用于亚微米颗粒测量的后向散射光谱法

针对后向散射光谱粒径测量法对亚微米颗粒测量准确度较差的问题,提出了一种采用紫外光作为光源的测量方法.通过快速傅里叶变换计算了粒径为0.25~1 μm的聚苯乙烯亚微米颗粒的后向散射频谱,将频谱峰值对应的频率值与相应的颗粒粒径进行线性回归,各粒径值相对于回归直线的平均误差为±0.02 μm. 结果表明,本文提出的300~400 nm的紫外光适用于测量0.25~1 μm的亚微米颗粒,相比目前国外最新的采用可见光谱或红外光谱的方法准确度提高了一个数量级,同时该方法也适用于测量双峰分布亚微米颗粒系.     

chirp-z重组算法及其在电力设备绝缘监测中的应用

在电力系统中,在线带电监测电力设备的绝缘性能,实现电网故障的预测和诊断是智能电网对电气设备绝缘性能自动化测量的重要要求。其中,通过谐波分析结算介质损耗,是测量绝缘性能的一种重要方法。为了提高谐波结算的实时性,文章采用了线性调频Z变换（Chirp-Z）及其双实序列在线重组算法,对介质损耗测量中电流电压的谐波计算进行了优化,很好地解决了测量中谐波和间谐波干扰难题,实现了高精度局部解谱,而耗时不到常规Chirp-Z算法的一半。该方法在涉及谐波计算的有限资源无线分布测量系统中获得了很好的应用。     

Fast evaluation of quadrature formulae on the sphere

Recently, a fast approximate algorithm for the evaluation of expansions in terms of standard -orthonormal spherical harmonics at arbitrary nodes on the sphere has been proposed in [S. Kunis and D. Potts. Fast spherical Fourier algorithms. J. Comput. Appl. Math., 161:75-98, 2003]. The aim of this paper is to develop a new fast algorithm for the adjoint problem which can be used to compute expansion coefficients from sampled data by means of quadrature rules.

We give a formulation in matrix-vector notation and an explicit factorisation of the spherical Fourier matrix based on the former algorithm. Starting from this, we obtain the corresponding factorisation of the adjoint spherical Fourier matrix and are able to describe the associated algorithm for the adjoint transformation which can be employed to evaluate quadrature rules for arbitrary weights and nodes on the sphere. We provide results of numerical tests showing the stability of the obtained algorithm using as examples classical Gauß-Legendre and Clenshaw-Curtis quadrature rules as well as the HEALPix pixelation scheme and an equidistribution.

     

Simultaneous denoising and enhancement of signals by a fractal conservation law

In this paper, a new filtering method is presented for simultaneous noise reduction and enhancement of signals using a fractal scalar conservation law which is simply the forward heat equation modified by a fractional anti-diffusive term of lower order. This kind of equation has been first introduced by physicists to describe morphodynamics of sand dunes. To evaluate the performance of this new filter, we perform a number of numerical tests on various signals. Numerical simulations are based on finite difference schemes or fast Fourier transform. We used two well-known measuring metrics in signal processing for the comparison. The results indicate that the proposed method outperforms the well-known Savitzky-Golay filter in signal denoising.     

润滑接触中弹性变形的快速数值计算

研究了弹性变形的计算特点 ,并在简单回顾卷积算法的基础上给出了一种利用快速傅立叶变换 (FFT)和离散圆卷积计算弹性变形的方法 .计算表明 ,通过对压力信号和影响系数 -响应函数 (Green函数 )进行简单的预处理 ,可以获得准确的弹性变形 ,其计算精度和多层网格积分法相当 ,而计算速度则是多层网格积分法的 3倍左右 ,是一种准确、高效的数值计算方法