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Presentation given at 49th Annual Technical Meeting for the Society of Engineering Sciences in the Materials - Processing, Microstructure, Performance Relations Symposia on October 12, 2012 at Georgia Tech in Atlanta, GA.
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Higher-Order Microstructure Statistics for Next Generation Materials Taxonomy
Tony Fast
University of California Santa Barbara, Materials Engineering
Olga Wodo, Baskar Ganapathysubramanian
Iowa State University, Mechanical Engineering
Surya R. Kalidindi
Drexel University, Mechanical Engineering
From Materials Selection
μS informatics distill rich spatial and temporal information into tractable, usable, and searchable bi-direction SPP linkages
From Materials Selection to Microstructure (μS) Informatics…
A. 2-pt Correlation Function – Statistical correlation between random points in space/time
B. Chord Length Distribution – length and orientation of chords in a heterogeneous medium
C. Interfacial Surface Distribution - The principal curvatures of surfaces in the μS.
A. B. C.
Effective statistics are contained in μS InformaticsStatistical spatial distributions capture traditional effective statistical measures
C. Kwon, Yongwoo, Morphology and topology of interfaces during coarsening via nonconserved and conserved dynamics, Northwestern, Thesis, 2007.
Benefits of Using n-Point Correlations• Ground Truth• Fit naturally in higher-orderhomogenization and localization theories
The Microstructure is a stochastic processDistributions provide a framework to effectively compare microstructures
Mic
rost
ruct
ure
Aut
ocor
rela
tion
-
- =
=
HT1 HT2 Difference
Extremely Large Dimensional Spaces!
The comparison of μS is dubious due to the lack of origin.
Autcorrelation contains all of the information in its respective μS.
MS informatics benefits from dimensional reductionReducing the number of random variables for feature selection and extraction in discrete materials systems
Improve Empirical Fitting:
Porous Bi-layers in Fuel Cells
Microstructure Taxonomy:
MS Mapping of α-βTitanium
VfKalidindi, S.R., S.R. Niezgoda, and A.A. Salem, Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM, 2011. 63(4): p. 34-41.
A. Çeçen, T. Fast, E. C. Kumbur, and S. R. Kalidindi, Data-driven Approaches to Establishing Microstructure-property Relationships: Application to Transport through Porous Structures, submitted, 2012.
Principal Component Analysis: Reduced embedding of linearly independent variables that correspond to decreasing levels of variance starting with the highest (Dd)
>6e6 Variables~1e6 Variables
μS Taxonomy of Continuous Material Feature An Application to Organic Blends in Solar Cells
10% FAST PHASE SEPARATION 90% SLOW GRAIN COARSENING
FINAL STRUCTURES
11 Distinct TopologiesMany Topologies
Simulation data provided by Olga Wodo and Baskar Ganapathysubramanian at ISU.
Isosurfaces of atomic fraction1100 Datasets
Use data driven techniques to classify the final topology before the simulation is complete. i.e. Reduce Redundancy, Time Savings
End Goal
Develop Microstructure Taxonomies of the Final Structuresi.e. Build Utilities for Continuous Materials Features
First Goal
First-Order Higher-Order
Discrete
Continuous
μS function of continuous materials featuresInformatics benefit from a generalized higher-order microstructure description
H
hs
hhs vm
1
10,11
hs
H
h
hs mmPrimitive Basis
Function
nsm
nm1nm3
nm5
nm6
nm2
poreblack
solidwhitem
s
shs /1
/0
N
N
hts
hts
hs
hs mmmm 1
1
0~~
Local conformation of pixels
ssss ,,~
210~~ h
shs
hs
hs mmmm
shs fm 1 sh
s fm 2
μS informatics workflow is a systemMicrostructure Descriptor, Statistics, PCA, etc are isolated modules
Systems analysis allows one to prove the efficacy of methods
HO Descriptors
NP CorrelationsPCA/k-means
Future Work
1100 Datasets
Reduced embedding of final topologiesPCA projection changes with the number of basis functions and the gradient
Hard clustering in the PCA space allows the final topologies to be classified qualitatively
Each point indiciates a 21x21x21 μS where each color is a different topology
Augmented embedding combines gradientsPCA embedding changes when different descriptors are combined
Data-mining with k-means clusteringAutomated topology recognition and quantitative metrics
k-Means Clustering: A data-mining approach that creates partitions based on the means of clusters to automatically classify datapoints.
Sensitivity – metric for accurate classification
Specificity – metric for accurate nonclassification
Classification CasesTP – Correct classificationTN – Correct nonclassificationFP – Incorrect classificationFN – Incorrect nonclassification
Range = 0 to 1
Quantitative Measures of ClusteringSensitivity and specificity analysis of PCA embedding
AF
FG
SGAF
FG
SG
AF – Atomic FractionFG – First GradientSG – Second Gradient
ClockwiseFG,SGAF,SGAF,FGAF,FG,SG
• An automated data-mining technique was successfully developed for 3D systems with continuous μS features.
• A generalized higher-order μS descriptor was developed using the primitive basis.
• Higher-order descriptors prove that higher-order terms play a strong role in developing structure-structure databases.
• This system naturally clusters in PCA, but other DR techniques show improvement.
• μS informatics are necessary to automatically disseminate structure-structure relationships of large collections of multi-dimensional datasets
ConclusionsHigher-Order Microstructure Statistics for Next Generation Materials Taxonomy
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