INFLUENCE OF SYSTEMATIC EXPERIMENTAL UNCERTAINTIES IN THE EVALUATION OF NUCLEAR DATA
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1 INFLUENCE OF SYSTEMATIC EXPERIMENTAL UNCERTAINTIES IN THE EVALUATION OF NUCLEAR DATA Cyrille De Saint Jean, Pascal Archier, Gilles Nguere, Pierre Lecnte, D. Bernard, C. Carmuze and T. Nicl CEA/DEN/Cadarache JEFF-CHANDA Jint Winter Meeting Nvember, 20/24, 2017 JEFFDOC-1880 PAGE 1
2 OUTLINES 1 Reminders, cntext and bjectives 2 Bayesian inference (Generalize least square and Mnte-Carl) 3 Systematic Micrscpic Uncertainties: A. What? B. Marginalizatin C. Cvariances 239 Pu, an example 4 5 Integral Data Assimilatin ans Syst. Uncertainties A. What? B. Single experiment (JEZEBEL) Cvariances 239 Pu, an example C. Several experiments : PU-SOL-THERM Syst. Uncertainty D. A psitive aspect f Syst. Uncertainties Cnclusins and Perspectives
3 CROSS SECTIONS KNOWLEDGE EVALUATION IN THE RESONANCE RANGE AND HIGHER 1 Issues : Systematic experimental uncertainties t ( M, x, ) Phenmenlgical Nuclear reactin mdel theries + Parameters Mdel defects (Epistemic Uncertainties) Integral experiment assimilatin Cmmn Physics frm RRR t Cntinuum x a, E, a, R' c x a, a c, R, D0, S a x 2, ac, dc, V, W,... r x,,... g g
4 Micrscpic and Integral experiments 1 Micrscpic experiments Transmissin measurements at JRC/Geel (GELINA) Fine reslutin in energy All reactins: (n,), (n,f), (n,n ), (n,xn) Outging particles (n,, a...) caracterized in terms f spectrum/multiplicity/angular distributin Systematic uncertainties (nrmalizatin, backgrund, detectr efficiency ) Neutrn flux in MINERVE Integral experiments Integrated measurements in angle/energy/space Better verall precisin) <3% (1s) fr difficult regins Representativity w/t t Industrial cncepts: keff, reactivity effects, flux/pwer distributin Integral experiments crrelatins (systematic uncertainties) EvaluatinPrcessingTransprt cde feedback ND 20 NOVEMBRE 2017 Oscillatin measurements in Minerve
5 CROSS SECTIONS KNOWLEDGE EVALUATION IN THE RESONANCE RANGE AND HIGHER 1 Nuclear reactin mdels Experiments (micrscpic/integral) Bayesian 20 NOVEMBRE inference 2017 technique Evaluatin f uncertainties (variances and crrelatins) R Matrix Optical Mdels Statistical Mdel Transmissin Mdels
6 CROSS SECTIONS KNOWLEDGE EVALUATION IN THE RESONANCE RANGE AND HIGHER 1 Micrscpic Micrscpic Integral Nuclear reactin mdels Experiments (micrscpic/integral) Bayesian 20 NOVEMBRE inference 2017 technique Evaluatin f uncertainties (variances and crrelatins) Micrscpic
7 CROSS SECTIONS KNOWLEDGE EVALUATION IN THE RESONANCE RANGE AND HIGHER 1 Nuclear reactin mdels Experiments (micrscpic/integral) Bayesian 20 NOVEMBRE inference 2017 technique Evaluatin f uncertainties (variances and crrelatins) GLS BMC
8 Mdel p( x EVALUATIONS AND UNCERTAINTIES GENERAL MATHEMATICAL FRAMEWORK Bayesian inference (prbability density): M, y, U ) = p( x Μ, U ) dx p( x M, U p( y M, x, U ) ) p( y M, x, U ) 2 Mdel parameters New measurements a priri infrmatin Frmulatin: psterir[p(x y,u)] prir[p(x U)] likelihd[p(y x,u)] Estimatin f the first tw mments f the a psteriri distributin PAGE 8
9 EVALUATIONS AND UNCERTAINTIES GENERAL MATHEMATICAL FRAMEWORK 2 Bayesian inference (prbability density): Maximum Entrpy Principle Laplace apprximatin (Sammy,Refit,Cnrad, SOK ) Mnte-Carl (BMC, Frward-Backward ) Estimatin f a cst functin (Generalized Chi-square) 2 GSL = T 1 x x M x x m T 1 y t ( x) M y t ( x) y x m Estimate 1 st tw mments f with Mnte-Carl Sample f p( x Μ, U ) x Fr each k assciate a weight Fr ex. Likelihd L k [ y M p(x M, y,u ) x k p(, xk,u )] PAGE 9
