Stochastic simulation as a basis for optimizing microstructural - - PowerPoint PPT Presentation

Lori Graham-Brady*, Kirubel Teferra**, Michael Uchic***, Michael Groeber***

*Department of Civil Engineering, Johns Hopkins University **US Naval Research Laboratory (formerly JHU) ***US Air Force Research Laboratory

*supported by the US Air Force Research Laboratory through the Center of Excellence

• n Integrated Materials Modeling

Stochastic simulation as a basis for optimizing microstructural characterization protocols

Role le o

• f U

Unc ncertaint nty Q y Quant ntification i n in: n: “The Digital Material Workflow”

Uncertainty Quantification Mechanical Modeling/Testing Characterization

Collection+Digital Processing 1 Collection+Digital Processing i Collection+Digital Processing N

Digital Structure Model Real Material

Idealization 1 Idealization i Idealization N

Property/ Response Collection+Digital Processing Examples:

Collection – resolution, data modes, scan rate, averaging, etc. Processing – forward model, size filtering, averaging, segmentation method, smoothing, etc.

Idealization Examples:

Structure Model – mesh type, smoothing, synthetic surrogate, ‘representative’ volume, etc. Response Model – constitutive description, empirical v. physics- based, explicit structure v. analytical/statistical, etc.

Role le o

• f U

Unc ncertaint nty Q y Quant ntification i n in: n: “The Digital Material Workflow”

Uncertainty Quantification Mechanical Modeling/Testing Characterization

Collection+Digital Processing 1 Collection+Digital Processing i Collection+Digital Processing N

Digital Structure Model Real Material

Idealization 1 Idealization i Idealization N

Property/ Response Collection+Digital Processing Examples:

Collection – resolution, data modes, scan rate, averaging, etc. Processing – forward model, size filtering, averaging, segmentation method, smoothing, etc.

Idealization Examples:

Structure Model – mesh type, smoothing, synthetic surrogate, ‘representative’ volume, etc. Response Model – constitutive description, empirical v. physics- based, explicit structure v. analytical/statistical, etc.

Sens nsitivity S y Study i y in S n Structure-P

• Property R

y Rela lations nshi hip

Idealization 1 Idealization i Idealization N

Structures from Virtual Collection Experiments & Reconstruction/Processing ‘Round-Robin’ Meshing & Simulation DoE Comparison of Simulated Properties/Responses

• Various representation, meshing & simulation techniques lead to range of responses
• Quantify confidence bounds on material properties/responses as P(Error)
• Generate instantiations of microstructure consistent with statistics of data

Microstructure S Simu mula lation: E n: Elli llipsoidal Gr l Growth T h Tessella llation ( n (Te Teferra & & Gr Graha ham-B m-Brady, C , Comp. M . Mat. S . Sci. 2 . 2015)

Variations ns i in ho n homo mogeni nized s stress-s

• strain b

n beha havior f for v varyi ying ng s sample le si size ze

Role le o

• f U

Unc ncertaint nty Q y Quant ntification i n in: n: “The Digital Material Workflow”

Uncertainty Quantification Mechanical Modeling/Testing Characterization

Collection+Digital Processing 1 Collection+Digital Processing i Collection+Digital Processing N

Digital Structure Model Real Material

Idealization 1 Idealization i Idealization N

Property/ Response Collection+Digital Processing Examples:

Collection – resolution, data modes, scan rate, averaging, etc. Processing – forward model, size filtering, averaging, segmentation method, smoothing, etc.

Idealization Examples:

Structure Model – mesh type, smoothing, synthetic surrogate, ‘representative’ volume, etc. Response Model – constitutive description, empirical v. physics- based, explicit structure v. analytical/statistical, etc.

Role le o

• f U

Unc ncertaint nty Q y Quant ntification i n in: n: “The Digital Material Workflow”

Uncertainty Quantification Mechanical Modeling/Testing Characterization

Collection+Digital Processing 1 Collection+Digital Processing i Collection+Digital Processing N

Digital Structure Model Real Material

Idealization 1 Idealization i Idealization N

Property/ Response Collection+Digital Processing Examples:

Collection – resolution, data modes, scan rate, averaging, etc. Processing – forward model, size filtering, averaging, segmentation method, smoothing, etc.

Idealization Examples:

Structure Model – mesh type, smoothing, synthetic surrogate, ‘representative’ volume, etc. Response Model – constitutive description, empirical v. physics- based, explicit structure v. analytical/statistical, etc.

Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m)

Level of uncertainty affected by choices made (“knobs turned”) during characterization:

• dwell time
• polishing time
• spatial resolution, …

Every Data Point Has: 1) Location Uncertainty 2) ‘Value’ Uncertainty Sources of Location Uncertainty

1) Material Removal/Sample Translation Error

• planarity, removal/translation variability,

etc. 2) Distortions

• optics, sample positioning, drift, etc.

Sources of ‘Value’ Uncertainty

1) Physical Interaction with Sample

• probe size, surface topology, etc.

