A multiscale Galerkin method for the hypersingular integral equation reduced by the harmonic equation

The aim of this paper is to investigate the numerical solution of the hypersingular integral equation reduced by the harmonic equation. First, we transform the hypersingular integral equation into 2π-periodic hypersingular integral equation with the map x=cot(θ/2). Second, we initiate the study of the multiscale Galerkin method for the 2π-periodic hypersingular integral equation. The trigonometric wavelets are used as trial functions. Consequently, the 2j+1 × 2j+1 stiffness matrix Kj can be partitioned j×j block matrices. Furthermore, these block matrices are zeros except main diagonal block matrices. These main diagonal block matrices are symmetrical and circulant matrices, and hence the solution of the associated linear algebraic system can be solved with the fast Fourier transform and the inverse fast Fourier transform instead of the inverse matrix. Finally, we provide several numerical examples to demonstrate our method has good accuracy even though the exact solutions are multi-peak and almost singular.     

Denoising of sensor signals for the flange thickness measurement based on wavelet analysis

A railway wheelset is subject to normal wear due to large part to friction contact between the wheelset and the rail. Because the wear of wheelset will bring the hidden security troubles to the operation of the railway, it is very important to measure the wheelset's geometrical parameters, especially the flange thickness. The optoelectronic method is proposed and can dynamically measure the flange thickness on line. Fast Fourier transform and wavelet analysis methods are used to denoise the sensor's signals. It is found that the wavelet transform produces a much better way of denoising of the signals compared with the fast Fourier transform. Comparisons of the flange thickness measurement with the wheelset creeping and the optoelectronic system are presented. The root-mean-square errors of the flange thickness with the manual measurement with the wheelset creeping and the optoelectronic method measurement with the wavelet analysis are 0.22 and 0.18, respectively. The changing range of manual measurement is much larger than that of the optoelectronic method because of the difference between every operator's measuring standard. Measurement results of the optoelectronic method show that the system has better repeatability and reliability compared to the manual measurement.     

Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction

In the context of time-accurate numerical simulation of incompressible flows, a Poisson equation needs to be solved at least once per time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is one of the most time consuming and difficult to parallelise parts of the code.     

基于组合FFT的多核北斗软件接收机并行捕获算法

目前数字信号处理器已经由单核系统发展为多核并行系统,可通过并行执行任务加快信号处理速度。北斗C_(B2I)码是GPS C/A码码长的两倍,若使用传统捕获算法将会延长信号捕获时间。基于此问题,提出了一种基于组合FFT的并行捕获算法。该算法将信号奇偶点分开进行并行处理,可将单次FFT变换点数减半,并通过高效利用多核资源加快信号捕获速度。为了验证算法性能,对比了传统算法和改进后算法的PTP值。仿真结果表明,两算法PTP均值分别为2.961和2.938,改进后算法未降低捕获精度。最后,以多核嵌入式平台为基础分析了两算法的单核运算量,结果表明:当待处理的信号点数由1000增加到256 000时,改进后算法单核乘法运算量减少比例由33%增加到了40%,而加法计算量始终减少50%,改进后算法可达到快速捕获的效果。     

光学相干层析成像色散补偿研究

针对通过增加光源谱宽度来提高光学相干层析成像系统分辨率时样品色散特性的限制作用,分析了色散与光学相干层析成像系统纵向光程分辨率的约束关系.根据物质色散特性,采用数值变换方法对光学相干层析成像相干成像信号进行了色散补偿.实验使用了中心波长1 550 nm 自激发辐射光源和光纤迈克尓逊干涉结构,对水和光学快速扫描延迟线引入的二阶和三阶色散进行了数值补偿并通过相位修正因子来改善补偿效果.确定了一种普适的、快速的数值色散补偿方法.在对水中盖玻片和生物组织和的光学相干层析成像图像的色散补偿实验中取得了良好的效果,证明了方法的可行性.     

基于PPG的心率和呼吸频率的测量研究

利用光电容积脉搏波描记法(PhotoPlethysmoGraphy,PPG)测量人体生理参数具有操作简单、性能稳定和适应性强等优点.采用反射式光电测量法获得桡动脉PPG信号,对PPG信号做快速傅里叶变换,分析频域实现人体心率和呼吸频率的检测.实验结果表明利用快速傅里叶变换获得的心率和呼吸频率与监护仪获得的相应数据之间有...     

干涉条纹图像处理的相位解包新方法

干涉图的处理是光干涉计量中的关键技术.采用泰曼一格林型干涉系统,建立被测物与干涉相位之间的数学模型,通过MATLAB软件,实现对被测参数的自动化测量.基于二维快速傅里叶方法的基本原理,提出一种新的相位解包算法--菱形种子算法,通过识别1个种子点,然后依次向相邻4点扩展,再把这4个点作为第二批种子点,依次向各自的4点邻域扩展,以菱形轨迹遍历所有的有效信息点,以到达整幅图像相位解包的目的.采用该算法测量薄膜样片的厚度,测试结果与ZYGO测试结果比较,PV误差为0.036 4λ,RMS最大误差为0.003λ,证明该算法虽然处理的是单幅干涉图,但可以得到高精度的相位分布.