论文标题
部分可观测时空混沌系统的无模型预测
Fitting the grain orientation distribution of a polycrystalline material conditioned on a Laguerre tessellation
论文作者
论文摘要
与谷物微观结构相关的分布的描述有助于物理学家了解材料及其特性的过程。本文提出了一种一般的统计方法，用于分析3D laguerre tessellation数据集中晶粒的晶体方向，该数据集代表多晶材料的微观结构。我们引入了复杂的随机模型，该模型可以替代昂贵的实验室实验：在拉瓜尔乳胶上的条件下，我们建议用于分布立方晶体晶格方向的相互作用模型，其中这种相互作用是在乳胶中相邻晶粒的方向之间的相互作用。我们讨论了基于最大伪样性的参数估计和模型比较方法以及使用模拟检查模型检查的图形程序。我们的方法用于分析代表镍形状存储合金的数据集。
The description of distributions related to grain microstructure helps physicists to understand the processes in materials and their properties. This paper presents a general statistical methodology for the analysis of crystallographic orientations of grains in a 3D Laguerre tessellation dataset which represents the microstructure of a polycrystalline material. We introduce complex stochastic models which may substitute expensive laboratory experiments: conditional on the Laguerre tessellation, we suggest interaction models for the distribution of cubic crystal lattice orientations, where the interaction is between pairs of orientations for neighbouring grains in the tessellation. We discuss parameter estimation and model comparison methods based on maximum pseudolikelihood as well as graphical procedures for model checking using simulations. Our methodology is applied for analysing a dataset representing a nickel-titanium shape memory alloy.
