针对微动目标特征提取问题,该文提出了一种正弦调频Fourier-Bessel变换(Sinusoidal Frequency Modulation Fourier-Bessel Transform,SFMFBT),并基于SFMFBT提出了一种雷达目标微动频率的精确提取方法。首先给出了SFMFBT的定义,分析了变...针对微动目标特征提取问题,该文提出了一种正弦调频Fourier-Bessel变换(Sinusoidal Frequency Modulation Fourier-Bessel Transform,SFMFBT),并基于SFMFBT提出了一种雷达目标微动频率的精确提取方法。首先给出了SFMFBT的定义,分析了变换的相关性质,并通过频率提取误差分析给出了一种修正方法,最后讨论了离散信号处理中的若干问题。相比于傅里叶-贝塞尔变换,SFMFBT将k分辨率参数引入Bessel函数基,克服了其对应频率不可细分的缺陷,并且通过误差分析提高了信号分解精度,从而将Bessel函数基引入特征提取领域,拓展了其应用范围。仿真结果表明该方法同样适用于微动群目标频率提取与回波分离重构,且在SNR>0 dB条件下具有较好的鲁棒性。展开更多
A new method is presented for dealing with asymmetrical Abel inversion in this paper.We separate the integrated quantity into odd and even parts using Yasutomo's method. The asymmetric local value is expressed as ...A new method is presented for dealing with asymmetrical Abel inversion in this paper.We separate the integrated quantity into odd and even parts using Yasutomo's method. The asymmetric local value is expressed as the product of a weight function and a symmetric local value. The symmetric distribution is expanded into Fourier-Bessel series. The coefficients of the series are determined by the use of a least-square-fitting method.展开更多
Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients. The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain....Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients. The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain. Zeros of the generated transcendental equation and the relationship of orthogonality are employed to find the unknown coefficients. Several numerical and graphical examples are explained and discussed.展开更多
针对齿轮故障诊断中采集到的振动信号常伴有噪声干扰且故障特征难以提取的问题,以傅里叶-贝塞尔级数展开(Fourier-Bessel series expansion,FBSE)为基础,提出了一种将FBSE和基于能量的尺度空间经验小波变换(energy scale space empirica...针对齿轮故障诊断中采集到的振动信号常伴有噪声干扰且故障特征难以提取的问题,以傅里叶-贝塞尔级数展开(Fourier-Bessel series expansion,FBSE)为基础,提出了一种将FBSE和基于能量的尺度空间经验小波变换(energy scale space empirical wavelet transform,ESEWT)相结合的齿轮振动信号降噪方法,即FBSE-ESEWT。首先,将采集到的齿轮振动信号利用FBSE技术获得其频谱,以替代传统的傅里叶谱,接着凭借能量尺度空间划分法对获取的FBSE频谱进行自适应分割和筛选,以精确定位有效频带的边界点。随后通过构建小波滤波器组得到信号分量并进行重构,以减小噪声和冗余信息干扰;然后,为捕捉到更全面的特征信息将处理后的信号进行广义S变换得到时频图,输入2D卷积神经网络进行故障诊断验证算法可行性。通过对Simulink仿真信号和实际采集信号进行实验,结果表明,相对于原始经验小波变换(EWT)、经验模态分解(EMD)等方法,FBSE-ESEWT具有更好的降噪效果,信噪比提高了13.96 dB,诊断准确率高达98.03%。展开更多
The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential supports related to a Bessel type of(LCT)so called canonical Fourier-B...The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential supports related to a Bessel type of(LCT)so called canonical Fourier-Bessel transform.展开更多
Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet k...Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.展开更多
Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofpropertie...Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofproperties allows MEE materials to respond to mechanical,electric,and magnetic stimuli,making them versatile forvarious applications.This paper investigates the static and time-harmonic field solutions induced by the surface loadin a three-dimensional(3D)multilayered transversally isotropic(TI)linear MEE layered solid.Green’s functionscorresponding to the applied uniform load(in both horizontal and vertical directions)are derived using the Fourier-Bessel series(FBS)system of vector functions.By virtue of this FBS method,two sets of first-order ordinarydifferential equations(i.e.,N-type and LM-type)are obtained,with the expansion coefficients being Love numbers.It is noted that the LM-type system corresponds to the MEE-coupled P-,SV-,and Rayleigh waves,while the N-typecorresponds to the purely elastic SH-and Love waves.By applying the continuity conditions across interfaces,the solutions for each layer of the structure(from the bottom to the top)are derived using the dual-variable andposition(DVP)method.This method(i.e.,DVP)is unconditionally stable when propagating solutions throughdifferent layers.Numerical examples illustrate the impact of load types,layering,and frequency on the response ofthe structure,as well as the accuracy and convergence of the proposed approach.The numerical results are usefulin designing smart devices made of MEE solids,which are applicable to engineering fields like renewable energy.展开更多
文摘A new method is presented for dealing with asymmetrical Abel inversion in this paper.We separate the integrated quantity into odd and even parts using Yasutomo's method. The asymmetric local value is expressed as the product of a weight function and a symmetric local value. The symmetric distribution is expanded into Fourier-Bessel series. The coefficients of the series are determined by the use of a least-square-fitting method.
