International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Enhanced Bayesian Networks approach to risk assessment of spent fuel ponds Tolo, Silvia; Patelli, Edoardo; Beer, Michael; Broggi, Matteo Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Enhanced Bayesian Networks approach to Risk Assessment of SpentFuel PondsSilvia ToloPh.D. student,Institute for Risk and Uncertainty, Univ. of Liverpool, Liverpool, UKEdoardo PatelliLecturer, Institute for Risk and Uncertainty, Univ. of Liverpool, Liverpool, UKMichael BeerProfessor, Institute for Risk and Uncertainty, Univ. of Liverpool, Liverpool, UKMatteo BroggiResearch Associate, Virtual Engineering Centre, Univ. of Liverpool, Daresbury Scienceand Innovation Campus, Warrington, UKABSTRACT: A model for the risk assessment of spent nuclear fuel ponds subject to the risk of floodingis proposed. The methodology adopted is based on the enhancement of Bayesian Networks approachwith Structural Reliability Methods, in order to overcome the limitations of classic Bayesian Networks(such as the use of only discrete variables in case of exact inference calculations). The computationaltool developed for the methodology mentioned is briefly described together with the application to areal-case study. The related results are discussed and compared to those previously obtained by tradi-tional Bayesian Network analysis. Finally, a brief discussion about the advantages and drawbacks of theapproach adopted is provided.1. INTRODUCTIONThe attention about issues related to nuclear safetyis evidently high, particularly after the FukushimaDaiichi nuclear power plant accident. Whilst mostof these concerns are focused on the vulnerabilityof the reactors themselves, less attention has beenpaid to the spent fuel ponds which have the poten-tial to be more vulnerable to failures than the re-actor containment building. Furthermore, as recog-nized by the Nuclear Regulatory Commission, evenif the likelihood of a zirconium fire due to the expo-sure of spent fuel is generally very low, the conse-quences of a similar event would be highly signifi-cantCollins and Hubbard (2001). For these reasonsthe study of the vulnerability of such installationsto external events, such as extreme weather condi-tions, results relevant in view of a more general andaccurate risk assessment of nuclear facilities. Thiskind of analysis implies the use of flexible modelsable to simulate not only the complexity of the sys-tem under study but also different scenarios. Forexample, assessing the impact of natural hazardson technological installations, the climate changeeffect on extreme weather hazards cannot be ne-glected. Furthermore, a complete evaluation of therisk requires models suitable for long-term decisionmaking support but also for real time risk assess-ment, in order to lead the decision makers even incase of imminent danger.This study proposes a generic model for the quan-tification of the risk of exposure of the spent nuclearfuel stored in a fuel pond. The model aims to meetthe requirement of flexibility mentioned before. Itconsists of a simple and intuitive framework whichintegrates climate change models in order to assesspresent and future risks of exposure of spent fuel incase of flooding of the storing facility. A previousimplementation of the model [Silvia Tolo (2014)],112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015based on the use of traditional Bayesian Networks(BNs), highlighted the potential and limitations ofsuch an approach in the field of risk assessment oftechnological failures triggered by natural hazards.In light of this, a new methodology (firstly sug-gested by Straub and Kiureghian (2010)) has beenadopted.2. METHODOLOGYThis section aims to give an overall idea of the theo-retical background of the methodology adopted andto briefly described the computational tool devel-oped for its application.2.1. Bayesian NetworksBNs are statistical graphical models which providethe factorization of the joint probability distributionassociated with an event of interest exploiting in-formation about the conditional dependencies ex-isting among the variables. BNs consist of a vari-able number of nodes, representing the variables ofthe problem modelled. The nodes are connected toX1X3 X2Figure 1: Example of an elementary BNeach other by edges (commonly represented as ar-rows) expressing informal or causal dependencies.Only nodes among which exists some sort of de-pendency are linked, whilst those that are not joinedrefer to variables that are conditionally independentof each other. With regards to the BN introduced inFig. 