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Advanced Mathematical Methods for
Gamma Ray Based Nuclear Safeguards
Measurements
Ram Venkataraman
Canberra Industries (AREVA BDNM)
Presented at the IAEA Symposium on International Safeguards
October 20 – 24, 2014, Vienna, Austria
The contributions of the co-authors is gratefully acknowledged
Canberra
Andrey Bosko (now with the IAEA)
Frazier Bronson
Nabil Menaa
Gabriela Ilie
William Russ
IAEA
Ludovic Bourva (now with Canberra)
Alain Lebrun
Vladimir Nizhnik
Andrey Berlizov
Seokryung Yoon
Introduction Mathematical methods for computing gamma ray efficiencies such as
In Situ Object Calibration Software (ISOCS) are very attractive for
gamma ray based Nuclear Safeguards applications.
Accuracy of quantitative results will depend on how closely does the
efficiency calibration match the item being assayed.
ISOCS Uncertainty Estimator
Many of the characteristics of
items encountered in the field
are “Not Well Known” (NWK)
The matrix composition, density and
fill height
Weight fraction of U in matrix is not
known.
Container dimensions
ISOCS Uncertainty Estimator
(IUE) software tool can be used
to estimate uncertainties due to
NWK
Advanced-IUE
Advanced ISOCS (or Advanced IUE) takes it one step further.
Automated determination of efficiency calibration most consistent with gamma ray
spectrum measured in the field.
A-IUE developed by Canberra in close collaboration with the IAEA
A-IUE Algorithm Flow:
Container with Unknown
distribution of radioactive
material
Platform (could be rotating)
Radiation Sensor
High Voltage Power Supply
Collimator & Shield
Pre-Amplifier Amplifier
Analog to Digital
Convertor
Multi-Channel Analyzer for Signal
Processing
Pre-loaded Software and
Set up Files for Data
Acquisition & Automated
Analysis
Pre-Analysis with initial efficiency
(using guesstimated
geometry parameters)
Best Efficiency solution and Uncertainty Estimation
Final Analysis with Best Efficiency.
Nuclide Identification and
Activity Quantification
Report Nuclide Activities and Uncertainties
EXECUTE AUTOMATED
ANALYSIS
Benchmarks/Figure of Merits - Isotopics,U or Pu Mass
Isotopic analysis results of U or Pu Gamma ray spectra of items using codes
MGAU, MGA, & FRAM
MGAU (U measurements): U Enrichment used as benchmark
MGA: (Pu measurements): Relative efficiencies used as benchmark
FRAM: (U or Pu measurement): Enrichment for U, Relative efficiency for Pu
User-defined enrichment
MGAU and MGA are distributed as Canberra products and therefore are
seamlessly integrated with Genie2000 software.
Isotopic results are stored by Genie2000 directly in the measured spectrum; results
can be extracted without having to access an external file.
Isotopic results are representative of the shape of the efficiency curve; not
the magnitude (because of the “infinitely thick” sample conditions).
Isotopic benchmark used in combination with U (or Pu) mass benchmark
U (or Pu) mass in the ISOCS model compared with measured mass
Measured mass: obtained using measured peak areas, the gamma ray yields and the ISOCS
calculated peak efficiencies at U or Pu gamma ray energies of interest. Activity is converted to
mass by using the specific activities of the nuclides.
Benchmarks/Figure of Merit - Line Activity Consistency Evaluation (LACE),
- Multiple Counts of same item
LACE Benchmark:
Useful in measurements of a
nuclide emitting multiple
gamma lines.
Works best when gamma lines
span a wide energy range (e.g. 152Eu)
Multi-Count: A given item
counted at multiple
geometries
Source parameters that give a
consistent mass results with
the multiple-count data
Powerful benchmark that
boosts confidence in the
verification.
UNIFORM
SOURCE
DISTRIBUTION
A-IUE
CALIBRATION
PO
SIT
ION
1
PO
SIT
ION
2
Count 1
Count 2
Routines used in IUE to search for Efficiency Solution
Best Random Fit (BRF)
large number of random ISOCS models by varying the NWK parameters
within the range indicated by the user
Efficiencies from each trial model is compared against one or more
benchmarks, and the FOMs are calculated.
Individual FOMs obtained for each benchmark are then combined
together into a single Composite FOM.
Models are then ranked from the best to worst according to their
Composite FOM values.
Computes the mean efficiency and standard deviation based on the best
models; user defines the number of best models to be used
The mean efficiencies which represent the most consistent solution are
used in the analysis of the gamma ray spectrum.
Search is carried out until the user-set convergence is reached for
various energy ranges, or when the max. no. of models is reached
(default is 2000 models).
Routines used in IUE to search for Efficiency Solution
Smart search using Downhill
Simplex
involves continuously improving the
FOMs of models represented by
points in the solution space at the
vertices of a multidimensional form,
or simplex.
An initial simplex is established with
one vertex more than the number of
free parameters, and all of these
point models are evaluated.
The points are sequentially improved
by simultaneously adjusting all of
the free parameters in the point with
the worst FOM.
After the worst point is improved
and is no longer the worst point, the
new worst point is improved
Simplex vs. Best Random Fit
Simplex
Advantage: Short computation
times; tens of minutes; < 1 hour
even for highly attenuating
geometries
Disadvantage: Solution could
fall into local minimum
Mitigation: Convergence Check
option implemented. Perturbs
the solution space and confirms
convergence with original
results
Best Random Fit
Disadvantage: For highly
attenuating geometries, could
take several hours.
