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

Sandia National Laboratories is a multimis- DE-NA-0003525. SAND NO. 2018-4438 C Daniel Ries 1 PRESENTED BY Characteristics from SEM Images for Inverse Prediction sion laboratory managed and operated by Utilizing Distributional Measurements of Material Nuclear Security Administration under contract for the U.S. Department of Energy’s National subsidiary of Honeywell International, Inc., lutions of Sandia, LLC., a wholly owned National Technology and Engineering So- 1 Sandia National Laboratories 2 Los Alamos National Laboratory Contributors: John R. Lewis 1 , Adah Zhang 1 , Christine M. Anderson-Cook 2 , Marianne Wilkerson 2 , Gregory L. Wagner 2 , Julie Gravelle 2 , Jacquelyn Dorhout 2

2 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. going in opposite direction of causality. May 2, 2018 ⇒ This approach is referred to as inverse prediction because it’s

3 Bench-Scale Uranium Data May 2, 2018 • 18 runs • 5 production factors • Temperature (C): 21.5, 35, 50 • Sitr Rate (rpm): 170, 280, 400 • Flow Rate of NH 4 OH (mL/min): 2.5, 5, 7.5 • Ending pH: 5, 8, 10.5 • U:8MHNO 3 (mg/mL): 50, 100, 200 • 2 areas on slide examined at 5000x, 10000x, 15000x, 25000x • 8 total SEM images per run

4 Sample SEM Image With Segmentation in MAMA Software May 2, 2018

5 45 12 13 14 15 16 17 18 N i 120 93 100 57 33 10 67 26 20 20 56 66 33 55 38 42 6 48 11 9 Bench-Scale Uranium SEM Data Run Using MAMA (Morphological Analysis of MAterials) software, the following are measured for each particle in each SEM image: 8 Table: Number of particles analyzed for each of the 18 experimental runs. May 2, 2018 1 2 3 4 7 6 5 • Major ellipse • Vector area • Minor ellipse • Convex hull area • Ellipse aspect ratio • Pixel area • Diameter aspect ratio • Vector perimeter • Circularity • Convex hull perimeter • Perim convexity • Ellipse perimeter • Area convexity • ECD

6 Using Distributional Responses 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. May 2, 2018 However, a single sample has multiple particles ⇒ multiple

7 Average Response For Select Responses and Inputs May 2, 2018

8 than or equal to x Cumulative Distribution Function May 2, 2018 A CDF is a function of x that returns the probability of being less Defjnition: Cumulative Distribution Function (CDF) PDF CDF 1.0 0.30 P(X < 16) = 0.8 0.8 0.25 P(X < Response) 0.20 0.6 Frequency 0.15 0.4 0.8 0.10 0.2 0.05 0.00 0.0 10 12 14 16 18 20 10 12 14 16 18 20 Response Response

9 Bench-Scale Distributional Responses May 2, 2018 PDF CDF 20 1.00 15 0.75 StirRate StirRate Frequency 170 170 CDF 10 0.50 280 280 400 400 5 0.25 0 0.00 0.8 0.9 0.8 0.9 Perimeter Convexity Perimeter Convexity

10 100) Understanding Performance Via Simulation May 2, 2018 Simulated Y : For each X, a distribution Y values are sampled (size Simulated X : 100 different values of X Study 1 0 Mean Y −1 −2 0.0 2.5 5.0 7.5 10.0 X • Mean of Y is constant for all values of X • As X increases, variance of the response increases

11 Understanding Performance Via Simulation May 2, 2018 Study 1.00 x 0.75 CDF of Y 7.5 0.50 5.0 2.5 0.25 0.00 −10 −5 0 5 10 Values of Y

12 Understanding Performance Via Simulation PMSE for standard method: 18.1! q: number of response variables N: observations per experimental run n: number of experimental runs PMSE: Prediction Mean Squared Error (smaller means less left unexplained) May 2, 2018 Study n=50 n=100 0.6 variable q=1 0.5 q=2 PMSE 0.4 N 0.3 50 0.2 100 0.1 −0.5 0.0 0.5 −0.5 0.0 0.5 ρ

13 Bench-Scale Uranium Distributions of Select May 2, 2018 Responses StirRate FlowRate 1.00 1.00 0.75 0.75 170 2.5 CDF CDF 0.50 0.50 280 5 0.25 0.25 400 7.5 0.00 0.00 0.8 0.9 0.8 0.9 Perimeter Convexity Perimeter Convexity StirRate FlowRate 1.00 1.00 0.75 0.75 170 2.5 CDF CDF 0.50 0.50 280 5 0.25 0.25 400 7.5 0.00 0.00 −7.5 −5.0 −2.5 0.0 2.5 5.0 −7.5−5.0−2.5 0.0 2.5 5.0 log Vector Area log Vector Area StirRate FlowRate 1.00 1.00 0.75 0.75 170 2.5 CDF CDF 0.50 0.50 280 5 0.25 0.25 400 7.5 0.00 0.00 1 2 3 1 2 3 Ellipse Aspect Ratio Ellipse Aspect Ratio

14 76.99 84.84 84.28 3.33 2.71 16.64 Functional-1 Y 85.30 16.89 3.37 2.79 16.41 Table: Root PMSE using original scale data. ratio, perimeter convexity, ecd, area convexity ratio, perimeter convexity, ecd, area convexity aspect ratio, and perimeter convexity Inverse Prediction on Bench-Scale Uranium Functional-3 Y 2.65 Standard-5 Y Data UNO3ratio StirRate FlowRate EndpH 3.42 Temp 83.31 135.70 3.67 3.72 19.74 Functional-5 Y 79.35 81.53 May 2, 2018 • Standard-5 Y: Standard method using vector area, ellipse aspect • Functional-5 Y: Functional method using vector area, ellipse aspect • Functional-3 Y: Functional method using only vector area, ellipse • Functional-1 Y: Functional method using only vector area

15 Conclusions We presented a method that utilizes the SEM morphology distributional responses directly to perform inverse prediction over the current standard method. particles per run to estimate the cdf well. experiment. as the number of experimental runs increases, as evidenced by simulation study. May 2, 2018 • Simulation study and real data results show improvements • Simulation study suggests that we only need to analyze ≈ 50 • Real data results are only based on a small 18-run • We expect signifjcant improvements in predictive capability

16 Thank you! Contact: dries@sandia.gov May 2, 2018