ANS Best Estimate Plus Uncertainty International Conference BEPU 2018 - PDF document

1 ANS Best Estimate Plus Uncertainty Inter
ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 BEST ESTIMATE PLUS UNCERTAINTY (BEPU): WHY IT IS STILL NOT WIDELY USED E. Ivanov, A. Sargeni, F.Dubois, and G. Bruna Institut de Radioprotection et de Sûreté Nucléaire, BP 17, 92262 Fontenay - aux - Roses, France evgeny.ivanov@irsn.fr , antonio.sargeni@irsn.fr , franck.dubois@irsn.fr , giovanni.bruna@irsn.fr ABSTRACT The Institute for Radioprotection and Nuclear Safety (IRSN) , as the technical support organization (TSO) for French public Authorities , shall participate in policy making on nuclear safety and radiation protection. In the framework of its current activity, IRSN performs analysis and comparison of different safety assessment approaches, including Best Estimate Plus Uncertainty (BEPU). Despite BEPU is not yet worldwide recognized , the authors consider it a s a promising way to stimulate an involvement of a new generation of numerical tools and high - fi delity experiments data in the practice of safety and conceptual design . The present paper discusses enabling factors and constraints for BEPU from the technical and global point of view, relying on scientific background as well as on current practice with respect to its potential role in regulation and in decision making processes. 1. INTRODUCTION The Institute for Radioprotection and Nuclear Safety (IRSN) , a s the technical support organization (TSO) for French public Authorities , is in charge of safety assessment of nuclear reactors in operation and / or under design , as well as of nuclear fuel cycle facilities. According to its duties, IRSN is accustomed to evaluate the performance of different asse ssment approaches including Best Estimate Plus Uncertainty (BEPU) [1] . BEPU is considered by the authors a promising tool able to provide a risk informed assessment of margins and to combine Deterministic Safety Analysis and Probabilistic Safety Analysis (DSA and PSA) [2] relying upon hi gh fidelity simulation and representative experiments . The present paper presents an investigation on BEPU potential contribution to the safety assessment and decision making processes 1 , relying on scientific background and current practice . 2. GENERAL REMARKS The idea to combine the best estimate values with their uncertainties is not only a nuclear engin

2 eering prerogative. B ibliography on
eering prerogative. B ibliography on BEPU provides with numerous references mainly relied to financial or actuary mathematics, or to decision making pr ocess. They agree on predictive capabilities of best estimate tools presuming at the same time that quality of prediction can be characterized by precisely quantified uncertainties. 1 It is to be mentioned that BEPU is widely used outside the nuclear engineering domain, e. g., for financial and health risks perception applications. ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 The main application of the method in nuclear engineering dates back fort y years ago when it was adopted to investigate the risk of failure of heat removal system, relying, therefore, on Best Estimate System Thermal Hydraulics (SYS TH) simulations [1] . Since then , no additional wide use of such a methodology is known 2 , except for recent applications in the criticality safety domain [3] . Even if nowadays the BEPU has not got maturit y enough to overcome the traditional conservatism of safety assessment practices , nevertheless the lessons learned from the Fukushima - Daiichi ca tastrophe and the crucial need to implement and deploy innovation s could open a window for BEPU , since they require a better and a deep er understanding of the accidental processes, the safety limits and the performance of means deployed to accident managem ent . In the present paper, investigation is aimed at addressing under which conditions the BEPU could became a practicable approach, which further development will be needed to enable that and which constraints will remain ever. 3. PRINCIPLES OF AN ANA LYSIS Investigating potential performance of BEPU as an assessment tool means answer ing the following questions :  What kind of benefits can BEPU bring in the assessment process?  Wh at are the major obstacles preventing BEPU to spread it ?  How can these issues b e addressed in order to facilitate BEPU deployment ? Th is approach includes personal and collective experiences (1) on safety assessment, and (2) on lessons learned from relevant domestic and international scientific projects. It should be emphasized that B EPU implies, that is a major advantage, using experts - independent

