Wavelet Theory Research Articles

Underwater Small Target Classification Using Sparse Multi-View Discriminant Analysis and the Invariant Scattering Transform

Sonar automatic target recognition (ATR) systems suffer from complex acoustic scattering, background clutter, and waveguide effects that are ever-present in the ocean. Traditional signal processing techniques often struggle to distinguish targets when noise and complicated target geometries are introduced. Recent advancements in machine learning and wavelet theory offer promising directions for extracting informative features from sonar return data. This work introduces a feature extraction and dimensionality reduction technique using the invariant scattering transform and Sparse Multi-view Discriminant Analysis for identifying highly informative features in the PONDEX09/PONDEX10 datasets. The extracted features are used to train a support vector machine classifier that achieves an average classification accuracy of 97.3% using six unique targets.

Analysis and prediction of mesoscale eddy kinetic energy variations in the Kuroshio extension

The Kuroshio Extension (KE) region, a crucial area in the Northwest Pacific Ocean, exhibits eddy kinetic energy with various scales of periodicity. Understanding how to extract its characteristic features and analyze and predict their periodic correlations has become vital for studying the regulatory mechanisms of eddy kinetic energy in the KE region. This paper first introduces a mesoscale eddy hybrid identification algorithm based on the flow field vector and the closed flow field. Using this algorithm, we gather mesoscale eddy identification data from the KE region to extract the monthly average series of five typical features of the KE region. Subsequently, wavelet theory is applied to analyze the cycles of these main features, identifying the common cycles of the KE region as the primary focus for analyzing the vorticity kinetic energy. This analysis includes cycle correlations with globally recognized indices, and it predicts these correlations. Further analysis of the main characteristic cycles through wavelet theory reveals that the KE region's eddy kinetic energy is significantly influenced by solar activity over long periods and by the North Pacific ocean-atmosphere interaction over shorter, interannual periods. Finally, this paper introduces a W-LSTM (Wavelet Decomposition based Long Short-term Memory Networks) prediction model based on wavelet decomposition for the KE region, covering January 2023–December 2023. The model demonstrates its effectiveness, achieving a Root Mean Square Error (RMSE) of 0.2530 and a correlation coefficient of 0.8259 between the predicted data and the actual observations.

Novel method to determine bedrock from a single sensor based seismic reflection signal using Haar wavelet transform

The determination of bedrock depth is crucial across various earth sciences and related fields. Geophysical techniques, notably the continuous wavelet transform, are increasingly employed to map subsurface bedrock structures. This method allows the transformation of 1D time domain seismic reflection signals into a 2D image, providing time–frequency representations for feature extraction. Leveraging the advantages of wavelet theory, particularly the Haar wavelet known for its simplicity and compact support, this study utilizes continuous Haar wavelet local maxima lines to enhance bedrock analysis. Seismic reflection data is acquired using an extremely sensitive geophone as a receiver along with a high dynamic range data logger. The Common Midpoint (CMP) approach, coupled with optimized offset distances, is utilized to ensure robust data quality and signal strength. Simple sources, such as a sledgehammer, generate sound waves for data collection prior to borehole drilling, correlating acquired data with lithogeological information. This research emphasizes the significance of adjusting parameters like sampling frequency, choice of wavelet, and optimal offset distances. The methodology employed, involving a single geophone, a one-channel data recorder, and a basic sledgehammer as a sound source, offers an inexpensive, straightforward, and non-invasive approach. The study demonstrates the effectiveness of Haar wavelet local maxima lines in accurately determining bedrock depth, producing results closely aligned with both predicted and actual depths.

A review of wavelet theory and its applications in structural and earthquake engineering

A review of wavelet theory and its applications in structural and earthquake engineering

Development of Seismic Fragility Functions for Reinforced Concrete Buildings Using Damage-Sensitive Features Based on Wavelet Theory

In this study, wavelet-based damage-sensitive features are employed to derive the seismic fragility functions/curves for reinforced concrete moment-resisting frames. Two different wavelet transform functions, namely, Bior3.3 and Morlet mother wavelet families, were applied to absolute acceleration time histories of building frames to extract the wavelet-based and refined wavelet-based damage-sensitive features (i.e., DSF and rDSF). The accuracy of seismic assessments and certainty in predicting structural behavior strongly depend on the specific optimal intensity measures selected, reliability of wavelet-based damage-sensitive features, and some such intensity measures as PGA, PGV, PGD, Sa, and Sdi as the conventionally utilized measures to detect the damage state of a structure. These measures were examined against their statistical properties of efficiency, practicality, proficiency, coefficient of determination, and sufficiency to select the appropriate optimal intensity measures, which were then used to drive the fragility curves disclosing the failure or other damage states of interest. For the purposes of this study, three different concrete moment-resisting frames with four-, eight-, and twelve-story building frames were adopted for implementing the proposed approach. The findings demonstrate that the wavelet-based damage-sensitive features (DSFs/rDSF) simultaneously satisfy all the statistical properties cited above. This is evidenced by the low variance and dispersions observed in the frame damage state predictions by the fragility functions derived from the wavelet-based DSF when compared with those derived from the classical fragility analyses such as spectral acceleration at the first mode period of the structure. A final aspect of the study concerns the superior performance and efficiency of the fragility curves derived by the Bior3.3 wavelet-based DSF over those derived from Morlet wavelet-based DSF.

