Uncertainty propagation with AGS
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1 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
2 Contents Uncertinty propgtion with A (Anlysis of eel pectr Exmples Reporting of OF-cross section dt in EXFOR
3 Experimentl oservles rnsmission Rection exp N C in out C B B in out exp N Cr B C B r
4 Response / (/ns Response / (/ns (n, mesurements: 03 Rh(n, Flux mesurement Cpture mesurement 0 4 C C w 0 0 B B w ime Of Flight / ns exp N Cr B C B r N Bi Au ime Of Flight / ns
5 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
6 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
7 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
8 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
9 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
10 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
11 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
12 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
13 A :, g(, k (n, dim k (n, dim, nd not correlted nd in A-formt k dim
14 A :, g(, k (n, dim k (n, dim, nd not correlted nd in A-formt k dim
15 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
16 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
17 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
18 A commnds
19 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
20 rnsmission fctor Counts Counts Clcultion of trnsmission mple in mple out 0 5 C in B in 0 5 C out B out exp C N C in out B B in out ime / s ime / s ime / s
21 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 % E- 0.59E- 0.35E-4 0.4E E- 0.50E E- 0.67E- 0.45E-4 0.8E- -0.0E- 0.50E E- 0.73E- 0.54E-4 0.E- -0.E- 0.50E E- 0.78E- 0.6E-4 0.4E- -0.3E- 0.50E E-.07E-.5E-4 0.5E- -0.5E- 0.45E E-.0E-.04E E- -0.4E- 0.4E E- 0.93E- 0.86E E- -0.E- 0.35E E- 0.84E- 0.7E E- -0.8E- 0.30E E- 0.76E- 0.57E E- -0.5E- 0.5E E- 0.77E- 0.59E E- -0.6E- 0.5E E- 0.85E- 0.73E E- -0.9E- 0.9E E- 0.98E- 0.97E E- -0.3E- 0.35E E- 3.75E- 4.06E E- -.8E- 0.50E E- 3.89E- 5.3E E- -.3E- 0.5E E- 3.80E- 4.46E E- -.3E- 0.50E E- 3.77E- 4.3E E- -.0E- 0.50E-
22 ime-of-flight / ns A Output -> Covrince mtrix ime-of-flight / ns
23 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
24 Residuls rnsmission Residuls rnsmission pecify trget chrcteristics 4 Pu:.5 x 0-5 t/ Powder/metl smple 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 Holes = 0.33 = 5 me n =.90 me Neutron Energy / e Neutron Energy / e
25 Cpture mesurements pecify how dt reduction ws done nd use proper reference Weighting function with threshold e.g. Borell et l., NIM A577 ( without threshold e.g. Aondnnno et l. NIM A5 ( Correction for -ry ttenution 3 Normliztion internl/externl sturted resonnce neutron flux monitor 4 Bckground fixed ckground filters CK CEN
26 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 +/ 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 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 t/ 36 U 0 m luminium No continer 5 me Recommendtion IRMM & N - IAEA [] NE 60 ( [] NIM A 79 (98, 3 [3] NIM A 8 (985, 7 [4] NIM A 53 (004, 39
27 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 +/ 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
28 IAEA recommendtion
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