Adjustment of nuclear data libraries using integral

benchmarks Henrik Sjöstrand1,UU , Petter HelgessonUU ,

Erwin AlhassanUU

UUUppsala University, Department of Physics and Astronomy

1henrik.sjostrand@physics.uu.se

1

Uncertainty reduction using benchmarks

• Idea of using benchmarks for TENDL calibration is not new. – Petten method for

best estimates • Here:

– Multiple correlated benchmarks

– Multiple isotopes within one benchmark

CW 2017

2

Cases available Benchmarks from ICSBEP Handbook were used in this work. • Method 1: Pu-Met-Fast

– Re-evaluation of previously obtained data. (TENDL2012)

• Method 2: IEU-Met-Fast and HEU-Met-Fast – Curtesy of Steven Van

Der Marck – TENDL2014

Benchmark example – 239Pu Jezebel. Picture taking from the ICSBEP Handbook

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Uncertainty reduction

Prior keff distribution

Simulations: MCNP

Validation with a set of benchmarks

Posterior

Physical models parameters: TALYS based system (T6)

1st level of constraint: Differential data

A large set of acceptable ND libraries

2nd level of constraint: Integral benchmarks

Assign weights to random files

Weighted random files

Simulations: mcnp etc.

Applications: Criticality, burnup, Fuel cycle etc.

Random nuclear data from the 1st step is used as the prior for the 2nd step.

2

2i

iw eχ

−=

4

The posterior is constrained by both the differential and integral data

5

Benchmark consists of multiple isotopes contributing to ND uncertainty

I.e., a deviation between C and E can be due to any of these isotopes.

6

Important to also include the calculation uncertainty

22 ,, 2

,

2 2 2 2,,

overall pwher

2 2,

e

2

p j

( ), , ,B i B

i jB B j

B statE Ej ND p otherC j

C Ei randomfile j isotope B benchmarkχ

σ

σ σ σσ σ σ σ≠

−= = = =

= + = + + +∑

∑

Method 1: Use benchmarks to calibrate the ND for a specific isotope (here Pu239). Varying a single isotope at a time (here Pu239,240,241).

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Important to also include the calculation uncertainty

• Main idea: if the calculation deviates from the benchmark value it can be due to σE, σstat, an error in the isotope that we are calibrating, any of the other isotopes in the benchmark, or other errors not accounted for.

• Note: the σE in, e.g., ICSBEP, includes both the actual experimental uncertainty, but also uncertainties in transferring the experiment to a benchmark (e.g., densities).

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22 ,, 2

,

2 2 2 2,,

overall pwher

2 2,

e

2

p j

( ), , ,B i B

i jB B j

B statE Ej ND p otherC j

C Ei randomfile j isotope B benchmarkχ

σ

σ σ σσ σ σ σ≠

−= = = =

= + = + + +∑

∑

Benchmark exp. errors are correlated

Database for the International Criticality Safety Benchmark Evaluation Project (DICE), https://www.oecd-nea.org/science/wpncs/icsbep/dice.html

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Working with covariances How can COVE be determined? 1. Careful analysis of the

experiments. 2. Using DICE. 3. Here: guessing,

checking sensitivity of results, and try to be conservative.

COVC is also strongly correlated

( ) ( ),

,

2 1

,

B j

B j

Ti

E C j

C E COV C E

COV COV COV

χ −= − −

= +

,,overall pwhere p j

stat ND pC jCOV COV COV≠

= + + ∑10

Before and after calibration

Calibration Validation

TENDL2012 250 randomfiles

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Comment on results • Decreased ND uncertainty

to more ‘realistic values’. • Small improvement of the

best-estimates. – Strong correlations

• The inclusion of COVC and ρexp=0.5 affects the ND uncertainty but not the mean values. – If COVC is included the

results are quite insensitive to the value of ρexp.

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Method 2 • All isotopes of interest are

varied simultaneously • Intrinsically the

uncertainty of the different isotopes are taking into account simultaneously

• Investigated for U8 and U5.

( ) ( )

2

,

,

2

2 1

i

B j

B j stat

iT

i

E

w e

C E COV C E

COV COV COV

χ

χ

−

−

=

= − −

= + 13

Importance of benchmark exp. correlation

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Importance of benchmark exp. correlation 2

15

Before and after calibration

Calibration Validation

ρexp=0.6 1000 TENDL2014 files

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Difficult to fit the experimental data?

• Wrong model parameter distribution? • Model defects?

– Solution Gaussian Processes? • To small experimental uncertainties or wrong

experimental covariance matrix.

17

Adding 80 pcm experimental uncertainty to hmf1 and imf7_4

Calibration Validation

TENDL2014 1000 randomfiles

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Method 1 vs. Method 2 Method 2 -hypothesis • Better calibration of the best

estimate- due to higher degree of freedom

• Smaller posterior ND uncertainty – negative correlations between isotopes.

• Higher cost in terms of random files needed. I.e., the method produce lower average weights.

Proposal • Use Method 1 for the

complete models to determine the uncertainty for minor isotopes (e.g. 234U) and Method 2 for the major isotopes (235, 238U).

Limitation of this work • To few effective randomfiles • ENDF/B-VII.0 used as

background library

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How is the uncertainty reduced? • Using integral data introduce

correlations: between isotopes and between different parts of the ND file.

• Difficult to improve nuclear physics

• Improve understanding of reactor behavior.

D. Rochman et al., EPJ Nuclear Sci. Technol. 3, 14 (2017)

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Conclusion Methods for the inclusion of integral experiments for nuclear data calibration and uncertainty reduction within the TMC method were presented. It was stressed that calculation uncertainties should be included.

– The correlation between the benchmarks are important

– Important to take into account the multiple isotopes within the benchmarks

,over

2

all pwhere

2

p j

2stat NDC jσ σ σ

≠

= + ∑21

THANK YOU FOR YOUR ATTENTION!

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Acknowledgment • Figures for slide 18 where provided with curtsey from

Dimitri Rochman

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References 1. Alhassan, E., et al. On the use of integral experiments

for uncertainty reduction of reactor macroscopic parameters within the TMC methodology, Progress in Nuclear Energy, 88, pp. 43-52. (2016)

2. D. Rochman, et al. Nuclear data correlation between different isotopes via integral information , submitted to EPJ/N, Sept. 2017

3. D. Rochman et al., EPJ Nuclear Sci. Technol. 3, 14 (2017)

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