Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.

Simulation of stochastic wind field for large complex structures based on modified Fourier spectrum

Simulation for stochastic wind field is very important in analyzing dynamic responses of large complex structures due to strong wind.The typical simulation method is the spectrum representation method (SRM),but the SRM has drawbacks of inferior precision in lower frequency and slow calculating speed.In view of this,the modified Fourier spectrum method (MFSM) is introduced into the simulation of stochastic wind field in this paper.In this method,phase information of wind velocity time history is determined by cross power spectral density (CPSD) between adjacent points,and the wind velocity time history with time and space correlation is generated by iterative modification for CPSD considering auto power spectral density (APSD).Simulation of the wind field for a long-span bridge is undertaken to verify the effectiveness of the MFSM.Simulation results of the SRM and the MFSM are compared.It can be concluded that the MFSM is more accurate and has higher calculation speed than the SRM.

A Fourier spectrum-based strain energy damage detection method for beam-like structures in noisy conditions

In this paper,the Fourier spectrum-based strain energy damage detection method for beam-like structures is proposed based on the discrete Fourier transform.The classical strain energy damage detection method localizes damage by the comparison of the strain energy between the intact and inspected structures.The evaluation of the 2nd-order derivative term in the strain energy plays a crucial part in the comparison.The classical methods are mostly based on a numerical derivative estimation for this term.The numerical derivative,however,introduces additional disturbances into damage indications.To address this problem,a discrete Fourier transform-based strain energy is proposed with the emphasis of enhancing the performance in noisy condition.The validations conducted on the simulated and experimental data show that the developed method is effective enough for composite beam damage detection in noisy environments.

A theoretical method based on Fourier spectrum analysis for the focusing performances of the X-ray compound refractive lenses

It is important to predict the intensity distribution in focusing plane for designing the X-ray compound refractive lenses. On the basis of analyzing the structure of X-ray compound lenses and comparing it with Praunhofer diffraction system, it is concluded that the X-ray focusing system can be regarded as a kind of Praunhofer diffraction system. Therefore, a method based on Fourier spectrum analysis is presented to predict the intensity distribution in the focusing plane for the X-ray lenses. A brief analysis on the relationship between the parameters of X-ray lenses and their focusing performance is also given in this paper.

Femtosecond laser processing stainless steel foil and its Fourier spectrum detection

In this paper, we use femtosecond laser pulse to scribe 304 stainless steel foil, detect the Fourier transform infrared spectrum of the sample before and after processing, confirm the "cold processing" and "thermal processing" and their mutual conversion, and determine the "cold processing" parameter window. The ablation threshold and incubation coefficient of 304 stainless steel foil are calculated, and the effects of scanning speed and effective pulse number on the ablation threshold are analyzed. The ANSYS software is used to simulate the radial and axial temperature distributions of the surface on 304 stainless steel foil sample and the heat-affected zone with a femtosecond laser fluence of 10 J/cm2 and an effective number of pulses of 1 200 are obtained. In the aspect of spectral detection, the Fourier transform infrared spectra of the sample before and after processing are measured and two processing mechanisms of "cold processing" and "hot processing" are confirmed, which proves that we can achieve the conversion between "cold processing" and "hot processing" by changing the laser fluence and determine the "cold processing" laser fluence range.

Fourier Power Spectrum Analysis of Exons for the Period-3 Behavior

The period-3 behaviors of 105 exons from 20 genes in human were studied by Fourier power spectrum. The results indicated that not all exons show the period-3 behavior. The exons were adjusted in order to make them accord with the order of the protein translated, and we found that the period-3 character is relation to the length of exons and the bases distribution in the three codon position. Furthermore, as long as the exons with period-3 behavior accord with the order of protein translated, they would exhibit the synonymous codons usage preference, and the codons with g/c at the third position are used in higher frequency. The results are significant to the gene prediction and the research on the introns.

Spectrum of Signals on the Quaternion Fourier Transform Domain

The quaternion Fourier transform plays a vital role in the representation of two-dimensional signals. This paper characterizes spectrum of quaternion-valued signals on the quaternion Fourier transform domain by the partial derivative.

