Orthogonal Wavelet Research Articles

Interannual Covariation of the North American and African Summer Monsoons

ABSTRACTThe North American summer monsoon (NASM) and the North African summer monsoon (NAFSM) are two vital subsystems of the global monsoon. To date, the potential inter‐monsoon relationship between the NASM and NAFSM has not been fully understood. To fill this gap, we investigate the NASM–NAFSM relationship on the interannual timescale during the period of 1979–2022. Based on statistical methods (including correlation, empirical orthogonal function and cross wavelet analyses), we identify a noteworthy interannual covariation of the NASM and NAFSM. This observed NASM–NAFSM covariation can be explained by atmospheric circulation anomalies associated with sea surface temperature (SST) anomalies in the tropical central‐eastern Pacific and tropical Atlantic, suggesting the critical roles of tropical Pacific–Atlantic SST anomalies in shaping the NASM–NAFSM covariation. The results of Coupled Model Intercomparison Project Phase 6 (CMIP6) models indicate that a model's ability to simulate the NASM–NAFSM covariation tends to be related to its ability to reproduce the modulating effects of the tropical Pacific–Atlantic SST anomalies. These results have potential implications for seasonal forecasts of the NASM and NAFSM variations, suggesting that the NASM and NAFSM can be considered simultaneously in climate predictions.

Wavelets for Self-Calibration of Aerial Metric Camera Systems

In this paper, wavelets are applied to develop new models for the self-calibration of aerial metric camera systems. It is well known and mathematically proven that additional parameters (APs) can compensate image distortions and remaining error sources by a rigorous photogrammetric bundle-block adjustment. Thus, kernel functions based on orthogonal wavelets (e. g., asymmetric Daubechies wave- lets, least asymmetric Daubechies wavelets, Battle-Lemarié wavelets, Meyer wavelets) are used to build the wavelets-based family of APs for self-calibrating digital frame cameras. These new APs are called wavelet APs. Its applications in rigorous tests are accomplished by using aerial images taken by an airborne digital mapping camera in situ and practical calibrations. The test results demonstrate that these orthogonal wavelet APs are applicable and largely avoid the risk of over-parameterization. Their external accuracy is evaluated using reliable and high precision check points in the calibration field.

Large eddy simulation of a swirling kerosene spray flame: A proper orthogonal decomposition and wavelet transform analysis on the flow structure and hydroxyl species field

Large eddy simulation of a swirling kerosene spray flame: A proper orthogonal decomposition and wavelet transform analysis on the flow structure and hydroxyl species field

Detecting Gravitational-wave Bursts from Black Hole Binaries in the Galactic Center with LISA

Stellar-mass black hole binaries (BHBs) in galactic nuclei are gravitationally perturbed by the central supermassive black hole (SMBH) of the host galaxy, potentially inducing strong eccentricity oscillations through the eccentric Kozai–Lidov mechanism. These highly eccentric binaries emit a train of gravitational-wave (GW) bursts detectable by the Laser Interferometer Space Antenna (LISA)—a planned space-based GW detector—with signal-to-noise ratios up to ∼100 per burst. In this work, we study the GW signature of BHBs orbiting our galaxy’s SMBH, Sgr A*, which are consequently driven to very high eccentricities. We demonstrate that an unmodeled approach using a wavelet decomposition of the data effectively yields the time-frequency properties of each burst, provided that the GW frequency peaks between 10−3 and 10−1 Hz. The wavelet parameters may be used to infer the eccentricity of the binary, measuring log10(1−e) within an error of 20%. Our proposed search method can thus constrain the parameter space to be sampled by complementary Bayesian inference methods, which use waveform templates or orthogonal wavelets to reconstruct and subtract the signal from LISA data.

Sorted sample- wavelet feature clustering based on the range for classification of multiple nutrient deficiencies in tomato plants

