IAEA-CN-184/61 Y. GOTO, T. KATO, K.NIDAIRA. Nuclear Material Control Center, Tokai-mura Japan.

Transcription

1 IAEA-CN-84/6 Establshmt of accurat calbrato curv for atoal vrfcato at a larg scal ut accoutablt tak RRP - For strgthg stat sstm for mtg safguards oblgato. GOO. KAO K.NIDAIRA Nuclar Matral Cotrol Ctr oka-mura Jaa goto@jmcc.or.j Abstract. aks ar stalld a rrocssg lat for st ful ordr to accout soluto of uclar matral. h carful masurmt of volum taks s crucal to mlmt accurat accoutg of uclar matral. h calbrato curv rlatd wth th volum ad lvl of soluto ds to b costructd whr th lvl s dtrmd b dffrtal rssur of d tubs taks. Mor tha o calbrato curvs ddg o th hght ar commol ald for ach tak but t s ot lctl dcdd how ma sgmts ar usd whr to slct sgmt or what ordr of olomal curv. Hr w rst th ratoal costructo tchqu of gvg otmum calbrato curvs ad thr charactrstcs. h tak calbrato work has b coductd th cours of cotract wth Jaa afguards Offc JGO) about safguards formato tratmt.. Itroducto Calbrato curvs var accordg to who draw thm bcaus thr was ot adquat statstcal algorthm to dtrm th dgr of calbrato curv ad cut ots ddg o th hght of th tak. hrfor followg ots ar focusd ths ar. - What dgr of olomal curvs should b usd? - Whr to slct th cut ot sgmt) a tak? Of cours th dtrmato coffct of rgrsso could b bttr f ou chos th hghr dgr of rgrsso. Howvr t s ot arorat to cras th dgr of olomal curv. It should b bst to dtrm th arorat lowr dgr of rgrsso for th calbrato quato from th statstcal vw ots. Rgardg th sgmt t should b cssar to stablsh th statstcal aroach to dtrm th cut ot for sgmt. Du to th abov raso ths ar dscrbs th statstcal aroach of dtrmato for th dgr of calbrato curv ad cut ots for sgmts.. Costructo of calbrato curv. Raw data for costructo of calbrato curv h varous covrsos should b ald bfor mlmtg th rgrsso aalss btw hght ad volum. - Hght drvd from rssur masurd b d tub th tak h quato blow dcats th covrso from dffrtal rssur P ) dst ) ad acclrato of gravt g) to hght H). P H g Dst s stadardzd b th stadard tmratur 5 dgr s hr usd)

2 - Volum drvd from wght of watr h quato blow dcats th covrso from th wght of watr th ot W) to volum cotad th tak V). W V h dst s also stadardzd b th stadard tmratur 5 dgr s hr usd) h corrcto b tmratur should b ald carfull bfor mlmtg multl rgrsso aalss for th costructo of th calbrato curv. Furthrmor othr corrctos ar ald.g. thrmal cotracto/aso of th tak tslf ad d tub ar buoac ffcts o th volum. Howvr th corrcto of ar colum wght for maomtr lvl rssur loss lvl d tub bubbl form ffct at t of lvl tub b bubblg ovr rssur ar ot ald bcaus thos corrctos ar glgbl ad thos corrcto maks th covrso mor coml wh w us th calbrato curv. h most mortat thg s to us th sam covrso ad corrctos as tal calbrato for th matral accoutac.. Procdur of costructo hr ar followg 5 sts to costruct th calbrato curv.. I th frst st data aalst rforms th covrso from dffrtal rssur to hght of th lqud cotad th tak.. I th scod st covrso from wght to volum of th watr cotad th tak.. h calbrato oratos ar coductd mor tha oc ordr to avod th sstmatc rror. Hraftr th frst calbrato s calld as Ru th scod calbrato s calld as Ru ad so o. h volum of hl udr th d tub amog svral rus s lkl dffrt. It s cssar to adjust th hl volum of svral rus to b sam. h adjustmt s show th fgur whch s calld Algmt. 4. Multl rgrsso aalss s ald to th data btw volum ad hght aftr algmt. h dtald rocss s dscrbd th t ssso. hs st s ma ot of ths ar. 5. h calbrato curvs ar dtrmd aftr th abov rocdurs. Fgur. Calbrato curv costructo flow

3 Fgur. Algmt for svral rus. Multl Rgrsso Aalss for tak calbrato h statstcal multl rgrsso aalss s ald to th rlato btw hght ad volum th tak. hs scto dscrbs th dtald statstcal algorthm for costructg calbrato curv... Producg th calbrato curv h tabl blow dcats th data for hght ad volum at th calbrato. abl. Notato of th hght ad volum Numbr) Hght) Volum) : : : h modl of th multl rgrssos for dgr s dfd as follows. ) ~ N Vctor ad matr rgardg volum hght coffct ad rror ar dscrbd as follows. h modl of th multl rgrssos ar dscrbd b usg vctor ad matr as follows. I N ~ h vctor of rsdual volum s dscrbd as follows. Rsdual sum of squars s dfd as follow.