实测风场的随机Fourier谱研究

根据国内某大桥桥址处实测风速资料,获得了该地区风场10 m高平均风速U10、地面粗糙度z0的统计概率特征,以及纵向脉动风速Fourier谱曲线;基于Kolmogrov理论,提出了随机Fourier谱经验公式,应用随机建模理论和非线性优化技术,获得了实测风场的随机Fourier幅值谱函数以及基本随机变量的概率密度函数。与实测资料Fourier谱样本集合的比较表明,本文建立的随机Fourier谱能够很好地表征实测资料Fourier谱的随机性。同时,通过实测风速资料,进一步验证了本文提出的随机Fourier谱具有很好的通用性。

基于随机Fourier谱的地震动合成研究

本文基于与物理随机模型相对应的随机Fourier谱,通过对地震动非平稳性及其所受影响机制的分析,建立了非平稳地震动合成的新方法。通过引入基本相位差谱,并将初始相角视为随机变量,以相位差谱的分布特性、随机地震动的统计特征以及对结构随机反应的影响为原则,利用计算机程序生成相位差谱,提出了基于随机Fourier谱的合成地震动方法。同时,利用快速FFT技术提高合成精度。根据本文提出的合成方法获得的地震动具有非平稳特性,将为后续研究工作提供合理的地震动加速度时程。

脉动风速互随机Fourier谱函数

为了在随机Fourier谱中考虑风场的空间相关性,首先在经验物理关系的意义上定义了互随机Fourier谱,其表达式由两个随机过程的随机Fourier谱和一个可以反映风场空间相关性的随机相干函数组成;然后,利用现场实测风速资料,研究并建立了实际风场的随机相干函数的经验物理模型;最后,基于假设检验理论,确定了互随机Fourier谱函数中基本随机参数及其概率密度信息。实例表明,建立的互随机Fourier谱函数可以在概率的意义上很好地表征实际风场的空间相关性。

脉动风速功率谱与随机Fourier幅值谱的关系研究

功率谱密度函数是随机过程在频域内的重要特征量,但由于其本质上是平稳过程的频域数值特征,致使其很难全面反映原始随机过程的概率信息,这就需要从更本源的意义上考察随机过程。本文试图从Fourier随机函数的角度反映随机过程,将经典的功率谱密度函数中具有物理意义的可测变量看作随机变量,利用功率谱与Fourier幅值谱的关系,定义了随机Fourier幅值谱;以Davenport谱为例,证实当地面粗糙度服从对数正态分布、10m高度基本风速服从极值Ⅰ型分布时,可通过功率谱构造具有物理意义的随机Fourier幅值谱。通过实测风速Fourier谱与随机Fourier幅值谱的比较,证明随机Fourier幅值谱的概念具有合理性。

利用灰度图提高 Fourier变换轮廓术的测量精度

在 FTP测量中 ,常利用 π相移方法来消除零频 ,以避免频谱混叠 ,提高 FTP的测量精度。此时 ,测量系统中包含相移装置 ,增加了系统的复杂性。然而 ,人们常常忽略了灰度图中包含的信息在 FTP测量中的作用。本文提出了在 FTP测量中利用一帧灰度图来提高测量精度的方法。该方法测量装置简单 ,又可以达到π相移的效果 ,在实际的 FTP测量中的意义。

Fourier变换光谱学的一种光谱分辨率增强方法

本文提出了一种基于特征值分析与线性拟合 (EALF)的超分辨率谱估计方法。其实质是在光谱的Fourier变换域内进行信号处理 ,以使复原谱的分辨率突破仪器函数的限制。EALF由总体最小二乘参数估计、特征值分析频率估计和最小二乘拟合振幅估计三个步骤来实现。本文将介绍EALF谱估计的原理 ,通过仿真实验验证原理的正确性 ,讨论关键技术 ,并总结EALF相对于其他Fourier变换光谱分辨率增强技术的主要优点。

