Download - Microstructure Informatics
GA Tech: S.R. Kalidindi, D.M. Turner, LANL: S.R. Niezgoda, Drexel: A. Cecan, C. Kumbur, Teledyne: B. Cox, LLNL: H. Bale, UCSB: F. Zok ISU: O. Wodo, Basker G., Dartmouth: U. Wegst, OSU: H. Fraser, P. Collins
Novel and Enhanced Structure-Property-Processing Relationships with Microstructure Informatics
Tony Fast
University of California Santa Barbara
Materials Department
Structural Materials Seminar, UCSB, December 7, 2012
Materials Genome Initiative for Global Competitiveness
DIGITAL DATAInformatics• Data Transparency• Data Sharing• Data Transfer• Data Retrieval• Data Analysis
“Advanced data-sharing techniques at all stages of the development continuum will be the driving force behind the Initiative and help build the scholarly record.”
Materials Genome Initiative for Global Competitiveness, June 2011.
U. Wegst, Dartmouth
H. Bale, LLNL
From Materials Selection
Materials selection relies on effective material descriptors.
From Materials Selection to Microstructure (μS) Informatics…
• Advances in characterization and computational materials science are contributing to the materials data deluge.
H. Fraser, OSU.
Each module is self-contained
μInformatics workflow is a systemA robust paradigm to address dimensionality challenges in materials science
μInformatics is material and hierarchy independent statistical framework aimed to distill rich physical data into tractable forms that facilitate structural taxonomies and bi-direction
structure-property-processing homogenization and localization relationships. It provides a foundation for rigorous microstructure sensitive materials design.
Future Work
Image Segmenting extracts important features of the μSA necessary evil in data-driven materials science
Hough transform Methods
Raw Segmented(EM/MPM) @ bluequartz.net
Segmentation
Modules
Image Segmentation uses image processing and DSP methods to minimize the human interaction necessary to analyze digital images. Most problems are subjective and ill-posed.
Ceramic Matrix Composite
Virtual Metallic
Kalidindi, 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.
Aluminum in Epoxy
First-Order Higher-Order
Discrete
Continuous
H
hs
hhs vm
1
10,11
hs
H
h
hs mmPrimitive Basis Function
Salient Descriptors
nsm
nm1nm3
nm5
nm6
nm2
poreblack
solidwhitem
s
shs /1
/0
N
N
hts
hts
hs
hs mmmm 1
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0~~
Gradients contain local conformation
Local conformation of pixels
ssss ,,~
210~~ h
shs
hs
hs mmmm
shs fm 1 sh
s fm 2
Segmentation
Modules
The primitive basis converts any μS to a digital signalInformatics benefit from a generalized higher-order microstructure description
Extensible to any number of discrete phases
Other Basis Functions: Legendre, Generalized Spherical Harmonics, Chebyshev
𝑓 𝑟hh′= 1
𝑆∑𝑠=1
𝑆
𝑚𝑠h𝑚𝑠+𝑟
h′
A. 2-pt Correlation Function – Statistical correlations between random points in space/time which reveal systematic patterns in the microstructure
B. Chord Length Distribution – length and orientation of chords in a heterogeneous medium
C. Interfacial Surface Distribution - The principal curvatures of interfacial surfaces in the μS.
A.
B. C.
Statistical distributions are the crux of μInformaticsDistributions capture traditional effective statistical measures
Chen et al., Morphological and topological analysis of coarsened nanoporous gold by x-ray nanotomography, Advanced Physics Letters 2010.
The rich internal structure of the material is the microstructure. However, the μSprovides statistical, not deterministic material information.
Statistical
Modules
The Microstructure as a stochastic processDistributions provide a framework to effectively compare microstructures
Mic
rost
ruct
ure
Aut
ocor
rela
tion
-
- =
=
HT1.1 HT1.2 Difference
The direct comparison of the μS is useless due to the lack of origin.
(+) Provide a ground truth and metric space for comparison, or there is a natural origin(+) Autocorrelation contains all of the information in its respective μS.
(+) Amenable to homogenization and localization relationships (-) Very large dimensionality
Statistical
Modules
Data-mining modules are the vehicle for linkagesDimensionality reduction, classification, and regression
Regression methods allow the salient microstructure features to be connected with homogenized and localized properties in static and evolving materials. (Structure-Property and Structure-Processing)
Clustering and classification provide methods to automatically identify microstructures with certain performance or structural criterion. Ideal for searching the intrinsically large space of microstructures.