文摘Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients. The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain. Zeros of the generated transcendental equation and the relationship of orthogonality are employed to find the unknown coefficients. Several numerical and graphical examples are explained and discussed.
文摘针对齿轮故障诊断中采集到的振动信号常伴有噪声干扰且故障特征难以提取的问题,以傅里叶-贝塞尔级数展开(Fourier-Bessel series expansion,FBSE)为基础,提出了一种将FBSE和基于能量的尺度空间经验小波变换(energy scale space empirical wavelet transform,ESEWT)相结合的齿轮振动信号降噪方法,即FBSE-ESEWT。首先,将采集到的齿轮振动信号利用FBSE技术获得其频谱,以替代传统的傅里叶谱,接着凭借能量尺度空间划分法对获取的FBSE频谱进行自适应分割和筛选,以精确定位有效频带的边界点。随后通过构建小波滤波器组得到信号分量并进行重构,以减小噪声和冗余信息干扰;然后,为捕捉到更全面的特征信息将处理后的信号进行广义S变换得到时频图,输入2D卷积神经网络进行故障诊断验证算法可行性。通过对Simulink仿真信号和实际采集信号进行实验,结果表明,相对于原始经验小波变换(EWT)、经验模态分解(EMD)等方法,FBSE-ESEWT具有更好的降噪效果,信噪比提高了13.96 dB,诊断准确率高达98.03%。
文摘The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential supports related to a Bessel type of(LCT)so called canonical Fourier-Bessel transform.
文摘Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.
基金The National Science and Technology Council of Taiwan(Grant No.NSTC 111-2811-E-516 A49-534)provided financial support for this study。
文摘Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofproperties allows MEE materials to respond to mechanical,electric,and magnetic stimuli,making them versatile forvarious applications.This paper investigates the static and time-harmonic field solutions induced by the surface loadin a three-dimensional(3D)multilayered transversally isotropic(TI)linear MEE layered solid.Green’s functionscorresponding to the applied uniform load(in both horizontal and vertical directions)are derived using the Fourier-Bessel series(FBS)system of vector functions.By virtue of this FBS method,two sets of first-order ordinarydifferential equations(i.e.,N-type and LM-type)are obtained,with the expansion coefficients being Love numbers.It is noted that the LM-type system corresponds to the MEE-coupled P-,SV-,and Rayleigh waves,while the N-typecorresponds to the purely elastic SH-and Love waves.By applying the continuity conditions across interfaces,the solutions for each layer of the structure(from the bottom to the top)are derived using the dual-variable andposition(DVP)method.This method(i.e.,DVP)is unconditionally stable when propagating solutions throughdifferent layers.Numerical examples illustrate the impact of load types,layering,and frequency on the response ofthe structure,as well as the accuracy and convergence of the proposed approach.The numerical results are usefulin designing smart devices made of MEE solids,which are applicable to engineering fields like renewable energy.
