Identify the unconstrained

subspaceCorresponds to null singular values

Mentor: K. Bledsoe With: P. Hausladen, M. Blackston, J. Lefebvre Program: NESLS / Reactors and Nuclear Systems Division / Nuclear Security Modeling Group

Uncertainty Quantification for Inverse Radiation Transport

Aaron M. Bevill – University of Michigan

Signal ProcessingGain correction

Pulse-shape discrimination

Intrinsic efficiency

Object

Coded aperture

mask

Organic

scintillator

bank

Counts

y

z

Hidden parameters

True source distribution

Sampled data

~50K count rates

Forward model

Calibrated ray tracing

Parameters’ confidence region

~1M voxels’ source intensity

Quantity-of-interest confidence interval

Total source intensity

Hit pattern

Mask

intersections

Predicted

counts

3D Geometry

Cross-validation resultsPredicted minus measured

Chi-squared

confidence testReject holdup distributions

that are unlikely to produce

the data

Confidence regionAll non-negative distributions

that pass the test

Confidence intervalLower and upper bound on

holdup

Define confidence interval Evaluate confidence interval

s0 (neutrons / second)

s1

(neutr

ons / s

econd)

First, find the

CR (green

arrows)

Second, seek

min(s0 + s1) &

max(s0 + s1)

(white arrows)

CR bounded

by white oval

Convex optimization problemsSolved using Newton’s method with logarithmic barriers

Result: 3.43 < s0 + s1 < 4.52 (blue dotted lines)

Hidden parameters

True characteristics

Sampled data

4 to 8 count rates

Forward model

Transport

linearized response

Parameters’ Bayesian posterior

Mean and covariance of 2 to 6 parameters

Generalized Linear Least Squares

Linear Equality Constraints

Transform the problemSo that the residuals follow a

standard normal distribution

Minimize squared

residualsUsing linear algebra

Calculate covariance

GLLSOn the unconstrained subspace

Underdetermined Problems

Overdetermined Problems

Linearize the problem

Singular value

decomposition

This work was funded by DOE's National Nuclear Security Administration.

Open-source air sampling missions during

aboveground US nuclear weapons testing

from 1945 to 1963 provided diagnostic data,

however; these parameters do not address the

needs of National Technical Nuclear Forensics

to inform attribution. To fill this gap Oak Ridge

National Laboratory is developing the Airborne

Planning Tool, which provides predictive data

based on specified routes to optimize the

collection of quality volatile samples

(r-value > 1.0) with a sufficient quantity of

equivalent fissions for radiochemical analysis.

Nuclear Preparedness: Air Sampling for Today and the Future

Introduction

Samuel J. Cope, North Carolina State University, NESLS Intern

Mentor: Vincent J. Jodoin, Nuclear Security Modeling, RNSD

Active Air Sampler Networks

Airborne Planning Tool

Additional Developments

Right: EPA RadNet System for national

radiation monitoring

Below: IMS map for radionuclide stations

Conclusions

• Volatile-air-sample collection is necessary for

rapid nuclear forensics

• The Airborne Planning Tool optimizes

- fixed air sampler locations

- aircraft collection flight missions

• Qualitative and quantitative predictive results

as specified for radiochemical analysis

This work was funded by the Office of Defense Nuclear

Nonproliferation Research and Development (NA-22), within

the U.S. Department of Energy's National Nuclear Security

Administration and the Next Generation Safeguards Initiative

(NA-24).

• GIS export for collection-mission path

• Fixed sampler placement optimization

• Average particle density sensitivity

• Verification and validation of DELFIC and

HYSPLIT integration

• Fractionation ratio display for sample quality

Airborne Planning Tool GUI: Buster-Jangle Sugar shot

sample collection path and particle mass distribution

Equivalent fissions per cubic meter collected along the specified mission

Dose rate and cumulative dose at the exterior of the plane over the

specified mission

• 79 of 80 radionuclide stations mapped with

high-volume samplers and HPGe detectors

• Only sensitive to particulate gamma emitters

• 90% detection of 1 kt explosion debris within

14 days

• Commercially available, automatic system

sends data to International Data Center

• Design requirement of 300 cfm;

up to 650 cfm

International Monitoring System (IMS)

