Model Order Reduction Methods for Discrete Systems via Discrete Pulse Orthogonal Functions

This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.

Walsh Hadamard Transform Based Transceiver Design for SC-FDMA with Discrete Wavelet Transform

This article proposes a new transceiver design for Single carrier frequency division multiple access(SCFDMA)system based on discrete wavelet transform(DWT). SCFDMA offers almost same structure as Orthogonal frequency division multiple access(OFDMA)with extra advantage of low Peak to Average Power Ratio(PAPR). Moreover,this article also suggests the application of Walsh Hadamard transform(WHT)for linear precoding(LP)to improve the PAPR performance of the system. Supremacy of the proposed transceiver over conventional Fast Fourier transform(FFT)based SCFDMA is shown through simulated results in terms of PAPR,spectral efficiency(SE)and bit error rate(BER).

A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.

A CLASS OF COMPACTLY SUPPORTED ORTHOGONAL SYMMETRIC COMPLEX WAVELETS WITH DILATION FACTOR 3

When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex that illustrate the corresponding results. wavelets. In the end, there are several examples

Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets

The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.

CONSTRUCTION OF WAVELET BASES WITH VANISHING MOVEMENT

A kind of mother wavelet with good properties is constructed for any N greater than or equal to 2, which is differentiable for N times, converges to Zero at the order of O( I t I-N)( t --> infinity) and has N - 2 order of vanishing movement and some property of symmetry meanwhile. A computation example for N = 4 is also given.

Characterizations of Orthogonal Vector-valued Multivariate Wavelet Packets

In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.

A Novel Radial Basis Function Neural Network Approach for ECG Signal Classification

ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental aim of this work is tofind the R-R interval.To analyze the blockage,different approaches are implemented,which make the computation as facile with high accuracy.The information are recovered from the MIT-BIH dataset.The retrieved data contain normal and pathological ECG signals.To obtain a noiseless signal,Gaborfilter is employed and to compute the amplitude of the signal,DCT-DOST(Discrete cosine based Discrete orthogonal stock well transform)is implemented.The amplitude is computed to detect the cardiac abnormality.The R peak of the underlying ECG signal is noted and the segment length of the ECG cycle is identified.The Genetic algorithm(GA)retrieves the primary highlights and the classifier integrates the data with the chosen attributes to optimize the identification.In addition,the GA helps in performing hereditary calculations to reduce the problem of multi-target enhancement.Finally,the RBFNN(Radial basis function neural network)is applied,which diminishes the local minima present in the signal.It shows enhancement in characterizing the ordinary and anomalous ECG signals.

A Wavelet Transform Method to Detect P and S-Phases in Three Component Seismic Data

The discrete time wavelet transform has been used to develop software that detects seismic P and S-phases. The detection algorithm is based on the enhanced amplitude and polarization information provided by the wavelet transform coefficients of the raw seismic data. The algorithm detects phases, determines arrival times and indicates the seismic event direction from three component seismic data that represents the ground displacement in three orthogonal directions. The essential concept is that strong features of the seismic signal are present in the wavelet coefficients across several scales of time and direction. The P-phase is detected by generating a function using polarization information while S-phase is detected by generating a function based on the transverse to radial amplitude ratio. These functions are shown to be very effective metrics in detecting P and S-phases and for determining their arrival times for low signal-to-noise arrivals. Results are compared with arrival times obtained by a human analyst as well as with a standard STA/LTA algorithm from local and regional earthquakes and found to be consistent.

不同容量下并网模式交流微电网短路故障早期检测与区域定位

随着分布式电源(distributed generation,DG)的容量变化,微电网原有的供电结构发生改变,使得潮流大小、方向和功率结构发生变化,对快速检测和定位微电网中的短路故障区域提出了挑战。在MATLAB/Simulink中搭建低压交流微电网模型;通过高尺度小波能量谱算法对微电网与大电网公共连接点(point of common coupling,PCC)处检测到的电流进行分解,提取适应不同容量情况的短路故障特征值,实现了不同容量下微电网短路故障的早期检测;利用小波能量谱特征结合基于正交最小二乘法(orthogonal least square,OLS)的径向基函数(radial basis function,RBF)神经网络算法提出一种适用于不同容量微电网的短路故障区域定位方法,并进行仿真验证;在此基础上设计并网模式微电网短路故障保护硬件系统,并进行实验验证。结果表明,所设计的保护系统能够快速、准确地同时实现并网模式下交流微电网短路故障的早期检测与区域定位。

