Fractal Brownian motion model of ship radiated noise

On the basis of the fractal geometry, a nactional Brownian Motion (FBM) model for the noise radiated by ship was established, under which its fractal dimension has been obtained and the Fractal Characteristic Vector (FCV) was constructed in the fractional Brownian random field (FBRF). By using of them, a new technique of the characteristic analysis for target recognition in the underwater acoustics was presented. A comparative experiment for classification shows us that the FCV can be used as essential quantity by which some defects existing in the methods to do the characteristic extraction elsewhere can be remedied.

Combinatorial fractal Brownian motion model

To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.

On p-variation of bifractional Brownian motion

In this paper we study p-variation of bifractional Brownian motion. As an applica-tion, we introduce a class of estimators of the parameters of a bifractional Brownian motion andprove that both of them are strongly consistent; as another application, we investigate fractalnature related to the box dimension of the graph of bifractional Brownian motion.

IMAGE OBJECT DETECTION BASED ON FRACTIONAL BROWNIAN MOTION

Fractional Brownian motion, continuous everywhere and differentiable nowhere, offers a convenient modeling for irregular nonstationary stochastic processes with long-term dependencies and power law behavior of spectrum over wide ranges of frequencies. It shows high correlation at coarse scale and varies slightly at fine scale, which is suitable for and successful in describing and modeling natural scenes. On the other hand, man-made objects can be constructively well described by using a set of regular simple shape primitives such as line, cylinder, etc. and are free of fractal. Based on the difference, a method to discriminate man-made objects from natural scenes is provided. Experiments are used to demonstrate the good efficiency of developed technique.

Research on Extraction Method of Surface Information Based on Multi-Feature Combination Such as Fractal Texture

Because of the developed economy and lush vegetation in southern China, the following obstacles or difficulties exist in remote sensing land surface classification: 1) Diverse surface composition types;2) Undulating terrains;3) Small fragmented land;4) Indistinguishable shadows of surface objects. It is our top priority to clarify how to use the concept of big data (Data mining technology) and various new technologies and methods to make complex surface remote sensing information extraction technology develop in the direction of automation, refinement and intelligence. In order to achieve the above research objectives, the paper takes the Gaofen-2 satellite data produced in China as the data source, and takes the complex surface remote sensing information extraction technology as the research object, and intelligently analyzes the remote sensing information of complex surface on the basis of completing the data collection and preprocessing. The specific extraction methods are as follows: 1) extraction research on fractal texture features of Brownian motion;2) extraction research on color features;3) extraction research on vegetation index;4) research on vectors and corresponding classification. In this paper, fractal texture features, color features, vegetation features and spectral features of remote sensing images are combined to form a combination feature vector, which improves the dimension of features, and the feature vector improves the difference of remote sensing features, and it is more conducive to the classification of remote sensing features, and thus it improves the classification accuracy of remote sensing images. It is suitable for remote sensing information extraction of complex surface in southern China. This method can be extended to complex surface area in the future.

Numerical study on permeability characteristics of fractal porous media

The fractal Brownian motion is utilized to describe pore structures in porous media. A numerical model of laminar flow in porous media is developed, and the flow characteristics are comprehensively analyzed and compared with those of homogeneous porous media. Moreover, the roles of the fractal dimension and porosity in permeability are quantitatively described. The results indicate that the pore structures of porous media significantly affect their seepage behaviors. The distributions of pressure and velocity in fractal porous media are both non-uniform;the streamline is no longer straight but tortuous. When Reynolds number Re < 1, the dimensionless permeability is independent of Reynolds number, but its further increase will lead to a smaller permeability. Moreover, due to the higher connectivity and enlarged equivalent aperture of internal channel network, the augment in porosity leads to the permeability enhancement, while it is small and insensitive to porosity variation when ε < 0.6. Fractal dimension also plays a significant role in the permeability of porous media. The increase in fractal dimension leads to the enhancement in pore connectivity and a decrease in channel tortuosity,which reduces the flow resistance and improves the transport capacity of porous media.