Advantage: If one is willing to
tolerate long computation
times, BRF will give a good
solution
Mitigation: Option to speed up
BRF; the software automatically
narrows down the specified
variation ranges for NWK
parameters based on the
results of the initial batch of
random ISOCS models.
Verification and Validation
Measurement spectra provided by the IAEA – mostly U but
also some Pu spectra.
Canberra sources were also measured.
U measurements (IAEA spectra):
Uranyl Nitrate solutions in High Density PolyEthylene vials with various
fill heights and concentrations; 15 – 30 g of U
“CBNM” standard with 169.7 g of low enriched uranium (LEU: 2.95%,
4.46%) in U3O8
“SU-135” standard with 848 g LEU (3.105%) in U3O8
Uranium Carbide samples similar to what is encountered in the field;
mixture of graphite and U; known matrix weight (2 to 3 kg), but unknown
U weight fraction; HEU: 20%-50; U mass range of 800 g – 1600 g
Example: Uranium Carbide Spectrum, and measurement geometry
Count 1
Count 2
Uranium Measurement Results
Each U spectrum analyzed using the
following benchmarks:
MGAU + U mass
FRAM + U mass
User-defined enrichment + U
mass
LACE + U mass
CBNM & SU-135 standards counted
at 2 different geoms.
Majority of the A-IUE results are
within ±20%of expected mass
Simplex agrees with BRF to within
±10%
Outlier: U Carbide spectrum with
LACE + U mass benchmark and
Simplex
Plutonium Measurements
Except for Plutonium 1,
expected masses were not
available for other Pu items.
One could only draw
conclusions based on the
consistency of results among
various benchmarks
Plutonium 1 is a spectrum
measured at Canberra (CRM). Pu
mass known
A-IUE results were between 8%-10%
of the expected Pu mass.
0.1
1
10
100
0 5 10 15 20
Op
tim
ize
d p
luto
niu
m
ma
ss
, g
Optimization case
Plutonium 1
Plutonium 2
Plutonium 2 (no Pu)
Plutonium 3
Plutonium 4 (no Pu)
Results from Best Random Fit
Results from Simplex
241Am + 152Eu Point source inside 208 liter drum matrix
Efficiency model Activity for
Position 1, mCi
Activity for
Position 2, mCi
Weighted
average activity,
mCi
Measured
/Expected
Uniform source
distribution 9.20 +/- 0.17 1.22 +/- 0.03 1.38 +/- 0.02 0.351
Point source in the middle 10.60 +/- 0.20 1.53 +/- 0.03 1.74 +/- 0.03 0.442
BRF (LACE) 3.70 +/- 0.06 4.42 +/- 0.14 3.81 +/- 0.06 0.966
BRF (Multi) 3.88 +/- 0.13 3.78 +/- 0.13 3.82 +/- 0.09 0.969
BRF (Multi + LACE) 3.73 +/- 0.04 4.15 +/- 0.04 3.94 +/- 0.03 0.998
Simplex (LACE) 3.50 +/- 0.07 4.60 +/- 0.09 3.88 +/- 0.05 0.983
Simplex (Multi) 4.36 +/- 0.08 4.36 +/- 0.09 4.36 +/- 0.06 1.106
Simplex (Multi + LACE) 4.09 +/- 0.08 4.04 +/- 0.08 4.06 +/- 0.03 1.029
Efficiency model Activity for
Position 1, mCi
Activity for
Position 2, mCi
Weighted
average activity,
mCi
Measured
/Expected
Uniform source
distribution 17.22 +/- 1.73 0.55 +/- 0.06 0.57 +/- 0.06 0.145
Point source in the middle 23.27 +/- 2.34 0.75 +/- 0.08 0.77 +/- 0.08 0.196
BRF (LACE) 4.15 +/- 0.31 4.30 +/- 0.54 4.19 +/- 0.27 1.069
BRF (Multi) 4.45 +/- 0.94 2.97 +/- 0.78 3.57 +/- 0.60 0.910
BRF (Multi + LACE) 4.28 +/- 0.29 3.71 +/- 0.12 3.79 +/- 0.11 0.967
Simplex (LACE) 3.86 +/- 0.39 4.57 +/- 0.46 4.15 +/- 0.30 1.058
Simplex (Multi) 22.49 +/- 2.26 4.04 +/- 0.41 4.62 +/- 0.40 1.179
Simplex (Multi + LACE) 4.87 +/- 0.49 3.55 +/- 0.36 4.02 +/- 0.29 1.025
152Eu results
241Am results
Field ISOCS Utility
This utility is focused on the ease of use by IAEA inspectors in the field
and was designed to fully support the Expert-Inspector concept.
Conclusions
The A-IUE prototype software was developed by Canberra in
close collaboration with the IAEA.
The A-IUE automatically determines the efficiency calibration
that is consistent with the gamma ray spectrum measured in
the field.
A-IUE was thoroughly tested using the measurement spectra
provided by the IAEA, and measurements done at Canberra’s
factory.
Acknowledgement: The A-IUE project was funded by the U.S.
Support Program: USSP Task USA A 1607 "Development of
ISOCS Self Modeling Capabilities" A.267. The authors
gratefully acknowledge the support from USSP.
Thank You!
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