Uncertinty propgtion with A J. Heyse, C. Prdel, P. chilleeeckx EC JRC IRMM tndrds for Nucler fety, ecurity nd fegurds (N3 H.I. Kim Koren Atomic Energy Reserch Institute Nucler t Center
Contents Uncertinty propgtion with A (Anlysis of eel pectr Exmples Reporting of OF-cross section dt in EXFOR
Experimentl oservles rnsmission Rection exp N C in out C B B in out exp N Cr B C B r
Response / (/ns Response / (/ns (n, mesurements: 03 Rh(n, Flux mesurement Cpture mesurement 0 4 C C w 0 0 B B w 0-0 0-4 0 4 0 5 0 6 0 7 ime Of Flight / ns exp N Cr B C B r N Bi Au 0 0 0 4 0 5 0 6 0 7 ime Of Flight / ns
A concept: full covrince informtion Anlysis of eel pectr (A rnsforms count rte spectr into oservles (trnsmission, yields Full uncertinty propgtion strting from counting sttistics Output: complete covrince mtrix pecil formt for covrince mtrix Reduce spce for dt storge (EXFOR ocument the sources of uncertinties due to ech step in the dt reduction process erify the contriution of ech quntity introducing correlted uncertinty component! C. Bstin, Int. oc. Opticl Eng. 867 (997 6 X z z : uncorrelted prt n vlues : correlted prt dim. (n x k
Relile experimentl dt nd results (P Requires Understnding of the mesurement process (scientific ckground experimentl oservles mesurement model Well documented experimentl oservles, including ll experimentl detils (input prmeters, systemtic effects ll uncertinty components (correlted nd uncorrelted Propgtion of uncertinties (uncorrelted & correlted not complicted UP : Note : UP & Q sed on norml proility distriutions A-formlism (concept X X X Q: q q z q ( q z q (q q (z h(q
OF - spectrum nd prmeter vector f(, only chnnel-chnnel opertions (, (, OF spectrum(counts (,..., k dim. n prmeter vector f(, digonlelements yi : : g g,ik,ik fi f y k i k f only chnnel chnnelopertions 3 : symmetricnd positive definite Cholesky trnsformtion
OF - spectrum nd prmeter vector f(, only chnnel-chnnel opertions (, (, OF spectrum(counts (,..., k dim. n prmeter vector f(, dim (k,k dim (n,k f digonl only chnnel chnnel : digonl dim (n,k digonl, n - vlues
OF - spectrum nd prmeter vector f(, only chnnel-chnnel opertions (, (, OF spectrum(counts (,..., k dim. n prmeter vector f(, dim (n,k A - formt digonl, n - vlues numer of vlues to e stored dim. (n, k+ k = totl numer of correlted uncertinty components
OF - spectrum nd prmeter vector f(, only chnnel-chnnel opertions (, (, OF spectrum(counts (,..., k dim. n prmeter vector f(, correltedcomponents uncorrelted components A - formt numer of vlues to e stored dim. (n, k+ k = totl numer of correlted uncertinty components
OF - spectrum nd prmeter vector Exmple: (, (, OF spectrum(counts ( prmeter vector dim. dim. n f(, g,i dim (n, f i y i ( ( f only chnnel chnnel f : g i,ii y digonl digonl i
OF - spectr in A formt nd prmeter vector g(,,, nd not correlted Input Output (, dim. k f(,, (, f (, dim. k uncorrelted components (, f (, dim. k correltedcomponents
A :, g(, k (n, dim k (n, dim, nd not correlted nd in A-formt k dim
A :, g(, k (n, dim k (n, dim, nd not correlted nd in A-formt k dim
A : g(,,, nd not correlted nd in A-formt dim k dim (n, k dim (n, k dim (n,k (n,k (n,k (n,k (k = k + k + k correltedcomponents dim n uncorrelted components
A File formt n k : numer of dt points (OF : numer of quntities introducing correlted uncertinty components : uncorrelted prt (n vlues X : mtrix dimension (n x k contins the contriution of ech quntity creting correlted uncertinty component Oservle (dimension n with k sources of correlted uncertinties C. Bstin, Int. oc. Opticl Eng. 867 (997 6
A File formt torge spce Covrince mtrix n elements (e.g. 3k x 8 ytes A representtion n (k+ elements (3k, 0 corr. 8 5 M X Oservle (dimension n with k sources of correlted uncertinties Informtion Covrince mtrix no seprtion etween components A representtion seprtes uncorrelted nd correlted components (void PPP verify impct of ech individul component
A commnds
A, cript for trnsmission dt # crete gs-file gs_mpty RFAK # red smple out scler=oout,cmout gs_getx RFAK /CAER=$scler /FROM=spout.his /AIA=OU # red smple in scler=oin,cmin gs_getx RFAK /CAER=$scler /FROM=spin.his /AIA=IN /IKE=A0OU C N C in out B B in out # ded time correction dtcoef=coef gs_idtc RFAK,A0OU /IME=$dtcoef /PC= gs_idtc RFAK,B0IN /IME=$dtcoef /PC= # normlize to centrl monitor nd divide y in width gs_vgr RFAK,C0OU /CMC= gs_vgr RFAK,0IN /CMC= #clculte ckground contriution gs_func RFAK /FUN=f0 /PARFIE=PAROU /AIA=BOU /IKE=A0OU gs_func RFAK /FUN=f0 /PARFIE=PARIN /AIA=BIN /IKE=A0OU #sutrct ckground gs_lico RFAK,E0OU,0BOU /AIA=OUNE /PAR=.0,-.0 gs_lico RFAK,F0IN,H0BIN /AIA=INNE /PAR=.0,-.0 #crete trnsmission fctor gs_divi RFAK,I0OUNE,J0INNE /AIA=RFAK