4 ) ) Dffrtat wth rsct to Du to th modl of multl rgrsso th followg quato ca b dscrbd. I V V E ) ) ) hrfor th followg quato could b drvd from abov quato. ) ) V E h dstrbuto of coffct N ~ h dtald matr of varac for coffct s dscrbd as follow. ) Followg quato dcats th cofdc lvl 95% t F.5 ) ) Whr Hothss tst for dtrmato for th dgr of quato hs scto coctrats o th statstcal tst rgardg dtrmato for th dgr of quato. h uros of th tst s to fd th lowst dgr of quato b statstcal aroach. I ordr to slct arorat dgr of quato followg sts maks t ossbl to choos dgr ratoall. Cosdrg th tratmt of data sml th hghst dgr of quato s dtrmd as cubc. h followg hothss tst s dfd frst. H : It s ot ffctv for mtgatg th varac of calbrato curv b chagg hghr dgr. H : It s ffctv for mtgatg th varac of calbrato curv b chagg hghr dgr. h dtald mthodolog of th tst s as follows. Notato : quato squars for lar sumof Rsdual : Rsdual sum of squars for quadratc quato : Rsdual sum of squars for cubc quato : Dgr of frdom for lar quato : Dgr of frdom for quadratc quato : Dgr of frdom for cubc quato F : F tst statstc btw lar ad quadratc quato

5 F : F tst statstc btw quadratc ad cubc quato h followg F statstc s usd for th tst btw lar ad quadratc quatos. F. F statstc dcats how much amout of rsdual sum of squars could b dcrasd b chagg lar to quadratc quato. If th F statstc cd F at dsrd fals alarm 5% or % t could b ffctv to chag lar to quadratc quato. % fals alarm s rcommdd ths ar. h followg F statstc s usd for th tst btw quadratc ad cubc quato. F s dstrbutd wth th followg dgr of frdom F If th F statstc cd F at dsrd fals alarm % t could b ffctv to chag quadratc to cubc quato. h adquat dgr of quato s dtrmd b th abov statstcal tst... Hothss tst for dtrmato for th cut ots gmts) hr ar sts to dtrm th cut ots for th sgmts. t. Fd th rosctv cut ot h rosctv cut ot s foud b th mmum total rsdual sum of squars. h tabl blow dcats how to fd th rosctv cut ot. h mamum dgr of quato s dfd as cubc. Du to th mamum dgr of quato th calbrato rocss rqurs mor tha 4 data ots. h fgur blow shows th flow of cratg th tabl to calculat th total rsdual sum of squars wth sgmts. h gr sold l dcats th dgr of quato ad rsdual sum of squars for sgmt b usg data from ) to 55). O th othr had th blu dottd l dcats sgmt wth data from 66) to ). h data surroudd b rd crcl s th total rsdual sum of squars. h rosctv cut ot s th mmum valus for rsdual sum of squars all data. h followg tabl ad fgur dcat th aml of fdg th rosctv cut ot. h cut ot s 79.86mm) th aml. abl. How to calculat th total rsdual sum of squars wth sgmts at ach hght

6 Fgur. Eaml of fdg th rosctv cut ot t. Dtrm o sgmt or two sgmts? h ma ot of ths tst s to fd whthr t s ffctv or ot b dvdg sgmt to sgmt. h crtcal lmt s dfd as fals alarm %. h coct of ths tst s show as follows. Notato : Rsdual sum of squars for sgmt : otal rsdual sum of squars for sgmts : Dgr of frdom for sgmt : Dgr of frdom for sgmts F : F tst statstc btw sgmt ad sgmts h followg F statstc s usd to tst th sgfcac btw sgmt ad sgmts F F s dstrbutd wth th followg dgr of frdom F statstc dcats how much amout of rsdual sum of squars could b dcrasd b chagg F statstc cds sgmt to sgmt. If th F at rqurd fals alarm 5% or % t could b ffctv to chag sgmt to sgmts. % fals alarm s rcommdd ths documt. h tabl blow dcats th F tst btw sgmt ad sgmts to dcd whthr t s ffctv to dvd sgmt to sgmts or ot. h followg fgur shows th comarso btw sgmt ad sgmts of th rsdual volum from calbrato curv. Du to th fgur t s obvous that th sarato of sgmts cotrbuts to rduc th sum of squars. h dvdg rocss s ratd for ach of dvdd sgmts utl th rocss has o statstcal sgfcac o calbrato works.