1, the node X1 is called the parent of X2 andX3, which are also referred to as its children. Nodesthat have no parents are defined as roots. Generally,on the basis of the Bayes’ theorem, the joint proba-bility modelled by any BN with nodes X1,X2, ...,Xncan be expressed as:P(x1...xn) =∏iP(xi | pi) (1)where pi refers to the outcomes assumed by the par-ents of the node Xi, whose state is represented by xi.Then, the joint probability associated with the BNof Fig. 1 is:P(x1,x2,x3) = P(x1)P(x2|x1)P(x3|x1) (2)A complete overview of Bayesian networks is pro-vided by Pearl and Russell (2000).2.2. Bayesian Networks Enhanced with system re-liability methodsExact inference algorithms are robust and well es-tablished methods for the computation of inferencein BNs. These are restricted to only discrete orGaussian nodes, often implying the necessity to dis-cretize continuous random variables and hence im-poverishing the quality of the information. The in-tegration of the BN approach with system reliabilitymethods allows to avoid this practise. The resultingstrategy is commonly known as Enhanced BayesianNetworks (EBNs). The role of system reliabilitymethods is to reduce the initial EBN (including dis-crete as well as continuous random variables) to atraditional BN on which is possible to compute ex-act inference. More in details, each node child ofat least one continuous has to be defined as do-mains in the outcome space of its parents (deter-ministic nodes) or by a PMF that is parametrizedby the parent nodes (random nodes). The use ofsystem reliability methods, not only allows to asso-ciated to discrete nodes children of continuous con-ditional probability values (as in traditional BNs)but also erases the dependency of the node from itsnon-discrete parents. Hence, the links among con-tinuous and discrete nodes can be completely re-moved, finally allowing the elimination of all con-tinuous nodes. In light of Eq.1, the joint probabilityassociated to the reduced network in Fig.2 can becomputed solving the integral in Eq.3:P(D1,D2) =∫C1p(D1)p(D2|D1,C1) f (C1)dC1(3)where p(D1),p(D2|D1,C1) are the probability val-ues associated to the discrete nodes D1,D2 whilstf (C1) is the probability density function associatedto the continuous node C1. Considering the Markovcondition, hence the independence of the node D1212th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015D1D2C1 D1D2Figure 2: Example of an elementary EBN and its re-duced network, where C refers to a continuous whilstD1 and D2 to a discrete nodefrom the continuous node C1, the solution of the in-tegral in Eq.4 is reduced to:P(D1|D2) =∫C1p(D2|D1,C1) f (C1)dC1 (4)In light of the initial hypothesis, the state of thenode D2 can be expressed as domain in the outcomespace of the nodes C1 and D2. The integral can bethan expressed as:P(D1|D2) =∫Ωd2D2,d1f (C1)dC1 (5)where Ωd2D2,d1 is the domain that defines the eventD2 = d2 in the space of C1 given D1 = d1. The in-tegral in Eq.5 appears in the form common to struc-tural reliability problems and can be easily solvedusing structural reliability methods. Please refer toStraub and Kiureghian (2010) for further details.2.3. Computational toolsThe EBN methodology briefly outlined in the pre-vious section has been implemented in the generalpurpose software OpenCossan [Patelli et al. (2012)]in an object oriented fashion. The computationaltool developed provides the graphical and numeri-cal implementation of models as well as the reduc-tion of EBNs to traditional BNs. Two main optionsare provided to the user for this procedure: the firstrelies on the use of First Order Reliability Method,providing a less computational expensive analysisat cost of poorer accuracy, the second is based onthe use of Monte Carlo methods. The computationof inference in the network it is possible thanks tothe interaction of the tool with the Bayes Toolboxfor Matlab [Murphy et al. (2001)].3. MODELThe overall aim of the model is to evaluate the riskof exposure of the spent fuel stored in a spent fuelpond of a nuclear facility in light of the impact ofa flooding (Fig.3). For the sake of clarity, the de-scription of the model proposed below is organizedin three sections, according to the aim of as manydifferent subsets of the network.3.1. Natural-technological interaction sectionThe upper part of the network (Fig.4) aims tomodel the direct effects of natural events on thenuclear facility and its surroundings. Three mainmechanisms of external flooding are considered:coastal, river and surface water