EPA RadNet

• >130 continuous high-volume samplers

across all 50 states

• 40 additional deployable monitors

available for dispatching

• Automated gamma measurements

• Alerts to laboratory staff in response to

significant increases in radiation levels

• Custom Hi-Q design, ~35 cfm

Left: Knoxville EPA RadNet air sampler unit by Hi-Q

Top Right: NaI(Tl) gamma detector above filter

Bottom right: 4-in.-diameter polyester filter with debris

• Industrial designs by Staplex, F&J, Hi-Q,

ThermoFisher Scientific, and Tisch

Environmental

• Portable designs capable of up to 70 cfm

Above: Boeing WC-135 US Air Force

radiation “sniffer” plane

Below: Mushroom cloud following

detonation of the Buster-Jangle Sugar shot

• Aerosol-collection mission planning

• DELFIC (cloud rise) + HYSPLIT (aerosol transport)

• Determination of optimal placement of fixed

samplers and deployable samplers

LEGEND:

EPA RadNet air sampler

IMS Radionuclide Aerosol Sampler

Left: Staplex high-volume portable sampler

Right: F&J low-volume portable air sampler

Off-the-Shelf Air Samplers

Acknowledgements:

Repeating History: A Review of Air Sampling Techniques and Their

Application to Modern Nuclear Forensics

• What are we looking for?

– Characteristic debris from a nuclear explosion(i.e., fallout or airborne particles)

• Refractory elements (Zr, W, Mo)

• Volatile elements (I, Xe, Br)

• Air Sampling v. Fallout Sampling

– Fallout sampling:collection of debrisafter it has landedon the ground

– Air sampling:collectionof debris mid-transport

• Ground-based airsampling (portable vs.stationary)

• Aerial sampling

– Manned vs.unmanned

– Various flight paths Acknowledgments:

• Timeline:

– 1945: First nuclear weapon tested (Trinity)

– 1946–1962: US weapon development

program operated, air sampling occurred

– 1963: Limited Test Ban Treaty is

implemented, only underground

detonations allowed

– 1992: U.S. Weapon testing ceased

– Present day: R&D of technical nuclear

forensics capabilities

• What is nuclear forensics?

– Techniques used to characterize and

support attribution of nuclear material

before/after detonation of a device

• Destructive (radiochemistry)

• Non-destructive (radiation detection)

BackgroundEmilie K. Fenske, University of Tennessee, NESLS

Mentor: Vince J. Jodoin, Nuclear Security Modeling, RNSD

Historic Air Sampling

Historic Air Sampling Data and Fallout Modeling

A Comparison

What’s Next?

• Main sample criteria: Volatile particles

• Valuable data include:

– Equivalent fissions (EF/m3)

– Particle sizes

– Ratio of volatile/refractory mass chains

• Airborne Planning Tool (APTool) underdevelopment

– Similar to Fallout Planning Tool

– Placement of air samplers in scenarios:fixed vs. portable

– Additional capabilities?

• Review and application of current airsamplers

Can an air sampler collect

adequate samples for

nuclear forensics?

Historic air sampling data &

assessment

Historic air sampling data &

assessment

Fallout modeling (DELFIC)

Fallout modeling (DELFIC)

Airborne particulate modeling

Airborne particulate modeling

Overlay of weapon test Buster-Jangle Sugar DELFIC

results and air sampler locations.

High volume ground-based air

sampler located at the Nevada

Test Site.

• SS-23: Operation Sandstone Report, 1948.

• WT-811: Distribution and Characteristics of Fallout, Upshot-Knothole, 1953.

• WT-1178: Distribution and Characterization of Fallout, OperationTeapot, 1955.

• DELFIC: Department of Defense Fallout Prediction System,1979.

• Defense Land Fallout Interpretive Code (DELFIC)

– Fallout prediction/planning tool (GUI)

– Used for DOE exercises with a focus onrefractory samples close to GZ

– Models transport of fallout, NOT airborneparticles

• Cannot directly compare air sampling data

• Applicable results include:

– Plume movement

– Volatile/refractory sample locations

Preliminary Conclusions

• Based on historic ground-based air sampling

data, adequate samples can be obtained for

radiochemical analysis.

• 1010–1012 equivalent fissions possible

• Based on DELFIC results: 50–100 miles from

GZ, samples collected should be volatile.

Historical data (equivalent fissions) from

weapon test Teapot Met at three distances from

GZ (and at ± 6 mi perpendicular to hot line)

Yes/NoYes/No

SamplerOnset

time* (hr)

Cessation

time* (hr)

Distance from GZ

(mi.)

