基于小波分解与分形内插相结合的地形数据压缩方法

地形匹配制导中需要使用大量的地形数据，因此有效的地形数据压缩技术是非常重要的。传统的地形数据压缩方法主要采用线性内插的方法，但这对于地形起伏较大的山区地形失真太大，不能满足高精度导航的要求。本文基于小波分解与分形内插相结合的方法，提出了一种新的地形数据压缩方法，它具有压缩比高，保真性好，解码快的特点，特别适合山区地形数据的压缩。     

基于分数阶理论的铁路基础设施形变监测数据分析与挖掘

北斗高精度定位系统因噪声等因素会产生一定范围内的随机误差,这导致传统模型难以直接对监测数据进行精准分析,因此提出基于分数阶理论的北斗监测数据分析方法,从数据整体趋势角度挖掘铁路基础设施形变演化规律。首先,给出分数阶分析方法的理论框架,并对基础理论进行详细介绍;其次,提出利用α稳定分布对原始数据进行概率密度拟合,实现数据的非高斯特性估计;再次,通过长程相关特性和多重分形特性挖掘隐藏在监测数据中的深层次趋势特征,从数据分数阶特性维度分析未来变化趋势;最后,所提分析方法应用于国内某重载铁路的基础设施形变监测,实验结果表明所提出的分析方法能够在噪声干扰下实现北斗监测数据的精准分析,能够对各组监测数据的演化规则和铁路基础设施形变程度进行精准判别。     

一种分形DGS单元结构设计及其在微带电路中的应用

文章设计出了一种新型的DGS单元——Minkowski分形哑铃DGS单元，并将其应用于微带电路的设计中。利用HFSS软件对相关电路模型进行仿真，结果表明，具有相同尺寸的一阶分形单元电路（缺口深度P=2／3）与普通的哑铃形DGS单元电路比较，谐振频率降低了1．1GHz。利用此分形单元设计电路，可以达到电路小型化的效果。     

Advanced fractal approach for unsupervised classification of SAR images

Unsupervised classification of Synthetic Aperture Radar (SAR) images is the alternative approach when no or minimum apriori information about the image is available. Therefore, an attempt has been made to develop an unsupervised classification scheme for SAR images based on textural information in present paper. For extraction of textural features two properties are used viz. fractal dimension D and Moran’s I. Using these indices an algorithm is proposed for contextual classification of SAR images. The novelty of the algorithm is that it implements the textural information available in SAR image with the help of two texture measures viz. D and I. For estimation of D, the Two Dimensional Variation Method (2DVM) has been revised and implemented whose performance is compared with another method, i.e., Triangular Prism Surface Area Method (TPSAM). It is also necessary to check the classification accuracy for various window sizes and optimize the window size for best classification. This exercise has been carried out to know the effect of window size on classification accuracy. The algorithm is applied on four SAR images of Hardwar region, India and classification accuracy has been computed. A comparison of the proposed algorithm using both fractal dimension estimation methods with the K-Means algorithm is discussed. The maximum overall classification accuracy with K-Means comes to be 53.26% whereas overall classification accuracy with proposed algorithm is 66.16% for TPSAM and 61.26% for 2DVM.     

Scaling analysis and model estimation of solar corona index

A monthly average solar green coronal index time series for the period from January 1939 to December 2008 collected from NOAA (The National Oceanic and Atmospheric Administration) has been analysed in this paper in perspective of scaling analysis and modelling. Smoothed and de-noising have been done using suitable mother wavelet as a pre-requisite. The Finite Variance Scaling Method (FVSM), Higuchi method, rescaled range (R/S) and a generalized method have been applied to calculate the scaling exponents and fractal dimensions of the time series. Autocorrelation function (ACF) is used to find autoregressive (AR) process and Partial autocorrelation function (PACF) has been used to get the order of AR model. Finally a best fit model has been proposed using Yule-Walker Method with supporting results of goodness of fit and wavelet spectrum. The results reveal an anti-persistent, Short Range Dependent (SRD), self-similar property with signatures of non-causality, non-stationarity and nonlinearity in the data series. The model shows the best fit to the data under observation.     