2) Software/Hardware Interaction

• detector noise, indexing methods, etc.

Collection+Digital Processing 1 Collection+Digital Processing i Collection+Digital Processing N

True material microstructure Collection experiments & reconstruction/processing Reconstructed microstructure, unknown error

Variability of boundary position

Physical experiment Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m)

Collection+Digital Processing 1 Collection+Digital Processing i Collection+Digital Processing N

True material microstructure Collection experiments & reconstruction/processing Reconstructed microstructure, unknown error

Variability of boundary position

Physical experiment

Ground-truth, or “phantom” microstructure Virtual collection experiments & reconstruction/processing Compare digital and “phantom” microstructure, “known” error

Virtual “experiment” Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m)

Collection+Digital Processing 1 Collection+Digital Processing i Collection+Digital Processing N

True material microstructure Collection experiments & reconstruction/processing Reconstructed microstructure, unknown error

Variability of boundary position

Physical experiment

Ground-truth, or “phantom” microstructure Virtual collection experiments & reconstruction/processing Compare digital and “phantom” microstructure, “known” error

Virtual “experiment” Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m) Valuable uncertainty quantification – enables optimization of data collection parameters!

Cons nstraine ned O Optimi mization P n Proble lem m

Data Collection Data Cleanup Cheapest technique within error tolerance

Minimize: E(Cost) such that P

~

(Error) <ε

(P

i(E),Ci)

(P

i(E),Ci)

(P

i(E),Ci)

(P

i(E),Ci)

(P

~ i(E),Ci)

(P

~ i(E),Ci)

(P

~ i(E),Ci)

(P

~ i(E),Ci)

Framework to be a communication tool for modeler & experimentalist to exchange requirements/constraints

• Simple objective function to start (time of data collection):
• Similarly simple constraint function (error in mean grain size dist.):
• Minimize cost under the constraint that expected value of CDF of

grain size is within tolerance of target CDF

• Trick is to calculate CDF(s,y)

y=(tδ, Δx, Δz), parameters to be optimized CDFT(s) = target CDF known and computed from “ground truth” microstructure D = threshold on error of CDF difference CDF(s,y) = CDF of reconstructed microstructure from EBSD simulation

Optimi mization F n Formu mula lation n

Error P Propagation i n in F n Feature R Represent ntation ( n (Forward P Proble lem) m)

10 20 30 40 50 60 70 5 10 15 20 % Zero Solutions Data Collection Time (milliseconds/pixel)

Original Data Reprocessed Data

(using M. DeGraef dictionary comparison)

• Data clean-up required to address

unindexed pixels

• Relationships may be sensitive to

microscope, software, etc.

• Data clean-up tools may alter

relationships

Simple le p process mo model l

• Scan locations in

phantom microstructure according to Δx and Δz

• Identify

probability of unindexed data (per tδ)

• Generate

unindexed data

• Filter simulated

data using Dream3D data cleanup

10 20 30 40 50 60 2 4 6 8 10 dwell time (dx1=.5 dz=.5) constraint (not including errthresh) 30 40 50 60 70 80 90 0.2 0.4 0.6 0.8 1 1.2 1.4 dx1 (tdwell=30 dz=.5) constraint (not including errthresh) 5 10 15 20 25 0.1 0.2 0.3 0.4 0.5 dz (tdwell=30 dx1=.5) constraint (not including errthresh)

Lack of smoothness suggests implicit filtering to be an appropriate optimization tool Smo moothne hness o

• f c

cons nstraint nt f func nction n

Incorporate%error%into% constraint%formula0on% (barrier,%penalty%method)%

Execute%op0miza0on%algorithm%(e.g.,% implicit%filtering,%interior%point% method)%

Generate%phantom% microstructure% Dream3D:%iden0fy%baseline% sta0s0cs%from%phantom% Generate%N%sets%of%ini0al% guesses%to%parameters% X0

1, X0 2, …, X0 N

Point%by%point%virtual% data%collec0on% Dream3D:%data%cleanO up%and%error%analysis%

Obtain%N%candidate%sets%of%

• p0mal%parameters%

%X1, X2, …, XN Select%global%op0mal%solu0on% (automated%or%by%user)

Overview o

• f O

Optimi mization P n Procedure

EXA XAMPLE: i : isotropic mi microstructure

• Optimal solution captures size

distribution with minimal cost

• Does NOT capture shape well
• Can tune constraint function

to match other statistics

EXA XAMPLE: i : isotropic mi microstructure

• Optimal solution more costly than under previous constraint
• Optimal solution still efficient
• Captures shape better
• Trade-off of accuracy vs. efficiency apparent

• Slicing across grain is more efficient than slicing along grain
• Same accuracy constraint/threshold in both

EXA XAMPLE: r : rolle lled mi microstructure

Incorporate%error%into% constraint%formula0on% (barrier,%penalty%method)%

Execute%op0miza0on%algorithm%(e.g.,% implicit%filtering,%interior%point% method)%

