Dyadic Bivariate Fourier Multipliers for Multi-Wavelets in L^2(R^2)

The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation(where A is any expansive matrix with integer entries and|det A|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium(1998) and Z. Y. Li, et al.(2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L~2(R~2). In this paper, we choose 2I2=(~2~0)as the dilation matrix and consider the 2 I2-dilation orthogonal multivariate waveletΨ = {ψ, ψ, ψ},(which is called a dyadic bivariate wavelet) multipliers. We call the3 × 3 matrix-valued function A(s) = [ f(s)], where fi, jare measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)( ψ(s), ψ(s), ψ(s)) ~T=( g(s), g(s), g(s))~ T is a dyadic bivariate wavelet whenever(ψ, ψ, ψ) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L.Shi(2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising.

基于Multi-Agent的水电站变压器故障诊断系统

为了精准、快速完成水电站变压器的故障诊断,设计基于Multi-Agent的水电站变压器故障诊断系统。变压器状态监控agent将检测到的变压器故障信息发送给系统管理agent,系统管理agent通过通信agent将变压器故障信息发送给变压器故障诊断agent,变压器故障诊断agent利用小波变换方法提取变压器故障特征,并将其作为IFOA-SVM模型输入,完成变压器故障分类后,获取变压器故障诊断结果,该结果通过通信agent显示给用户。实验表明,该系统可有效诊断变压器故障诊断,诊断成功率受系统故障信息丢失率的影响较小,诊断耗时、耗能小,并具有较高故障诊断成功率。

Strategies for multi-step-ahead available parking spaces forecasting based on wavelet transform

A new methodology for multi-step-ahead forecasting was proposed herein which combined the wavelet transform(WT), artificial neural network(ANN) and forecasting strategies based on the changing characteristics of available parking spaces(APS). First, several APS time series were decomposed and reconstituted by the wavelet transform. Then, using an artificial neural network, the following five strategies for multi-step-ahead time series forecasting were used to forecast the reconstructed time series: recursive strategy, direct strategy, multi-input multi-output(MIMO) strategy, DIRMO strategy(a combination of the direct and MIMO strategies), and newly proposed recursive multi-input multi-output(RECMO) strategy which is a combination of the recursive and MIMO strategies. Finally, integrating the predicted results with the reconstructed time series produced the final forecasted available parking spaces. Three findings appear to be consistently supported by the experimental results. First, applying the wavelet transform to multi-step ahead available parking spaces forecasting can effectively improve the forecasting accuracy. Second, the forecasting resulted from the DIRMO and RECMO strategies is more accurate than that of the other strategies. Finally, the RECMO strategy requires less model training time than the DIRMO strategy and consumes the least amount of training time among five forecasting strategies.

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.

Wavelet Packet Domain LMS Based Multi-User Detection

An improved wavelet packet domain least mean square （IWPD-LMS） based adaptive muhiuser detection algorithm is proposed. The algorithm employs the wavelet packet transform to rewhiten the input data, and chooses the best wavelet packet basis according to a novel convergence contribution function rather than the conventional Shannon entropy. The theoretic analyses show that the inadequacy of the eigenvalue spread of the tap-input correlation matrix is ameliorated, thus the convergence performance is improved greatly. The simulation result of convergence performance and bit error rate（BER） performance as a function of the signal power to noise power ratio（SNR） are presented finally to prove the validity of the proposed algorithm.

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.

Power Quality Disturbance Classification Method Based on Wavelet Transform and SVM Multi-class Algorithms

The accurate identification and classification of various power quality disturbances are keys to ensuring high-quality electrical energy. In this study, the statistical characteristics of the disturbance signal of wavelet transform coefficients and wavelet transform energy distribution constitute feature vectors. These vectors are then trained and tested using SVM multi-class algorithms. Experimental results demonstrate that the SVM multi-class algorithms, which use the Gaussian radial basis function, exponential radial basis function, and hyperbolic tangent function as basis functions, are suitable methods for power quality disturbance classification.