Universal scaling laws for fully-developed magnetic field turbulence near and far upstream of the Earth’s bow shock

We analyze the multifractal scaling of the modulus of the interplanetary magnetic field near and far upstream of the Earth’s bow shock, measured by Cluster and ACE, respectively, from 1 to 3 February 2002. The maximum order of the structure function is carefully estimated for each time series using two different techniques, to ensure the validity of our high-order statistics. The first technique consists of plotting the integrand of the pth order structure function, and the second technique is a quantitative method which relies on the power-law scaling of the extreme events. We compare the scaling exponents computed from the structure functions of magnetic field differences with the predictions obtained by the She–Lévêque model of intermittency in anisotropic magnetohydrodynamic turbulence. Our results show a good agreement between the model and the observations near and far upstream of the Earth’s bow shock, rendering support for the modelling of universal scaling laws based on the Kolmogorov phenomenology in the presence of sheet-like dissipative structures.     

基于弹塑性理论的新型接触热导模型

提出了一种新型接触热导的模型。充分考虑界面上微凸体的变形,根据微凸体变形连续的特点,分别给出了弹性、弹塑性、塑性三种变形时的接触方程。用Weierstrass-Mandelbrot分形函数描述粗糙表面轮廓曲线,并考虑了接触点的基体热阻及其界面收缩热阻,构建了分形热阻网格模型,分析了接触热导与载荷的关系,与实验数据及模型、Mikic弹性模型和Yovanovich塑性模型的预测值进行了比较。结果表明:该模型能较好地预测界面接触热导,有其合理性。     

A novel virtual material layer model for predicting natural frequencies of composite bolted joints

A novel virtual material layer model based on the fractal theory was proposed to predict the natural frequencies of carbon fiber reinforced plastic composite bolted joints. Rough contact surfaces of composite bolted joints are modeled with this new proposed approach. Numerical and experimental modal analyses were conducted to validate the effectiveness of the proposed model. A good consistence is noted between the numerical and experimental results. To demonstrate the necessity of accurately modeling the rough contact surfaces in the prediction of natural frequencies, virtual material layer model was compared with the widely used traditional model based on the Master-Slave contact algorithm and experiments, respectively. Results show that the proposed model has a better agreement with experiments than the widely used traditional model (the prediction accuracy is raised by 8.77% when the pre-tightening torque is 0.5 N∙m). Real contact area ratio A* of three different virtual material layers were calculated. Value of A* were discussed with dimensionless load P*, fractal dimension D and fractal roughness G. This work provides a new efficient way for accurately modeling the rough contact surfaces and predicting the natural frequencies of composite bolted joints, which can be used to help engineers in the dynamic design of composite materials.     

图象的分形压缩方法

本文介绍一种适于对高分辨率（大数据量）遥感图象实现高倍（几十至几百倍）压缩的方法。文中简述分形几何的基本概念，给出了一种分形压缩的模型，以北航的图象分形压缩研究结果为例，阐述了分形压缩方法的特点。     

Fractal analysis of short and intermediate GRB and the fireball model

In the present work the possibility of the fractal analysis application for GRB temporal profiles was studied. We have analysed the 4B revised BATSE catalog: temporal profiles of GRB with t₉₀ < 3 s (287 short and 100 intermediate) were studied on TTE data, a sample of 278 intermediate GRB with t₉₀  3 s were studied on DISCSC data. An analysis of the background fractal dimension distributions obtained using TTE and DISCSC data (143 and 110 background regions, respectively), indicates that for both datasets background fractal dimensions D_bgr = 1.5 that the fractal dimension distributions obtained by using these data can be processed simultaneously. The change of the fractal index D_bgr for Poisson statistics – dominated sets with different coefficients of error in counting (up to 10) was studied and D_bgr = 1.5. The ranges of fractal dimension (0.80  D  2.25 for short and 0.85  D  2.01 for intermediate GRB) are shifted over range for theoretical fractal curve (1 < D < 2) due to the finite detector time resolution. There are four subgroups in fractal dimension distribution for short GRB (D = 1.05 ± 0.03, D = 1.31 ± 0.05, D = 1.51 ± 0.04, D = 1.90 ± 0.03) and six subgroups for intermediate one (D = 1.05 ± 0.09, D = 1.24 ± 0.08, D = 1.44 ± 0.07, D = 1.51 ± 0.08, D = 1.64 ± 0.07, D = 1.91 ± 0.1). Time profiles with fractal dimension smaller then background can be obtained by using models with many short chaotic processes in sources, for example, fireball model with shock waves. The range of fractal dimensions for the modelled temporal profiles is 1.213  D  1.400, which can correspond to subgroups of short and intermediate GRB with D = 1.31 and D = 1.24; moreover, the fractal dimension of a simulated indented event and GRB990208 are equal within the error limits for some model parameters and it is possible to obtain smooth temporal profiles with D = D_bgr.