去滑动均值趋势的DeWijs模型多重分形特征分析

摘要

运用去滑动均值算法，探讨了 De Wijs 模型的多重分形特征。结果显示，趋势波动函数 Fq(s)与尺度 s 具有较好幂律关系， Hurst 指数 h(q)与标度函数τ(q)都是随 q 变化的非线性函数，且随着富集参数 d 的增大，多重分形谱 f(α)曲线跨度越大，指示多重分形特征越明显。这表明去滑动均值算法是识别 De Wijs 模型的多重分形特征及区分其分形强度的有效方法，可为进一步应用于实验数据的非线性特征分析提供理论指导。%Multifractal detrending moving average analysis(MFDMA) is used to study the multifractal characteristics of the De Wijs model and identify the degree of enrichment d. The results show that fluctuation function Fq(s) and window size s have a better scaling law after detrending moving average (DMA). At the same time, Hurst exponent h(q) and scaling exponent τ(q) are non-linear function along with the change of q-order. As the increase of the degree of enrichment, the span of multifractal spectrum curve get more huge, showing the multifractal characteristics will be more clear. The results make us better to understand multifractal detrending moving average analysis is a good method to identify the multifractal characteristics of De Wijs model and distinct the multifractal strength, and further theoretical guidances can be provided to the nonlinear characteristic of the experimental data analysis.