Weighted Self-Adaptive Threshold Wavelets for Interpolation Point Selection Used in Interconnect MOR

As process technology development,model order reduction( MOR) has been regarded as a useful tool in analysis of on-chip interconnects. We propose a weighted self-adaptive threshold wavelet interpolation MOR method on account of Krylov subspace techniques. The interpolation points are selected by Haar wavelet using weighted self-adaptive threshold methods dynamically. Through the analyses of different types of circuits in very large scale integration( VLSI),the results show that the method proposed in this paper can be more accurate and efficient than Krylov subspace method of multi-shift expansion point using Haar wavelet that are no weighted self-adaptive threshold application in interest frequency range,and more accurate than Krylov subspace method of multi-shift expansion point based on the uniform interpolation point.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Multi-symplectic wavelet splitting method for the strongly coupled Schrodinger system

We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic wavelet collocation method and the symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.

Asymmetric Mean Annual Temperature Wavelets Surface Air Layer of Berlin for 1701-2021

The regularities of the dynamics of the average annual temperature of Ber­lin from 1701 to 2021 are revealed.A total of 65 wavelets were received.The temperature has a high quantum certainty,and the change in the aver­age annual temperature of Berlin was identified by a model that contains only two components for prediction.The basis of the forecast at 320 years makes it possible to look into the future until the year 2340.The forecast confirms the conclusions made in the CMIP5 report on global warming.With an increase in the number of components in the model up to five,the forecast is possible only until 2060.Therefore,the model with only two components is workable.The trend is characterized by a modified Man­delbrot equation showing exponential growth with a high growth rate of 1.47421.The wave equation also has an amplitude in the form of the Man­delbrot law(in mathematics,the Laplace law,in biology,the Zipf-Pearl law,in econometrics,the Pareto law),when the exponential growth activity is equal to 1.For 1701,the period of oscillation was 2×60.33333≈120.7 years.By 2021,the period decreased and became equal to 87.6 years.The trend is such that by 2340 the period of oscillation will decrease to 30.2 years.Such an increase in fluctuations indicates an imbalance in climate disturbances in temperature in Berlin.For Berlin,the last three years are characterized by sharp decreases in the average annual temperature from 11.8℃ to 10.5℃,i.e.by 12.4% in 2021.Therefore,the forecast is still unstable,as a further decrease in the average annual temperature of Berlin in the near future may change the picture of the forecast.

ICI elimination of M-band wavelet multi-carrier modulation system

To solve the inter carrier interference （ICI） elimination problem of an M-band wavelet multi-carrier modulation system, this paper analyzes the principle of the ICI caused by the Doppler frequency shift and its mathematical expression based on the M-band wavelet multi-carrier modulation system model. Through the analysis of the mathematical expression and combining with the perfect reconstruction conditions of the filter banks, we propose the design conditions of an M-band filter to reduce and eliminate the ICI. The impulse response model of the filter design conditions and an iterative algorithm is also established. The simulation results show that the proposed ICI reduction and elimination methods can effectively improve the system performance.

Quantum Biophysics of the Atmosphere:Asymmetric Wavelets of the Average Annual Air Temperature of Irkutsk for 1820-2019

The regularities of the dynamics of the average annual temperature of Irkutsk from 1820 to 2019 were revealed.It is proposed to use the sum of temperatures.However,this indicator requires the continuity of the dynamic series,so for Irkutsk the sum of temperatures could be accepted only from 1873.The first three terms of the general wavelet model gave a very high correlation coefficient of 0.9996.The second indicator is a moving average,calculated as the ratio of the sum of temperatures to the current time.Here the first three wavelets gave a correlation coefficient of 0.9962.In the dynamics of the average annual temperature from 1820 to 2019,86 wavelets were obtained,of which 47 affect the future.The temperature has a high quantum certainty,and the change in the average annual temperature of Irkutsk is obtained up to a measurement error of 0.05℃,and the identification process occurs as a full wavelet analysis.The basis of the forecast in 200 years makes it possible to replace the non-linear two-term trend with an oscillatory perturbation.With an increase in the number of terms in the model,the ordinate of the average annual temperature increases:for three terms,the temperature interval is from-2.95℃ to 2.61℃;for 12 members from -4.06℃ to 4.02°C;for the forecast for 47 members for 2020-2220,from -4.62℃ to 4.40°C.