Ratio*(140:99 M.C.)

Historic

Samples

(EF)

Sn

ap

pe

r F

ox Alamo -- -- 54 1.1 (volatile) 1.7E11

Crystal

Springs4.0 9.4 55 1.01 (volatile) 7.1E11

Groom

Mine2.1 7.6 24 1.1 (volatile) 7.9E11

Su

ga

r 29 0.11 0.23 3 0.55 (refract.) 8.7E9**

36 0.21 0.41 10 0.62 (refract.) 1.6E9**

39 0.35 0.67 16 0.68 (refract.) 1.4E9**

References:

This work was funded by the Office of Defense Nuclear

Nonproliferation Research and Development (NA-22) within

the U.S. DOE’s National Nuclear Security Administration.

*from DELFIC

**Calculated with an averaged concentration over 2 hours

Schematic of a ground-based

fallout collector (open-close

collector).

Schematic of filter locations on a B-17 for aerial air sampling.

DELFIC results (ratio of mass chains 140:99) of weapon

test Snapper Fox shown on Google Earth with pins

where air samplers were located.

Sensitivity Study of INDEPTH for Verification of Facility Spent Nuclear Fuel Declarations

Scott Richards – The University of Tennessee

Mentor: Brandon R. Grogan Program: NESLS Nuclear Security Modeling Group, Reactor and Nuclear Systems Division

To be able to distinguish if a prolonged cooling period hasoccurred, the isotopes of interest for the measurements shouldbe tracked through the forward ORIGEN calculation forpotential markers.

Rather than using indirectly measured quantities, INDEPTH cansolve using isotopics. To see more direct correlations,reconstructions with different groups of isotopes can beevaluated.

Results

Future Work

INDEPTH

INDEPTH finds aminimum within thesolution space byperforming a gradientsearch, based on the sumof square errors (SSE), ofthe measurement datagiven.

The forward ORIGENcalculations are done inINDEPTH as a singleirradiation and decay.

The accuracy of thecalculations is limited bythe degeneracy of thesolution. As the examplesto the right show, there isa spread of parametersthat result in the samesolution within theuncertainty.

Correlation and Convergence

The SSE is a measure of how well the foundsolution matches the measured data; however, itwas found not to be directly correlated to howwell the final INDEPTH parameters matched thecorrect parameters from the ORIGEN simulations

One of the goals of International Safeguards analysts is toverify the initial enrichments, burnups, and cooling timevalues of spent nuclear fuel declared by facilities usingnondestructive assay (NDA) measurements.

Motivation and Background

The three measurement types analyzed did show a uniformlyworse answer for all the cases with a long cooling time betweenirradiations (cases 3, 4, 10, 11, and 12), most notably in the casesfor which there was a simulated reactor shutdown event beforethe final irradiation cycle, such as cases 10 and 11. This result wasexpected, however the magnitude of the effect was not.

Scope of Study

The Inverse Depletion Theory (INDEPTH) code attemptsto reconstruct the initial enrichment and operatinghistory by using the Oak Ridge Isotope Generation(ORIGEN) code to simulate the irradiation and cooling ofthe fuel.

The study consisted of 13 different variations on the baseparameters of interest, with case 0 being the case the others areperturbations of and most closely simulating actual fuelconditions.

Each of the listed cases had 36 baseline combinations of assemblytype (2 BWR and 2 PWR designs), enrichments (2.0 and 3.5%),burnups (20 and 45GWd/MTU), and decay times (10, 20, and 30years).

All cases were solved by INDEPTH using absolute gammas, relativegammas, and absolute gammas with gross neutron countsgenerated by simulating irradiation and cooling with ORIGEN.

This work was funded under the Next Generation Safeguards Initiative—Spent Fuel project and the work was done as part of the NESLS internship at Oak Ridge National Laboratory

Varying most parameters had no tangible effecton error percentages. The only parameter thathad an effect was decay time between cycles.Generally, the longer the decay time betweencycles, the more inaccurate the results were.

In no case was the INDEPTH solution using relative gamma themost accurate solution. In fact, over the 5 factors of comparison,the absolute gamma measurement with gross neutron countswas as accurate or up to 10 times more accurate for the caseaverages.

Only in cases with extended cooling times between irradiationswas the added gross neutron information detrimental to theaccuracy of the solutions. The cause of this effect is currently beinginvestigated; it is possibly due to the way in which the 244Cminventory is changing, which cannot be reflected in the wayINDEPTH simulates the history.

