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

Abstract

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.

Low-cost approximate reconstructing of heterogeneous microstructures

“…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.…”

Statistical Reconstruction of Microstructures Using Entropic Descriptors

“…A digitized cross-section with a linear size of 170 pixels of the piece of concrete (Garboczi and Bentz 1998) with nanometre-sized pores and centimetre-sized aggregates has been used for testing different reconstruction methods (Jiao et al 2009;Tahmasebi and Sahimi 2013;Olchawa and Piasecki 2015). The binary target pattern is composed of non-uniform arrangement of irregular aggregates, which are relatively big in comparison to the size of the whole pattern.…”

“…The next significant improvement is the replacing one of the entropic pairs by a pair of distinct CFs and adding two respective weighting coefficients. The WDH method has been applied to islands, aggregates or compact clusters of various shapes and poly-dispersed in sizes by Olchawa and Piasecki (2015). The approach is concisely presented below.…”

“…The competition of the doubly-hybrid pairs ensures considering a wider spectrum of morphological features. We present part of the results with the neutral weighting factor α = 0.5 (Olchawa and Piasecki 2015). Here, for comparison purposes, the lineal-path L(k) function, additionally computed for both the concrete sample cross-section and its reconstruction, is shown in Fig.…”

“…1 The accuracy of the WDH reconstruction of a concrete microstructure supported by comparing different descriptors. a Comparison of the lineal-path L(k) function for the target concrete cross-section (the solid line) which is depicted in the upper inset (adapted from Jiao et al 2009) with that of the reconstructed microstructure with α = 0.5 (the filled circles), see the bottom inset (Olchawa and Piasecki 2015). In the both insets, the white phase corresponds to the cement paste, while the black (or grey) phase of the concentration 0.51 represents the stones.…”