Unified Monte Carlo evaluation method

Transcription

1 Unified Monte Carlo evaluation method IAEA Roberto Capote and Andrej Trkov IAEA Nuclear Data Section, Vienna, Austria Donald L. Smith, Argonne National Laboratory, USA

2 (Nuclear) Data Evaluation & correl From D. Neudecker, S. Gundacker, H. Leeb et al., ND2010, Jeju Isl., Korea 2

3 Definition of (Nuclear) Data Evaluation A properly weighted combination of selected experimental data (and modeling results if needed). Bayesian approaches (may use prior knowledge): Non-model GLSQ fit (standards) Model prior + experimental data: Deterministic: Model Prior (Sens) + GLSQ Stochastic (MC): UMC, TMC + UMC Hybrid: Model Prior (MC) + GLSQ All stochastic methods may be used to produce samples for TMC 3

4 i MONTE CARLO METHOD D.L. Smith, Covariance Matrices for Nuclear Cross-Sections Derived from Nuclear Model Calculations. Report ANL/NDM-159, Argonne National Laboratory, K K k 1 i k Vij i j i j i, j - energy indexes Monte Carlo calculation of covariance first tested by A. Koning Monte Carlo prior + GANDR (GLS) D.W. Muir, GANDR project (IAEA), Online at www-nds.iaea.org/gandr/. A. Trkov and R. Capote, Cross-Section Covariance Data, Th-232 evaluation for ENDF/B-VII.0 (MAT=9040 MF=1 MT=451); Pa-231 and Pa-233 evaluations for ENDF/B-VII.0 (MAT=9133 and 9137 MF=1 MT=451), National Nuclear Data Center, BNL ( 15 December

5 UMC-G a.k.a. Garage solution UMC-B a.k.a. Breakfast solution VS D.L. Smith San Diego 2007 R. Capote, A. Trkov Port Jefferson

6 UMC-G ( Garage Solution) 6 Donald L. Smith, ANL Argonne National Laboratory WPEC 2007 SG24

7 UNIFIED MONTE CARLO (UMC-G) D.L. Smith, A Unified Monte Carlo Approach to Fast Neutron Cross Section Data Evaluation, Proceedings of the 8th International Topical Meeting on Nuclear Applications and Utilization of Accelerators, Pocatello, July 29 August 2, 2007, p BAYES THEOREM & PRINCIPLE OF MAXIMUM ENTROPY p(σ) = C x L(y E,V E σ) x p 0 (σ σ C,V C ) p 0 (σ σ C,V C ) ~ exp{-(½)[(σ σ C ) T (V C ) -1 (σ σ C )]} L(y E,V E σ) ~ exp{-(½)[(y y E ) T ( V E ) -1 (y y E )]}, y=f (σ) y E, V E : measured quantities with n elements y C, V C : calculated using models with m elements UMC based on p(σ), GLS on the peak of the distribution 7

8 8 Unified Monte Carlo (UMC-B) 1) MC modeling (EMPIRE, TALYS, CCONE, CoH, ) {σ i } 2) For each random set {σ i } we calculate L(y E,V E σ i ) L(y E,V E σ i ) = exp{-(½)[(f (σ i ) y E ) T ( V E ) -1 (f (σ i ) y E )]} N exp w ( i ) i i 1, cov( N i, j ) exp w ( i ) i1 OUTPUT: 1) i 2) Stochastic set {σ i }, cov(, ) j exp w ( i) i j RC, D. L. Smith, A. Trkov, M. Meghzifene, A New Formulation of the Unified Monte Carlo Approach (UMC-B) and Cross-Section Evaluation for, J. ASTM International 9, JAI (2012) i j

9 Two variable toy model: ratio experimental data 9

10 EXPERIM MODEL RATIO CASE MODEL y1=210 +/- 63 (30%) y2=32 +/- 9.6 (30%) Cov(1,2) = 0.95 EXPERIM f1=y1= / (30%) f2=y2/y1= / (5%) ~ 43 Cov(1,2) = 0. y2 =43+/-2 vs 32+/- 9 10

11 EXPERIM MODEL COMBINED 5% exp. ratio unc., 95% model correl GLS 195 +/- 44 (22%) /- 7 (18%) COMBINED UMC 151 +/- 37 (25%) 30 +/- 7 (22%)

12 GLS FAILURE: ANALYSIS 5% exp. ratio unc. 95% model correlation (discrepant model vs data) Quantity Node 1 Node 2 Ratio BF/GLS METR/GLS METR/BF % exp. ratio unc. no model correlation Quantity Node 1 Node 2 Ratio BF/GLS METR/GLS METR/BF % exp. ratio unc. 95% model correlation Quantity Node 1 Node 2 Ratio BF/GLS METR/GLS METR/BF

13 Evaluation of 55 Mn(n,) cross section 13

14 Selection of experimental data (1) Raw data (EXFOR) 14

15 Selection of experimental data (2) Accepted and renormalized 15

16 Nuclear Data Sheets 110 (2009) 3107 Nuclear Data Sheets 108 (2009) 2655 p 0 (σ σ C,V C ) 16

17 UMC vs GLSQ: a real evaluation 55 Mn(n,) 17

18 Concluding remarks A careful selection and adjustment of raw experimental data is a critical step to achieve a consistent (non discrepant) database for the evaluation Linear case studied (no ratio data) : UMC-G and GLSQ are in excellent agreement Non-gaussian case studied (ratio data): GLSQ fails, UMC (Metr) solution obtained UMC-G (Metr), UMC-B and GLSQ applied to 55 Mn(n,γ) case (energy range 100 kev to 20 MeV) 18

19 19

20 UMC sampling schemes Brute Force approach: A set of independent {σ} METROPOLIS 1 approach: An stochastic Markov chain {σ} distributed following p(σ) If p(σ ) > γ p(σ(t)) then σ(t+1)=σ ; else σ(t+1)=σ(t) RC and D.L. Smith, Nucl. Data Sheets 109, 2768 (2008) (1)N. Metropolis et al., J. Chem. Phys. 21, 1087 (1953) 20

21 UMC-G: BF vs Metropolis Nuclear Data Sheets 109 (2008) 2768 An Investigation of the Performance of the Unified Monte Carlo Method of Neutron Cross Section Data Evaluation 21

22 Red.Chisq Red.Chisq UMC convergence Chisq Convergence GLS UMC: BF UMC: Metropolis E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 Histories 50 Chisq Convergence GLS UMC: BF UMC: Metropolis E+05 1.E+06 1.E+07 1.E+08 1.E+09 Histories 22