Direct parameter estimation for generalised balanced power diagrams
Direct parameter estimation for generalised balanced power diagrams
复制标题
广义平衡功率图的直接参数估计
DOI：
10.1080/09500839.2018.1472399
复制
发表时间：
2018
影响因子：
1.2
通讯作者：
D. Rowenhorst
中科院分区：
文献类型：
--
作者：
K. Teferra;D. Rowenhorst
摘要 通过镶嵌模型以数学方式表示其形态，有助于多晶材料微观结构的统计表征和合成再现。广义平衡功率图（GBPD）是一种曲面细分模型，在之前的研究中显示，它可以通过紧密匹配通过电子显微镜获得的显微照片来准确再现各种材料的微观结构形态。这些研究采用成本高昂的优化程序来确定最佳拟合模型参数，限制了模型的可扩展性。在这项工作中，结果表明，将曲面细分单元参数设置为使得相应颗粒的形状力矩匹配的值，可以得到与优化过程相称的拟合质量。这种拟合方法在拟合曲面细分参数时解耦了颗粒之间的相互作用，最值得注意的是，为所有模型参数提供了解析的封闭式表达式。这种参数拟合方法的性能在各种材料的多张显微照片上得到了证明，并且与最近发表的文献中报道的优化程序的性能进行了类似的比较。由于拟合的参数值是通过简单的计算获得的，因此该方法使得 GBPD 模型具有广泛的可扩展性，从而可以用于表示极大的表征数据集。
ABSTRACT The statistical characterisation and synthetic reproduction of a polycrystalline material's microstructure is assisted by mathematically representing its morphology by a tessellation model. The generalised balanced power diagram (GBPD) is a tessellation model that was shown in previous studies to accurately reproduce the microstructure morphology of various materials by closely matching micrographs obtained through electron microscopy. These studies employed costly optimisation procedures to determine the best-fit model parameters, limiting the scalability of the model. In this work, it is shown that setting the tessellation cell parameters to values such that the shape moments of the corresponding grains are matched results in a quality of fit that is commensurate with optimisation procedures. This fitting approach decouples the interaction among grains when fitting the tessellation parameters and, most notably, provides analytical, closed-form expressions for all the model parameters. The performance of this parameter fitting approach is demonstrated on multiple micrographs of various materials, and it compares similarly to the performance of optimisation procedures reported in recently published literature. As the fitted parameter values are obtained through trivial computations, this approach enables extensive scalability of the GBPD model such that it can be used to represent extremely large characterisation data sets.
影响因子：
1.6
作者：
A. Alpers;A. Brieden;P. Gritzmann;A. Lyckegaard;H. F. Poulsen
通讯作者：
H. F. Poulsen