基于瀑布过程的多重分形模型特性分析与检验

通过连乘瀑布过程的构建方法,采用对称的Beta分布拟合瀑布过程的乘数因子以及独立的pareto分布拟合瀑布过程的随机变量,建立网络流量多重分形模型。求解该模型合成流量的均值、方差、协方差的表达式,得出其具有正值、长相关、非二阶平稳特性。采用LBNL采集的数据DEC-PKT-1对其进行拟合检验,证明该模型在拟合真实网络流量时的有效性。     

空间目标RCS序列的多重分形分析

分析了空间目标RCS序列产生混沌的机理,将非线性理论中的多重分形分析法引入空间目标RCS序列的研究中,用多重分形分析法分析了空间目标RCS序列的混沌特性;实测数据计算结果表明,与旋转目标相比,三轴稳定目标RCS序列较复杂,这与实际分析的情况相符合,证明了该方法的有效性;另外,还证明了空间目标RCS序列服从多重分形分布。     

Al掺杂ZnO薄膜原子力显微图像的多重分形研究

用原子力显微镜观察溶胶-凝胶法制备Al掺杂znO薄膜的表面形貌,运用多重分形理论研究Al掺杂ZnO薄膜的原子力显微图像,多重分形谱可以很好地定量表征薄膜的表面形貌.结果显示:Al掺杂量为0.5 at.%的ZnO薄膜经550℃退火处理后,rms粗糙度为1.817,Al掺杂量为1.0 at.%的ZnO薄膜经600℃退火处理后,rms粗糙度增大到4.625,相应的分形谱宽△α从0.019增大到0.287,分形参数△f由-0.075变为0.124.     

A counterexample to the multifractal rigidity conjecture of piecewise linear Markov maps of the interval

A multifractal rigidity is the phenomena that the coincidence with the two multifractal spectra implies more strong relation between the given two dynamical systems. For the dimension spectrum of a Bernoulli measure defined on a repeller of a piecewise linear Markov map, Barreira, Pesin and Schmeling proved that a rigidity holds if the repeller is modelled by the full shift of two symbols. It was an open problem whether this rigidity holds in the case of three or more symbols. We give a negative answer to this problem by constructing a counter-example and we show that our counter-example is the unique one in the case of three symbols.     

基于MF-DCCA的呼吸道疾病与大气污染物相关性分析

针对呼吸道系统疾病与大气PM2.5、SO2浓度序列的相关性特征,应用多重分形消除趋势波动分析法(MF-DCCA),对张家界市永定区呼吸道系统疾病患病人数与大气PM2.5、S02浓度序列进行了研究.结果发现该地区呼吸道系统疾病患病人数与大气PM2.5、So2浓度的相关性具有长期持续特征和多重分形特征.随后对它们相关性多重...     

Mechanical Fault Diagnosis Based on Band-phase-randomized Surrogate Data and Multifractal

The vibration signals of machinery with various faults often show clear nonlinear characteristics.Currently,fractal dimension analysis as the common useful method for nonlinear signal analysis,is a kind of single fractal form,which only reflects the overall irregularity of signals,but cannot describe its local scaling properties.For comprehensive revealing of internal properties,a combinatorial method based on band-phase-randomized(BPR) surrogate data and multifractal is introduced.BPR surrogate data method is effective to eliminate nonlinearity in specified frequency band for a fault signal,which can be utilized to detect nonlinear degree in whole fault signal by nonlinear titration method,and the overall nonlinear distribution of fault signal is displayed in nonlinear characteristic curve that can be used to analyze the fault signal qualitatively.Then multifractal theory as a quantitative analysis method is used to describe geometrical characteristics and local scaling properties,and asymmetry coefficient of multifractal spectrum and multifractal entropy for fault signals are extracted as new criterions to diagnose machinery faults.Several typical faults include rotor misalignment,transversal crack,and static-dynamic rubbing fault are analyzed,and the results indicate that those faults can be distinguished by the proposed method effectively,which provides a qualitative and quantitative analysis way in the field of machinery fault diagnosis.     

基于多重分形的离心压缩机出口动态压力非线性特征研究及其在喘振识别中的应用

以800 kW离心压缩机系统的工作状态从平稳到喘振阶段的出口动态压力为分析对象,从多重分形角度研究了多重分形谱参数与出口动态压力之间的关系,着重研究了系统在喘振状态表现出的复杂非线性特征.通过控制系统出口防喘振阀的开度得到离心压缩机在不同工况下的出口动态压力.研究系统出口动态压力的结构函数在不同权重因子下的尺度特征和多...     

Spatiotemporal symmetry and multifractal structure of head movements during dyadic conversation.

This study examined the influence of sex, social dominance, and context on motion-tracked head movements during dyadic conversations. Windowed cross-correlation analyses found high peak correlation between conversants’ head movements over short (≈2-s) intervals and a high degree of nonstationarity. Nonstationarity in head movements was found to be positively related to the number of men in a conversation. Surrogate data analysis offsetting the conversants’ time series by a large lag was unable to reject the null hypothesis that the observed high peak correlations were unrelated to short-term coordination between conversants. One way that high peak correlations could be observed when 2 time series are offset by a large time lag is for each time series to exhibit self-similarity over a range of scales. Multifractal analysis found small-scale fluctuations to be persistent, τ(q) 0.5. These results are consistent with a view that symmetry is formed between conversants over short intervals and that this symmetry is broken at longer, irregular intervals. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

一种时间序列多重分形分析的改进方法及其应用

通过分析时间序列广义维数的不同计算方法,本文引入一种新的多重分形奇异测度概念,提出了一种时间序列多重分形分析的改进方法。该方法不仅计算量小,而且其得到的连续分段线性曲线序列的广义维数具有恒等于１ 的性质。由于现实中许多信号可以用连续分段线性曲线逼近,因此上述性质深入刻划了这类信号的一个共同特征。仿真结果表明,本文推导出的性质为信号奇异性检测开辟了一条新途径,利用本文方法还可以快速有效地提取实测舰船噪声的短时多重分维特征。     

An Airborne Radar Clutter Tracking Algorithm Based on Multifractal and Fuzzy C-Mean Cluster

For an airborne Iookdown radar, clutter power often changes dynamically about 80 dB with wide distributions as the platform moves. Therefore, clutter tracking techniques are required to guide the selection of const false alarm rate （CFAR） schemes. In this work, clutter tracking is done in image domain and an algorithm combining multifractal and fuzzy C-mean （FCM） cluster is proposed. The clutter with large dynamic distributions in power density is converted to steady distributions of multifractal exponents by the multifractal transformation with the optimum moment. Then, later, the main lobe and side lobe are tracked from the multifractal exponents by FCM clustering method.