3 statements. It means that the best e
statements. It means that the best estimate values as well as the quantified uncertainties should be validated against objective observations. Best estimate tools should be experimentally v alidated or, even more, they should be based on evidence - based modelling paradigm. Uncertainty quantification should also be done in a consistent way. While the best estimate computations could be tested against available experimental data, if any , the val idation of uncertainties seems an extremely non - trivial task. It is shown below (in following chapters) that consistency of uncertainty quantification can be achieved only using one or another Data Assimilation (DA) methodology . Summarizing the points addressed here above , it can be stated that a metrics f or BEPU analysis could be based on the following main axes :  Availability of a best estimate tool, a correct set of input data and a suitable algorithm for best estimate modelling process ,  Existence and affordability of representative high - fidelity experiment s suitable for comprehensive testing of the best estimate tool in a given application domain ,  Multi - lateral and / or international consensus of specific validation methodology for a giv en application domain . 2 For applications, we intend the cases of BEPU in volvement in decision making process, which are quite rare. However, many scientific results of uncertainties quantification, best estimate simulations etc. are available. Unfortunately their status can be characterized more as “for information” than as “f or support to decision making process”. ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 The main a dvantages of BEPU should be found in very complex simulations, i.e. in the possibility to predict phenomena, states and processes that have never been observed before and could not be simulated experimentally both i n a specific mock - up and / or in a power plant in operation, due to too high costs and / or risk. While Best estimate modeling allows predicting a value or a trajectory of the simulated process , the uncertainties quantification allows performing judgment how c redible such prediction could be . For BEPU the major challenges stand alongside with the major advantages. Objectiv iz ation of simulation and un

4 certainty quantification require confir
certainty quantification require confirmation on the basis of observations and experiments. In other words , BEPU heavily depends on the availability of representative and accurate experimental data , e.g. on suitable validation sets of experiments, including:  Plant Measurements and Observations (PMO) ,  M ock - up experiments in dedicated facilities , including res earch reactors, hot cells, hydraulic loops etc. ,  E xperiments of a benchmark - quality design ed to quantify the parameters of the physical models. PMO seems a more accessible source of information for any particular nuclear system , mainly if modern data mining techniques are adopted 3 . H owever , it is representative of the normal operation only; that requires extrapolation if:  The target system is an advanced or innovative one,  The onset parameters are beyond the range allowable for operation (that is a case for safety assessment). Moreover, mock - ups are designed to represent given applications (in accordance with experts‟ understanding of representativity) while benchmark experiments are focused on physics of processes and phenomena of interest. Nevertheless , Validation and Uncertainty Quantification (V&UQ) process accepts all kinds of experiments if they are consistently evaluated 4 . 4. ANALYSIS OF BEPU POT ENTIAL CAPABILITIES As mentioned above, the metrics of the investigation on BPU potential capabilities includes the following items:  A vailability of a Best Estimate code , a correct calculation model and a modelling methodology,  A ffor dability of representative tests based on high - fidelity experiment data,  Existence of standardized rules for uncertainties quantification in a given application domain. Thus, i t makes sense to begin further discussion with lessons learned from different projects in research and development and from recent cases of an assessment practice. 3 PMO in the past and nowadays are not yet sufficient for validation because of the limited on - site instrumentation capabilities and rather poor maturity of mathematic al approaches adopted for data interpretation. However we can see a positive tendency on PMO fidelity due to wider implementation of advanced equipment and data mining techniques . 4 One good pattern of IE evaluation is given in the ICSBEP [4] and IRPhEP