The phenomenon of physiological change in plants hyperpolarizes membrane potentials showing a significant change in electrophysiology. For plants to survive, develop, and reproduce, the proper ratio of nutrients is required. Malnourished plants exhibit unfavorable changes in their physiology. Nutrient deficiencies are one of the primary abiotic stresses occurred in plants which are commonly identified and classified through various hyperspectral imaging, and pattern recognition methods. In contrast to image-based methods, in this paper, the electrophysiological signal data of tomato plants in multiple nutrient deficiency states are classified. These electrical signals of tomato plants are acquired in healthy and in deficient states of calcium (Ca), manganese (Mn), nitrogen (N), and iron (Fe). The features are extracted by 7-level orthogonal wavelet decomposition using four different wavelets Daubechies (Db), Coiflet (Cf), Symlet (Sym), and Discrete Meyer (Dm). A novel range-based sorted sample clustering method is proposed to boost classification performance. Class assignment is performed in two modes homogeneous and non-homogeneous, where multi-class classification in non-homogeneous class assignment attained 99.4 % accuracy and in homogeneous class assignment a highest accuracy of 96.8 % is attained using the KNN classifier. Identifying nutrient deficiencies through electrophysiological signal analysis dominated the detection through imaging techniques, impacting a drastic change in crop protection practices.

A COMPARATIVE STUDY OF A CLASS OF LINEAR AND NONLINEAR PANTOGRAPH DIFFERENTIAL EQUATIONS VIA DIFFERENT ORTHOGONAL POLYNOMIAL WAVELETS

We propose a wavelet approach on different orthogonal polynomials for solving linear and nonlinear pantograph equations with stretch kind. The pantograph differential equation is a unique proportional delay functional differential equation class. It has been used to deal with numerous physics, mathematics, and engineering applications, such as quantum mechanics, control systems, electrodynamics, and number theory. This scheme is based on constructing the operational matrix for integration via different wavelets with their collocation nodes. This study aims to examine the numerical dynamics of the pantograph equation under stretch kind through different orthogonal polynomial wavelets. Illustrative examples are presented to highlight the flexibility of this scheme, and comparisons are made between the mentioned scheme and other existing schemes using tables and graphs. These numerical results correctly predict the applicability and effectiveness of the mentioned scheme.

Wavelet Transforms Significantly Sparsify and Compress Tactile Interactions.

As higher spatiotemporal resolution tactile sensing systems are being developed for prosthetics, wearables, and other biomedical applications, they demand faster sampling rates and generate larger data streams. Sparsifying transformations can alleviate these requirements by enabling compressive sampling and efficient data storage through compression. However, research on the best sparsifying transforms for tactile interactions is lagging. In this work we construct a library of orthogonal and biorthogonal wavelet transforms as sparsifying transforms for tactile interactions and compare their tradeoffs in compression and sparsity. We tested the sparsifying transforms on a publicly available high-density tactile object grasping dataset (548 sensor tactile glove, grasping 26 objects). In addition, we investigated which dimension wavelet transform-1D, 2D, or 3D-would best compress these tactile interactions. Our results show that wavelet transforms are highly efficient at compressing tactile data and can lead to very sparse and compact tactile representations. Additionally, our results show that 1D transforms achieve the sparsest representations, followed by 3D, and lastly 2D. Overall, the best wavelet for coarse approximation is Symlets 4 evaluated temporally which can sparsify to 0.5% sparsity and compress 10-bit tactile data to an average of 0.04 bits per pixel. Future studies can leverage the results of this paper to assist in the compressive sampling of large tactile arrays and free up computational resources for real-time processing on computationally constrained mobile platforms like neuroprosthetics.

Performance Evaluation of Fractal Wavelet Packet Transform on Wireless Communication Systems

The performance of the phase shift keying (PSK) modulation technique over additive white Gaussian noise (AWGN) and multipath propagation channels generally becomes worse for higher-order modes. Therefore, a new modulation technique should be provided in order to have a system that is capable of transmitting data with higher efficiency while maintaining better performance at the same time. This paper presents the development of a fractal wavelet packet transform incorporated within the M-ary PSK system, namely M-ary PSK orthogonal wavelet division multiplexing (OWDM), which is proposed to obtain high performance of modulation in terms of spectrum efficiency and bandwidth resources intended for wireless communication systems. To demonstrate performance improvement over a Rayleigh frequency selective fading channel and in the presence of AWGN noise, the proposed system was evaluated and compared to the basic modulation system and M-ary PSK employing orthogonal frequency division multiplexing (OFDM). The performance results show that M-ary PSK OWDM had better performance in comparison with M-ary PSK OFDM and the conventional system. By utilizing 16 subcarriers, QPSK OWDM achieved bit error rate performance improvement from 1.5 × 10-3 to 1 × 10-4 for Eb/N0 of 20 dB with efficient bandwidth.

