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、 SO2 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 多重分形特征的动力来源进行了分析, 通过随机重排和相位随机处理, 结果表明在不同时间尺度上的长期持续性影响 是其主要动力来源。进一步研究发现该地区呼吸道系统疾病与大气 PM2:5、 SO2 浓度序列的相关性在四个季节均具 有长期持续性的多重分形特征, 且夏季多重分形特征相对强于其他季节。     

镁质熔剂性球团矿相的多重分形谱

 球团矿相微观结构决定其冶金物理化学性能，为透视球团矿微观结构与其宏观冶金物理化学性能之间的依赖关系，需要解决的首要关键问题是矿相微观视觉特征的提取与定量表征。以镁质熔剂性球团微观矿相为研究对象，在直观分析矿相视觉特征的基础上，采用多重分形谱分析方法，提取矿相的微观多重分形谱定量表征值f（α），并分别深度挖掘由f（α）衍生出的对称度特征值Δf、谱宽特征值Δα、容量维特征值D（0）随碱度变化的迁移规律和随矿相检测位置变化的迁移规律。研究结果表明，矿相微观视觉特征在HSV颜色空间上呈现的颜色特征未在碱度变化和位置变化上存在显著差异性；矿相微观多重分形谱分析中，Δf、Δα、D（0） 3个特征值在碱度变化和位置变化上有显著的差异性，可以很好地表征碱度迁移规律和位置迁移规律。     

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-DFA的语音情感识别

针对语音情感线性参数在刻画不同情感类型特征上的不足,将多重分形理论引人语音情感识别中．通过分析不同语音情感状态下的多重分形特征,提取多重分形谱参数和广义hurst指数作为新的语音情感特征参数,并结合传统语音声学特征,采用支持向量机SVM对其进行语音情感识别．试验结果表明,该方法可使系统的准确率和稳定性得到有效提高．非线性参数的引人为语音情感识别提供了一个新的思路．     

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.     

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)     

Multifractal signatures of infectious diseases

Incidence of infection time-series data for the childhood diseases measles, chicken pox, rubella and whooping cough are described in the language of multifractals. We explore the potential of using the wavelet transform maximum modulus (WTMM) method to characterize the multiscale structure of the observed time series and of simulated data generated by the stochastic susceptible-exposed-infectious-recovered (SEIR) epidemic model. The singularity spectra of the observed time series suggest that each disease is characterized by a unique multifractal signature, which distinguishes that particular disease from the others. The wavelet scaling functions confirm that the time series of measles, rubella and whooping cough are clearly multifractal, while chicken pox has a more monofractal structure in time. The stochastic SEIR epidemic model is unable to reproduce the qualitative singularity structure of the reported incidence data: it is too smooth and does not appear to have a multifractal singularity structure. The precise reasons for the failure of the SEIR epidemic model to reproduce the correct multiscale structure of the reported incidence data remain unclear.     

岩石断裂面的各向异性分形和多重分形研究

针对表面结构的分形各向异性和奇异性特征，对岩石断裂表面的多重分形性质进行了研究。提出了一种新的分形测量方法---投影覆盖法，直接测量断裂表面的多重分形维数Ｄ∈［２，３），并引入粗糙性概率度量表面不规则性。研究表明，断裂表面的多重分形谱可提供有关断裂机制的更丰富的信息，不同载荷条件和断裂模式下形成的岩石断裂面具有明显不同的多重分形谱函数特征。     

基于多重分形去趋势波动分析的齿轮箱故障特征提取方法

齿轮箱故障信号通常是具有多标度行为的非平稳信号,去趋势波动分析(Detrended Fluctuation Analysis, DFA)不能准确揭示隐藏在这类信号中的动力学行为。多重分形去趋势波动分析(Multifractal Detrended Fluctuation Analysis, MF-DFA)是DFA方法的拓展,能够有效地揭示隐藏在多标度非平稳信号中的动力学行为。利用MF-DFA计算齿轮箱故障信号的多重分形奇异谱,而多重分形奇异谱的宽度、最大奇异指数、最小奇异指数和极值点对应的奇异指数都具有明确的物理意义,能够表征齿轮箱故障信号的内在动力学机制,适合作为齿轮箱振动信号的故障特征。提出一种基于MF-DFA的齿轮箱故障特征提取方法,将该方法用于包含正常、轻度磨损、中度磨损和断齿故障齿轮箱的故障诊断,并与DFA方法的结果进行了对比。结果表明,提出的方法对齿轮箱故障状态的变化非常敏感,能够完全分离相近的故障模式,有效地克服了传统DFA方法存在的缺陷,为齿轮箱的故障特征提取提供了一种新方法。     

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.