Generate%phantom% microstructure% Dream3D:%iden0fy%baseline% sta0s0cs%from%phantom% Generate%N%sets%of%ini0al% guesses%to%parameters% X0

1, X0 2, …, X0 N

Point%by%point%virtual% data%collec0on% Dream3D:%data%cleanO up%and%error%analysis%

Obtain%N%candidate%sets%of%

• p0mal%parameters%

%X1, X2, …, XN Select%global%op0mal%solu0on% (automated%or%by%user)

Overview o

• f O

Optimi mization P n Procedure

Incorporate%error%into% constraint%formula0on% (barrier,%penalty%method)%

Execute%op0miza0on%algorithm%(e.g.,% implicit%filtering,%interior%point% method)%

Generate%phantom% microstructure% Dream3D:%iden0fy%baseline% sta0s0cs%from%phantom% Generate%N%sets%of%ini0al% guesses%to%parameters% X0

1, X0 2, …, X0 N

Point%by%point%virtual% data%collec0on% Dream3D:%data%cleanO up%and%error%analysis%

Obtain%N%candidate%sets%of%

• p0mal%parameters%

%X1, X2, …, XN Select%global%op0mal%solu0on% (automated%or%by%user)

Overview o

• f O

Optimi mization P n Procedure

How many samples? Is phantom representative of actual? Possible adaptive approach?

Incorporate%error%into% constraint%formula0on% (barrier,%penalty%method)%

Execute%op0miza0on%algorithm%(e.g.,% implicit%filtering,%interior%point% method)%

Generate%phantom% microstructure% Dream3D:%iden0fy%baseline% sta0s0cs%from%phantom% Generate%N%sets%of%ini0al% guesses%to%parameters% X0

1, X0 2, …, X0 N

Point%by%point%virtual% data%collec0on% Dream3D:%data%cleanO up%and%error%analysis%

Obtain%N%candidate%sets%of%

• p0mal%parameters%

%X1, X2, …, XN Select%global%op0mal%solu0on% (automated%or%by%user)

Overview o

• f O

Optimi mization P n Procedure

What statistics matter? Possible use of computation models in error function evaluation?

Incorporate%error%into% constraint%formula0on% (barrier,%penalty%method)%

Execute%op0miza0on%algorithm%(e.g.,% implicit%filtering,%interior%point% method)%

Generate%phantom% microstructure% Dream3D:%iden0fy%baseline% sta0s0cs%from%phantom% Generate%N%sets%of%ini0al% guesses%to%parameters% X0

1, X0 2, …, X0 N

Point%by%point%virtual% data%collec0on% Dream3D:%data%cleanO up%and%error%analysis%

Obtain%N%candidate%sets%of%

• p0mal%parameters%

%X1, X2, …, XN Select%global%op0mal%solu0on% (automated%or%by%user)

Overview o

• f O

Optimi mization P n Procedure

Simple EBSD process model here, much room for improvement

Incorporate%error%into% constraint%formula0on% (barrier,%penalty%method)%

Execute%op0miza0on%algorithm%(e.g.,% implicit%filtering,%interior%point% method)%

Generate%phantom% microstructure% Dream3D:%iden0fy%baseline% sta0s0cs%from%phantom% Generate%N%sets%of%ini0al% guesses%to%parameters% X0

1, X0 2, …, X0 N

Point%by%point%virtual% data%collec0on% Dream3D:%data%cleanO up%and%error%analysis%

Obtain%N%candidate%sets%of%

• p0mal%parameters%

%X1, X2, …, XN Select%global%op0mal%solu0on% (automated%or%by%user)

Overview o

• f O

Optimi mization P n Procedure

Effect of clean- up protocols? Could be incorporated into optimized parameter set?

Incorporate%error%into% constraint%formula0on% (barrier,%penalty%method)%

Execute%op0miza0on%algorithm%(e.g.,% implicit%filtering,%interior%point% method)%

Generate%phantom% microstructure% Dream3D:%iden0fy%baseline% sta0s0cs%from%phantom% Generate%N%sets%of%ini0al% guesses%to%parameters% X0

1, X0 2, …, X0 N

Point%by%point%virtual% data%collec0on% Dream3D:%data%cleanO up%and%error%analysis%

Obtain%N%candidate%sets%of%

• p0mal%parameters%

%X1, X2, …, XN Select%global%op0mal%solu0on% (automated%or%by%user)

Overview o

• f O

Optimi mization P n Procedure

More sophisticated

• bjective

function?

Conc nclu lusions ns

Uncertainty Quantification Mechanical Modeling/Testing Characterization

Collection+Digital Processing 1 Collection+Digital Processing i Collection+Digital Processing N

Digital Structure Model Real Material

Idealization 1 Idealization i Idealization N

Property/ Response

• Uncertainty quantification required for full material workflow
• Uncertainty in data collection an interesting avenue for stochastic simulation
• Optimization framework established to minimize cost of data collection
• Increased sophistication can be incorporated – “plug & play” set-up