Restoration of Noisy 1/f Family Fractal Signal Based on Haar Wavelets and Wiener Filter

In order to restore noisy fractal Brownian motion(FBM),discrete fractional gaussiannoise(DFGN) combined with noise increments is decomposed by Haar wavelets based on Mallatalgorithm.Considering the correlation of detail coefficients,a bank of Wiener filters are used to estimatethe detail coefficients to reconstruct DFGN considering the estimated approximation coefficients in thecoarsest scale in the minimum mean square sense.Then,the reconstructed DFGN is used to restore FBM.In the digital simulation,in light of the restoration mean square error,we show that the suppose that thecorrelation of detail coefficients and the approximation coefficients in the coarsest scale for any Hurstcould be avoided is unrealistic.Moreover,we calculate the estimation root mean square error of the hurstparameter of the restored FBM to show the validity of our algorithm.

自驱动Janus微球的分数Brownian运动研究

Janus微球是形状规则但表面构成不同的特殊颗粒.在PIV实验平台上,以Pt-SiO2型Janus颗粒(Φ=1μm,Φ=2μm)为研究对象,获取了通过非对称催化分解H2O2产生自驱动情况下颗粒的不规则运动轨迹,通过统计得出不同观测时间下Janus颗粒在不同浓度H2O2溶液(0%,2.5%,5%,10%和15%)中的Hurst指数,实验清晰地表明了颗粒轨迹所具有的无规则运动与定向运动的叠加以及反常扩散特征.随后将这一复杂运动分解为随机的Brownian(布朗)运动、自驱动及随机转动的共同作用,并得出了不同因素所主导的特征时间尺度,合理地解释了所观察到的现象.

Subcooled pool boiling heat transfer in fractal nanofluids:A novel analytical model

A novel analytical model to determine the heat flux of subcooled pool boiling in fractal nanofluids is developed. The model considers the fractal character of nanofluids in terms of the fractal dimension of nanoparticles and the fractal dimen- sion of active cavities on the heated surfaces; it also takes into account the effect of the Brownian motion of nanoparticles, which has no empirical constant but has parameters with physical meanings. The proposed model is expressed as a function of the subcooling of fluids and the wall superheat. The fractal analytical model is verified by a reasonable agreement with the experimental data and the results obtained from existing models.

Fractal Surface Synthesis Based on Two Dimensional Discrete Fourier Transform

The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.

THE APPLICATION OF FRACTAL STUDY IN FORECASTING FLOOD CALAMITIES IN WUZHOU, GUANGXI

As a kind of sudden and common natural disast er, flood is characterize d by the temporal fraction. A date series of floods was established according to the catastrophic records in Wuzhou, Zhuang Autonomous Region of Gaungxi, P. R. China since 1949.By the means of the model of fractional brownian motion, we can imitate the temporal sequence of past and forecast the developin g trend in future, on the basis of which, the R/S analysis was employed to cal cul ate the temporal sequence, the ‘H' exponent and function R(τ)/S(τ) were d etermi ned. It is anticipated that the next catastrophic flood in Wuzhou will happen in 1999.

Analyzing Rotor Rotating Error by Using Fractal Theory

Based on the judgement of fractional Br ow nian motion, this paper analyzes the radial rotating error of a precision rotor. The results indicate that the rotating error motion of the precision rot or is characterized by basic fractional Brownian motions, i.e. randomicity, non -sequencity, and self-simulation insinuation to some extent. Also, this paper calculates the fractal box counting dimension of radial rotating error and judges that the rotor error motion is of stability, indicating that the motion range of the future track of the axes is relatively stable.

水下辅助导航的重力异常随机场分形插值研究

针对重力异常数据匮乏的地区,本文提出采用分形布朗运动(fractional Brownian motion,FBM)分形插值方法对重力异常随机场进行重构,实现可用于水下重力辅助导航的重力异常基准图生成.实验结果表明:分形插值方法作为一种粗插值是可行的,可为水下重力辅助导航系统的实现提供理论参考.