flooding. ThisTimeScenarioSeaWaveHeightWavePeakPeriodSeaWallInclinationCrestLevelSeaWaterLevelExtremePrecipitationReturnPeriodExtremePrecipitationWaveOvertoppingOutfallCapacityOutfallFailureDrainageSystemCapacityDrainageSystemFailureLocalSeaDefencesHeightFloodingSurroundingsGrossStationArea FloorAreaRatioFloodBarriersCapacityDischargeFailureFloodingStationAreaSeawallLengthHighTideDurationFigure 4: Section of the network modelling the directeffects of natural eventssection involves nodes either related to weatherconditions (ExtremePrecipitation, SeaWaterLevel,SeaWavePeriod, SeaWaveHeight) or representingfailures directly triggered by the natural event(DrainageSystem, FloodingSurroundings, Outfall,WaveOvertopping). The first category is generallyrepresented by continuous nodes, which better de-scribe the aleatory nature of such events. Coastalflooding is considered in terms of both sea waveovertopping of coastal defences and tidal flooding.The first case involves the modelling of the mech-anism of discharge of sea water inside the stationperimeter due to the action of sea waves overcom-ing the station protections (involving ExtremeSea-WaterLevel , SeaWaveHeight and SeaWavePeriod)[Hedges et al. (1998)]. Tidal flooding is assumedto affect only the surrounding area (FloodingSur-roundings). Also the river flooding mechanism canaffect the surroundings and it is mainly representedin the model by the edge joining the node Extreme-Precipitation and FloodingSurroundings.312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015TimeScenarioSeaWaveHeightWavePeakPeriodSeaWallInclinationCrestLevelSeaWaterLevel ExtremePrecipitationReturnPeriodExtremePrecipitationWaveOvertoppingOutfallCapacityOutfallFailureDrainageSystemCapacityDrainageSystemFailureLocalSeaDefencesHeightFloodingSurroundingsGrossStationArea FloorAreaRatio FloodBarriersCapacityDischargeFailureFloodingStationAreaSeawallLength HighTideDurationSpentFuelExposureCoolingSystemOnSiteACPlannedOutageEmergencySuppliesUnplannedOutageOffSiteACExternalPowerGridDelayInReactionNumberEmergencyDieselsEmergencySuppliesPowerSupplies OnSiteSubstation EmergencySuppliesHydrantSystemOrganizationalCultureTeam TrainingResources KnowledgeMachine AttitudeComplexityLoads&perceptionsErrorContext1ErrorContext2ErrorContext3ErrorContext4HumanErrorFigure 3: Overview of the BN model proposed for the risk assessment of spent nuclear fuel ponds subject to therisk of floodingSurface water flooding involves the events of fail-ure of the drainage system (DrainageSystem) dueto exceptionally heavy rainfall (ExtremePrecipita-tion) and the unavailability of the Outfall due to ex-treme sea level. The overall combination of theseflooding dynamics can lead to accumulation of wa-ter within the perimeter of the facility, event repre-sented by the node FloodingStationArea. The nodeTimeScenario allows to run analysis with regardsto a particular time interval of choice. Introducingevidence in the node, hence selecting the time sce-nario of interest, it is possible to take into accountthe influence of climate change on natural events.3.2. Internal failure sectionThe event of exposure of the spent nuclear fuel isbound by the availability of either cooling systemsor emergency supplies. If both these subsystemsare out of order, the event SpentFuelExposure is as-sumed to occur (Fig.5). The cooling system is ex-pected to fail if no electric power, either generatedon site (OnSiteAC) or supplied to the station fromthe external grid (OffSiteAC), is available.The failure of on-site generation can be attributedto power station outages, planned (e.g. due to re-fuelling or decommissioning) or unplanned (loss ofgrid or unplanned reactor shut-down); the failure ofemergency power supplies (EmergencyPowerSup-plies), such as emergency diesels, is also a pre-TimeScenarioSpentFuelExposureCoolingSystemOnSiteACPlannedOutage EmergencySuppliesUnplannedOutageOffSiteACExternalPowerGrid DelayInReactionNumberEmergencyDiesels FloodingStationAreaEmergencySuppliesPowerSupplies OnSiteSubstationEmergencySuppliesHydrantSystemFloodingSurroundingsFigure 5: Section of the network modelling internalfailurescursor event of station blackout. If both the out-age and the failure of emergency diesels occur, nopower generation is available on site. The loss ofpower from the external network can occur in thecase of failure of the power grid as well as on-siteelectric substations and connections (OnSiteSubsta-tion). The node EmergencySupplies refers to thelack of effective actions on the pond in the caseof unavailability of the cooling system. It can becaused by lack of supplies (loss of reservoirs Reser-voirs or EmergencyHydrantSystem) or by delay ofactions from the outside (DelayInReaction, e.g. theintervention of fire tenders) or the occurrence ofHumanError which nullify or prevent the action.412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Figure 6: Layout of the nuclear site with Sizewell B re-actor building(1), fuel building(2) and dry fuel cask(3).On the East of the site are located the so called BentHills(4), on the west the Sizewell A Power Station(5).Figure available from EDF (2014)3.3. Human Error sectionThe BN model proposed by Groth and Mosleh(2011) to quantify the probability of human errorsin case of significant incident at a nuclear powerplant has been integrated in the overall framework.This part of the network is linked to the rest of themodel through the causal dependency between thenodes HumanError and EmergencySupplies.3.4. Case studyThe nuclear power plant of Sizewell B (Fig.6) inEast Anglia, UK, operated by EDF Energy, hasbeen selected as real-world case study for the ap-plication of the BN model proposed.According to the flood maps provided by the En-vironment Agency [Environment Agency (2013)],the surrounding area is subject to risk of flooding.Moreover, EDF’s strategic target is to extend theoperational life of the installation postponing thedecomissioning date from 2035 to 2055 [Houlton(2013)]: it is then of particular interest to evaluatethe impact of climate change on the risks to whichthe facility is subject. Unlike British Magnox andAGR stations [ (Office for Civil Nuclear Securityand Industry)] the management strategy adopted forSizewell B revolves long term on site storage un-der water: the current rate of accumulation and cur-rent safety restrictions suggest that full capacity ofthe on site pond will be reached by 2015. SizewellB power plant is built on a plateau at 6.4m AboveOrdnance Datum (AOD) on the coast of East An-glia in the county of Suffolk. It shares a site of 97Hectares with Sizewell A station (no longer operat-ing) which lies on the southern side. The area to theeast of the station consists of a series of sand duneswhich slope down to the sea shore covering a widthof about 100m. These ridges provide a 10m highsea defence embankment along the east boundaryof the site. The site access road is located at anelevation of 3.5m AOD. The on-site electric substa-tion is connected to the external grid at three sep-arate 400kV points (two at Bramford, one at Nor-wich and one at Pelham) and provides connectionwith the external network for the import and exportof power. Adjacent to the reactor building, the fuelbuilding accommodates the pond where both newand used fuel is stored [Fullalove (1995)] under wa-ter. The fuel assemblies are located in the pool at adepth of water adequate to guarantee the coverageof the fuel for 24h in case of total loss of the coolingsystem. The availability of AC power on-site bindsthe working order of the cooling system in the fuelfacilities. All the building of the nuclear island areprovided with fire doors that can act as flood barri-ers up to a water depth of 1m [EDF (2012)].3.4.1. Input and Data SourcesA wide range of data sources has been adopted forthe application of the model to the Sizewell casestudy. Three different time scenarios has been con-Table 1: Characterization of the time scenariosadopted in the studyYear of reference Station stateScenario 1 2013 OperationalScenario 2 2055 OperationalScenario 3 2099 Closedsidered: one related to the actualised risk and twoto future hazards, evaluated using frequency andseverity forecasts for extreme events projected in2055 and 2099 (see Table I).In order to represent the hazards related to futurescenarios, projections have been adopted for the512th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015sea water level [Office (2013)] and extreme precip-itations [Francis (2011)] values, which have beenrepresented as continuous random variables. Thereturn period for the sea water level are shown inFig.7. All the predictions related to climate changeand adopted in the case study refer to a mediumemissions scenario SRES A1B according to IPCCclassification. Also the wave characteristics (Sea-1.5 2 2.5 3 3.5 4 4.5 5 5.5050001000015000Still Water Level [m]Return Period [y]  Today20552099Figure 7: Return period curves for extreme sea waterlevelWaveHeight and WavePeriod) are represented bycontinuous nodes. The probabilistic models havebeen implemented fitting historical data [CEFAS(2013)] to generalized extreme value distributions(see Table II and Fig.8) adopting the least squaresapproach. A linear correlation factor of -0.29 be-tween the two variables, represented by the con-tinuous line in Fig.9, has