基于多个无标度区的多重分形分析方法

用计算机模拟生成了多重分形结构,通过对比分析结构的解析多重分形谱和配分函数法计算得到的多重分形谱,总结出多重分形谱可以描述结构在某一无标度区内生长规律的特性,发现结构的各个无标度区都具有研究价值,针对传统方法不能充分利用数据的缺陷,提出了基于多个无标度区的多重分形谱计算方法.     

气液两相流波动信号多重分形去趋势波动分析

为了研究不同流型压差波动信号的分形特征,本文首先讨论了多重分形去趋势波动分析对周期信号、随机信号和混沌信号的识别能力,然后运用多重分形去趋势波动分析方法对水平管内气-液两相流压差波动信号进行分析.通过计算广义Hurst指数、尺度函数,多重分形谱,细致量化了压差波动信号的局部及不同层次的波动奇异性.研究结果表明:压差波动...     

混合交通流时间序列的去趋势波动分析

应用去趋势波动分析法研究交通流时间序列的复杂性,探讨了混合交通流时间序列演变行为的标度指数.根据标度指数的变化特征,进而揭示交通流时间序列所具有的长程相关性和短程相关性.通过分析发现,存在一密度ρ,当ρ₁<ρ<ρ₂时,交通流时间序列具有长程相关性;而当ρ<ρ₁或ρ>ρ₂时,交通流时间序列具有短程相关性,即密度的变化影响着标度指数的变化.另外分析了在不同慢车比率条件下时间序列的标度指数,发现慢车比率的变化 关键词： 混合交通流 去趋势波动分析 时间序列 长程相关     

多重分形降趋波动分析法和移动平均法的分形谱算法对比分析

多重分形降趋波动分析法(MFDFA)和多重分形降趋移动平均法(MFDMA)是用来估算一维随机分形信号多重分形谱的两种算法, 已被拓展应用于二维和高维分形信号的分析. 本文简要介绍了MFDFA和MFDMA算法及其在一维时间序列中的应用. 首次系统地从算法模型、计算统计精度、样本量的敏感性、无标度区选取的敏感性、矩选择的敏感性和计算量这六个方面对两种算法进行了对比分析, 以典型多重分形信号BMC信号为例, 分析两种算法的适用性和优劣性. 为实际应用中, 针对具体信号如何选用MFDFA或MFDMA算法, 以及两种算法的参数设置提供了有价值的参考.     

交通流突变点的无标度特征分析

交通流时间序列在不同时间尺度上具有不同的波动特征.为了分析交通流的突变特征,以一段实际的交通流量序列为研究对象进行实证研究.采用小波变换的方法求得交通流在不同尺度上的突变点,按照小波函数过零点数目将交通流的尺度划分为若干层次,并分析了交通流突变的层次性.计算表明:以突变点数目为测度时,在一定的尺度范围内,交通流在突变层次上的突变点数目满足自相似性特征.因此,交通流的突变在不同尺度上具有无标度性.     

去趋势波动分析方法中不重叠等长度子区间长度的确定

针对去趋势波动分析方法中参数不重叠等长度子区间长度s的选取,基于信息论的基本原理,提出使用符号分析方法对原始数据进行符号编码,并使用不同的方式对符号序列进行分段、计算互信息函数.细致描述了不同分段方式对原始混沌序列的信息编码能力,以此判断所采用的分段方式能否真实有效地还原原始序列所包含的全部信息.给出了确定最优分段个数或各分段长度的具体方式,确定了不重叠等长度子区间长度s的选取算法,以及判断所研究序列是否适用于去趋势波动分析方法,避免了以往参数s选取中随机性和主观性给计算结果带来的错误信息.进一步将该方法应用于实际温度资料,计算并分析中国1961—2000年逐日平均温度的去趋势波动分析指数分布状况.     

一种识别关联维数无标度区间的新方法

在计算关联维数过程中, 为了减少人为因素识别无标度区间带来的误差, 提出一种基于模拟退火遗传模糊C均值聚类识别无标度区间的新方法. 该方法根据无标度区间对应曲线的二阶导数在零附近波动的变化特征, 利用分类算法进行识别. 首先对双对数关联积分的离散数据进行二阶差分; 然后利用模拟退火遗传模糊C均值聚类方法对该数据进行分类, 选出在零附近波动的数据; 再剔除粗大误差保留有效数据; 最后进行统计分析识别出线性度最好的作为无标度区间. 应用新方法对两个著名的混沌系统Lorenz 和Henon 进行了仿真, 计算结果与理论值非常符合. 实验表明, 所提出的新方法与主观识别、K-means和2-means方法比较, 可以有效自动识别无标度区间, 减少误差, 计算结果更加精确.     

基于双树复小波变换的非平稳时间序列去趋势波动分析方法

多重分形去趋势波动分析是研究非平稳时间序列非均匀性和奇异性的有效工具, 针对该方法中趋势项难以确定的问题, 提出一种基于双树复小波变换的方法, 实现了非平稳信号的多重分形自适应去趋势波动分析. 利用双树复小波变换提取信号的多尺度趋势和波动信息, 通过小波系数的希尔伯特变换确定每个时间尺度不重叠子区间的长度, 使多重分形分析具有信号自适应性及较高的计算效率. 以具有解析形式分形特征的倍增级联信号和分数布朗运动时间序列为例验证本文方法的有效性, 所得结果与解析解相吻合. 与传统的多项式去趋势多重分形方法相比, 本文方法根据信号自身特点自适应地确定信号的趋势和不重叠等长度子区间长度, 所得结果更加精确. 对倍增级联信号时间序列取不同的长度, 验证了算法的稳定性. 分别与基于极大重叠离散小波变换和离散小波变换多重分形方法进行比较, 表明本文方法具有更精确的结果和更快的运算速度.     