Fingerprint Image Compression using Biorthogonal and Orthogonal Wavelets at Different Levels of Discrete Wavelet Transform

Fingerprint Image Compression using Biorthogonal and Orthogonal Wavelets at Different Levels of Discrete Wavelet Transform

Artificial neural network and discrete wavelet transform for inter-turn short circuit and broken rotor bars faults diagnosis under various operating conditions

Introduction. This work presents a methodology for detecting inter-turn short circuit (ITSC) and broken rotor bars (BRB) fault in variable speed induction machine controlled by field oriented control. If any of these faults are not detected at an early stage, it may cause an unexpected shutdown of the industrial processes and significant financial losses. Purpose. For these reasons, it is important to develop a new diagnostic system to detect in a precautionary way the ITSC and BRB at various load condition. We propose the application of discrete wavelet transform to overcome the limitation of traditional technique for no-stationary signals. The novelty of the work consists in developing a diagnosis system that combines the advantages of both the discrete wavelet transform (DWT) and artificial neural network (ANN) to identify and diagnose defects, related to both ITSC and BRB faults. Methods. The suggested method involves analyzing the electromagnetic torque signal using DWT to calculate the stored energy at each level of decomposition. Then, this energy is applied to train neural network classifier. The accuracy of ANN based on DWT, was improved by testing different orthogonal wavelet functions on simulated signal. The selection process identified 5 pertinent wavelet energies, concluding that, Daubechies44 (db44) is the best suitable mother wavelet function for effectively detecting and classifying failures in machines. Results. We applied numerical simulations by MATLAB/Simulink software to demonstrate the validity of the suggested techniques in a closed loop induction motor drive. The obtained results prove that this method can identify and classify these types of faults under various loads of the machine. References 31, table 1, figures 9.

Metaheuristic optimized time–frequency features for enhancing Alzheimer’s disease identification

Background:Alzheimer’s disease (AD) is a chronic disorder characterized by progressive cognitive dysfunctions and memory loss. Electroencephalography (EEG) is a non-invasive tool to detect AD using machine learning models and signal-derived features. Feature selection enhances AD detection performance, reduces training and testing time, and builds simpler models. Metaheuristic algorithms (MHAs) have successfully selected optimum features in several classification tasks and can be valuable in enhancing AD detection. Method:In this work, an AD detection model is proposed based on a systematic investigation of adaptive signal decomposition techniques and MHAs. The four techniques comprising empirical mode decomposition, variational mode decomposition, discrete wavelet transform, and Low-Complexity Orthogonal Wavelet Filter Banks (LCOWFBs) decompose EEG signals into subbands. Thirty-four features based on signal, temporal, spectral, and entropy analysis are extracted for each subband. The salient features are selected using seven different MHAs: particle swarm algorithm, salp swarm algorithm, reptile search (RSA), Grey Wolf, dwarf mongoose optimization, snake optimizer, and Fick’s law algorithm (FLA). Results:The two publicly available AD EEG datasets validated the performance of the proposed framework. LCOWFBs achieved the highest binary classification accuracy of 99.72% using 15 salient features selected by RSA and multi-class accuracy of 88.92% with seven salient features selected by FLA. The present method investigates brain regions that are affected by AD. Conclusion:The results indicate that the combination of LCOWFBs and RSA achieved maximum AD detection performance for both datasets with shorter computational time than earlier reported methods in the literature. The present model can be extended to identify chronic disorders, including hypertension, sleep disorders, and Parkinson’s disease.

A Lattice-Structure-Based Trainable Orthogonal Wavelet Unit for Image Classification

A Lattice-Structure-Based Trainable Orthogonal Wavelet Unit for Image Classification

Selection of wavelet generating function in voltage interruption detection

When using wavelet for voltage interruption detection, improper selection can lead to detection failure due to the differences in wavelet characteristics and the diversity of the generating function. Based on the analysis of wavelet characteristics, the modulus maximum principle is used to compare the detail coefficients after wavelet decomposition, and a method that should be followed for selecting the generating function is proposed. Here are four important points to consider: First, choose orthogonal wavelets that can decrease redundancy. Second, symmetry does not have a major effect. Third, higher-order vanishing moments and longer support lengths result in better singularity detection. Finally, the order of vanishing moments is more important than the support length. We establish a disturbance signal model with interruption occurring at the time of voltage zero crossing and select six types of wavelets: db1, db3, db6, db8, coif2, and coif3 for four-scale wavelet decomposition. The experimental results demonstrate the accuracy of the proposed method in this paper.

