Research Papers: Design Automation

A Machine Learning-Based Design Representation Method for Designing Heterogeneous Microstructures

[+] Author and Article Information
Hongyi Xu

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: hongyixu2014@u.northwestern.edu

Ruoqian Liu

Department of Electrical Engineering
and Computer Science,
Northwestern University,
Evanston, IL 60208
e-mail: rosanne@northwestern.edu

Alok Choudhary

Department of Electrical Engineering
and Computer Science,
Northwestern University,
Evanston, IL 60208
e-mail: choudhar@eecs.northwestern.edu

Wei Chen

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: weichen@northwestern.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 21, 2014; final manuscript received February 3, 2015; published online March 5, 2015. Assoc. Editor: Carolyn Seepersad.

J. Mech. Des 137(5), 051403 (May 01, 2015) (10 pages) Paper No: MD-14-1507; doi: 10.1115/1.4029768 History: Received August 21, 2014; Revised February 03, 2015; Online March 05, 2015

In designing microstructural materials systems, one of the key research questions is how to represent the microstructural design space quantitatively using a descriptor set that is sufficient yet small enough to be tractable. Existing approaches describe complex microstructures either using a small set of descriptors that lack sufficient level of details, or using generic high order microstructure functions of infinite dimensionality without explicit physical meanings. We propose a new machine learning-based method for identifying the key microstructure descriptors from vast candidates as potential microstructural design variables. With a large number of candidate microstructure descriptors collected from literature covering a wide range of microstructural material systems, a four-step machine learning-based method is developed to eliminate redundant microstructure descriptors via image analyses, to identify key microstructure descriptors based on structure–property data, and to determine the microstructure design variables. The training criteria of the supervised learning process include both microstructure correlation functions and material properties. The proposed methodology effectively reduces the infinite dimension of the microstructure design space to a small set of descriptors without a significant information loss. The benefits are demonstrated by an example of polymer nanocomposites optimization. We compare designs using key microstructure descriptors versus using empirically chosen microstructure descriptors as a demonstration of the proposed method.

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Fig. 1

SEM images of polymer nanocomposites, binary image, and correlation function-based characterization

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Fig. 2

Illustration of three levels of microstructure descriptors: composition, dispersion, and geometry

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Fig. 3

Framework of machine learning-based microstructure descriptor identification

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Fig. 4

Illustration of redundant microstructure descriptors. In microstructure I, area A, and major radius r can replace each other; in microstructure II, both are needed for a full microstructure representation.

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Fig. 5

(a) The permuted rank correlation matrix shows intracorrelated descriptor groups. Larger correlations are marked by darker colors. White color means the correlation is 0 (no correlation). The sequential numbers on X, Y axis represent different descriptors. Refer to the Appendix for the meanings of sequential numbers. (b) and (c): the binarized correlation matrix. The bright pixel means a correlation larger than or equal to the threshold; the dark pixel means a correlation smaller than the threshold. Two thresholds are tested: 0.9 and 0.8.

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Fig. 6

Sample images of damping system (evenly dispersed fillers) and dielectric system (clustering of fillers). In damping system, the bright part represents fillers; in dielectric system, the dark spots represent fillers.

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Fig. 7

Microstructure reconstructions using statistically learned descriptor set and empirical descriptor set

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Fig. 8

Comparison of optimal designs (Min: L, Max: P, Max: H) using key descriptors and empirical descriptors. (a) Single objective optimization for each objective; (b) multi-objective optimization with equal weights on objectives. Two examples of optimal microstructures, Max H by key descriptors and Max H by empirical descriptors, are also plotted.



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