Dimension reduction converts large dimensional data (D) to a reduced
space (d) based upon specific characteristics of the data
Data-Mining
Modules
Maaten, et al., Dimension Reduction: A Comparative Review, Tilburg centre for Creative Computing, Tilburg University, 2009.
Sensitivity – metric for accurate classification
Specificity – metric for accurate nonclassification
Range between 0 and 1
k-Means Clustering: A data-mining approach that creates cluster partitions based on the means of clusters to automatically classify datapoints.
Class in practice may indicate processing history, material system, tendency to failure (e.g. rank).
k-Means clustering for automatic feature recognitionQuantitative data-mining techniques
Data-Mining
Modules
K-means Clustering, Wikipedia
Linear dimension reduction with PCADimension reduction to deal with big data
Principal Component Analysis, Wikipedia
Data-Mining
Modules
Principal Component Analysis: Reduced embedding of linearly independent variables that correspond to decreasing levels of variance starting with the highest (Dd)
PCA (most DR methods) require a natural origin for the data-points
PCA is typical for linear systems and exploratory data analysis.
Many nonlinear techniques exist.
𝑈
W Improved homogenization relationships for diffusivity in porous media (sProp)
Localization meta-model for the evolution of a binary alloy (sProc)
Localization meta-model for medium contrast dual phase composites (sProp)
μS Taxonomy of α-β Ti (s-s)
μS Taxonomy of Organic Blends in Solar Cells (s-s)Data-MiningPCAAutocorrelationFirst-Order Signal130 Experiments
K-meansPCAAutocorrelationFirst-Order SignalN-pt StatisticsHigher-Order Signal1100 Simulations
RegressionPCAAutocorrelationFirst-Order SignalExperiments
RegressionN/AFirst-Order SignalSimulation
RegressionN/AHigher-Order Signal400 Simulation
μS informatics is a versatile framework that relies on workflowsPlug-n-play operations with modules provide solutions for diverse problems
μInformatics is a growing suite of modular functions that when combined into a workflow system provide solutions to traditional empirical relationships and emerging big data in materials science. μInformatics can be seamlessly applied to 1-D, 2-D,3-D, and 4-D physical datasets generated empirically and/or computationally.
ORKFLOW OUTLINE
Data-driven structural diffusion coefficients in fuel cellsRegressionN/AFirst-Order SignalSimulation RegressionPCAAutocorrelationFirst-Order SignalExperiments
XCTFIB-SEM
Tortuosity quantifies the topology of the porous medium in a matter. How curved of tortuous are the pores?Diffusivity is the ability of a substance (electrons, liquid, gas) to diffuse through a medium.
Data-driven structural diffusion coefficients in fuel cellsRegressionN/AFirst-Order SignalSimulation RegressionPCAAutocorrelationFirst-Order SignalExperiments
XCTFIB-SEM
MPL
GDL
RVE’s from the experimental data are input into a Fickian diffusion model to evaluate the diffusivity.
Each point is one RVE~1e6 variables
Data-driven fitting outperforms traditional fitting methods and extends the reach of the fit to both the GDL and MPL layers.
Diffusivity
Diff
usiv
ity
The Materials Knowledge SystemExtracting compact knowledge from boat loads of information
microstructure signal local response
Stress, strain, evolution
How can information about new structures be extracted?What knowledge is gained?
Many Inputs and Many Outputs Repetitive simulation is demanding
Simulation produces a lot of data, but what is determined about the system?
The Materials Knowledge SystemExtracting compact knowledge from boat loads of information
DSP representation of local structure-local response Localization relationship and its influence coefficients
Influence coefficients capture the combined point effects of the MS configuration on the local response
Strong implications on multi-scale modeling
microstructure signal local response influence coefficients
𝔍 (𝜀𝑠 )𝑘=∑𝑖=1
𝐼
𝐴❑𝑖𝑘𝑀
𝑖𝑘❑𝔍
An evolutionary meta-model for phase separation
A Materials Knowledge System for structure-processing relationships
Phase separation guided by a negative energy gradient Cahn Hilliard Relationship evolved by way of Euler forward
Double well potential free energy curve Simulated using Phase Field Model (PFM)
Concentration is continuous between spinodal points [.15, .23]- Bounds of microstructure
Interested in structure evolution of spinodal structure
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a
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cdfcDc 22
Cahn JW. On spinodal decomposition. Acta Metallurgica 1961;9:795.
