A supervised functional Bayesian inference model with transfer-learning for performance enhancement of monitoring target batches with limited data

To increase the monitoring performance of the batch process with serious nonlinearity, uneven-length, and limited-data issues, a supervised transfer-learning based functional Bayesian inference method is developed in this study. The raw uneven-length batch data are firstly transformed into functional data by choosing appropriate orthogonal wavelet basis functions (WBFs). Using the approximation coefficients representing the latent features that are inherent to the raw data, a Gaussian process model and a Bayesian inference method are applied based on the coefficients in each source batch process and the established models are transferred to enhance modeling performance for the target process with limited batches. In the proposed functional method, the unfolding operation is not needed for preprocessing, avoiding distortion of the raw data structure. With the compact support property of WBFs, within-batch detection can be implemented effectively to recognize faults earlier. The advantages of the proposed model are verified using a numerical case and an industrial polytetrafluoroethylene process.

Wavelet multi-scale analysis on particle dynamic characteristics of the vertical tubes in a horizontal-vertical pneumatic conveying system

To study the flow characteristics of particles in the vertical tube, the velocity is measured at the minimum pressure drop (MPD) by using a high-speed particle image velocimeter (PIV). Firstly, the pneumatic conveying system’s pressure drop and the particle velocity characteristics in the vertical tube were investigated. Then, for the axial fluctuation velocity of the particles, the continuous wavelet transform, and one-dimensional discrete orthogonal wavelet decomposition are used to reveal the dynamic characteristics of the particles based on the time-frequency characteristics, the contribution of wavelet levels to the energy of particle fluctuations, the auto-correlation of each wavelet level and the probability distribution of wavelet levels. The results demonstrate that large-scale movement dominates particle movement in the vertical tube, whereas small-scale movement increases as conveying height rises. The energy contribution of the low-frequency wavelet level is larger, and this contribution decreases with the acceleration of the particles along the tube. The high-frequency wavelet level’s auto-correlation coefficients decay more slowly and have a longer duration. At increasing wavelet levels, the skewness and kurtosis coefficients grow, and the departure of the Gaussian probability distribution becomes more obvious.

A hybrid two-dimensional orthogonal wavelet multiresolution and proper orthogonal decomposition technique for the analysis of turbulent wake flow

A hybrid two-dimensional orthogonal wavelet multiresolution and proper orthogonal decomposition technique is developed to analyze the wake flow behind a semi cylinder. The two-dimensional orthogonal wavelet analysis is first applied to decompose the measured velocity fields into four wavelet components based on their spatial scales. Then the extracted multi-scale structures are further investigated based on proper orthogonal decomposition. The modal energy distributions of multi-scale flow structures suggest that the dominance of first two POD modes is reduced and the relative energy becomes more distributed as the flow structure changes from large-scale to small-scale. The first two POD modes of intermediate-scale structure also appear in a mode pair and they are related to secondary resonance accompanied with large-scale flow oscillation. The POD mode 3 of intermediate-scale structure suggest the existence of symmetric vortex shedding pattern. The first two POD modes of small-scale structure also display a symmetrically distributed vortex pair and the distance between adjacent vortices is about half of the case of mode 3 of intermediate-scale structure. The PSD distributions of POD modes of multi-scale structures suggest that the bandwidth of PSD becomes less concentrated as the flow structure varies from large-scale to small-scale. Distinctive flow patterns associated with first and second order harmonics of fundamental flow oscillation can be successfully extracted from the dominating POD modes of intermediate-scale and small-scale structures. The proposed hybrid technique provides a tool for relate the most energetic flow events over a period of time with multi-scale structures cascaded in the turbulence flow.

General double-sided orthogonal planes split QFT and wavelet transform on functions and distribution spaces

General double-sided orthogonal planes split QFT and wavelet transform on functions and distribution spaces

A Novel Design of Symmetric Daub-4 Wavelet Filter Bank for Image Analysis

The orthogonal wavelet filter banks (FBs) consume large resources for hardware implementation due to their irrational coefficients. This results in reduction in speed of operation, huge memory requirement and increased power dissipation. In order to solve these issues, a low complex symmetric Daub-4 (8-tap) orthogonal wavelet FB is proposed in this brief. This is achieved by slightly altering the perfect reconstruction (PR) condition to make proposed FB symmetric and to obtain dyadic filter coefficients. The proposed wavelet FB is multiplier free and achieves considerably reduction in hardware and dynamic power consumption by reducing number of adders and shifters. This is verified by implementing the proposed wavelet FB on Kintex-7 field programmable gate array (FPGA) using vivado 2019.2 software from Xilinx. The proposed FB is tested for its suitability in applications such as image compression and medical image retrieval. Simulations results prove that the designed wavelet FB gives better performances in terms of PSNR for image compression and retrieval accuracy (ARP, ARR) for medical image retrieval on the benchmark images as compared to state-of-art methods.