5 [5] Handbooks. ANS Best Estimate Pl
[5] Handbooks. ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 4.1. Examples of international projects on treatment of uncertainties IRSN is accustomed to test its tools and methodologies participating in relevant international projects within IAEA CRPs and OECD - NEA sponsored activities. They are quite numerous; among them, we mention : in the field of SYS TH: BEMUSE, PREMIUM and SAPIUM projects [6] ; in the field of reactor design : OECD - NEA UAM - LWR project [7] ; in the field of in novative systems safety: ESFR - SMART Project granted by European Commission; in the field of criticality safety, the series of projects within OECD - NEA WPEC and WPNCS activities [8] , [9] and others. Numerous activities on the topic are carried - out within the NURESAFE European project and suppor ted by the NUGENIA Association. All of them have brought essential information on the approaches, the tools and the limits of applicability in different fields of endeavour. The majority of international projects provide unique opportunities to freely disc uss uncertainties treatments and evaluations and, then, to identify, on the consensus basis, ways for resolution. Another example is the OECD - NEA project “Uncertainty Analysis Modelling for Light Water Reactors” (UAM - LWR). It has been launched after decad es the scientific and engineering communities have being wondering upon the interest to quantify the confidence intervals for best - estimate simulation of design and safety related parameters of nuclear reactors [7] . UAM - LWR was split into the following items : 1) subdivision of the systems / scenarios into steps, 2) identification of the inputs, outputs and assumptions for each step, 3) evaluation of u ncertainties for each step and 4) propagation of the uncertainties along the entire flow of design studies scenarios. The whole UAM - LWR approach has been translated in to nine exercises that mix experimental data and numerical benchmarks going from neutroni cs to full scale system. IRSN participated in OECD - NEA/NSC/UAM - LWR and OECD - NEA/CSNI/BEMUSE, PREMIUM and SAPIUM and others activities with contributions in the benchmark development and analysis testing the in - house methods and tools and addressing all pla usible issues of consistent uncertainty quantification. 4.2. Lessons learned from projects on system thermal hydraulics Since SYS TH tool s play critical r

6 ole in the study of nuclear system beh
ole in the study of nuclear system behaviour and in the safety studies [1] , the n uclear engineering community pay increased attention to credibility of simulation and consistency of uncertainty quantification through d edicated benchmark - based projects: BEMUSE (2003 - 2008), PREMIUM (2012 - 2015) and others to evaluate a maturity of the best estimate simulation and uncertainty quantification [6] . Although BEMUSE confirmed sufficient maturity of error propagation techniques, further PREMIUM outcome s demonstrated that involved experimental data brought controversial correction of re - flooding in an application domain [10] . Findings were divergent among participants while they adopted similar methodologies (see Figure 1). The variables i n the figure represent tw o indicators ( criteria ) : (1) “informativeness” (that measures the precision of the uncertainty band), and (2) “calibration” (related to the discrepancy between predictions and experimental values). Each single output over there is attributed with two words : a title of tool (TRACE, RELAP, CATHARE, ATHLET, KORSAR and COBRA etc.), and an indication of data assimilation approach (like DIPE, CIRCE and FFTBM) 5 . 5 Scripts such as RELAP CIRCE 1 and RELAP CIRCE 2 indicate the use of th e same methodologies by different participants. Normally, in these situations, the results should be the same or at least very close, but it was not the case because of the clearly identified “user‟s effects” [10] , despite the high qualification of user should practically exclude rough mistakes. The divergences were likely engendered by the choice of sample numbers of ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 It must be mentioned that the IRSN tool is the home - made DIPE (Determination of Input Parameters Empir ical properties) [11] that provides information on uncertainties of input parameters for selected outputs on the basis of a given set of experiments . In practice, i t operates shifting the Best Estimate results and establishing the experimental based uncertainties of these shifts as shown i n the Figures 2a and 2b. Figure 1 – Informativeness and calibration for FEBA [10] . DIPE neglects measurement errors and discrepancies due to the nodalization of the benchmarks and models; it assumes also a contin

7 uous dependence of the solutions on in
uous dependence of the solutions on input parameters. Of course, it cannot give a deep insight in intrinsic uncertainties because it provides only with aggregated information on the “coverage” of given experiments . a) b) Figure 2 – Simplification of core configuration – development of a surrogate model [11] . It should be added that the findings of PREMIUM projects motivate launching of one more project SAPIUM [ 12 ] intended to elaboration of experimental - based benchmarks specification (stringent establishment of experimental uncertainties) and of relevant methodology of UQ. 4.3. Lessons learned from practice of criticality safety assessment The other important acknowledged field for implementation of BEPU is the criticality safety, a pure single - physics domain where the uncertainty due to nuclear data is a factor of ten higher than any other uncertainty in the integral experiments and a factor of 10 2 higher than the typical Monte - Carlo or discrete ordinate convergence limits. Generally speaking, all plausible sources of uncertainties can be gathered into two groups: (1) and nodalizations (2). Sampl es variations resulted in shift along “informativeness”, while variation of nodalization led to shift along “calibration” axes. ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018  The manufacturing processes, measurements, numerical approximations etc.,  The modelling parameters such as physical constants, models and assumptions. [9] . The u ncertainties of the first group - aleatory ones - are propaga ted using various stochastic and deterministic algorithms, while the uncertainty of the second group - epistemic ones - can be quantified and reduced using data assimilation / adjustment methodologies. The applicability of one of them - General Linear Le ast Squared Method (GLLSM) - has been illustrated and demonstrated by the quantification of biases and uncertainties for criticality safety cases [13] representing the non - conform states of a MOX fuel fabrication apparatus [12] . F our configurations were studied (see Table 2) parametrized vs. mo deration - humidity - as well as the Energy