134Cs + 137Cs + 154Eu degeneracy space: 5yrs cooled

134Cs + 137Cs + 244Cm degeneracy space: 5yrs cooled

134Cs + 137Cs + 244Cm degeneracy space: 15yrs cooled

Library Enrichments Burnup (GWd/MTU) Cooling Times (years)

BWR 8x8 2.00% 20 10, 20, 30

BWR 8x8 3.50% 20 10, 20, 30

BWR 8x8 3.50% 45 10, 20, 30

PWR 15x15 2.00% 20 10, 20, 30

PWR 15x15 3.50% 20 10, 20, 30

PWR 15x15 3.50% 45 10, 20, 30

BWR 10x10 2.00% 20 10, 20, 30

BWR 10x10 3.50% 20 10, 20, 30

BWR 10x10 3.50% 45 10, 20, 30

PWR 17x17 2.00% 20 10, 20, 30

PWR 17x17 3.50% 20 10, 20, 30

PWR 17x17 3.50% 45 10, 20, 30

Variants in Cases

Case

Number

Number of

Cycles

Length of

Cycle (d)

Length Down

between

cycles (d)

Power (MW/MTU)Burn

time (d)Notes

Case 0/Base 5 330 30 12.12/27.27 1650Closest to comparison data for

actual assemblies

Case 1 1 1770 0 11.30/20.45 1770

Closest to how INDEPTH

simulates conditions, with 3

back to back burn cycles and

one decay

Case 2 5 440 30 9.091/20.46 2200 Longer power cycles

Case 3 5 270 105 14.81/33.34 1350

Longer down times between

power cycles but similar

overall cycle length

Case 4 5 330 105 12.12/27.27 1650

Longer down times between

power cycles but same length

power cycles

Case 5 4 420 30 11.90/26.79 1680 Fewer cycles

Case 6 6 270 30 12.35/27.78 1620 More cycles

Case 7 5 330 30(20.20 or 10.10)/

(45.45 or 22.73)1650

Different powers on cycles

(first cycle higher)

Case 8 5 330 30(20.20 or 10.10)/

(45.45 or 22.73)1650

Different powers on cycles

(middle cycle higher)

Case 9 5 330 30(20.20 or 10.10)/

(45.45 or 22.73)1650

Different powers on cycles

(last cycle higher)

