Bayesian networks for comprehensive scenario analysis of nuclear waste repositories

Transcription

1 Bayesan networks for comprehensve scenaro analyss of nuclear waste repostores Edoardo Toson a,b, Aht Salo a, Enrco Zo b,c a. Systems Analyss Laboratory, Dept of Mathematcs and Systems Analyss Aalto Unversty b. Laboratory of sgnal and rsk analyss, Dpartmento d Energa oltecnco d Mlano c. har on Systems Scence and the Energetc hallenge École entrale ars and Supelec June 21, 2017

2 Scenaro analyss of nuclear waste repostory Deep geologcal dsposal of nuclear waste erformance Assessment: Many physcal and chemcal phenomena nteractng Long tme horon (10,000 1,000,000 years) Large aleatory uncertanty about the evoluton of the dsposal system Safety? Scenaro Analyss Scenaro 1 Scenaro 2 Scenaro Scenaro n

3 hallenges n scenaro analyss Revew of methodologes for Scenaro Analyss of nuclear waste repostores Very few repostores lcensed to date hallenges: 1 Buldng a system model to gude scenaro development Bayesan network (BN) of the dsposal system 2 3 Ensurng comprehensveness Treatng the epstemc uncertantes Algorthm to select whch smulatons to run for analyng scenaros onservatve aggregaton of multple experts belefs on probabltes n the BN

4 Defntons Set of nodesv and of drected arcs A Stochastc varables wth dscrete states d { } e.g. s shear 0, 5cm, 300cm ÎS FEs robabltes ndependent nodes Uncondtonal ce sheet Fracture dsplacement km_0 km_0_5 km_2 Dependent nodes ondtonal sheet Scenaros? ombnaton of FEs states ( ) n FE 1,, ce 0.56 cm_ cm_ cm_300 km_ km_0_ km_ FEs 3 states per FE 3 7 2,187 scenaros Radologcal consequence

5 Bayesan network safety State of unacceptable consequences ÎS Each scenaro : Occurs wth probablty auses falure wth probablty Õ ÎV ÎV Õ ^ D FE ÇV V Overall falure probablty of the dsposal system å ÎS V Õ ^ Õ D FE ^ ÎV ÎV ÇV V V ^ ure! Safety: Sum over all scenaros robablty of the scenaro < e ure probablty n the scenaro How to obtan these probabltes?

6 Expert udgments Set of experts at each nodee, ÎV Experts belefs on the probabltes For each probablty multple values e.g. d d shear shear V cm_300 km_2 Weght to expert e at node w e ESTEM UNERTANTY d d shear shear V cm_300 km_2, e 1 d d shear shear V cm_300 km_2, e 2 d shear å d shear dshear V d d shear shear V, e we cm_300 km_2 cm_300 km_2 d eîe shear d d shear shear V cm_300 km_2, e 3 æ ö æ å æ ö Õå Õ å å è ø è ø è ÎS, h V, k V, l ç w ç ç h w ^ k wl D FE ^ Î Î Î Ç Î ^ V h E V V k E V lîe ö ø

7 Optmaton What values of the weghts? Assgn values to obtan the most conservatve estmate of the falure probablty, gven the elcted belefs Optmaton model: FEs & Experts weghts Radologcal consequence Expert 1 Expert 2 Expert 3 ce sheet w e, max Î V, w e å eîe ³ w eîe 0 e 1 Salne water upconng Fracture dsplacement hlorde concentraton Nearfeld Buffer anster breach Radonuclde dscharge

8 Determnstc tools n the BN (1/2) Some dependences modeled by determnstc tools (computer codes, laboratory experments) Better capure the physcal phenomena Resourcentensve smulatons (tme, cost) Nearfeld Buffer anster breach Radonuclde dscharge q NF q B D Neglgble Below lmt Beyond lmt l_y_0 l_y_0 mm_ l_y_100 l_y_0 mm_ l_y_100 l_y_100 mm_ l_y_1000 l_y_100 mm_ l_y_100 l_y_1000 mm_ l_y_1000 l_y_1000 mm_ Very strong assumpton! Soon removed D q NF q B r

9 Determnstc tools n the BN (2/2) depends on the realaton of the table å Fnte dscrete set of table realatons Nearfeld Buffer anster Radonuclde dscharge breach q NF q B D Neglgble Below lmt Beyond lmt l_y_0 l_y_0 mm_ l_y_100 l_y_0 mm_ l_y_100 l_y_100 mm_ l_y_1000 l_y_100 mm_ l_y_100 l_y_1000 mm_ l_y_1000 l_y_1000 mm_ MONOTONTY! ÎS V Õ ^ Õ D FE ^ ÎV The nterval may not be conclusve for assessng safety, f e Î[ l,u ] ÎV ÇV 1 2, 790 V Î[ l, u ] 8 [ 0,0.709] e 0.05 Run smulaton Fll n the correspondng row Dscard realatons Update nterval Here, at the begnnng: OMREHENSVENESS

10 Smulatonselecton algorthm Algorthm for teratvely selectng next smulaton Assgn a conclusvty score to each smulaton Run the smulaton wth the hghest score Nearfeld Buffer anster Radonuclde dscharge breach q NF q B D Neglgble Below lmt Beyond lmt l_y_0 l_y_0 mm_0 l_y_100 l_y_0 mm_ nterval contans lmt nterval does not contan lmt l_y_100 l_y_100 mm_1 l_y_1000 l_y_100 mm_ l_y_100 l_y_1000 mm_950 l_y_1000 l_y_1000 mm_950 l_y_1000 l_y_1000 mm_950 Neglgble Below lmt Beyond lmt [ 0,0] [ 0,0] [ 0.016,0.709] nterval wdth Smulaton s score: 0.78

11 Selected smulatons Nearfeld Buffer anster Radonuclde dscharge breach q NF q B D Neglgble Below lmt Beyond lmt l_y_1000 l_y_100 mm_1 l_y_100 l_y_1000 mm_1 l_y_100 l_y_100 mm_950 l_y_1000 l_y_100 mm_950 l_y_100 l_y_1000 mm_950 l_y_1000 l_y_1000 mm_ [ ] e [ ] 0.05 [ ] [ ] [ ] [ ] [ ]

12 Summary and next steps Methodology to address challenges n Scenaro Analyss of nuclear waste repostory hallenge Addressed by Next steps Buld a system model Bayesan network (BN) of FEs and Tmedependent BN to gude scenaro radologcal consequence Technques for dentfyng the development Scenaro: combnaton of FEs states most mportant falure scenaros Ensure Algorthm to select whch smulatons to More than one dependence comprehensveness run for analyng scenaros, untl a modeled by determnstc tools conclusve nterval for the falure Remove assumpton of nteger probablty s found probabltes Treat the epstemc Aggregaton of multple experts belefs More types of constrants on uncertantes on probabltes n the BN to ensure a weghts conservatve estmate of the falure robabltydependent weghts probablty (or bounds thereof)