M-band wavelet network for machine anomaly detection from a frequency perspective

The autoencoder (AE) is widely utilized in deep anomaly detection, but it lacks explainability due to the complexity of nonlinear mapping. One approach to address this issue is incorporating wavelet theory, which shares similarities in decomposition and reconstruction procedures. However, the perfect reconstruction property of wavelet theory conflicts with AE-based anomaly detection. To tackle this problem, we introduce a novel deep anomaly detection method from a frequency perspective. A learnable M-band wavelet network (MWNet) is designed to offer a flexible frequency band structure for signal representation. Subsequently, with the aid of sparsity constraint, MWNet dynamically focuses on key components within each frequency band. A learnable hard threshold function with a threshold maximization constraint is proposed to retain the essential frequency band of normal signals. After training, the MWNet is exclusively capable of well reconstructing normal signals, thereby producing a noticeable reconstruction error difference between normal and abnormal signals. Extensive experiments on both simulated and experimental datasets validate the effectiveness of the proposed method. The corresponding Python codes are available at https://github.com/albertszg/MbandWaveletNet.

Shearlet Transform Applied to a Prostate Cancer Radiomics Analysis on MR Images

For decades, wavelet theory has attracted interest in several fields in dealing with signals. Nowadays, it is acknowledged that it is not very suitable to face aspects of multidimensional data like singularities and this has led to the development of other mathematical tools. A recent application of wavelet theory is in radiomics, an emerging field aiming to improve diagnostic, prognostic and predictive analysis of various cancer types through the analysis of features extracted from medical images. In this paper, for a radiomics study of prostate cancer with magnetic resonance (MR) images, we apply a similar but more sophisticated tool, namely the shearlet transform which, in contrast to the wavelet transform, allows us to examine variations along more orientations. In particular, we conduct a parallel radiomics analysis based on the two different transformations and highlight a better performance (evaluated in terms of statistical measures) in the use of the shearlet transform (in absolute value). The results achieved suggest taking the shearlet transform into consideration for radiomics studies in other contexts.

Research on Energy Hierarchical Management and Optimal Control of Compound Power Electric Vehicle

In response to the challenges posed by the low energy utilization of single-power pure electric vehicles and the limited lifespan of power batteries, this study focuses on the development of a compound power system. This study constructs a composite power system, analyzes the coupling characteristics of multiple systems, and investigates the energy management and optimal control mechanisms. Firstly, a power transmission scheme is designed for a hybrid electric vehicle. Then, a multi-state model is established to assess the electric vehicle’s performance under complex working conditions and explore how these conditions impact system coupling. Next, load power is redistributed using the Haar wavelet theory. The super capacitor is employed to stabilize chaotic and transient components in the required power, with low-frequency components serving as input variables for the controller. Further, power distribution is determined through the application of fuzzy logic theory. Input parameters include the system’s power requirements, power battery status, and super capacitor state of charge. The result is the output of a composite power supply distribution factor. To fully exploit the composite power supply’s potential and optimize the overall system performance, a global optimization control strategy using the dynamic programming algorithm is explored. The optimization objective is to minimize power loss within the composite power system, and the optimal control is calculated through interpolation using the interp function. Finally, a comparative simulation experiment is conducted under UDDS cycle conditions. The results show that the composite power system improved the battery discharge efficiency and reduced the number of discharge cycles and discharge current of the power battery. Under the cyclic working condition of 1369 s, the state of charge of the power battery in the hybrid power system decreases from 0.9 to 0.69, representing a 12.5% increase compared to the single power system. The peak current of the power battery in the hybrid power system decreases by approximately 20 A compared with that in the single power system. Based on dynamic programming optimization, the state of charge of the power battery decreases from 0.9 to 0.724. Compared with that of the single power system, the power consumption of the proposed system increases by 25%, that of the hybrid power fuzzy control system increases by 14.2%, and that of the vehicle decreases by 14.7% after dynamic programming optimization. The multimode energy shunt relationship is solved through efficient and reasonable energy management and optimization strategies. The performance and advantages of the composite energy storage system are fully utilized. This approach provides a new idea for the energy storage scheme of new energy vehicles.