Case 10 5 330 30 12.12/27.27 1650300 day decay between the

4th and 5th cycle

Case 11 5 330 30 12.12/27.27 1650900 day decay between the

4th and 5th cycle

Case 12 5 330 30 12.12/27.27 1650900 day decay between the 1st

and 2nd cyle

Case Burnup Down Enrich Burn Power

0 31.37% 129.05% 123.71% 30.41% 29.47%

1 62.24% 215.32% 223.05% 36.22% 63.89%

2 28.64% 136.40% 123.54% 46.48% 28.52%

3 6.37% 22.01% 4.02% 251.58% 81.22%

4 6.43% 41.11% 5.23% 260.12% 83.16%

5 49.04% 118.78% 157.67% 60.80% 47.80%

6 50.39% 131.97% 158.32% 51.90% 46.54%

7 40.04% 111.86% 115.33% 20.91% 25.83%

8 59.57% 120.12% 145.06% 35.74% 47.96%

9 24.59% 94.87% 53.50% 30.39% 30.26%

10 8.72% 25.24% 7.99% 174.34% 81.56%

11 8.00% 23.72% 8.96% 312.03% 97.79%

12 15.46% 77.93% 10.46% 357.55% 121.14%

Absolute Gamma/Relative Gamma Error

Case Burnup Down Enrich Burn Power

0 13.69% 74.95% 12.34% 35.51% 22.12%

1 10.91% 20.60% 9.89% 50.99% 14.74%

2 8.89% 66.17% 8.59% 38.86% 16.63%

3 7.12% 85.59% 41.48% 44.84% 16.13%

4 7.58% 115.06% 59.92% 48.59% 15.54%

5 17.14% 54.73% 18.99% 66.52% 28.09%

6 12.85% 69.25% 13.47% 44.15% 23.29%

7 19.29% 91.40% 12.66% 22.37% 22.90%

8 11.04% 78.45% 11.82% 32.72% 23.26%

9 7.78% 90.28% 3.85% 45.73% 24.44%

10 8.01% 94.24% 70.72% 44.07% 24.40%

11 10.11% 108.95% 59.65% 38.96% 20.35%

12 16.62% 85.48% 61.01% 42.86% 8.30%

Absolute Gamma+Gross Neutron Count/Relative Gamma Error

Case Burnup Down Enrich Burn Power

0 43.64% 58.08% 9.98% 116.77% 75.05%

1 17.52% 9.57% 4.43% 140.78% 23.07%

2 31.05% 48.51% 6.95% 83.62% 58.31%

3 111.86% 388.93% 1031.33% 17.82% 19.86%

4 117.92% 279.87% 1145.82% 18.68% 18.69%

5 34.95% 46.08% 12.05% 109.40% 58.75%

6 25.50% 52.48% 8.51% 85.07% 50.04%

7 48.19% 81.71% 10.98% 106.95% 88.68%

8 18.53% 65.31% 8.15% 91.53% 48.50%

9 31.65% 95.16% 7.20% 150.46% 80.77%

10 91.87% 373.40% 885.24% 25.28% 29.91%

11 126.46% 459.34% 665.95% 12.49% 20.81%

12 107.54% 109.69% 583.03% 11.99% 6.85%

Absolute Gamma+Gross Neutron Count/Absolute Gamma Error

Initial comparison of fallout modeling codes within Fallout Planning Tool (FPTool) and

Specialized Hazard Assessment Response Capability (SHARC)

Atomic fallout modeling provides emergency

response teams with critical maps, data, and

projections used to plan for or react to atmospheric

nuclear explosions. Current modeling programs

have room for improvements in their outputs in

terms of accuracy and precision when compared to

exposure data of known historical events and in

providing direct predictions on radiation health and

safety. Two modeling codes named AIRborne

RADiation (AIRRAD) and DEfense Land Fallout

Interpretive Code (DELFIC) are being compared to

understand the advantages of each model.

Introduction

Katie M. Cook – Texas A&M UniversityMentor: Vincent Jodoin Program: NESLS Nuclear Security Modeling (NSM) Group Nuclear Security and Isotope Technology Division (NSITD)

Method

Based on comparing code manuals and file structures:

– DELFIC offers dynamic cloud rise with wind andmeteorological updates in time while this is notpossible with AIRRAD.

– More specifically, DELFIC accounts forfractionation in exposure calculations.

– AIRRAD utilizes a computed grid rotation anglewhich is not used in DELFIC.

– DELFIC output files include a parameter recapand more detailed annotations over AIRRAD

Results

To identify differences between DEFLIC and

AIRRAD based on:

– Code manuals

– File structures

– Map types

– Ease and usability

Objectives

• Codes AIRRAD and DELFIC are utilized within the

programs Fallout Planning Tool (FPTool) and

Specialized Hazard Assessment Response

Capability (SHARC).

• 7 historical atomic tests and 3 different map types

were used for comparisons.

• FPTool and SHARC produce different types of

fallout projection maps based on date, designated

exposure duration, location, and shot data.

Method

• Above are two examples of map types generated from SHARC for twodifferent atomic tests, representing a sampling of the total 84 maps generatedbetween SHARC and FPTool.

• DELFIC overlays are often more conservative with larger hot spot areas andlarger overall projections which are also shown in the above maps.

• Initial generated DELFIC overlays tend to be cut off more frequently (alsoshown above), but map domains can be updated in the input file.

• Runtimes for AIRRAD and DELFIC range from 12 – 30 seconds for eachmap type per each historical atomic test.

• SHARC offers an auto-calculate grid for DELFIC that can increase runtimefor larger map overlays compared to AIRRAD or standard DELFIC runs.

Results

• Both AIRRAD and DELFIC can be run through the

SHARC graphical user interface (GUI) for easy

map generation.

• FPTool better utilizes the capabilities of DELFIC

map types due to special overlay tab in GUI.

• DELFIC is currently providing higher resolution

and more conservative overlays in the selected

map types analyzed.

• Due to the ability to update wind and

meteorological data in time, DELFIC is better

suited for modeling offsite clouds that have

travelled for longer times than onsite clouds.

• Both DELFIC and AIRRAD provide similar high

and low exposure data per each map type for

each historical atomic test.

• Neither AIRRAD or DELFIC had faster runtimes

for the selected tests analyzed.

