Spatially resolved pair correlation functions for structure processing taxonomies - ICME 2013
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Transcript of Spatially resolved pair correlation functions for structure processing taxonomies - ICME 2013
Spatially Resolved Pair Correlation Functions
for Structure-Processing Taxonomies
DATA
SO
UR
CES
Chandler Becker
Al Molecular Dynamics Peter Voorhees, John Gibbs
X-CT Al-Cu Solidification Karl Jacobs, Xin Dong
Polymer MD
MAT
SCI
DATA
SCI
Tony Fast
Materials Data Analyst
μInformatics is material AGNOSTIC statistical framework aimed to distill
rich physical data into tractable forms that facilitate structural taxonomies and bi-directional structure-property/processing
homogenization and localization relationships. It provides a foundation
for rigorous microstructure sensitive materials design.
3 Statistical Modules
5 Value Assessment
4
Data-Mining Modules
2
μS Signal Processing Modules
Experiment & Simulation
Objective & Subjective μS
metrics
DSP and image segmentation
“HUGE influence on μI”
1
Physical Models
DSP
Spatial
Statistics
MKS Dimension
Reduction
MICROSTRUCTURE
INFORMATICS (μI)
Hey, I don’t know what direction to
hold this microscope image so I’m going home!
MATERIAL / population RVE / sample Materials science Statistics
?
? ?
Difference Between
Direct comparison of microstructures is most often
impractical which demands novel statistical interpretations.
Statistically speaking, you probably never
will, so stay here and use some statistics!
reveal
Statistical correlations between random points in space/time which reveal systematic patterns
in the microstructure. Contains the original μS within a translation & inversion.
Difference Between
Mate
rial In
form
atio
n
Sp
atia
l Co
rrela
tion
Objective
Comparison
𝑚𝑠ℎ A digital signal of the microstructure at a position maybe voxel in the volume, s,
of S total positions for a channel, h, of H total channels. The channels describe
material features (e.g. phase, angle, curvature) using a prescribed basis function.
𝑓𝑟ℎℎ′ =
1
𝑆 𝑚𝑠
ℎ𝑚𝑠+𝑟ℎ′
𝑆
𝑠=1
Evenly Gridded
Spatial Domain
& Outside Cell
Inside Cell
k-d tree range to
find point indices in
each partition
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An Algorithm for Point
Cloud Spatial Statistics
Provides a look-up table for material features
Build a kd-tree & partition the spatial domain
Build: O(N) & Search: O(log(N))
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes
Combining Domains - The μS Function
𝑚 𝑠′
ℎ is the average of the weighted average of Legendre Polynomials of the
processed digital signal in each partition.
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𝑚 𝑠′ℎ =
𝐴𝑖𝑚𝑖ℎ
𝑖∈𝑃 𝐴𝑖 𝑖∈𝑃
Position of the Partition(𝑠′)
𝑑𝑥
Material Features: Orientation, Phase, Category, Curvature, Volume Fraction,…
Correlation Function Visualization
Correlation Function Visualization
Correlation Function Visualization
HEAT TREATED α-β TITANIUM
Microstructure Taxonomies
Albeit these datasets are sampled from different
processing routes, the taxonomy is a structure-structure relationship that doesn’t
track processing history because the images are sampled after heat treatment.
Principal Components Analysis Reduces D variables to d variables. Each axis corresponds to the
i-th greatest direction of variance.
Kalidindi, Surya R.; Niezgoda, Stephen R.; Salem, Ayman A
,"Microstructure informatics using higher-order statistics and efficient data-mining protocols", "JOM" , 2011
POLYMER SIMULATIONS Xin Dong, Karl Jacobs,GA Tech
Each point indicates
the statistics, or a
structure, in a simulation.
Each color is a different
initial structure & lines
track history.
Initial Stages
★Final Structure
Al Molecular Dynamics
Chandler Becker, NIST
Liquid
Crystalline
SOLIDIFICATION
OF AL-CU ALLOYS 20% Vf
15% Vf
Peter Voorhees, John Gibbs
Northwestern University
Interfacial curvatures between Al & Cu
during solidification rendered from X-CT
2 different volume fractions
Chandler Becker
Al Molecular Dynamics Peter Voorhees, John Gibbs
X-CT Al-Cu Solidification Karl Jacobs, Xin Dong
Polymer MD
Le Fin