基于改进切尾均值的矿井图像去噪算法

现有矿井图像去噪算法对于复杂噪声的去除效果有限,且处理速度不能满足实时监控需求。针对该问题,提出一种基于改进切尾均值的矿井图像去噪算法。首先,采用切尾均值滤波器对图像噪声进行初步滤除,同时引入二次检验机制处理残留的噪声点,通过引入离散系数提升算法对不同像素的区分能力,增强去噪性能;其次,采用基于极值数量的分类处理及再次检验机制,有效减少残留噪声问题;然后,在小波函数中引入新的控制变量优化软阈值函数和硬阈值函数,构建双阈值函数,结合Radon变换增强对线性特征的处理,增强对矿井图像的检测能力;最后,采用均方误差(MSE)与峰值信噪比(PSNR)进行图像质量评价。实验结果表明:相较于切尾均值算法、硬阈值算法、软阈值算法,基于改进切尾均值的矿井图像去噪算法处理的图像的MSE增长相对缓慢,MSE最小,图像去噪效果最好;引入离散系数后,去噪图像的MSE相较于引入前低300 dB左右,PSNR相较于引入前高20 dB左右,引入离散系数能有效减少噪声点对算法的影响;相较于卡尔曼遗传优化算法、变换域图像去噪算法、交叉分支卷积去噪网络,基于改进切尾均值的矿井图像去噪算法处理的图像MSE分别降低了27,21,13 dB,PSNR分别提升了8,6,3 dB,去噪耗时分别缩短了0.20,0.16,0.14 s。

斯里兰卡极端降水时空演变特征及趋势预测

斯里兰卡是中国“一带一路”倡议的重要节点国家,极端降水对当地社会经济威胁较大,极易引发灾害。选取当地10个气象站2008—2020年的逐日降水资料,基于RClimDex模型计算斯里兰卡6个极端降水指标,利用经验正交函数分析、Morlet小波分析和重标极差法(R/S分析)等,分析极端降水事件的时空演变特征。结果表明:极端降水指数在时间分布上,除持续干旱指数(CDD)呈减少趋势外,其他各指数均为上升趋势;极端降水指数空间差异表现为北部沿海平原地带的极端降水强度高于南部沿海平原,拉特纳普勒市以西地区为斯里兰卡降水事件的多发区;极端降水指数周期性明显,绝大多数极端降水指数以6~7 a为第一主周期。R/S分析表明当地极端降水事件未来持续可能性较大。研究成果可为斯里兰卡极端气候预测、生态环境保护、防灾减灾工作等提供决策支持。

青海省多年地表感热通量的时空变化特征

选取青海省35个气象站观测数据,基于CHEN-WENG感热系数方案,计算了1980—2017年青海省地表感热通量。利用小波分析、Mann-Kendall突变检验和经验正交函数法(Empirical Orthogonal Function,EOF),对感热通量的时空变化特征及其影响因子进行分析。结果表明:(1)1980年以来,青海省全年和各季节感热通量总体上均呈上升趋势,并具有28 a的主周期和约18 a的副周期,冬季的周期变化较为复杂;(2)全年和各季节感热通量与地气温差存在显著相关性,2004—2017年受地气温差增大的影响上升;(3)全年、春季和秋季感热通量与风速存在显著相关性,1980—2004年受风速减小的影响感热通量下降;(4)夏季降水与感热通量呈显著负相关;(5)从空间上看,全年以及春季感热通量呈现出显著的东西分异,秋、冬季表现出一定程度的南北分异。

基于相对湿润指数的浙江省茶叶气象干旱特征分析

【目的】研究浙江省茶叶气象干旱的演变规律,为茶叶安全生产优化布局提供科学依据。【方法】利用浙江省68个地面气象观测站50 a(1971—2020年)的逐日气温、降水量、日照时数等数据,基于相对湿润指数、正交经验函数和小波分析法等分析浙江省茶叶气象干旱的时空分布规律。【结果】浙江省茶叶生产夏季干旱的强度和发生频率高于秋季,且均呈现西高东低的分布,中西部尤其金衢盆地的干旱强度和频率为全省最强,浙北地区次之,沿海地区最小。茶叶夏季干旱站次比呈逐年下降的趋势,秋季则呈现先升后降的趋势,2000年以后夏秋两季出现极端大范围茶叶气象干旱的年份增多。茶叶夏季和秋季干旱强度的正交经验函数第一模态表现为全省变化一致性,第二模态中沿海局部地区和内陆呈反相位变化,夏秋两季干旱强度的主模态时间序列分别存在2-6、2-4、6-10 a的振荡周期。【结论】浙江省在夏季和秋季出现茶叶气象干旱的频率在下降,但出现极端干旱的概率在增加,应重点加强茶叶主产区干旱监测预警能力建设,提升防旱抗旱能力。

1961—2020年黄河源区降水时空变化特征研究

基于1961—2020年黄河源区16个雨量站点的逐日降水资料,应用线性趋势法、Mann-Kendall(MK)检验、滑动t检验、Pettitt检验、小波分析、经验正交分解(EOF)方法对黄河源区年降水、季节降水、汛期降水的变化趋势及时空分布特征进行分析。结果表明:(1)黄河源区年降水以10.0 mm/10 a的趋势显著增加;除冬季呈不明显的减少趋势外,春季、夏季、秋季和汛期降水同样呈增加趋势。(2)黄河源区降水除春季无明显突变外,全年、夏季、秋季、冬季和汛期的对应突变年份分别为2015年、1998年、2018年、2016年和2019年。(3)黄河源区年降水存在3~7 a、6~12 a、9~13 a和16~24 a的变化周期,第一、第二主周期为19 a和11 a,两种主周期都经历了3次“丰-枯”变化;年降水存在2种模态,4种降水表现类型,2种模态的年份数为35 a和13 a。研究成果可为黄河源区防汛抗旱及上游水库群水资源调度提供参考。