Conclusions

AIRRAD or DELFIC DELFIC

Fallout projection

map

Location

Date

Fission yield

Fission type

Wind speed

Wind direction

Air pressure

Relative humidity

Altitudes

Map Type

I would like to thank Sandia National Laboratory for allowing me to assist with this project as well as Murray Purves and Jordan Lefebvre within the NSM Group for consistent software help. This work was funded by the National Nuclear Security Administration.

Acknowledgements

Sunbeam Johnnie Boy early population effectsHardtack II Humboldt groundshine overlay

AIRRAD DELFIC Comparison AIRRAD DELFIC Comparison

FPTool example map overlay from

atomic test Buster-Jangle Sugar

Quantifying Variations in Spent Nuclear Fuel Isotopic Concentrations for International Safeguards

Prediction and identification of isotopics of spent nuclear fuel(SNF) is of critical importance to international safeguards. Tothis goal, the Spent Fuel Nondestructive Assay (NDA)project seeks to predict isotopics of SNF. Of particularemphasis are non-standard reactor operating conditions,such as extended downtimes between cycles.

As more countries look to either reprocess or utilize SNFrepositories, it is important to be able to validate operatordeclarations with respect to SNF properties. Theseproperties include burnup, initial enrichment, and coolingtime.

Introduction

Michael Cooper, University of Tennessee, Knoxville

Mentor: Brandon Grogan Program: NESLS | Division: Nuclear Security and Isotope Technology | Group: Nuclear Security Modeling

To accomplish the goals highlighted, the Oak Ridge Isotope

Generation (ORIGEN) simulation code was used to model a

number of irradiation scenarios and calculate the

concentrations of isotopes of interest. ORIGEN allows for

the simulation of nuclear fuel being irradiated and decayed

in a reactor setting, based off of user inputs. This code is a

part of the SCALE software package.

For this project, a total of 156 ORIGEN runs were

performed, based on permutations of 13 irradiation history

cases wherein there were 2% and 3.5% enrichments, as

well as burnups of 20 and 45 gigawatt days per metric ton of

uranium (GWd/MTU).

Method

The results of this project show that variations in the

irradiation history of SNF can significantly alter the resulting

isotopic composition. This is important as NDA isotopes are

used to verify operator declarations. If the radiation

signatures do not match declared reactor operations, there

is a possibility of abnormal reactor behavior. The following

figures illustrate isotopic changes for several conditions.

Case 0 is the base case, with 5 uniform 300 day irradiation

cycles and 30 days downtime between cycles.

Results

This project looked at the effects of varying irradiation

histories and initial conditions for 4 fuel assembly types.

Varying the assembly type had a minimal effect between

PWR and BWR assemblies. Varying burnup and enrichment

altered the isotopics as has already been published. The

new contribution of this project is the information that altering

the irradiation history such as introducing extended

downtimes or longer irradiation periods with lower per cycle

power, can significantly alter the concentrations of NDA

isotopics. While burnup and cooling time are the major

determinants of isotope ratios, changes in the cycle history

can have a significant impact.

Summary

Figure 1. This figure shows the differences of 244Cm Isotopic

concentration for the 13 cases that were run.

Figure 1 shows that for case 11, which has a 900 day

downtime between the last two cycles, there is a 2.2%

decrease in the concentration of 244Cm. A decrease of 244Cm

could be mistaken for SNF with a slightly lower burnup if the

extended reactor downtime is not considered.

Figure 2. This figure shows the ratios of 134Cs/137Cs for

case 0 and case 11.

Figure 3 shows that altering the irradiation history can

significantly affect the NDA ratio of 134Cs/137Cs. This effect is

especially pronounced for cases 10 and 11. Case 11 has a

900 day decay between the 4th and 5th cycles, and case 10

has a 300 day decay between the same cycles. This decay

period allows 134Cs to decay away faster than 137Cs due to

its 2.07 year half-life. Case 9 shows a higher ratio of134Cs/137Cs due to that case having a higher last cycle

power, boosting the amount of fresh 134Cs.

Figure 2 shows that when there is an extended downtime

between reactor cycles, the important NDA isotopic ratio134Cs/137Cs is decreased by approximately 21.6% at

discharge and throughout cooling. This finding is very

important for NDA analysts who are examining gamma ray

signatures of SNF, and attempting to calculate

characteristics such as burnup from the SNF.

Figure 3: This figure shows how 134Cs/137Cs mass ratios vary

significantly due to changes in irradiation history. All cases

here are 10 years post-discharge.