脉动风速随机Fourier波数谱研究

从物理机制出发,建立了具有扎实物理基础的脉动风速随机Fourier谱模型.首先,基于大气湍流物理图景,阐述了湍流中的涡旋尺度和风速能谱不同子区的对应关系.以脉动风速在剪切含能子区和惯性子区所符合的不同幂次规律为基础,建立了随机Fourier谱模型,指出上述两个子区分界波长lc对应实际物理过程中含能大涡尺度和平衡范围涡旋尺度的分界值.本质上,lc是一个随机变量,影响lc的主要因素是湍流涡量和剪切率的比值.利用实测数据,建立了lc和剪切率以及Fourier谱模型中各参数的关系.最后,以地面粗糙度和10min平均风速为基本随机变量,湍流强度为牵连随机变量,得到了分界波长的分布以及以双线性函数为特征的随机Fourier波数谱.理论预测结果和实际观测结果符合良好.

中药材芡实的X射线衍射Fourier图谱分析研究

目的:建立中药材芡实的鉴定分析新方法。方法:采用粉末X射线衍射Fourier图谱鉴定法。结果:获得芡实的标准X射线衍射Fourier图谱和特征标记峰值,发现芡实的淀粉属于A型淀粉,标准药材粉末的结晶度为33.2%。结论:X射线衍射Fourier谱鉴定法可用于中药材芡实的品质评价。

α-Si3N4单晶纳米线的Fourier变换红外光谱和Raman光谱分析

将单晶硅片在流动的氨气和氮气混合气体中加热到1250℃,不用催化剂,实现了大量高纯度单晶Si3N4纳米线的生长。用X射线衍射方法分析了所制备Si3N4纳米线的相结构,用扫描电子显微镜和高分辨透射电子显微镜观察了其微观形貌。Si3N4纳米线生长机理为气–固机制。Fourier变换红外光谱与Raman光谱分析表明:产物的吸收与振动模式呈现了典型的α-Si3N4的特征;与α-Si3N4块体材料相比,部分峰位发生了蓝移,也有几个峰位发生了少许的红移,这是α-Si3N4纳米材料小尺寸效应与表面效应的综合体现。

Fourier变换光谱学退卷积技术的理论研究

介绍了 Fourier变换光谱退卷积技术的原理 ,通过数学推导从理论上对退卷积光谱的特性进行了分析 ,分别讨论了退卷积技术的两个重要参量 ,即退卷积系数和切趾长度 ,对复原光谱的线宽和信噪比的影响 ,从而得到三个结论 :1 )退卷积技术的分辨率增强能力在实际中由于受到噪音的限制而不能无限提高 .2 )对于光谱中宽度不同的谱线 ,退卷积将导致它们之间的峰高比失真 .3)在选定退卷积系数和切趾长度以满足谱线形状和宽度的要求后 ,只有通过选择合适的切趾函数来满足信噪比的要求 .研究还发现 ,退卷积过程相当于一个带通滤波器 ,其中高通滤波器是退卷积函数 ,低通滤波器是切趾函数 。

Hilbert spectrum and intrinsic oscillation mode of dynamic response of a bilinear SDOF system: influence of harmonic excitation amplitude

Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.

基于椭圆Fourier描述子的旋转机械振动信号分析

基于椭圆Fourier描述子,对转子同一截面上相互垂直的两个传感器测取的同源振动信号进行融合分析,从理论上推导出滤波轴心轨迹的表达式。研究对比全谱、全息谱和矢谱,建立三种谱分析方法的统一理论框架,给出三种谱分析方法的理论表达式,并设计利用一次快速Fourier变换实现三种谱图的数值方法。在融合全谱、全息谱和矢谱三种谱分析方法的基础上,提出基于椭圆Fourier描述子的矢椭谱分析方法,用于分析转子的同源振动信号。应用对比验证了矢椭谱的简洁可行性。

基于分数阶Fourier变换的经验模式分解方法研究

在分析了经验模式分解(EMD)及分数阶Fourier变换的基础上,提出了一种基于分数阶Fourier变换的经验模式分解方法,并且深入探讨了该方法的分解特性。对仿真和实际振动信号的分析结果表明,对直接采用经验模式分解分析结果不够明确的信号,基于分数阶Fourier变换的经验模式分解方法对信号进行分析是比较有效的方法。