Fluid-Dynamic and Aeroacoustic Characterization of Side-by-Side Rotor Interaction

An investigation of twin corotating rotors’ interaction effects was performed by load (thrust and torque) measurements, flow field dynamics through Time-Resolved Particle Image Velocimetry, and acoustic emissions using a microphone array. Two rotors, each with a diameter of D = 393.7 mm and equipped with three blades, were investigated in a side-by-side configuration, to simulate a multirotor propulsion system. The mutual distance between the propellers is 1.02 D, and four different rotating speeds, i.e., 2620, 3500, 4360, and 5200 RPM, were explored. In such a configuration, thrust and torque undergo a reduction compared to that found for a single propeller configuration. The level of aerodynamic load fluctuations increases as well. The interaction of the wakes produces a recirculation region at the external periphery of the shear layers. An innovative approach involving the coupling of Proper Orthogonal Decomposition (POD) and Wavelet Transform has been employed to investigate the dominant structures within the flow and their mutual influence. The results reveal that the interacting wakes are dominated by a wave-like motion pulsating at Harmonics of the Blade Passing Frequency (HBPF) of 1/3. Higher orders of POD modes capture coherent vortical structures, including tip vortices pulsating at HBPF = 1. The aeroacoustic investigation shows that the noise level, in terms of the Over All Sound Pressure Level, presents a remarkable increment concerning that generated by the single propeller.

Establishing a quantitative assessment methodology framework of water conservation based on the water balance method under spatiotemporal and different discontinuous ecosystem scales

Water conservation (WC) is an essential terrestrial ecosystem service that mitigates surface runoff and replenishes groundwater, which has received considerable attention under the dual pressures of climate change and human activity. However, there is insufficient understanding of the trends in WC changes on temporal (annual, monthly, daily), spatial, and ecosystem scales. This study proposed a quantitative assessment methodology framework (QAMF) for analyzing the spatiotemporal variation of WC under different discontinuous ecosystems. The QAMF mainly used models and methods such as the hydrological model (SWAT), calibration and uncertainty program (SWAT-CUP), WC calculation formula (water balance method), and spatial analysis method (empirical orthogonal function and wavelet analysis). It was applied to the source region of the Yellow River (SRYR), where the ecological landscape pattern underwent varying degrees of degradation, and WC capacity decreased. The results show that: Firstly, the constructed SWAT in the SRYR had high accuracy, and the proposed formula for calculating WC was suitable for multi-temporal scale analysis of WC in spatially distributed discontinuous basins. Secondly, the annual and monthly WC were respectively 81.00–184.13 mm and −28.58–107.64 mm, and daily WC was positive during extreme precipitation periods and negative during dry periods. The regulating effect of WC was fully reflected on the daily scale, partially reflected on the monthly scale, and absent on the annual scale. Third, the crucial WC area was mainly distributed in the southeast, and there was a significant primary yearly cycle of WC in the SRYR. Finally, different ecosystems exhibited different WC capabilities, and protecting the diversity of ecosystems played an essential role in maintaining and improving the WC function in the SRYR. This project has great scientific significance and technological support for scientifically evaluating the WC capacity in the SRYR.

Self-similar, spatially localized structures in turbulent pipe flow from a data-driven wavelet decomposition

This study aims to extract and characterize structures in fully developed pipe flow at a friction Reynolds number of $\textit {Re}_\tau = 12\,400$ . To do so, we employ data-driven wavelet decomposition (DDWD) (Floryan & Graham, Proc. Natl Acad. Sci. USA, vol. 118, 2021, e2021299118), a method that combines features of proper orthogonal decomposition and wavelet analysis in order to extract energetic and spatially localized structures from data. We apply DDWD to streamwise velocity signals measured separately via a thermal anemometer at 40 wall-normal positions. The resulting localized velocity structures, which we interpret as being reflective of underlying eddies, are self-similar across streamwise extents of 40 wall units to one pipe radius, and across wall-normal positions from $y^+=350$ to $y/R=1$ . Notably, the structures are similar in shape to Meyer wavelets. Projections of the data onto the DDWD wavelet subspaces are found to be self-similar as well, but in Fourier space; the bounds of self-similarity are the same as before, except streamwise self-similarity starts at a larger length scale of $450$ wall units. The evidence of self-similarity provided in this study lends further support to Townsend's attached eddy hypothesis, although we note that the self-similar structures are detected beyond the log layer and extend to large length scales.