基于去趋势波动分析方法确定极端事件阈值

极端事件或者极值事件脱离了自身的正常演化状态,是系统演化的极端状态或系统受到外界扰动而导致的异常状态.去趋势波动分析法得到的指数是衡量系统在某一时间尺度内演化的长程相关性的参数,系统的长程相关性不受极端事件的影响或影响很小.基于这一思想,提出了利用去趋势波动分析法确定极端事件的阈值方法,并验证了该方法的有效性.使用该方法对北京极端高温事件、极端低温事件和极端降水事件进行了分析和讨论,确定北京1951—2004年极端高温、极端低温事件和极端降水事件的阈值.50余年来,北京极端高温和低温事件在20世纪70年代 关键词： 去趋势波动分析 极端事件 阈值     

基于多分辨分析的高炉铁水含硅量波动多重分形辨识

以包钢6号高炉、邯钢7号高炉和莱钢1号高炉在线采集的铁水含硅量(［Si］)的时间序列为样本, 利用多分辨分析剔除样本的长期趋势,对样本保留的波动趋势进行多重分形特征辨识. 通过计算广义Hurst指数、尺度函数、多重分形谱, 全面、细致量化了序列的局部及不同层次的波动奇异性. 计算结果表明: 去除长期趋势后, 三座高炉［Si］序列的波动呈现显著多重分形特征, 这样的波动过程仅用单一的Hurst指数或box维数来描述是不够的. 关键词： 多分辨分析 铁水含硅量 波动 多重分形     

Effects of quantization on detrended fluctuation analysis

Detrended fluctuation analysis(DFA) is a method foro estimating the long-range power-law correlation exponent in noisy signals.It has been used successfully in many different fields,especially in the research of physiological signals.As an inherent part of these studies,quantization of continuous signals is inevitable.In addition,coarse-graining,to transfer original signals into symbol series in symbolic dynamic analysis,can also be considered as a quantization-like operation.Therefore,it is worth considering whether the quantization of signal has any effect on the result of DFA and if so,how large the effect will be.In this paper we study how the quantized degrees for three types of noise series(anti-correlated,uncorrelated and long-range power-law correlated signals) affect the results of DFA and find that their effects are completely different.The conclusion has an essential value in choosing the resolution of data acquisition instrument and in the processing of coarse-graining of signals.     

Application of long-range correlation and multi-fractal analysis for the depiction of drought risk

By using the multi-fractal detrended fluctuation analysis method, we analyze the nonlinear property of drought in southwestern China. The results indicate that the occurrence of drought in southwestern China is multi-fractal and longrange correlated, and these properties are indifferent to timescales. A power-law decay distribution well describes the return interval of drought events and the auto-correlation. Furthermore, a drought risk exponent based on the multi-fractal property and the long-range correlation is presented. This risk exponent can give useful information about whether the drought may or may not occur in future, and provide a guidance function for preventing disasters and reducing damage.     

Chaotic SVD method for minimizing the effect of exponential trends in detrended fluctuation analysis

The Detrended Fluctuation Analysis (DFA) and its extensions (MF-DFA) have been used extensively to determine possible long-range correlations in self-affine signals. However, recent studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. In this study, a smoothing algorithm based on the Chaotic Singular-Value Decomposition (CSVD) is proposed to minimize the effect of exponential trends and distortion in the log-log plots obtained by DFA techniques. The effectiveness of the technique is demonstrated on monofractal and multifractal data corrupted with exponential trends.     

Multifractal detrended fluctuation analysis for clustering structures of electricity price periods

A new model is proposed to investigate the structure of electricity price in different time periods. A popular method — the multifractal detrended fluctuation analysis (MF-DFA) method is employed to analyze the features achieved from three types of electricity price data after filtering some trends by Fourier detrended fluctuation function. Twelve multifractal parameters are calculated and selected as the characteristic indicators for comparison. Moreover, the minimum number of indicators is determined so that the discriminant accuracy reaches maximum based on Fisher’s linear discriminant algorithm (Fisher’s LDA) for each time period. These indicators form a multi-dimensional space, in which each point represents a price time series. This allows us to cluster the three price time periods, namely, the low price time periods, the average price time periods and the peak price time periods. Fisher’s LDA is employed to evaluate the discriminant accuracy on these three kinds of time periods. Our analysis is then applied to the data in California1999–2000 and PJM2001–2002 electricity markets to demonstrate the applicability of our methods.     

Relationships of exponents in multifractal detrended fluctuation analysis and conventional multifractal analysis

Multifractal detrended fluctuation analysis (MF-DFA) is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis (DFA), which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression τ(q)=qh(q)-1 stipulating the relationship between the multifractal exponent τ(q) and the generalized Hurst exponent h(q). As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as τ(q)=qh(q)-qH'-1, where H' is the nonconservation parameter in the universal multifractal formalism. The singular spectra, α and f(α), are also derived according to this new relationship.