rnsmission fctor Counts Counts Clcultion of trnsmission mple in mple out 0 5 C in B in 0 5 C out B out 0 4 0 3 exp C N C in out B B in out 0 4 0 3 0 0 00 000 ime / s.0 0.8 0 0 00 000 ime / s 0.6 0.4 0. 0.0 0 00 000 ime / s
Output A_PUX C = + = + X X H u u B in B out N B in / B in : 0.0 % B out / B out : 5.0 % N / N : 0.5 % 800 600 0.999 0.79E- 0.59E- 0.35E-4 0.4E- -0.08E- 0.50E- 600 400 0.999 0.86E- 0.67E- 0.45E-4 0.8E- -0.0E- 0.50E- 400 300 0.999 0.9E- 0.73E- 0.54E-4 0.E- -0.E- 0.50E- 300 4000 0.999 0.97E- 0.78E- 0.6E-4 0.4E- -0.3E- 0.50E-........................... 6000 6800 0.899.30E-.07E-.5E-4 0.5E- -0.5E- 0.45E- 6800 7600 0.88.4E-.0E-.04E-4 0.53E- -0.4E- 0.4E- 7600 8400 0.70.5E- 0.93E- 0.86E-4 0.54E- -0.E- 0.35E- 8400 900 0.594.06E- 0.84E- 0.7E-4 0.55E- -0.8E- 0.30E- 900 0000 0.50 0.98E- 0.76E- 0.57E-4 0.56E- -0.5E- 0.5E- 0000 0800 0.504.00E- 0.77E- 0.59E-4 0.57E- -0.6E- 0.5E- 0800 600 0.58.09E- 0.85E- 0.73E-4 0.58E- -0.9E- 0.9E- 600 400 0.707.E- 0.98E- 0.97E-4 0.60E- -0.3E- 0.35E-........................... 964000 97000 0.999 5.9E- 3.75E- 4.06E-4 3.98E- -.8E- 0.50E- 97000 980000.037 6.09E- 3.89E- 5.3E-4 4.04E- -.3E- 0.5E- 980000 988000.00 6.0E- 3.80E- 4.46E-4 4.05E- -.3E- 0.50E- 988000 996000.00 5.9E- 3.77E- 4.3E-4 3.96E- -.0E- 0.50E-
ime-of-flight / ns A Output -> Covrince mtrix ime-of-flight / ns
Relile model prmeters from experiment Requirements: Well documented experimentl oservles in EXFOR Including: - experimentl detils (, n, N, - ll uncertinty components (correlted nd uncorrelted, A-formt - response function of OF-spectrometers Recommendtion IAEA / IRMM sed on the A system
Residuls rnsmission Residuls rnsmission pecify trget chrcteristics 4 Pu:.5 x 0-5 t/.0 0.8 Powder/metl smple 0.6 0.4 iterture = 5 me FI = 36.5 me n =.00 me n =.46 me Arel density + uncertinty 4 0 rin size of powder smple -4.0 Homogeneity 0.8 0.6 0.4 Holes = 0.33 = 5 me n =.90 me 4 0-4.5.6.7.8 Neutron Energy / e Neutron Energy / e
Cpture mesurements pecify how dt reduction ws done nd use proper reference Weighting function with threshold e.g. Borell et l., NIM A577 (007 66 without threshold e.g. Aondnnno et l. NIM A5 (004 454 Correction for -ry ttenution 3 Normliztion internl/externl sturted resonnce neutron flux monitor 4 Bckground fixed ckground filters CK CEN
emplte for cross section dt in EXFOR Min Reference Fcility EINA,3 Neutron production 4 Primry neutron production trget Urnium ime resolution primry em (ns 4 ns Modertor mteril H O urfce imensions continers 00 x 00 mm (mm x mm or dimeter in mm hickness (mm 40 mm Experimentl detils Mesurement type Flight pth length (m (modertor trget (detector: fce to fce distnce Fission (8.8 +/- 0.006 m Angle 8 deg (with respect to norml of modertor Bem dimensions imeter 55 mm (mm x mm or dimeter in mm mple ype (metl, powder Electrodeposition Chemicl composition UO Atomic undnce of min element 99.973 t% 36 U Weight per unit re (g/cm (09.9 +/-.3 Ug/cm eometry urfce dimensions imeter (50.0 +/- 0. mm (mm x mm or dimeter in mm hickness of min element (t/ Bcking Continment description emperture 5.354 0-6 t/ 36 U 0 m luminium No continer 5 me Recommendtion IRMM & N - IAEA [] NE 60 (008 00-06 [] NIM A 79 (98, 3 [3] NIM A 8 (985, 7 [4] NIM A 53 (004, 39
emplte for cross section dt in EXFOR etector ype Frisch gridded ionistion chmer Mteril CH 4 (00% s pressure s flow t tm eometry Flux normliztion Rection 0 B(n, Cross section from ENF/B-I.8 Atomic undnce of min element 93.0 t% 0 B rget thickness (8.05 +/- 0.0 0 B g/cm urfce dimensions imeter (50.0 +/- 0. mm ( 36 U- 0 B : ck to ck Normliztion uncertinty (OF-independent.5 % t ime-of-flight of first chnnel 3000 ns ime-of-fligth in width / ns Column Energy (reltivistic formul, = 8.38 m e Column ield in rn/t Column 3 Uncertinties (t sigm level otl (normliztion not included Column 4 Uncorrelted contriution (vrince Column 5 Other sources creting correlted ed time 0 B [col 6] uncertinty components Bckground 0 B [col.7, 8,9] ed time 36 U [col. 0] Bckground 36 U [col.,,3] escription of A Output
IAEA recommendtion