Efficient ground motion conditional simulation method for nonstationary multivariate processes based on Kriging method and orthogonal discrete wavelet transform

Conditional ground motion simulation methods preserve more physical features of actual ground motions than unconditional methods by including actual earthquake records. This study developed a conditional multivariate nonstationary process simulation method based on the combination of the Kriging method and the orthogonal discrete wavelet transform (DWT). The Kriging method is used to ensure the spectral coherences between simulations as prescribed and is extended to nonstationary random processes by applying it to the average power spectral density (APSD) of ground motions. The ground motions' DWT wavelet coefficients are assumed to be uniformly time-modulated stationary processes whose time-modulating functions are the envelopes of the seed record's wavelet coefficients. The APSD and the envelopes together outline the energy distribution of the random field in both the time and frequency domain features. The power spectral densities of the stationary random processes' DWT coefficients are derived and used to estimate the APSD of the ground motions' DWT coefficients. Approaches to realizing uniformly time-modulated stationary processes with prescribed APSDs and envelope functions are developed. Monte Carlo simulations were conducted to verify the new method's effectiveness. Results show that both the target APSD and coherences can be well approximated, but precise approximation cannot always be realized in the high-frequency range. The new approach possesses a simple structure, involves simple algorithms, and applies to time-independent spectral coherence models, making it an efficient method compared with existing methods.

Misalignment-Related Defect Detection using Discrete Wavelet Transform

Induction motors are most commonly used in many industries, including petrochemicals, oil, and steel. A single failure in any of the induction motor's components or sub-components can result in a plant shutdown. The plant will suffer significant financial losses as a result. It is crucial to diagnose different types of faults in induction motors. Various condition monitoring techniques diagnose faults in induction motors in the early stages. Vibration analysis is most commonly used among different condition monitoring techniques due to its higher accuracy than other methods. Vibration analysis is used to detect various types of faults in induction motors. The acceleration vibration data corresponding to multiple types of defects are gathered from publicly available web resources. The primary objective of this research work is to explore the severity of horizontal and vertical misalignment defects utilizing a signal processing approach. To achieve this objective, Discrete Wavelet Transform (DWT) is used to detect abnormal behavior of the induction motor. The Daubechies-4(db4) wavelet is chosen as a mother wavelet. As Daubechies wavelet is an orthogonal wavelet, the percentage energy in all decomposed sub-band will equal the original energy of the signal. The energy level of sub-bands is compared with the healthy condition of the motor to detect significant changes in motor fault.

Wavelet analysis of supersonic shock-boundary-layer interaction

We present a wavelet analysis of supersonic shock-boundary-layer interaction. We have used direct numerical simulation data for supersonic flow over a compression ramp and performed orthogonal anisotropic wavelets. The wavelet-based method of extracting coherent structures is applied to the flow vorticity field, decomposed into coherent and incoherent contributions using thresholding of the wavelet coefficients. The statistics of the coherent part of vorticity are close to the statistics of the total field. The study aims to improve our understanding of the shock-boundary-layer interaction, the role of vorticity, and the relationship between the flow's coherent and incoherent vorticity components with the near-wall sound. Our analysis shows a substantial correlation between the incoherent part of vorticity components and wall-pressure fluctuations.

Hermite Wavelet Method for Nonlinear Fractional Differential Equations

Nonlinear fractional differential equations (FDEs) constitute the basis for many dynamical systems in various areas of engineering and applied science. Obtaining the numerical solutions to those nonlinear FDEs has quickly gained importance for the purposes of accurate modelling and fast prototyping among many others in recent years. In this study, we use Hermite wavelets to solve nonlinear FDEs. To this end, utilizing Hermite wavelets and block-pulse functions (BPF) for function approximation, we first derive the operational matrices for the fractional integration. The novel contribution provided by this method involves combining the orthogonal Hermite wavelets with their corresponding operational matrices of integrations to obtain sparser conversion matrices. Sparser conversion matrices require less computational load, and also converge rapidly. Using the generated approximate matrices, the original nonlinear FDE is converted into an algebraic equation in vector-matrix form. The obtained algebraic equation is then solved using the collocation points. The proposed method is used to find a number of nonlinear FDE solutions. Numerical results for several resolutions and comparisons are provided to demonstrate the value of the method. The convergence analysis is also provided for the proposed method.