RegressionN/AFirst-Order SignalSimulation
Iterations of PFM used to calibrate coefficients Discretization contains 125 discrete points on a 20x20
spatial domain
Time derivative of concentration is captured extremely accurately by MKS method
IC provide accurate simulation resultsRegressionN/AFirst-Order SignalSimulation
• From an initial starting structure, ONE set of influence coefficients can be used to evolve the material structure
Time Derivative
MSE Error
IC are amenable to numerical integrationRegressionN/AFirst-Order SignalSimulation
Attenuated Error
Magnitude of influence coefficients decay rapidly with distance Influence coefficients can be easily extended to larger domains by
zero-padding with complexity
RegressionN/AFirst-Order SignalSimulation
Influence coefficients can be used to scale the simulation
63ta
Ø Padding
Original
63ta
Scaled
20x20:
100x100:
RegressionN/AFirst-Order SignalSimulation
Scaled linkages are provide accurate predictions
complexity vs. complexity
Time Derivative
MSE Error
RegressionN/AFirst-Order SignalSimulation
Scaled IC allow for scaled evolution simulations
Meta-modeling of moderate contrast strain fields in composites
A Materials Knowledge System for Structure-Property relationships
2
1
E
E
FEMε=5e-4
MICROSTRUCTURE
RESPONSE
Contrast (nonlinearity) – Young’s modulus ratio First-order microstructure descriptors are ineffective for high contrast
Results are presented for uniaxial 1-1 strain Calibrating coefficients for other modes is trivial
Random distribution of phases in 21x21x21 microstructure
RegressionN/AHigher-Order Signal400 Simulation
52
1 E
E10
2
1 E
E
Case 1: First Order Case 2 – 7: Second Order Case 8-9: Seventh Order
Influence coefficients accurately capture the response fieldsRegressionN/AHigher-Order Signal400 Simulation
HOIC of increasing order captures local information better Drastic improvement of linkages of FOIC
Accuracy has a strong dependence on nonlinearity Cross Validation (omitted) yields agreement between
training and validation sets.
Case 9: Seventh-Order to First Neighborhood and Second-Order to Sixth Neighborhoods
153 influences coefficients have finite memory and decay to zero at larger distances
FEM required 45 min on supercomputer MKS required 15 seconds on a desktop computer
MKS – NlogN(N)
Scalability of the influence coefficientsRegressionN/AHigher-Order Signal400 Simulation
Data-MiningPCAAutocorrelationFirst-Order Signal130 ExperimentsMicrostructure taxonomy of α-βTitanium
Kalidindi, 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.
Each point in the PCA indicate ONE μS, or ~6e6 variables. Microstructures generated by similar heat treatments naturally
cluster together in the reduced embedding.
PCA Embedding
H., Fraser, OSU
μS Taxonomy of Continuous Material States An Application to Organic Blends in Solar Cells
10% FAST PHASE SEPARATION 90% SLOW GRAIN COARSENING
FINAL STRUCTURES
11 Distinct TopologiesMany Topologies
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
K-meansPCAAutocorrelationFirst-Order SignalN-pt StatisticsHigher-Order Signal1100 Simulations
Microstructure taxonomy of binary organic blendsK-meansPCAAutocorrelationFirst-Order Signal1100 Simulations
Each point describes 21^3 variables and each color is a different topology Binning and microstructure features effect the clustering quality
Hard clustering in the PCA space allows the final topologies to be classified qualitatively
Microstructure taxonomy of binary organic blendsK-meansPCAN-pt StatisticsHigher-Order Signal1100 Simulations
Different choices of local state descriptions lead to different levels of clustering
Class A
Class B
Class C
Good Identification
Poor I
dent
ificat
ion
AF
FG
SGAF
FG
SG
AF – Atomic FractionFG – First GradientSG – Second Gradient
Quantitative Measures of Clustering
Sensitivity and specificity analysis of PCA embeddingK-meansPCAN-pt StatisticsHigher-Order Signal1100 Simulations
Sensitivity (Classification) and specificity (Nonclassification) provide a valuation on the usefulness of difference embeddings
to automatically search the space of microstructures.
PCA embedding can be used to visualize 3-D processing historyμInformatics collectively can visualize SPP linkages
Each path is defined by the spinodal decomposition and grain coarsening simulation. The paths are created by a reduced
embedding of the N-pt statistics of 21x21x21 periodic microstructures.
PCA embedding can be used to visualize 3-D processing historyμInformatics can collectively visualize bidirectional SPP linkages
Structure-Processing MKSProcessing History
Structure-PropertyHomogenization
Structure-PropertyLocalization
Using a stochastic framework, μInformatics provides an agile framework that allows data science to address the problems of scale
in emerging materials science problems.
contact: [email protected]