Multi-objective scheduling and optimization for smart energy systems with energy hubs and microgrids

This paper introduces a novel model for optimizing microgrid systems by integrating multi-purpose renewable energy (MEM) and cutting-edge technologies, including electric vehicles (EVs). The proposed MEM demand response programs encompass various energy sources such as wind energy, multi-carrier energy storage technologies, boilers, combined heat and cooling units, EVs, P2G (power-to-gas), and demand response capabilities. The primary objective is to minimize the total operational cost of the microgrid system. A distinctive aspect of the proposed method lies in considering the prices of all energy carriers as unknown variables. Market prices are integrated into the modeling process, incorporating scenarios with reasonable probabilities and taking into account demand-side management programs. Moreover, the model allows for customizable programming of different parts of the multi-energy microgrids, with a focus on maintaining convexity principles for the operating area of each CHP (combined heat and power) unit. To tackle the unique complexity of this optimization problem, a developed blue whale optimization algorithm is proposed. This algorithm builds upon the main whale optimization algorithm (WOA), a promising population-based optimization approach. However, the effectiveness of WOA heavily relies on the careful setting of exploration and exploitation parameters, which may lead to being trapped in local optima. To address this challenge, the paper introduces a self-adaptation modification based on wavelet theory to enhance the WOA's performance. The proposed model and optimization method are thoroughly evaluated through simulation studies for different scenarios, showcasing their efficacy in achieving cost-efficient and sustainable microgrid operation. The combination of MEM and emerging technologies like EVs, along with the improved optimization algorithm, marks a significant contribution to advancing the planning and operation of microgrid systems towards low-cost, reliable, and environmentally-friendly energy solutions.

A novel tool for voltage event characterization based on the Wavelet theory

The actual methods for analyzing the starting point of any event are unable to define correctly this kind of phenomena with enough accuracy. Methods based on RMS calculation often have substantial errors in time and highly depend on the phase of the voltage waveform. In spite of this previous disadvantage, these methods are being used in most of the PQ analyzers. This paper develops a novel method to characterize accurately the parameters that define each event (dips, swells and interruptions), mainly the duration, start and end instant by the calculation of the root mean square value during the disturbance. The wavelet theory will be used in the development of the method

Analysis model of flood spatiotemporal change characteristics based on k-means clustering algorithm

<p>In order to analyze the spatiotemporal change characteristics of regional flood disaster, analyze the main change characteristics and hydrological response of precipitation distribution in Guangxi, and improve the comprehensive utilization efficiency of water resources, this paper introduces the k-means clustering algorithm to design an analysis model of spatiotemporal change characteristics of flood disaster. First of all, obtain the flood data in Guangxi and the observation data of the national meteorological station within 5 km, complete the collection of the basic data of mountain flood disasters. Based on the collected data, an analysis was conducted on the spatial and temporal distribution of flash floods in the Guangxi region. Secondly, the Kriging spatial interpolation method was used to analyze the spatial distribution of precipitation data in Guangxi. The Mann-Kendall trend test was then employed to examine the trend of precipitation-related statistical parameters over time. Additionally, wavelet theory was applied to analyze the time series of annual precipitation and precipitation with different durations in Guangxi. Subsequently, the k-means clustering algorithm was introduced to construct a model for analyzing the spatiotemporal characteristics of flood changes, determining the concentration and duration of precipitation in different years in the region. Finally, analyze the spatiotemporal change characteristics of flood events in different seasons under various indicators, and realize the analysis of flood spatiotemporal change characteristics. The research results indicate that the Frank Copula function fits the best correlation between annual precipitation and temperature, and can better characterize the correlation between the two. The Frank Copula function has the best fitting effect on the correlation between precipitation and temperature in autumn in Guilin, summer in Nanning, and summer and winter in Beihai. In Guangxi Zhuang Autonomous Region, the annual precipitation shows a gradually decreasing trend, especially at R and P stations. In summary, the Frank Copula function can effectively characterize the correlation and trend of precipitation and temperature in different seasons and regions of Guangxi.</p>

Analysis of Electrical Signal Disturbances. A New Strategy.