been considered. In0.5 1 1.5 2 2.5 3 3.5 4 4.500.511.52Significant Wave Height [m]PDF  Figure 8: Generalized extreme value model of the wavesignificant height probability distributionTable 2: Parameters of generalized extreme value dis-tributions computed with maximum likelihood estima-tionParameter WaveHeight WavePeriodShape Parameter 0.268026 0.00512954Scale Parameter 0.280391 1.45702Location Parameter 0.539845 4.62444the implementation of the overtopping model allthe waves have been considered normally incidentto the seawall and no integration with off-shorenear-shore wave transformation models has beenconsidered. This simplificative hypothesis and theresulting strongly conservative approach make thecontribution of climate change totally negligible.Hence, the effect of climate change on wave con-dition nodes has been neglected.0 1 2 3 4 5Hm05 10 15 20024Tp [s]Hm0 [m] 5101520Tp [s]  Figure 9: Analysis of the correlation between signifi-cant wave height(Hm0) and peak period(Tp)Table 3: References for the model inputEvent ReferencePower Grid Failure Nack (2005)Hydrant System Failure TECDOC (1989)On-site Substation Failure Nack (2005)Planned Outage EDF (2013)Unplanned Outage EDF (2013)Power Supplies Failure Plants (2007)Human Error (section) Groth and Mosleh (2011)Dissimilarly from the upper part of the network,the nodes involved in the remaining sections of themodel are all discrete. The input associated withsuch nodes have been deduced either from previousstudies or, more generally, from data available inliterature. Table III shows the references related tonodes for which probability values have been col-lected or derived from the available literature. Thestate of the remaining events involved in the bottompart of the network is considered to be directly in-ferable from the outcomes of their precursor nodes,according to Section ResultsThe analysis of the model has required the evalua-tion of 156 system reliability problems. The over-612th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015all risk of exposure of the spent fuel grows alongwith the three scenarios considered. This trend canbe mainly explained with the analogous growth ofthe probability of on-site flooding which, as fore-seeable on the basis of the climate change projec-tions, results significantly affected by the expectedintensification of extreme weather events in time.In spite of this, as shown in Table 4, in none ofthe time periods considered the probability of fuelexposure assumes significant values, remaining be-low an order of magnitude of 10−10. On the con-trary, the probability of flooding events in the areasurrounding the station, reaches not negligible val-ues in particular with reference to the 2099 sce-nario. It must be pointed out that this estimatescould be strongly affected by the conservative ap-proach resulting from the hypothesis discussed insection 3.4.1.Table 4: Quantification of risks of several eventsEvent Scenario1 Scenario2 Scenario3(Today) (2055) (2099)On-site Flooding 0 1.11E-16 1.10E-10Cooling System 1.74E-11 1.74E-11 1.27E-10Spent Fuel Exposure 2.61E-17 1.09E-16 3.32E-12Flood Surroundings 6.14E-05 2.57E-04 1.80E-03Several what-if scenarios have been analysed inorder to estimate the risk of exposure conditional tofailure of different subsystems. As shown in Table5, the failure of the drainage system and the occur-rence of human error alone slightly increase the fi-nal risk of accident. On the contrary, the the failureof the cooling system significantly rises the prob-ability of spent fuel exposure which, in this case,grows up to an order of magnitude of 10−2 in the2099 scenario. Finally, BNs allow also to easilytake into consideration the combination of simulta-neous occurrence of more failures events, such asshown in Table 5 for the failure of drainage systemand the lack of reaction of operators. In this case,the combination of the two accident scenarios con-tributes to the overall growth of the risk of spentfuel exposure more than what previously seen forthe two separate events.Table 5: Risk of Spent Fuel ExposureWhat if...? Scenario1Scenario2Scenario3(Today) (2055) (2099)Cooling S. Failed 1.50E-06 6.27E-06 2.61E-02Drainage S. Failed 1.26E-16 6.15E-16 3.36E-09Surroundings Flooded 4.25E-13 4.25E-13 1.84E-09Human Error 1.07E-15 4.48E-15 3.35E-12Human Error &Drainage S. Failed 1.74E-11 1.74E-11 1.86E-094. CONCLUSIONSA model for the assessment of the risk of expo-sure of spent nuclear fuel has been proposed. Themethodology adopted is based on the enhancementof BNs using structural reliability methods and ithas been implemented in the general