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为了理解各式各样的具有广义自相似性特征的尺度不变性系统,提出了1个称之为GSI(generalized scale invariance)的理论体系.它阐述了大小尺度可以相互关联而不需要引入任何1个特有(具体)尺度的最普通情形.在二维线性GSI理论的基础上,形成了2个重要的各向异性尺度不变性量化模型:SIG(scale invariant generator)模型和S-A(spectrum-area)模型.SIG模型通过在频率域中估计GSI理论中代表旋转和层化程度的尺度不变性生成元的参数来量化各向异性尺度不变性.而S-A模型通过从二维频率域中能谱密度大于P元素集的面积与P之间关系的非参数模型对各向异性尺度不变性进行量化.如果研究的对象是1个混合模式(多个不同尺度的过程或作用叠加而形成的),S-A模型不仅可以对异性尺度不变性进行量化,还可以对该混合模式进行分解.系统阐述了GSI理论、SIG模型和S-A模型,并将SIG模型和S-A模型结合提出了既能对混合模式进行分解又能对分解后模式的各向异性尺度不变性进行量化的模型.
In order to understand a wide range of scale-invariant systems with generalized self-similar features, a theoretical system called GSI (generalized scale invariance) is proposed, which states that size scales can be related to each other without introducing any 1 Based on the two-dimensional linear GSI theory, two important quantitative models of anisotropy scale invariance are formed: scale invariant generator (SIG) and spectrum-area (SA) Model.SIG model quantifies the anisotropy scale invariance by estimating the parameters of the scale invariance generator in the GSI theory in the frequency domain, The non-parametric model of the relationship between the area of P element sets and P quantifies the anisotropy-scale invariance.If the object of study is a mixed model (formed by overlaying several processes or actions of different scales), the SA model It not only can quantify the invariance of the scale of the opposite sex, but also decompose the mixed mode.It expounds the GSI theory, SIG model and SA model systematically, and combines SIG model and SA model He proposed a model that can both decompose mixed modes and quantify the invariance of the anisotropic scale of the decomposed mode.