A joint treatment for signal analysis based in both Fourier and Wavelet theory is presented. Distinguishing from harmonics and transient disturbance components present on an electrical signal, the former part is extracted by means of Fourier methods, while the latter is subjected to multiresolution treatment in order to split disturbance low frequency components with high frequency components. Numerical experiments are performed over a variety of signals with a given harmonic content, which are classified according to the kind of low frequency disturbance (voltage sag, swell and momentary interruption) and high frequency disturbance (oscillatory transient) present. In every case, a good compression rate is achieved and disturbance components in an efficient way are extracted. Finally, characteristic plots of the low frequency disturbances are obtained for classification purposes.

Mid-frequency vibration analysis of built-up structures using WFE-SEA method

The idea of classifying built-up structures into hybrid deterministic-statistical subsystems is formed as a framework to deal with the dynamical response in the mid-frequency region. This paper explores the potential combination of the wavelet finite element method and SEA, resulting in the hybrid WFE-SEA method, to achieve a solution with reduced computational burdens and increased accuracy. The development of the hybrid WFE-SEA method commences with the formulation of a 3-D B-spline wavelet theory, utilizing the semi-orthogonality of B-spline wavelet. A multi-resolution analysis of this theory facilitates the creation of a 3-D B-spline wavelet on an interval element model, incorporating nodes distributed on both the surface and inside of the hexahedron. Subsequently, the 3-D B-spline wavelet on an interval element is integrated with SEA theory, producing in a hybrid WFE-SEA framework suitable for examining dynamic problems of built-up structures. The energy-balance equation is derived by coupling the 3-D B-spline wavelet theory with diffuse field reciprocity relation to estimate the mid-frequency dynamic response. Furthermore, the validity of the proposed approach is rigorously assessed by comparing it against detailed mid-frequency analyses, including the hybrid FE-SEA method and the hybrid ES-FE-SEA method. The conclusion highlights the substantial agreement of the present hybrid method with other approaches, achieved at a small cost in terms of degrees of freedom.

Wavelet sets, scaling sets and generalized scaling sets on Vilenkin group

Wavelet sets provide a range of wavelets that can be analyzed with ease. The constructions of wavelet sets and scaling sets in different settings are studied in several papers in the literature. Wavelet sets provide a good source of examples and counterexamples in wavelet theory. In this paper we have studied properties of (multi)wavelet sets and associated wavelets for Vilenkin group. Further, results related to scaling sets and generalized scaling sets are given along with some characterizations.

High-order adaptive multiresolution wavelet upwind schemes for hyperbolic conservation laws

We present a novel system of high-order adaptive multiresolution wavelet collocation upwind schemes, implemented in a meshfree framework, for solving hyperbolic conservation laws. Our approach constructs asymmetrical wavelet bases with interpolation properties to achieve the upwind property and address nonlinearities in hyperbolic problems. An adaptive algorithm based on multiresolution analysis in wavelet theory is designed to capture moving shock waves and identify new localized steep regions. To suppress the Gibbs phenomenon, we propose an integration average reconstruction method based on the Lebesgue differentiation theorem. These numerical techniques enable the wavelet collocation upwind scheme to provide a general framework for devising satisfactory adaptive wavelet upwind methods with high-order accuracy. We perform several benchmark tests for 1D hyperbolic problems to verify the accuracy and efficiency of the proposed wavelet schemes. Notably, our wavelet collocation upwind schemes successfully solve the two interacting blast waves problem when discretizing the spatial derivatives in the physical space directly. This is in contrast to classical high-order schemes that usually involve transforming variables back and forth between physical and characteristic spaces with many local projections. Our results indicate the robustness, stability, and efficiency of our proposed schemes for strong shock wave interaction problems.

Modeling the total outflow of reservoirs using Wavelet-developed approaches: a case study of the Mahabad Dam reservoir, Iran

Abstract Lack of water reserves in artificial reservoirs poses serious challenges in meeting various human requirements, especially during periods of water scarcity. In the current research, the Total Outflow (TO) of the Mahabad Dam reservoir has been estimated under six scenarios including the Monthly Cumulative Rainfall (MCR), Snow Water Equivalent (SWE), Stream Flow (SF), Mean Temperature (T), Pan Evaporation (Ep), Sediment Flushing Gate Outlet (SFGO), Penstock Outflow (PO), Evaporation Losses (EL), Cumulative Non-Scheduled Discharge (CNSD), Live Storage Volume (LSV), Water Surface Area (WSA), Monthly Water Level (MWL), Total Allocated Water (TAW), and Generated Power (GP) variables for the 2001–2021 period. Estimation of TO is accomplished via individual and wavelet-developed (W-developed) data-mining approaches, including Artificial Neural Networks (ANNs), wavelet-ANNs (WANNs), adaptive neuro-fuzzy inference system (ANFIS), wavelet-ANFIS (WANFIS), Gene Expression Programming (GEP), and wavelet-GEP (WGEP). The obtained values of RMSE for WGEP1–WGEP6 models account for 5.917, 2.319, 4.289, 8.329, 10.713, and 9.789 million cubic meters (MCM), respectively, based on the following scenarios: reservoir inlet elements, reservoir outlet elements, consumption, storage characteristic, climate, and energy. This research revealed that combining the wavelet theory (WT) with individual models can be a powerful method to improve the modeling performance in the TO estimation.

