高速旋转机械用消除频率混叠现象的小波变换算法研究

高速旋转机械由于其工作转速高、控制精度高，其故障信号又属于微弱突变信号，造成常规监测方法准确率偏低，成为制约高速旋转机械故障监测进一步发展的最大障碍。本文设计了一种消除小波分解和重构过程中产生的频率混叠的算法。该算法利用傅里叶变换和傅里叶逆变换构成Mallat小波变换在分解和重构过程中所需的严格正交镜像滤波器，从而达到Mallat小波变换过程中必须具有的理想截止特性，最终去除掉多余的频率成分。利用改进前后的小波算法对实际信号进行分析，结果表明，本文设计的Mallat小波变换改进算法可消除信号分析中出现的频率混叠现象。     

时分MIMO滑坡雷达稀疏成像算法

针对现用于成像的MIMO山体滑坡雷达均匀线性阵列数目过多、数据处理复杂度高的问题，引入稀疏阵列时分地基MIMO雷达模型，提出一种基于逆傅里叶变换和混合匹配追踪算法的成像方法。首先通过对雷达回波信号作逆傅里叶变换实现距离向压缩，并进行近似相位补偿，然后采用一种基于时延补偿因子稀疏基的压缩感知算法实现方位向压缩。同时针对多目标成像的伪影点问题，方位向数据压缩引入子空间追踪算法和正交匹配追踪算法的结合算法重构出高分辨率且没有伪影的二维图像。根据真实的山体滑坡监测成像场景参数，通过数值仿真验证了该方法能够在低于传统均匀阵列的天线数目情况下实现目标高质量成像，且具有一定的抗噪性。     

光学显微定位系统定位精度分析

为了提高光学显微定位系统对细胞微生物识别定位的精度：一方面，必须改进手眼标定方法；另一方面，需要提高全局图像识别的准确性，因此，提出一种两步法对系统进行手眼标定。首先，通过标定固定靶标来确定系统原点，并得到视觉模块相对于系统原点的转换关系；然后，根据每次拍照的起始点位置、拍照的数量和移动的步长求解出全局图像相对于系统原点的转换关系；最后，为了进一步提高全局转换关系的准确度，提出一种基于傅里叶变换的误差矫正方法，利用傅里叶变换求解出视觉模块在移动过程中的误差，并加入系统进行补偿。实验结果表明，误差补偿之后，系统X轴方向的误差均值从10.23 μm降为-0.002 μm，Y轴方向的误差均值从6.9 μm降为-0.50 μm，显微定位系统的平均定位精度达到了99%以上。结果表明，所提方法可很好地用于光学显微定位系统对细胞微生物进行高精度的自动化抓取。     

Numerical Solutions of Diffusion Equations in Multi-Dimensional Slab Geometry by Fourier Expansions

Solutions of multi-dimensional neutron diffusion equations in Cartesian coordinates are obtained in the form of regionwise multi-dimensional Fourier series. Equations for two- and three-dimensional problems are derived. A critical and a source problem in two dimensions, and a one-regional source problem in three dimensions are numerically studied.

Two kinds of Fourier series are numerically examined from the viewpoint of rapidity of convergence of the series.

To obtain the value of the flux more accurately, a method is presented which contributes to improvement of the flux profile.     

Image‐based Continuous Displacement Measurements Using an Improved Spectral Approach

Digital Image Correlation algorithms capable of determining continuous displacement fields are receiving growing attention in the field of mechanical properties identification. In this paper, we develop an Improved Spectral Approach (ISA) to reconstruct continuous displacements based on their Fourier decomposition. This approach leads to a time and memory‐efficient algorithm, thanks to the fast Fourier transform. Moreover, the Fourier‐based decomposition enables accurate heterogeneous measurements. Improvements consist in increasing the accuracy and convergence rate as well as dealing with non‐periodic displacements and images. Furthermore, a theoretical framework is presented to quantify the noise sensitivity of the ISA from which useful information is retrieved. The approach is evaluated using synthetic images deformed by heterogeneous displacement fields. Comparisons show that the introduced modifications lead to lower uncertainties by one order of magnitude in the case of non‐periodic images and displacement field studied. Moreover, first‐order (SO1) and second‐order (SO2) subset‐based Digital Image Correlation algorithms are compared with the ISA. The comparisons herein reveal that the uncertainties of the ISA are 6–9 times smaller than those of the SO1 due to insufficiency of the first‐order shape function for the estimation of heterogeneous displacements, while being slightly smaller than those of the SO2. Moreover, as the image smoothness decreases, the uncertainties of the SO2 deviate from those of the ISA and the exact displacements. The presented approach shows great potentials for challenging applications such as strain measurements at microstructural levels.     

Detecting Change Points by Fourier Analysis

The cumulative sum (CUSUM) is a basic diagnostic tool in the analysis of change-point data. It is shown that Fourier analysis of the CUSUM can be a useful supplementary tool in such analyses. The technique is applied to three data sets that have appeared previously in the statistical literature.     

Ethyl group as matrix modifier and inducer of ordered domains in hybrid xerogels synthesised in acidic media using ethyltriethoxysilane (ETEOS) and tetraethoxysilane (TEOS) as precursors

Hybrid silica xerogels favourably combine the properties of organic and inorganic components in one material; consequently these materials are useful for multiple applications. The versatility and mild synthetic conditions provided by the sol-gel process are ideal for the synthesis of hybrid materials. The specific aims of this study were to synthesise hybrid xerogels in acidic media using tetraethoxysilane (TEOS) and ethyltriethoxysilane (ETEOS) as silica precursors, and to assess the role of the ethyl group as a matrix modifier and inducer of ordered domains in xerogels. All xerogels were synthesised at pH 4.5, at 60 °C, with 1:4.75:5.5 TEOS:EtOH:H₂O molar ratio. Gelation time exponentially increased with the ETEOS molar ratio. Incorporation of the ethyl groups into the structure of xerogels reduced cross-linking, increased the average siloxane bond length, and promoted the formation of ordered domains. As a result, a transition from Qⁿ to Tⁿ signals detected in the ²⁹Si NMR spectra, the Si–O structural band in the FTIR spectra shifted to lower wavelength, and a new peak in the XRD pattern at 2θ < 10° appeared in the XRD patterns. Mass spectroscopy detected fragments with high numbers of silicon atoms and a polymeric distribution.     

数字信号处理的时频分析方法综述

现代数字信号处理方法众多,时频分析在此领域应用广泛并仍然具有发展潜力。介绍了数字信号处理的时频分析方法的发展,从短时傅里叶变换,到Wigner-Ville分布,小波变换,希尔伯特-黄变换,EEMD,分别论述了5种方法的原理以及优缺点。