Speeding up of microstructure reconstruction: I. Application to labyrinth patterns

Piasecki, R.; Olchawa, W.

doi:10.1088/0965-0393/20/5/055003

Cited by 9 publications

(14 citation statements)

References 21 publications

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“…In this way, various random two-phase microstructures are modelled by different spatial arrangements of the phase-corresponding voxels. The present approach is based on one of entropic descriptors (EDs) that describes the average multi-scale spatial inhomogeneity of a given microstructure [28,29,32,33]. However, the estimation of the spatial inhomogeneity is related to the scale of its description.…”

Section: The Methodsmentioning

confidence: 99%

Low-cost approximate reconstructing of heterogeneous microstructures

Olchawa¹,

Piasecki²,

Wiśniowski³

et al. 2016

Computational Materials Science

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We propose an approximate reconstruction of random heterogeneous microstructures using the two-exponent power-law (TEPL). This rule originates from the entropic descriptor (ED) that is a multi-scale measure of spatial inhomogeneity for a given microstructure. A digitized target sample is a cube of linear size L in voxels. Then, a number of trial configurations can be generated by a model of overlapping spheres of a fixed radius, which are randomly distributed on a regular lattice. The TEPL describes the averaged maximum of the ED as a function of the phase concentration and the radius. Thus, it can be used to determine the radius. The suggested approach is tested on surrogate samples of ceramic and carbonate. In each of the cases, fifty low-cost trials provided a few good enough candidates to a selection of the optimal reconstruction. When a better accuracy is planned, the final reconstructions can serve as the starting configurations. Then, the resulting reconstructions should be competitive indeed to those starting with random configurations.Comment: In Figure 3, the repeated by mistake Fig. 2b is replaced by the correct Fig. 3b, published versio

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Section: The Methodsmentioning

confidence: 99%

Low-cost approximate reconstructing of heterogeneous microstructures

Olchawa¹,

Piasecki²,

Wiśniowski³

et al. 2016

Computational Materials Science

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“…Thus, the usage of four hybrid EDs for the mentioned above types of patterns was a preferred choice in Piasecki (2011). It was applied also to the stochastic reconstruction of complex labyrinth patterns by Piasecki and Olchawa (2012). The next significant improvement is the replacing one of the entropic pairs by a pair of distinct CFs and adding two respective weighting coefficients.…”

Section: The Cost Function For 2d Complex Composite Materialsmentioning

confidence: 99%

Statistical Reconstruction of Microstructures Using Entropic Descriptors

et al. 2018

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We report a multiscale approach of broad applicability to stochastic reconstruction of multiphase materials, including porous ones. The approach devised uses an optimization method, such as the simulated annealing (SA) and the so-called entropic descriptors (EDs). For a binary pattern, they quantify spatial inhomogeneity or statistical complexity at discrete lengthscales. The EDs extract dissimilar structural information to that given by two-point correlation functions (CFs). Within the SA, we use an appropriate cost function consisting of EDs or comprised of EDs and CFs. It was found that the stochastic reconstruction is computationally efficient when we begin with a preliminary synthetic configuration having in part desirable features.Another option is low-cost approximate reconstructing of the entire multiphase medium beyond the SA technique. The information included in the target ED-curve was utilized for this purpose. For a given volume fraction the low-cost trial microstructures can be generated in two ways. In the first one, applied to ceramics and carbonate samples, the interpenetrating spheres generate a number of trial configurations. In the second one, with phase-EDs, here used to the sandstone sample, the overlapping superspheres do it. Both methods use a radius determined from the EDs-linked two-exponent power-law. However, the supersphere deformation parameter allows controlling of the spatial inhomogeneity of prototypical microstructures. At last, even for a hypothetical ED-curve (under reasonable assumptions), the specific microstructure can be found, if it is realizable for a given volume fraction. In general, the EDsbased methods offer a compromise between computational efficiency and the accuracy of reconstructions.

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“…When the entropic descriptors (EDs) only are included in the objective (cost) function, the speeding-up of a labyrinth microstructure reconstruction can be achieved in a simple way [21]. Here, we propose a significant modification of this kind of reconstruction in order to apply it to patterns of islands of miscellaneous shapes and poly-dispersed in sizes.…”

Section: Weighted Doubly-hybrid Reconstructionmentioning

confidence: 99%

“…To obtain a well-balanced influence of ED and CF part in (3.3), the equal number of considered scales is applied. Let us note that the present form of energy differs from the previously considered one [20,21], where two pairs of binary entropic descriptor and its grey-scale counterpart are included.…”

Section: Weighted Doubly-hybrid Reconstructionmentioning

confidence: 99%

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Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands

Olchawa

Piasecki

2015

Computational Materials Science

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H I G H L I G H T S  A weighted doubly-hybrid method of statistical reconstruction of patterns isreported.  The weighting factors account in part for an irregularity of islands shapes.  A final pattern has the same value of interface and number of islands as the target.  This competitive approach offers morphologically credible patterns.A B S T R A C T We report a fast, efficient and credible statistical reconstruction of any two-phase patterns of islands of miscellaneous shapes and poly-dispersed in sizes. In the proposed multi-scale approach called a weighted doubly-hybrid, two different pairs of hybrid descriptors are used. As the first pair, we employ entropic quantifiers, while correlation functions are the second pair. Their competition allows considering a wider spectrum of morphological features. Instead of a standard random initial configuration, a synthetic one with the same number of islands as that of the target is created by a cellular automaton. This is the key point for speeding-up of microstructure reconstruction, making use of the simulated annealing technique. The program procedure allows requiring the same values for the reconstructed and target interface. The reconstruction terminates when three conditions related to the accuracy, interface and number of islands are fulfilled. We verify the approach on digitized images of a thin metallic film and a concrete sample cross-section. For a given accuracy, our method significantly reduces the number of accepted Monte Carlo steps when compared to the standard approach. At the same time, it provides credible shapes and similar areas of islands, keeping their number and the total interface of the target. To the best of our knowledge, this is the first attempt to obtain such an outcome. The cost-effective reconstructions suggest that the present technique could also be used for patterns of islands with strongly jagged border lines.

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Speeding up of microstructure reconstruction: I. Application to labyrinth patterns

Cited by 9 publications

References 21 publications

Low-cost approximate reconstructing of heterogeneous microstructures

Low-cost approximate reconstructing of heterogeneous microstructures

Statistical Reconstruction of Microstructures Using Entropic Descriptors

Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands

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