8 corresponding to the Average Letharg
corresponding to the Average Lethargy of neutrons causing Fission (EALF). Biases and uncertainties were estimated using two approaches: traditional one, based on weighted average bias , and Data Assimilation (see Figures 3a and 3b) here below [13] . Data assimilation technique relying on Bayesian approaches extrapolates observations to an application area using prior uncertainties (in gre y on Figure 3b) establishing posterior biases (columns on Figure 3b) and reduced (posterior) uncertainties (error bars). Figure 3 illustrates how far physics - based extrapolation of observations 6 (200÷300 pcm) to the application increases a bias (~ 4000 pcm ) which should be imposed as a safety margin. All studies were performed using the IRSN home - made code system BERING based on GLLSM 7 [13] that allo ws visualizing contribution of each IE on correction of biases, uncertainties and nuclear data (see Figure 4). Different colours of individual experiments contribution on Figure 4 demonstrate contradictions - similar to SYS TH - due to compensation effect [13] . Table 2. Application objects – criticality safety cases of 239 Pu – containing systems. Safety case Case 1 Case 2 Case 3 Case 4 humidity ε = 0.1% ε = 1% ε = 3% ε = 5% EALF 4 keV 1 keV 300 eV 90 eV a b Figure 3 – Traditional mean biases (a) versus GLLSM (b) for 239 Pu containing systems [13] . 6 Observation in our case is a Calculation - to - E xperiment (C/E) ratio 7 The same could be done using many other code systems [9] ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 It can be roughly concluded that in the field of criticality safety all potential methodological problems have been solved. Further progres s should be achieved adding new experiments data in the Bayesian - based estimations. Figure 4 – Contributions of the different benchmarks on 239 Pu cross sections adjustment [13] . 4.4. Extrapolation beyond operational parameters: quantification of mechanical energy release in core disruptive accidents One more example of application of multi - physics best - estimate simulation to safety assessment is the so - called Borax Transient 8 [14] of the Material Testing Reactor (MTR), such as the Jules Horowitz Reactor (JH R) (see Figure 5a an

9 d b). All existing experiments on the t
d b). All existing experiments on the topic including among others Special Power Excursion Test Reactor (SPERT) are very poorly representative of the JHR in terms of geometry and topology (see Figures 5 c and d). a b c d Figure 5 – Jules Horowitz Reactor (JHR): global view (a) and scheme of core (b) [14] and SPERT - IV/D - 12/25 core (c) and fue l element (d) [15] 8 The BOiling water ReActivity eXperiment (BORAX) is a referent Mastered Severe Accidents (MSA) where mechanical energy releases in steam explosion caused degradation or even melt - down of either parts or even the entire core. ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 Extrapolation of the existing data to JHR is complicated because the transients in this reactor are both of coupled and multi - physics nature. So that, major parameters from current multi - phys ics tool have been adjusted upon accurate reference single - physics tools 9 to quantifying power peak and energy released in several postulated cases (see Figure 6) [14] . Figure 6 – Bounded Best Estimate and assimilated calculations [14] . 4.5. Activities relevant to European project ESFR - SMART BEPU can also be applied if the Best Estimate solution is not fully available , that is the case for Sodium Cooled Fast Reactors (SFR) when quantifying uncertainties at several strategically selected snap - shots derived using multi - physics transient calculations [16] . For example , f igure s 7a and 7 b show schematic view on snap - shots , 7 c and 7 d present power and reactivity evolution. It is well known that, at nominal operating conditions, fast reactor cores are not in their most reactive configuration, thus enabling sharp power excursion during a Cor e Disruptive Accident (CDA) due to a coolant voiding and / or relocation of materials. CDA is a fully multi - physics process the predictive capabilities of which are quite poor. As said, the power excursions are due to re - criticality engendered by relocatio n of materials, while the degradation of structures results from both power excursions and an insufficient heat removal. The safety assumptions were based on the following statements: - The biggest amount of mechanical energy is released during the first p rompt criticality (first power peak ) and is lim