10 COVARIANCES EVALUATION STRATEGY 2 20 NOVEMBRE 2017 CEA 10 AVRIL 2012 PAGE 10
11 MICROSCOPIC EXPERIMENT SYSTEMATIC UNCERTAINTIES 3 Cunting rates: statistical uncertainties The mre yu cunt, the lwer is the uncertainty Uncrrelated bins Nrmalizatin, efficiency,. Asympttic uncertainties Cnstants Lng range crrelatins Bayesian Inference issues : ex 239 Pu Analysis f capture (Gwin 73) ; Syst. Unc.~ 3% «Classical» (GLS/BMC) fr fissin and radiative widths Obviusly bad result (see Fig.) Due t the likelyhd pdf and experimental cvariance 2 GSL = T 1 x x M x x T 1 y t ( x) M y t ( x) Slutin: Marginalisatin f pdf s m y x m 20 NOVEMBRE 2017 PAGE 11
12 SYSTEMATIC EXPERIMENTAL UNCERTAINTIES MARGINALIZATION? 3 Marginalizatin philsphy t( ( x), ) Mdel parameters «nuisance» parameters Nuisance parameters are necessary during cmparisns with experiments (data reductin, nrmalizatin, ), but nt fr the final evaluatin t( ( x), ) y + Cvariances p( x, M, y, U ) Marginalizatin f the prbability density: p ( x M, y, U ) = d p( x, M, y, U ) Marginalizatin : estimatin f at least the first tw mments f the marginal prbability density PAGE 12
13 SYSTEMATIC EXPERIMENTAL UNCERTAINTIES MARGINALIZATION 3 Analytical methd* : Full cvariance kept: with and Hybrid Mnte-Carl/GLS**: 1. Sampling f nuisances parameters fllwing its pdf : θ k 2. Fr each realizatin k, d a GLS x k +M k 3. Use ttal variance cvariance therem n the K-Statistic Full Mnte-Carl*** : duble Mnte Carl integratin (BMC) * B. Habert et al., Nuc. Sci. Eng., 166, 276 (2010) + PhD Thesis ** C. De Saint Jean et al., Nuc. Sci. Eng., 161, 363 (2009). *** E. Privas PhD thesis + C. De Saint Jean et al., EPJ Web (ND2016) PAGE 13
14 Example : Pu239 3 Reslved Resnance Range Unreslved Resnance Range and Cntinuum Analysis f main EXFOR experiments (E<2500 ev) with R-Matrix cde CONRAD. Marginalizatin f Exp. systematic uncertainties (nrmalizatin, backgrund, ) Fit f JEFF3.2 with CONRAD in huse mdels Marginalizatin f Exp. systematic uncertainties (nrmalizatin, backgrund, ) * G. Nguere, P. Archier et C. De Saint Jean : JEFFDOCs (04/15 ; 11/15 ; 04/16) PAGE 14
15 Example : Pu239 3 High impact f Exp. Systematic Uncertainties Lng range crrelatins (~0.8-1) High uncertainties ~ % (Thermal Capture; Fissin in Fast range) ~1000 pcm n MISTRAL2 (EOLE Reactr) and ASTRID (FR prttype) Energy dmain treated separatly Beware f ptential impact fr Fast Reactr (URR) * G. Nguere, P. Archier et C. De Saint Jean : JEFFDOCs (04/15 ; 11/15 ; 04/16) Additinal Experimental infrmatin PAGE 15 needed
16 Systematic Uncertainties fr Integral Experiments 4 Systematics Uncertainties ** (see WPEC/SG33-SG39): Fuel cmpsitin uncertainties Detectr efficiencies and calibratins One experiment analyzed It will increase the initial uncertainty Several experiments It will increase the initial uncertainty It will give a crrelatin cefficient between the experiments What are the effect n Integral Data Assimilatin r Nuclear Data Validatin? PAGE 16
17 * C. De Saint Jean et al, Nuclear Data Sheet 123 (2015), x Integral Data Assimilatin and Fast energy range : 239 Pu Data assimilatin f JEZEBEL* Limited nuclear data adjustement () but with tw schemes RRR, OMP, Fissin And/r Multigrup bbbbb,... (x) g Neutrn/Gamma Transprt Integral Data Assimilatin n Parameters 4 JEZEBEL is an indirect measurement f χ + υσ f Here : Fcus n XS E~ pcm!!! Need f a cherent ( Micrscpic) prir (previus analysis)