Analysis of non-sinusoidal non-stationary modes of electric networks based on the wavelet transformation

Subject of research: methods for calculating and analyzing non-sinusoidal non-stationary modes of electrical networks.
 Purpose of research: development of a method for calculating active and reactive power, as well as the power of distortion of non-sinusoidal modes of electrical networks based on the theory of wavelet transform.
 Object of research: electrical networks and power supply systems containing a non-linear load, which is the cause of non-sinusoidal modes.
 Methods of research: packet wavelet transform of currents and voltages; theory of electrical circuits.
 Main results of research: The paper proposes the idea of using the wavelet transform for frequency decomposition of currents and voltages of non-sinusoidal non-stationary modes of electrical networks. Based on the wavelet coefficients, it is proposed to calculate the active, reactive power and distortion power of non-sinusoidal modes.

Effectiveness of Wavelet Denoising on Secondary Ion Mass Spectrometry Signals

Wavelet theory has already achieved huge success. For Secondary Ions Mass Spectrometry (SIMS) signals, denoising the secondary signal, which is altered by the measurement, is considered that an essential step prior to applying such a signal processing technique that aims enhance the SIMS signals.The most efficient and widely used wavelet denoising method is based on wavelet coefficient thresholding. This process involves three important steps; wavelet decomposition: the input signals are decomposed into wavelet coefficients, thresholding: the wavelet coefficients are modified according to a threshold, and reconstruction: the modified coefficients are used in an inverse transform to obtain the noise-free-signal. Several researchers have used thresholding wavelet denoising techniques.
 The choice of wavelet type and the level of resolution can have a significant influence; it is important to note that the choice of resolution level depends on the type of signal we are dealing with, the nature of the present noise, and our specific goals for the denoised signal. It is generally recommended to test different resolution levels and evaluate their impact on the quality of the denoised signal before making a final decision. Moreover, the results obtained in wavelet denoising can be significantly influenced by the selection of wavelet types. The chosen wavelet type plays a crucial role in the extraction of signal details. Indeed, the effectiveness of denoising the MD6 sample has been demonstrated by the results obtained with sym4, db8, Haar and coif5 wavelets? These wavelets have effectively reduced noise while preserving crucial signal information, leading to an enhancement in the quality of the denoised signal.

Wavelets and stochastic theory: Past and future

In the paper, authors report on the interdisciplinary and extremely complex link between wavelets and stochastic processes. An insight into the history of wavelets has been provided presenting the fundamental conception of wavelets, as well as wavelet theory that emerged from stochastic processes. The multiresolution analysis corresponds to the Kolmogorov system which is a regular stationary stochastic process. It presents a significant link to the measurement problem in terms of positional notation which the wavelet domain hidden Markov model should be derived from. The optimal representation arises to be an issue requiring further elaboration extended to the general measurement and wavelet frames.

Super-resolution reconstruction method of ground penetrating radar signals based on wavelet theory and its application in reverse time migration

The finite difference time domain (FDTD) method was used to solve the Maxwell’s equation to obtain the reverse time migration (RTM) of ground penetrating radar (GPR) signals, namely, the FDTD-RTM. In order to ensure that the correct numerical solution of iterative calculation was achieved, it was necessary to obtain high-resolution signals, which greatly limits the applicability of FDTD-RTM in engineering. Based on the characteristics of wavelet multi-resolution analysis, this study proposed a super-resolution signal reconstruction method to improve signal resolution, with the view to completely solving the problem of FDTD-RTM limitation caused by insufficient signal sampling using GPR. The results of electromagnetic simulation showed that the signals reconstructed by the above method were highly similar to the signals sampled with the same resolution. On this basis, reverse time migration electromagnetic simulation and physical model tests were designed. The results of both experiments showed that the under-sampled GPR signals could achieve FDTD-RTM following super-resolution reconstruction, and that the migration imaging results of the target were basically consistent with the design scheme. The signal super-resolution reconstruction method based on the wavelet theory was thus shown to successfully achieve the overall application of FDTD-RTM in GPR signal analysis.