ABSTRACT

Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physically inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the starting point of the investigation. Isotonic regression allows to take into account ordering relations and leads to more efficient and accurate results when the underlying assumptions actually hold. The main goal in this paper is to test order relations in a model inspired by a materials science application. The statistical estimation procedure is described considering three different scenarios according to the knowledge of the variances: known variance ratio, completely unknown variances, and variances under order restrictions. New likelihood ratio tests are developed in the last two cases. Both parametric and non-parametric bootstrap approaches are developed for finding the distribution of the test statistics under the null hypothesis. Finally an application on the relation between geometrically necessary dislocations and number of observed microstructure precipitations is shown.

摘要

研究金属机械性能的主要决定因素并非易事。已知的 2D 微观结构特征和 3D 机械性能之间的物理启发定性关系可以作为研究的起点。当基本假设实际成立时，等渗回归允许考虑排序关系并导致更有效和更准确的结果。本文的主要目标是测试受材料科学应用启发的模型中的顺序关系。根据方差的知识，考虑三种不同的场景来描述统计估计过程：已知方差比、完全未知的方差和订单限制下的方差。在最后两种情况下开发了新的似然比检验。参数和非参数自举方法都被开发用于在零假设下寻找检验统计量的分布。最后显示了几何必要位错与观察到的微观结构析出数量之间关系的应用。