18 * C. De Saint Jean et al, EPJ Web, ND2016 (2017) Integral Data Assimilatin and Fast energy range : 239 Pu Data assimilatin f JEZEBEL* Limited nuclear data adjustement () but with tw schemes 4 Bayesian Mnte-Carl ~ GLS Results: cherent fr bth methds With a cherent ( Micrscpic) prir Results: cherent fr bth schemes ½
19 Integral Data Assimilatin and Fast energy range : 239 Pu Data assimilatin f JEZEBEL Full nuclear data adjustement (,, )* 4 Results are very sensitive t prirs Even fr this clean case, crss crrelatins are intrduced between (,, ) ENDF issue ; GND? Uncertainty reductin ~ E 250 pcm is lw : Unrealistic? Syst. Unc.? * C. De Saint Jean et al, Nuclear Data Sheet 123 (2015),
20 Systematic Uncertainties fr Integral Experiments Example f Pu-Sl-Therm serie 4 First Integral Experiment : PU-SOL-THERM WATER-REFLECTED 11.5-INCH DIAMETER SPHERES OF PLUTONIUM NITRATE SOLUTIONS Fissile cncentratin (g/l) 73 (H1)/(Pu240,Pu242,Pu241,Pu239,Pu238) (H1)/(Pu241,Pu239) Vecteur istpique : 238Pu 239Pu 240Pu 241Pu 242Pu 0.01% 95.01% 4.67% 0.31% 0.01% Keff = ± E/C-1 (T4) = pcm Secnd Integral Experiment : PU-SOL-THERM WATER-REFLECTED 12-INCH DIAMETER SPHERES OF PLUTONIUM NITRATE SOLUTIONS Fissile cncentratin (g/l) (H1)/(Pu240,Pu239) (H1)/(Pu239) Vecteurs istpiques : 239Pu 240Pu 96.88% 3.12% Keff = ± E/C-1 (T4) = - 12 pcm Integral Data Assimilatin f Bth PST n Pu Nuclear Data With a crrelatin cefficient : r = 0 r 1
21 Systematic Uncertainties fr Integral Experiments Example f Pu-Sl-Therm serie 4 Identical uncertainty reductin n 239 Pu capture crss sectin Very different trends between r = 0 r 1
22 *D. Bernard et al., Nuclear Data Sheet 118 (2014), Systematic Uncertainties fr Integral Experiments A psitive use pssible! 4 FLATTOP GODIVA Δρ - = 235 U + reflectr 238 U 235 U Reflectr Privas et al. Cntains fuel with equivalent caracteristics New interpretatin f standard Integral Experiments* Cntains fuel with cmmn Syst. Uncertainties Cnceive integral experiments with Syst. Uncertainty can permit t reach different Nuclear Data PAGE 22
23 Systematic Uncertainties fr Integral Experiments Validatin ; Figure f merit ; 4 Reduced χ O. Cabells, jefdc-1843 Reduced value will be impacted by crrelatins Cnclusins n the quality f the Library culd be changed
24 Systematic Uncertainties fr Integral Experiments Validatin ; Figure f merit ; 4 Cumulative χ O. Cabells, jefdc-1843 Very usefull t identify utliers What happens when crrelatins exists?
25 Cnclusins 5 Evaluatin f systematic uncertainties is f prime interest fr Nuclear Data evaluatrs Micrscpic Experiments: Still high Syst. Uncertainties n Fissin (Cntinuum), Capture f Fissile istpes Mainly related t nrmalizatin, backgrund, detectrs efficiency, Create Evaluated Nuclear Data with lng range (and high) crrelatins Integral Experiments: A prper lk n Syst. Uncert. fr Integral Experiments is paramunt G back t pre-icsbep (Experimental reprts?) If n infrmatin be careful in the chice (r = 0 r 1) Syst. Uncert. will change adjustments results (trends r uncertainty reductin) SG46 Culd be psitive!! Lk at integral experiments such as gdiva/flattp Innvative Integral Experiments t be studied PAGE 25
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