Characteristics from SEM Images for Inverse Prediction sion - - PowerPoint PPT Presentation

Sandia National Laboratories is a multimis- sion laboratory managed and operated by National Technology and Engineering So- lutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. SAND NO. 2018-4438 C

Utilizing Distributional Measurements of Material Characteristics from SEM Images for Inverse Prediction

PRESENTED BY

Daniel Ries1 Contributors: John R. Lewis1, Adah Zhang1, Christine M. Anderson-Cook2, Marianne Wilkerson2, Gregory L. Wagner2, Julie Gravelle2, Jacquelyn Dorhout2

1Sandia National Laboratories 2Los Alamos National Laboratory

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Introduction

Experiments are being conducted at US National Labs in nuclear forensics with the goal of exploring the impact of different production and processing parameters on materials produced. Underlying Goal: Build a model from which interdicted materials can be matched to their original production environments using morphology information from SEM images of the interdicted material. ⇒ This approach is referred to as inverse prediction because it’s going in opposite direction of causality.

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Bench-Scale Uranium Data

• 18 runs
• 5 production factors
• Temperature (C): 21.5, 35, 50
• Sitr Rate (rpm): 170, 280, 400
• Flow Rate of NH4OH (mL/min): 2.5, 5, 7.5
• Ending pH: 5, 8, 10.5
• U:8MHNO3 (mg/mL): 50, 100, 200
• 2 areas on slide examined at 5000x, 10000x, 15000x, 25000x
• 8 total SEM images per run

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Sample SEM Image With Segmentation in MAMA Software

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Bench-Scale Uranium SEM Data

Using MAMA (Morphological Analysis of MAterials) software, the following are measured for each particle in each SEM image:

• Vector area
• Convex hull area
• Pixel area
• Vector perimeter
• Convex hull perimeter
• Ellipse perimeter
• ECD
• Major ellipse
• Minor ellipse
• Ellipse aspect ratio
• Diameter aspect ratio
• Circularity
• Perim convexity
• Area convexity

Table: Number of particles analyzed for each of the 18 experimental runs.

Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Ni 120 93 100 57 45 33 67 26 20 20 56 66 33 55 38 42 6 48

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Using Distributional Responses

However, a single sample has multiple particles ⇒ multiple measurements of same characteristic for one set of experimental conditions! This allows us to consider distributional responses instead of single number summaries. Standard Approach (Aggregation): For each experimental run, take the average over all measurements for each response variable. Our Approach: Estimate cumulative distribution functions (cdf) for each response of each experimental run.

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Average Response For Select Responses and Inputs

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Cumulative Distribution Function

Defjnition: Cumulative Distribution Function (CDF)

A CDF is a function of x that returns the probability of being less than or equal to x

10 12 14 16 18 20 0.00 0.05 0.10 0.15 0.20 0.25 0.30

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Response Frequency

0.8

10 12 14 16 18 20 0.0 0.2 0.4 0.6 0.8 1.0

CDF

Response P(X < Response)

P(X < 16) = 0.8

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Bench-Scale Distributional Responses

5 10 15 20 0.8 0.9

Perimeter Convexity Frequency StirRate

170 280 400

PDF

0.00 0.25 0.50 0.75 1.00 0.8 0.9

Perimeter Convexity CDF StirRate

170 280 400

CDF

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Understanding Performance Via Simulation Study

Simulated X: 100 different values of X Simulated Y: For each X, a distribution Y values are sampled (size 100)

−2 −1 1 0.0 2.5 5.0 7.5 10.0

X Mean Y

• Mean of Y is constant for all values of X
• As X increases, variance of the response increases

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Understanding Performance Via Simulation Study

0.00 0.25 0.50 0.75 1.00 −10 −5 5 10

Values of Y CDF of Y

2.5 5.0 7.5

x

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Understanding Performance Via Simulation Study

n=50 n=100 −0.5 0.0 0.5 −0.5 0.0 0.5 0.1 0.2 0.3 0.4 0.5 0.6

ρ PMSE variable

q=1 q=2

N

50 100

PMSE: Prediction Mean Squared Error (smaller means less left unexplained) n: number of experimental runs N: observations per experimental run q: number of response variables PMSE for standard method: 18.1!

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Bench-Scale Uranium Distributions of Select Responses

0.00 0.25 0.50 0.75 1.00 0.8 0.9

Perimeter Convexity CDF StirRate

170 280 400 0.00 0.25 0.50 0.75 1.00 0.8 0.9

Perimeter Convexity CDF FlowRate

2.5 5 7.5 0.00 0.25 0.50 0.75 1.00 −7.5 −5.0 −2.5 0.0 2.5 5.0

log Vector Area CDF StirRate

170 280 400 0.00 0.25 0.50 0.75 1.00 −7.5−5.0−2.5 0.0 2.5 5.0

log Vector Area CDF FlowRate

2.5 5 7.5 0.00 0.25 0.50 0.75 1.00 1 2 3

Ellipse Aspect Ratio CDF StirRate

170 280 400 0.00 0.25 0.50 0.75 1.00 1 2 3

Ellipse Aspect Ratio CDF FlowRate

2.5 5 7.5 May 2, 2018

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Inverse Prediction on Bench-Scale Uranium Data

UNO3ratio StirRate FlowRate EndpH Temp Standard-5 Y 83.31 135.70 3.67 3.72 19.74 Functional-5 Y 79.35 81.53 3.42 2.65 16.89 Functional-3 Y 84.84 84.28 3.33 2.71 16.64 Functional-1 Y 76.99 85.30 3.37 2.79 16.41 Table: Root PMSE using original scale data.

• Standard-5 Y: Standard method using vector area, ellipse aspect

ratio, perimeter convexity, ecd, area convexity

• Functional-5 Y: Functional method using vector area, ellipse aspect

ratio, perimeter convexity, ecd, area convexity

• Functional-3 Y: Functional method using only vector area, ellipse

aspect ratio, and perimeter convexity

• Functional-1 Y: Functional method using only vector area

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Conclusions

We presented a method that utilizes the SEM morphology distributional responses directly to perform inverse prediction

• Simulation study and real data results show improvements
• ver the current standard method.
• Simulation study suggests that we only need to analyze ≈50

particles per run to estimate the cdf well.

• Real data results are only based on a small 18-run

experiment.

• We expect signifjcant improvements in predictive capability

as the number of experimental runs increases, as evidenced by simulation study.

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Thank you!

Contact: dries@sandia.gov

May 2, 2018