Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media
Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media
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具有对称性的随机场的随机模型和生成器：在弹性随机介质细观建模中的应用
DOI：
10.1137/120898346
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Christian Soize
中科院分区：
文献类型：
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作者：
J. Guilleminot;Christian Soize
本文关注的是为矩阵值非高斯随机场构建一类新型广义非参数概率模型。更具体地说，我们考虑这样的情况：随机场可以在实数对称正定矩阵集合的某个子集中取值，该矩阵相对于给定的正交变换呈现稀疏性和不变性。在线性弹性的背景下，这种情况通常出现在异质微观结构的多尺度分析中，其中本构弹性矩阵可能表现出一些材料对称性，并且可能属于对称正定实矩阵集合的给定子集 $\mathbb{M}_n^{sym}(\mathbb{R})$。首先，我们提出了一种基于信息论框架的总体方法，并为随机场定义了特定的代数形式。该表示涉及两个独立的不确定性来源，即，一个几乎肯定保留拓扑......
This paper is concerned with the construction of a new class of generalized nonparametric probabilistic models for matrix-valued non-Gaussian random fields. More specifically, we consider the case where the random field may take its values in some subset of the set of real symmetric positive-definite matrices presenting sparsity and invariance with respect to given orthogonal transformations. Within the context of linear elasticity, this situation is typically faced in the multiscale analysis of heterogeneous microstructures, where the constitutive elasticity matrices may exhibit some material symmetry properties and may then belong to a given subset $\mathbb{M}_n^{sym}(\mathbb{R})$ of the set of symmetric positive-definite real matrices. First, we present an overall methodology relying on the framework of information theory and define a particular algebraic form for the random field. The representation involves two independent sources of uncertainties, namely, one preserving almost surely the topological...