Piasecki Ryszard, Olchawa Wiesław, Frączek Daniel, Bartecka Agnieszka
Institute of Physics, University of Opole, Oleska 48, 45-052 Opole, Poland.
Department of Materials Physics, Opole University of Technology, Katowicka 48, 45-061 Opole, Poland.
Materials (Basel). 2020 Jun 17;13(12):2748. doi: 10.3390/ma13122748.
The main goal of our research is to develop an effective method with a wide range of applications for the statistical reconstruction of heterogeneous microstructures with compact inclusions of any shape, such as highly irregular grains. The devised approach uses multi-scale extended entropic descriptors (ED) that quantify the degree of spatial non-uniformity of configurations of finite-sized objects. This technique is an innovative development of previously elaborated entropy methods for statistical reconstruction. Here, we discuss the two-dimensional case, but this method can be generalized into three dimensions. At the first stage, the developed procedure creates a set of black synthetic clusters that serve as surrogate inclusions. The clusters have the same individual areas and interfaces as their target counterparts, but . Then, from a given number of easy-to-generate synthetic cluster configurations, we choose the one with the lowest value of the cost function defined by us using extended ED. At the second stage, we make a significant change in the standard technique of simulated annealing (SA). Instead of swapping pixels of different phases, we randomly move each of the selected synthetic clusters. To demonstrate the accuracy of the method, we reconstruct and analyze two-phase microstructures with irregular inclusions of silica in rubber matrix as well as stones in cement paste. The results show that the two-stage reconstruction (TSR) method provides convincing realizations for these complex microstructures. The advantages of TSR include the ease of obtaining synthetic microstructures, very low computational costs, and satisfactory mapping in the statistical context of inclusion shapes. Finally, its simplicity should greatly facilitate independent applications.
我们研究的主要目标是开发一种有效的方法，该方法具有广泛的应用范围，用于对具有任意形状紧凑夹杂物（如高度不规则晶粒）的非均匀微观结构进行统计重建。所设计的方法使用多尺度扩展熵描述符（ED），该描述符可量化有限尺寸物体配置的空间非均匀程度。这项技术是先前阐述的用于统计重建的熵方法的创新发展。在这里，我们讨论二维情况，但该方法可以推广到三维。在第一阶段，所开发的程序创建一组黑色合成簇，用作替代夹杂物。这些簇具有与目标夹杂物相同的单个面积和界面，但是。然后，从给定数量的易于生成的合成簇配置中，我们选择使用扩展ED定义的成本函数值最低的那个。在第二阶段，我们对模拟退火（SA）的标准技术进行了重大改变。我们不是交换不同相的像素，而是随机移动每个选定的合成簇。为了证明该方法的准确性，我们重建并分析了橡胶基质中含有不规则二氧化硅夹杂物以及水泥浆中含有石头的两相微观结构。结果表明，两阶段重建（TSR）方法为这些复杂的微观结构提供了令人信服的实现。TSR的优点包括易于获得合成微观结构、计算成本非常低以及在夹杂物形状的统计背景下具有令人满意的映射。最后，它的简单性应极大地促进独立应用。
