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首页> 外文期刊>Philosophical Magazine Letters >Direct parameter estimation for generalised balanced power diagrams
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Direct parameter estimation for generalised balanced power diagrams

机译：广义平衡电源图的直接参数估计

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摘要

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.
机译：通过曲面细胞化模型来辅助多晶材料微观结构的统计表征和合成繁殖。广义平衡功率图（GBPD）是一种曲面细胞化模型，其在先前的研究中显示，通过通过电子显微镜获得的显微照片精确地再现各种材料的微观结构形态。这些研究采用了昂贵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，示出了将曲面细胞的细胞参数设定为值，使得相应晶粒的形状矩具有与优化程序相称的拟合质量匹配。该配件方法在拟合曲面细分参数时与颗粒相互作用，并且最特别地为所有模型参数提供分析，闭合形式表达式的谷物之间的相互作用。在各种材料的多个显微照片上证明了该参数拟合方法的性能，它与最近公开文献中报告的优化程序的性能相似。随着拟合参数值通过琐碎的计算获得，该方法可以实现GBPD模型的广泛可扩展性，使得它可以用于表示极大的表征数据集。

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