7 Rsdual VolumL) Rsdual VolumL) abl. Hothss tst for dtrmato for th cut ots gmt Hght Dfto Notato Eaml h umbr of data N 6 Rsdual sum of squars sgmt ~ Dgr of frdom Poulato varac 9.46 ~ / sgmts / ~ / otal of sgmts F tst h umbr of data N / Rsdual sum of squars / Dgr of frdom 6 / Poulato varac h umbr of data N / 7 Rsdual sum of squars / 9.47 Dgr of frdom / Poulato varac.49 Rsdual sum of squars / + /.857 Dgr of frdom / / 9 / / / / / F statstc / % F statstc F 5% / / / /.94 Cocluso / / / / / / / / It s ffctv to dvd sgmt to sgmts Rsdual Volum wth sgmt Hght mm) Rsdual Volum wth sgmts Hght mm) Rsdual VolumL)= Volum ord from ot)-volum drvd from calbrato curv) Blu dot th rght fgur: rsdual volum at st gmt Gr squar th rght fgur: rsdual volum at d sgmt Fgur4. Comarso btw sgmt ad sgmts for th rsdual volum.4 Dtrmato of calbrato curv.4. Dtrmato of calbrato curv h calbrato curvs ar costructd aftr dtrmg th cut ots dgr of quato. It s also mortat to stmat th matr of varac for coffct aftr calculatg th calbrato quato. h tabl blow shows th aml of dtrmato for th calbrato curvs.

8 abl4. Lst of th costructd calbrato curv gmt mm) Calbrato Curv = = ) ) ) = ) ) ) = ) ) ).4. Rvw of roosd aroach h fgur blow dcats th comarso btw w aroach ad covtoal aroach for rsdual volum ad masurmt ucrtats. I cocluso th w aroach could mak t ossbl to rduc th masurmt ucrtats wthout crasg th dgr of calbrato curv. I othr words th rlablt of calbrato has b mrovd b alg th w aroach. Blu dot: Rsdual volum b w aroach -Blu sold l: Error of calbrato curv b w aroach σ) Rd tragl: Rsdual volum b covtoal aroach Rd dottd l: Error of calbrato curv b covtoal aroach σ) Fgur5. Comarso btw covtoal ad w aroach. Cocluso h k ots of w aroach ar dtrmato of dgr of quato ad cut ot b statstcal F tst. h F tst could fd th arorat quato to mmz th masurmt ucrtats for calbrato curv. h calbrato rocss ca b dmostratd b th NMCC custom rogram ad cotrbuts to drawg uform calbrato curvs. h w aroach ca b ctd to mrov th rformac of calbrato works th followg ots. ) Rmoval of arbtrar dtrmato h w statstcal aroach s abl to lmat th arbtrar choc for cut ots. It also cotrbuts to avodg th us of ucssar hghr ordr olomal. h NMCC custom rogram s avalabl to draw ractcall bst calbrato curvs oc calbrato data ar obtad. )Otmzd dtrmato for dgr of quato ad cut ot for sgmt h w aroach ca fd th adquat dgr of quato ad bst cut ot for sgmt wthout kowg blurt of th tak. ) Assssmt of th ucrtats for calbrato curv It s mortat to assss th ucrtats of th calbrato curv b valuatg th varac of th calbrato curv. h ucrtats of th calbrato curv ca b usd for th rjcto lmt for th rodc r-vrfcato of th calbrato curv.

9 Rfrcs [] akauk KAO oshk GOO Kazuo NIDAIRA Costructo of Calbrato Curv for Accoutac ak 8 INMM Jaa [] asush Nagata Masahko Muchka Itroducto of multl classfcato aalss asu sha Co.. Ltd. Publshrs [] Jos F. A ak Volum Calbrato Algorthm Nuclar matrals maagmt 984 [4] GoldmaA.. t.al. h Aalss of ak Calbrato Data from vral Rus Procdgs of th 5 th aual mtg of INMM 984