Acknowledgments: This work was funded by the National Nuclear Security Administration.

Sigma=2%

Sigma=6%

Sigma=10%

N=2 N=4 N=8

Optimizing Training Noise Level

Characterization of Machine Learning Performance for Plutonium Production Predictions

• Models built with limited sets of nuclides for

deployability.

• How to measure core-averaged burnup from a

few specimens when local burnup is highly

variable?

• Factors affecting local burnup include:

– Position throughout core (radial & axial)

– Position within fuel pin (radial & axial)

– Operating temperature

– Neutron flux spectrum

• Many of these factors will be unknown.

Burnup as a Probe for Pu Production

Adam Drescher – The University of Texas at Austin

Mentor: Ken Dayman, Program: NESLS, Group: Nuclear Security Modeling, Division: Nuclear Security and Isotope Technology

• Can you make accurate measurements if the

operating temperature is unknown?

• Tradeoffs associated with training on a multi-

temperature dataset.

• Can the model discriminate between meaningful

and nuisance variations in the nuclide data?

• “Noise” could result from random errors in nuclide

measurements, or unspecified reactor operating

parameters such as temperature.

• Optimization problem with an ideal “level” of added

Gaussian noise.

• By adding Gaussian noise to training data,

predictions made on both clean and noisy testing

data were improved.

Reactor coreFuel pin

• A single core specimen is sufficient for determining

whole core plutonium production.

• A model can incorporate uncertainty in

measurements and reactor parameters while

achieving good burnup predictions

• A robust model for core-averaged burnup

predictions should incorporate many sources of

possible variation in fuel data.

Sets of Nuclides

Unknown Temperature?

Accounting for Noisy Data

Results & Conclusions

Developing a Model

• Reactor core-averaged burnup

• Multi-variate signature

• Deployability

• Invariant to biased core sample

• Accurate across a range of unknown parameters

• Measures a single fuel specimen

• Discriminates between meaningful and nuisancevariations in nuclide signatures

Pin Level Variations

What makes a good model?

Nuclide Concentration → Bavg

Estimated with

Bayesian inferenceNon-linear

basis

functions

Training data

Relevance Vector Machine Framework

Nested optimization problem

Sparse!

Integrated

feature

selection and

basis shaping!

• Probabilistic machine learning algorithm

• Multivariate statistical analysis

• Unique to ORNL: Integrated feature selection!

3D Inverse Depletion Challenges

Dataset Used For TrainingCombined Fuel Temp 600 K Fuel Temp 700 K

Da

tase

t U

se

d F

or Te

stin

g

Fu

el T

em

p 7

00

K

Fu

el T

em

p 6

00

K

Core Level Variations

404

39

460

39

15

6

1

10

100

1000

Actinides Actinides & Cesium Actinides Cs & Noble Gases

Ave

rage

Rel

ativ

e Er

ror

[%]

Nuclide Set

Average Error Predicting Noisy Data Burnups

Trained on Clean Data Trained on Noisy Data

Best Results

Acknowledgements: Support for my time on this project was provided by the

Consortium for Nonproliferation Enabling Capabilities. This work was funded by the

Office of Defense Nuclear Nonproliferation Research and Development (NA-22), within

the US Department of Energy’s National Nuclear Security Administration.

References

1. M.E. Tipping, “Sparse Bayesian learning and the relevance vector machine,”, The

Journal of Machine Learning Research, 1, 211-244 (2001)

2. K. Dayman, “Sparse Bayesian Regression with Integrated Feature Selection for

Nuclear Reactor Analysis”, International Conference on Mathematics &

Computational Methods Applied to Nuclear Science & Engineering

[2]

Reactor Fuel Data• Generated by TRITON

Training Data• Isotopics and

associated core-averaged burnups

RVM• Model Development

Burnup Predictions

Summary Statistics of Model Performance

Testing Data• Isotopics and

associated core-averaged burnups

Repeated for every considered set of parameters:• Sets of nuclides• Training and testing operating temperatures• Levels of Gaussian noise added

[1]

From Training on Values to Training on Distributions

[2]

• Goal: Position-independent signature of core-

averaged burnup despite highly position-

dependent local burnup.

The Rim Effect

Model fails if trained at the wrong temperature.

Models trained at multiple temperatures make good predictions across a range of temperatures.

• Can we extend the idea of training on a range of

possible values to other parameters besides

temperature?