Bayesian networks for scenario analysis of nuclear waste repositories

Transcription

1 Bayesan networks for scenaro analyss of nuclear waste reostores Edoardo Toson ab Aht Salo a Enrco Zo bc a. Systems Analyss Laboratory Det of Mathematcs and Systems Analyss - Aalto Unversty b. Laboratory of sgnal and rsk analyss Dartmento d Energa - Poltecnco d Mlano c. Char on Systems Scence and the Energetc Challenge - École Centrale Pars and Suelec November 07

2 Background Dee geologcal dsosal of nuclear waste For lcensng a reostory safety assessment Large aleatory uncertanty about the evoluton of the dsosal system Tycally addressed by scenaro analyss Safety? Scenaro Analyss Scenaro Scenaro Scenaro... Scenaro n

3 Motvaton Sent-nuclear-fuel reostory at Olkluoto Fnland Emhass on comrehensveness TURMET roect obectves: Systemate scenaro analyss for nuclear waste reostores Brng methodologcal advancements to hel acheve comrehensveness n scenaro analyss

4 Scenaro analyss rocess Structure of the rocess: Scenaro develoment o Identfcaton of the Features Events & Processes (FEPs) o System model of the dsosal system o Scenaro generaton Scenaro Develoment Identfcaton of Features Events and Processes (FEPs) System model (SM) Consequence analyss Aroaches to scenaro generaton: Scenaro generaton Pluralstc Probablstc Consequence Analyss

5 Challenges Methodologcal challenges n scenaro analyss: Buldng a system model as a framework for scenaro generaton Scenaro Develoment Identfcaton of Features Events and Processes (FEPs) System model (SM) Achevng comrehensveness Scenaro generaton Treatng the estemc uncertantes Consequence Analyss

6 FEPs and safety target Set of nodes FEPs and safety target and arcs Random varables wth dscrete states Z d d shear shear X shear State robabltes: d 0 X 00 cm dshear dshear dshear 0 S 00 cm FEPs Indeendent nodes Uncondtonal Deendent nodes Condtonal V Safety target

7 Scenaros and subscenaros A scenaro s a combnaton of FEP states FEPs... n FEP For a deendent node a subscenaro s a combnaton of states of ts arents D V V - Safety target

8 Safety State of the safety target ndcatng falure FEPs Total falure robablty of the dsosal system fal S V I V D \C V V C V C fal C V C aggregate over all scenaros ont robablty of scenaro and falure state Safety: fal fal Proagaton Safety target Falure!

9 Eert udgment At a gven node set of eerts Suose one s estmatng For the state-robablty vector multle eerts belefs Eert C ( ) Feasble regon for the state robabltes: Conve combnaton of eerts belefs Eert A ( ) P... : w b N b B b w b 0 b B w b Eert B ( )

10 Smulatons Relatonsh between the contnuous values of a node and of ts arents θ : b a b a X X X X V θ X Suose one s estmatng V Reeated Monte Carlo samlng a a a b b b subscenaros n n n θ n n n ˆ 0. ˆ 0.5 ˆ V V V Monte Carlo error ˆ ˆ ˆ k s k h N k h k h V V P Feasble regon for the state robabltes: Belong to ther ntervals Sum u to one

11 Falure-robablty nterval Otmaton to estmate bounds to the falure robablty Customed algorthm: smle + reduced gradents Thread eert udgment & smulatons falure-robablty nterval Estmaton of the falure-robablty nterval Bound Lower Uer Obectve functon Constrants mn ma fal I P P V fal S V D Eerts belefs Smulatons Feasble regons for state robabltes Otmaton Falurerobablty nterval V V V

12 Conclusveness & comrehensveness It can be challengng to assess safety The falure-robablty nterval s conclusve f t les ether: entrely below the mamum accetable threshold - Safe fal 0.8 entrely above the mamum accetable threshold - Unsafe Comrehensveness: P : P P P P P V S fal X P X P V V V D D S fal Eerts belefs Smulatons Feasble regons for state robabltes fal Otmaton fal Falurerobablty nterval fal Unsafe Safe 0 0 4

13 Comrehensveness & smulatons Achevng comrehensveness can be challengng f there are lmts to the number of smulatons For nstance f the subscenaros to be smulated are samled randomly: few smulatons for all subscenaros large Monte Carlo error wde state-robablty ntervals wde ossbly nonconclusve falure-robablty nterval ˆ h k ˆ V h k N s k ˆ V h k Ice sheet Subscenaros Fracture dslacement Smulatons 5 7 a n a b n n n a n θ b n b Can smulatons be erformed for a restrcted set of 8 resonsbly selected subscenaros? For nstance dentfed by rsk-mortance measures 0 Total 00

14 Addressng challenges n scenaro analyss Recall the methodologcal challenges n scenaro analyss: Buldng a system model as a framework for scenaro generaton Bayesan network of FEPs n whch scenaros and subscenaros are defned Achevng comrehensveness The subscenaros to be analyed wth more smulatons to obtan a conclusve falurerobablty nterval are dentfed Treatng the estemc uncertantes The estemc uncertanty about the values of the state robabltes s charactered by feasble regons

15 Comarson to former aroaches Pluralstc Scenaros selected by udgment Reresentatve/llustratve of the future Here robablstc scenaro analyss Probablstc (e.g. Yucca Mountan) Rgorous mathematcal framework Great comutatonal avalablty Large samle from ntal nodes then smulatons n cascade Here less comutatonal avalablty: ntegrate eert udgments and smulatons dentfy the regons of the robablty sace (subscenaros) to be analyed

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