Research Papers: Design Automation

Microstructure Representation and Reconstruction of Heterogeneous Materials Via Deep Belief Network for Computational Material Design

[+] Author and Article Information
Ruijin Cang, Yongming Liu, Max Yi Ren

Department of Mechanical Engineering,
Arizona State University,
Tempe, AZ 85287

Yaopengxiao Xu, Shaohua Chen, Yang Jiao

Department of Materials
Science and Engineering,
Arizona State University,
Tempe, AZ 85287

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 28, 2016; final manuscript received April 20, 2017; published online May 19, 2017. Assoc. Editor: Carolyn Seepersad.

J. Mech. Des 139(7), 071404 (May 19, 2017) (11 pages) Paper No: MD-16-1674; doi: 10.1115/1.4036649 History: Received September 28, 2016; Revised April 20, 2017

Integrated Computational Materials Engineering (ICME) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable ICME, it is required that (1) a structural feature space be identified to allow reconstruction of new designs, and (2) the reconstruction process be property-preserving. The majority of existing structural presentation schemes relies on the designer's understanding of specific material systems to identify geometric and statistical features, which could be biased and insufficient for reconstructing physically meaningful microstructures of complex material systems. In this paper, we develop a feature learning mechanism based on convolutional deep belief network (CDBN) to automate a two-way conversion between microstructures and their lower-dimensional feature representations, and to achieve a 1000-fold dimension reduction from the microstructure space. The proposed model is applied to a wide spectrum of heterogeneous material systems with distinct microstructural features including Ti–6Al–4V alloy, Pb63–Sn37 alloy, Fontainebleau sandstone, and spherical colloids, to produce material reconstructions that are close to the original samples with respect to two-point correlation functions and mean critical fracture strength. This capability is not achieved by existing synthesis methods that rely on the Markovian assumption of material microstructures.

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Fig. 1

(a) Samples and random synthesis results of material systems that are assumed to be Markovian [48]. (b) and (c) Random synthesis of the Ti–6Al–4V alloy microstructure following the synthesis algorithm from Ref.[48]. The synthesis is based on (b) a single sample and (c) 100 samples from Fig. 14. Image courtesy of Dr.Ramin Bostanabad.

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Fig. 2

(a) Three layers of human face features extracted at increasing length scales [54] and (b) a schematic comparison between an RBM and an autoencoder. ai (bj) and vi (hj) are the bias and state values of visible (hidden) layer, respectively. Wij indicates the weights between the visible and hidden layers.

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Fig. 3

(a) CRBM and pooling layers and (b) forward and backward probabilistic max-pooling procedures with 2 × 2 blocks

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Fig. 4

Input images and extracted features. Visualizations of filters for the five layers: The first layer has two filters, each with 12 orientations (see Sec. 3.1). Due to limited space, only the first 144 and 25 filters from the third and fourth layers, respectively, are shown.

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Fig. 5

Activation on different filters. From left to right, reconstructions when only the first, only the second, and both nodes from the fifth layer are activated, respectively.

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Fig. 6

Comparison between random reconstructions from (a) the fourth and (b) the fifth layers, sampled from the corresponding design spaces ({0, 1}1000 in (a) and {0, 1}30 in (b))

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Fig. 7

Postprocessing steps: Column (a) shows the original reconstruction and its third layer activations (288 channels) with enlarged sample channels; Column (b) shows the reconstruction after thresholding the third layer activations at 0.5; Column (c) shows the further improved reconstruction after skeletonization

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Fig. 8

(a) A threshold of 0.5 does not always guarantee valid reconstructions, see the second row (b) threshold can be fine-tuned based on a heuristic criterion: Here, we test a set of threshold values and pick the one that yields a volume fraction closest to the average volume fraction of reconstructions of the original samples (ρ = 0.51)

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Fig. 9

A comparison between random reconstructions (bottom) and the original samples (top) for four different material systems

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Fig. 10

Comparison between the samples (top) and their reconstructions (bottom). Details of the two fail to match.

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Fig. 11

The two-point correlation functions for the four different materials

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Fig. 12

(a) Comparison on critical fracture strength among the four material systems between the original samples (black), their corresponding reconstructions (gray), and random reconstructions (white) and (b) comparison on critical fracture strength among individual original images and the related reconstruction images (see figure online for color)

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Fig. 13

(a)–(c) Sample reconstructions (without skeletonization) based on models trained from 10, 50, and 100 samples, respectively. The variances among random reconstructions for these three cases are 0.2644, 0.2863, and 0.4205, respectively. The variance is calculated from 100 reconstructions in each case.

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Fig. 14

Ti–6Al–4V alloy

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Fig. 15

Pb–Sn (lead–tin) alloy

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Fig. 16

Pore structure of Fontainebleau sandstone

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Fig. 17

Two-dimensional suspension of spherical colloids




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