Wavelet Transform for Image Compression Using Multi-Resolution Analytics: Application to Wireless Sensors Data

The aggregation of data in recent years has been expanding at an exponential rate. There are various data generating sources that are responsible for such a tremendous data growth rate. Some of the data origins include data from the various social media, footages from video cameras, wireless and wired sensor network measurements, data from the stock markets and other financial transaction data, supermarket transaction data and so on. The aforementioned data may be high dimensional and big in Volume, Value, Velocity, Variety, and Veracity. Hence one of the crucial challenges is the storage, processing and extraction of relevant information from the data. In the special case of image data, the technique of image compressions may be employed in reducing the dimension and volume of the data to ensure it is convenient for processing and analysis. In this work, we examine a proof-of-concept multiresolution analytics that uses wavelet transforms, that is one popular mathematical and analytical framework employed in signal processing and representations, and we study its applications to the area of compressing image data in wireless sensor networks. The proposed approach consists of the applications of wavelet transforms, threshold detections, quantization data encoding and ultimately apply the inverse transforms. The work specifically focuses on multi-resolution analysis with wavelet transforms by comparing 3 wavelets at the 5 decomposition levels. Simulation results are provided to demonstrate the effectiveness of the methodology.

Classification of Multi-User Chirp Modulation Signals Using Wavelet Higher-Order-Statistics Features and Artificial Intelligence Techniques

Higher order statistical features have been recently proved to be very efficient in the classification of wideband communications and radar signals with great accuracy. On the other hand, the denoising properties of the wavelet transform make WT an efficient signal processing tool in noisy environments. A novel technique for the classification of multi-user chirp modulation signals is presented in this paper. A combination of the higher order moments and cumulants of the wavelet coefficients as well as the peaks of the bispectrum and its bi-frequencies are proposed as effective features. Different types of artificial intelligence based classifiers and clustering techniques are used to identify the chirp signals of the different users. In particular, neural networks (NN), maximum likelihood (ML), k-nearest neighbor (KNN) and support vector machine (SVMs) classifiers as well as fuzzy c-means (FCM) and fuzzy k-means (FKM) clustering techniques are tested. The Simulation results show that the proposed technique is able to efficiently classify the different chirp signals in additive white Gaussian noise (AWGN) channels with high accuracy. It is shown that the NN classifier outperforms other classifiers. Also, the simulations prove that the classification based on features extracted from wavelet transform results in more accurate results than that using features directly extracted from the chirp signals, especially at low values of signal-to-noise ratios.

基于BA-MKELM的微电网故障识别与定位

提出一种基于贝叶斯算法优化多核极限学习机的微电网故障识别和定位方法。针对极限学习机输入参数和隐含层节点数随机选取导致回归能力不足的问题,引入核函数,将多项式与高斯径向基核函数加权组合构成多核极限学习机建立故障识别与定位模型,并采用贝叶斯算法对多核极限学习机相关参数进行优化,进一步提高模型的逼近能力。为了验证所提模型的故障识别与定位性能,选用极限学习机和多核极限学习机分别建立故障诊断模型进行比较分析。实验结果表明,所提方法能够高性能地识别和定位微电网中任何类型的故障,识别和定位精度更高。