基于非正交离散变换的物理不可克隆函数可靠性提升算法

为了解决物理不可克隆函数(PUF)受外部环境和自身老化因素影响存在响应不稳定的问题,提出基于非正交离散(NOD)变换的PUF可靠性提升算法。首先,设计了一种重排序混淆器,将随机种子向量及PUF响应经重排序混淆器迭代处理后得到非正交混淆矩阵与混淆响应矩阵的内积,据此建立NOD谱,有效缓解了因PUF本身均匀性不足而产生偏向性密钥的问题;随后,通过分区编解码策略,赋予NOD谱一定的波动容错能力,将不稳定响应的影响限制在有限的范围,从而显著提高最终响应的可靠性。所提算法相较于传统基于纠错码的方法,需要的帮助数据更少。基于SRAM-XMC数据集进行实验,所提算法在对2949120组64位响应进行101次重复实验过程中平均可靠性达到99.97%,唯一性达到49.92%,均匀性达到50.61%。实验结果表明,所提算法能够在保证PUF响应均匀性与唯一性的同时有效提高可靠性。

光谱预处理小波基函数的选择对结合FIBS技术和机器学习的铝合金识别精确度影响研究

随着经济不断发展,工业建筑领域产生了大量的废弃铝合金材料,对废弃铝合金材料分类回收可以提升废弃资源的利用效率,缓解能源紧张。选取了工业领域常用的五种型号的铝合金,开展了等离子体丝诱导击穿光谱(FIBS)光谱预处理小波变换基函数对铝合金分类识别精度的影响的研究。分别采用bior2.2、bior2.4和bior2.6正交小波基函数对铝合金的FIBS光谱进行预处理,结合线性判别分析(LDA)、网格搜索优化的支持向量机(GSSVM)和反向传播神经网络(BPNN)实现了铝合金型号的快速分类识别。结果表明bior2.2、bior2.4和bior2.6正交小波基函数结合LDA-GSSVM实现铝合金型号的平均识别准确率为90%、100%和76.67%,结合LDA-BPNN实现铝合金型号的平均识别准确率为96.67%、100%和90%,因此选择合适的正交小波基函数对FIBS光谱预处理,对于提高铝合金型号识别准确率有较大作用。

基于深度学习的机载遥感通信系统自适应光学波前校正技术

自适应光学波前校正过程易受复杂背景、光照强度、噪声信号等问题的干扰,导致校正的效果降低。为了解决上述问题,提出基于深度学习的机载遥感通信系统自适应光学波前校正技术。通过相位差法实现自适应光学波前的探测,采用小波变换算法剔除其中的噪声,避免噪声对校正过程产生干扰。根据深度神经网络的预测与自学习能力构建动力学模型网络、策略网络与决策单元,通过与校正阈值的对比,完成机载遥感通信系统自适应光学波前的校正。实验结果表明,所提方法的斯特列尔比接近1,且校正时间短、校正效果好。

基于索周法的辽宁省干旱周期演变特征研究

为探究辽宁省不同气候特征区域年、季干旱周期性规律,基于辽宁省22个国家地面气象观测站1961~2020年逐日降水数据,首先采用旋转经验正交函数对研究区进行降水分区,再计算不同时间尺度的标准化降水指数,利用索周法分析各分区不同尺度标准化降水指数周期特征,并与Morlet小波周期分析的结果进行对比。研究表明,索周法可以很好地应用于干旱周期分析。年尺度上,Ⅰ、Ⅱ区存在7年左右的显著周期规律,Ⅲ区周期规律以5年为主。季尺度上,Ⅰ、Ⅱ区各季节的周期规律以4~7年为主,而Ⅲ区周期尺度稍长,各季节主要表现为6~9年,各分区不同时间尺度周期演变特征存在一定的差异。

太行山地区1973—2022年暴雨时空演变特征分析

基于太行山地区13个气象站点50 a的逐日降水数据,使用Mann-Kendall突变检验、信噪比检验、Sen’s斜率估计、小波分析法、正交函数分解等方法,对太行山地区的暴雨时空演变规律进行了研究。结果表明:(1)太行山地区年暴雨量波动幅度较大,根据拟合斜率和Sen’s斜率估计法的结果可知,太行山地区的暴雨量将会呈增多趋势;(2)Mann-Kendall突变检验和信噪比检验结果表明,2006年太行山暴雨量发生了由少变多的突变;(3)Morlet小波分析结果表明,在2017—2020间研究区暴雨量存在2~3 a的周期尺度变换;(4)该地区暴雨量经验正交函数(EOF)展开的前两个模态显示,暴雨量呈现全区一致变化以及西南—东北向的空间变化特征,这两个模态情境下的暴雨状况受到环流因子和地形的共同影响。