S波段雷达实测海杂波混沌分形特性分析

S波段海杂波信号表现了非线性和频谱时变性,传统的谱分析方法,无法反映该信号在时间上的演化规律。该文首先引入分形布朗运动模型,基于S波段雷达实测海杂波数据,计算了该分形模型的海杂波Hurst指数,进而求得了其分形维数。然后利用经典的Rosenstein方法,计算了S波段实测海杂波的最大Lyapunov指数,从而证实了S波段雷达海洋回波信号具有混沌分形特性。最后进行了计算机实验,验证了本文的结论。该文的工作为S波段海洋雷达的目标探测提供了一种新的途径。

我国证券市场波动的Hurst指数

证券市场的波动不服从布朗运动 ,而服从分数布朗运动。Hurst指数是描述分数布朗运动的重要指标。利用R/S分析方法计算出我国证券市场收益率序列的Hurst指数为 0 .6 8。从而说明我国证券市场的波动具有明显的持久性。

一种基于广义多尺度分形参数的小目标检测方法

复杂场景中小目标的检测是一个难点。本文从分数布朗随机场模型的描述出发，提出并构造了一种广义多尺度分形参数，用于描述图像的纹理信息。它可以作为区分分形集合与非分形集合的一种有效的测度。进一步，基于广义多尺度分形参数，本文提出了一种具有抗噪性能的稳健的目标提取算法，并用于海上小目标的提取。对于实际图像的实验结果表明，本算法具有极高的检测精度。

基于分形的纳米复合材料分散相分散均匀性描述

为了描述纳米填料填充复合材料分散相的分散均匀性 ,提出了一种基于分数布朗运动模型的纳米填料填充复合材料分散相分散均匀性描述方法。该方法将纳米填料填充复合材料TEM图像转化为分散相分布密度矩阵 ,估计分散相分布密度矩阵的H参数值 ,提取分散相分布密度波动的分形特征来定量描述分散相分布的均匀性。通过将该方法实际应用于聚合物基纳米填料填充复合材料分散相分散均匀性描述 ,证明了该方法能够正确描述纳米填料填充复合材料分散相的分散均匀性。

投资机会决策中分数布朗运动理论

根据现代期权理论将投资决策机会视作一种期权 ,当投资价值 (V)和初始支出 (C)是随时间变化的维纳过程时 ,根据 Black- Scholes公式给出投资机会的定价模型 .当 V和 C是 H(H≠ 1/2 )指数的分数布朗运动时 ,则 Ito微分方程形式将改变 ,Black- Scholes公式失效 .讨论了 H指数对投资决策的影响 ,给出此时根据

基于FBM的分形插值方法

系统阐述了分形插值的原理，介绍了分形布朗运动（ＦＢＭ）的概念及其构造方法，针对自然界实际系统分形特性，提出了实际ＦＢＭ系统分形特性的判别准则。在此基础之上提出了基于ＦＢＭ的分形插值方法，阐述了分形插值的基本条件；对于实际的裂隙结构，利用分形插值方法建立的模型进行了渗流计算，并与常规插值所得结果进行了比较。结果表明，对于具有分形特性的实际的复杂、非线性系统，利用基于ＦＢＭ的分形插值方法从大尺度来构造微观细节，能保持微观与宏观之间的相似性。

地震前兆观测资料的分形处理方法

本文从自仿射分形的角度探讨地震前兆观测资料的分形处理方法。在对自仿射分形的分维量测方法进行对比分析的基础上，给出了处理地震前兆观测资料较为适用的分形方法和满足计算需要的样本点数。从对部分水氡和地电阻率资料进行的处理分析中，得到了有益的启示：地震前兆时序观测资料可用分形方法处理分析，分维值（或Ｈ值）可反映观测资料的结构变化特征，其作为一个无量纲量为综合对比分析各类前兆现象，探讨地震前兆场的复杂性特征提供了有效的途径。