基于遥感多参数和IPSO-WNN的冬小麦单产估测

冬小麦是我国的主要粮食作物之一。为进一步准确地估测冬小麦产量,以陕西省关中平原为研究区域,选取冬小麦主要生育期与水分胁迫和光合作用等密切相关的条件植被温度指数(VTCI)、叶面积指数(LAI)和光合有效辐射吸收比率(FPAR)作为遥感特征参数,采用改进的粒子群算法优化小波神经网络(IPSO-WNN)以改善梯度下降方法易陷入局部最优的缺陷,并构建冬小麦产量估测模型。结果表明,IPSO-WNN模型的决定系数R2为0.66,平均绝对百分比误差(MAPE)为7.59%,相比于BPNN(R2=0.46,MAPE为11.80%)与WNN(R2=0.52,MAPE为9.80%),IPSO-WNN能够进一步提高模型的精度、增强模型的鲁棒性。采用灵敏度分析的方法探究对冬小麦产量影响较大的输入参数,结果发现,抽穗-灌浆期的FPAR对冬小麦产量影响最大,其次拔节期的VTCI、抽穗-灌浆期和乳熟期的LAI以及返青期和拔节期的FPAR对冬小麦产量的影响较大。通过IPSO-WNN输出获取冬小麦综合监测指数I,构建I与统计单产之间的估产模型以估测关中平原冬小麦单产,结果显示,估测单产与统计单产之间的R2为0.63,均方根误差(RMSE)为505.50 kg/hm^(2),相比于前人的研究较好地解决了估产模型存在的“低产高估”的问题,因此,本文基于IPSO-WNN构建的估产模型能够较准确地估测关中平原冬小麦产量。

基于增强多头注意力机制的Optuna-BiGRU测井岩性识别

测井岩性识别是油气勘探开发中至关重要的内容。针对现有算法模型在处理测井曲线数据时,无法有效捕获曲线内部深层关联和深度方向关系、拟合能力较弱、难以准确提取关键特征、噪声干扰以及模型超参数调优过程复杂困难等问题,提出了一种通过Optuna超参数优化双向门循环单元(Optuna-BiGRU)结合增强多头注意力机制(EMHA)的测井岩性识别模型——Optuna-BiGRU-EMHA模型。该模型引入残差机制和层归一化以改进多头注意力机制模块,并结合双向门循环单元(BiGRU)解决了处理测井数据时的问题,同时使用Optuna超参数优化框架和小波包自适应阈值方法分别解决了超参数调优和噪声干扰问题。首先通过交会图分析和敏感性箱线图分析选取自然伽马、深感应电阻率、中子-密度孔隙度、平均中子-密度孔隙度和岩性密度5个特征参数的测井数据,通过小波包自适应阈值方法对数据进行去噪,并将测井数据分割成数据块,然后利用Optuna框架优化BiGRU-EMHA模型超参数,最后通过实验对比K-近邻算法(KNN)、随机森林(RF)、极端梯度提升算法(XGBoost)、长短期记忆(LSTM)神经网络、BiGRU、双向长短期记忆(BiLSTM)神经网络、BiGRU-MHA、Optuna-BiGRU-EMHA等8种模型在测井岩性识别中的精度。结果表明:Optuna-BiGRU-EMHA模型识别准确率达到80%,相对于传统机器学习模型和深度学习模型,综合岩性识别准确率分别提高15.94%~23.14%和3.93%~15.94%,该模型为常规测井岩性识别提供了坚实的理论支持。

Wavelet analysis of pressure fluctuation signals in a gas-solid fluidized bed

It has been shown that much dynamic information is hidden in the pressure fluctuation signals of a gas-solid fluidized bed. Unfortunately, due to the random and capricious nature of this signal, it is hard to realize reliable analysis using traditional signal processing methods such as statistical analysis or spectral analysis, which is done in Fourier domain. Information in different frequency band can be extracted by using wavelet analysis. On the evidence of the composition of the pressure fluctuation signals, energy of low frequency (ELF) is proposed to show the transition of fluidized regimes from bubbling fluidization to turbulent fluidization. Plots are presented to describe the fluidized bed's evolution to help identify the state of different flow regimes and provide a characteristic curve to identify the fluidized status effectively and reliably.

Multi-features Based Approach for Moving Shadow Detection

In the video-based surveillance application, moving shadows can affect the correct localization and detection of moving objects. This paper aims to present a method for shadow detection and suppression used for moving visual object detection. The major novelty of the shadow suppression is the integration of several features including photometric invariant color feature, motion edge feature, and spatial feature etc. By modifying process for false shadow detected, the averaging detection rate of moving object reaches above 90% in the test of Hall-Monitor sequence.