purpose soft-ware OpenCossan. The computational tool ob-tained allows to take into consideration continuousrandom variables not renouncing to the advantagesand robustness of exact inference algorithms, at thecost of a higher, but still acceptable, computationalcost. Hence, the main advantage is the capability ofadequately represent aleatory uncertainty throughthe use of probabilistic models. This is a crucialaspect for risk analysis involving natural events andmore generally climate modelling variables.On the other hand, the tool proposed lacks the ca-pability of representing likewise epistemic uncer-tainty. Indeed, often lack of data prevents the im-plementation of suitable probabilistic models: inthis case, the adoption of intervals can be a moreaccurate choice for the representation of the infor-mation available. Furthermore, as pointed out insection 3.4.2, the current implementation does notallow to estimate the uncertainty affecting the out-put.These limitations can be overcome fully exploitingthe flexibility of the methodology adopted, as wellas the relative computation tool. Reliability meth-ods able to take into consideration a wider rangeof variable representations (e.g. intervals or othermodels of imprecise probabilities theory) can beadopted for the reduction of Enhanced BayesianNetworks including, hence, not only continuousand discrete variables. Future research will be ded-712th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015icated to the integration of these methods with thetraditional BN framework and the implementationof models for validation purpose.5. REFERENCESCEFAS (2013). “Sizewell waverider post recovery data.”available from:<http: // cefasmapping. uk/ >.Collins, T. and Hubbard, G. (2001). “Technical studyof spent fuel pool accident risk at decommissioningnuclear power plants.EDF (2012). “Eu stress test - sizewell b.” EDF Energy.EDF (2013). “Sizewell b community reports.” <http:// www. edfenergy. com/ download-centre>.EDF (2014). “Site boundary and development ar-eas.” <http: // www. suffolkcoastal. yourdistrict/ planning/ devcontrol/applications/ sizewell/ >.Environment Agency, E. A. (2013). “Flood-ing map sizewell area.” Contains Environ-ment Agency information, Environment Agencyand database right, available from: <http:// www. environment-agency. gov. uk/ >.Francis, T. (2011). “Extreme precipitation analysis atsizewell: Final report.” Met Office.Fullalove, S. (1995). Sizewell B: Power Station. ThomasTelford.Groth, K. and Mosleh, A. (2011). “Development and useof a bayesian network to estimate human error prob-ability.” ANS PSA 2011 International Topical Meet-ing on Probabilistic Safety Assessment and AnalysisWilmington, NC.Hedges, T., Reis, M., and OWEN, M. (1998). “Randomwave overtopping of simple sea walls: A new regres-sion model..” Proceedings of the ICE-Water Maritimeand Energy, 130(1), 1–10.Houlton, N. (2013). “Life extension of the edf energynuclear fleet.” EDF.Murphy, K. et al. (2001). “The bayes net toolboxfor matlab.” Computing science and statistics, 33(2),1024–1034.Nack, D. (2005). “Reliability of substation configura-tions.” Iowa State University, 7–8.Office, M. (2013). “Uk climate projections, dataavailable from:<>.Office for Civil Nuclear Security, D. o. T. and Industry.“The state of security in the civil nuclear industry andthe effectiveness of security regulation (April 2002 -March 2003).Patelli, E., Murat Panayirci, H., Broggi, M., Goller, B.,Beaurepaire, P., Pradlwarter, H. J., and Schuëller, G. I.(2012). “General purpose software for efficient un-certainty management of large finite element models.”Finite Elements in Analysis and Design, 51, 31–48.Pearl, J. and Russell, S. (2000). “Bayesian networks.ucla cognitive systems laboratory.” Report no., Tech-nical Report.Plants, N. P. (2007). “Industry-average performance forcomponents and initiating events at us commercialnuclear power plants.” Citeseer.Silvia Tolo, Edoardo Patelli, M. B. (2014). “Bayesiannetwork approach for risk assessment of a spent nu-clear fuel pond.” Second International Conferenceon Vulnerability and Risk Analysis and Management(ICVRAM) and the Sixth International Symposium onUncertainty, Modeling, and Analysis (ISUMA), Vul-nerability, Uncertainty, and Risk, 598–607.Straub, D. and Kiureghian, D. (2010). “Bayesiannetwork enhanced with structural reliability meth-ods: methodology.” Journal of engineering mechan-ics, 136(10):12481258.TECDOC, I. (1989). “508, survey of ranges of com-ponent reliability data for use in probabilistic safetyassessment.” IAEA, Vienna.8


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