10 ited at several hundred GWs; - The
ited at several hundred GWs; - The second and following power peaks are weaker and would not affect the safety barriers even more ; - The behaviour of the core can be substantiated by reactivity feedbacks. Figur e 8 shows the best estimate (non - conservative) power and reactivity swing vs. time during the transient. During the I st interval, from the very beginning of the transient to the end of the first power peak, the prompt criticality is achieved independently on the uncertainties. In the following interval (the II nd one) the prompt criticality might be achieved only if prior (non - constrained) uncertainty is considered and add ed , e.g. in a non - realistic assumption. And, finally, in the III rd interval both non - c onstrained and constrained uncertainties engender an energetic re - criticality. Experts‟ elicitations should be organized in a different manner for each of these intervals. 9 Those tools have been validated against representative experimental d ata. ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 a b c d Figure 7 - Snap - shots of core status in ULOF sequence (a and b), Power (c) and reactivity (d) evolution [16] . Thus even if the BEPU will not become a wide spread and acknowledged tool for assessment of the safety margins it could provide valuable inputs for further expert panel or individual judgments. Figure 8 - Revealed intervals of data assimilation and safety margins analysis [16] . These elements and intermediate conclusions addressed here above were proposed to research project ESFR - SMART supported by the European Commission aiming at the validation of safety related simulation of Sodium Cooled Fast Reactors. ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 5. DISCUSSION As far as the objective of BEPU is to remove conservatism , when performing assessment calculations the following conditions should be fulfilled [9] :  R elevant high - fidelity simulation tool should be available and affordable;  R elational database of the benchmark models based on representative sets of high - fidelity experiments data should be available and affordable too. Unfortunately , in everyday practice, these condit

11 ions could be fulfilled all together onl
ions could be fulfilled all together only for a very limited number of practical a pplications. It is too earlier, therefore, to propose adoption of BEPU as a universal tool for decision making in nuclear safety. It should be noted that conceptual systems of BEPU in different fields are very similar. Thus the PREMIUM project in SYS TH field operates with two entities to characterize experiments data: “calibrati on” and “informativeness” [6] . Data Assimilation for criticality safety proposes “bias ranking factor” (BRF) and “uncertainty reduction factor” (URF) [13] where “calibration” c orresponds to BRF and “informativeness” to URF. A mong the major outcome s of the recent international OECD - NEA exercises [6] , it is worth mentioning the well - established maturity in the uncertainty propagation for thermal - hydraulic codes. Nevertheless, a t the same time , a large spread among participants ‟ results ha s been revealed , which clearly underline s identifying needs for further improvements [6] , while the full applicability of the BEPU in criticality safety has been clearly proven [13] . Even if it must be acknowledged that the BEPU cannot become either a widely adopted or an internationally recognized technology [18] , nevertheless the BEPU principles can be applied for decoupling multi - physics models that allows testing and refuting of safety hypothesis, doubtful assumptions or/and unconformities [14] , [13] , [18] . Although many issues remained un - addressed or insufficiently addressed ( first of all at fully coupled multi - physics model ing ) the progress has been demonstrated in (1) system thermal hydraulics, (2) criticality safety and partially in (3) reactor physics applications. As t he US NRC considers BEPU a tool for informed decision [19] , elsewhere it could provide assessors (not deciders) with informed relevant inputs keeping mediation layer between simulation, assessment and decision - making p rocesses. 6. CONCLUSION Nowadays , Best Estimate Plus Uncertainties approach is frequently used to characterise the risks in different fields of actuarial mathematics [19] , finance and industry . O n the contrary as far as the industrial and nuclear applications are concerned, it remains confined at the second stage. In the field of safety, BEPU has been aimed, at first , at reducing the subjectivism of expert elicitation. It presumes reli

12 ance on evidence - based simulations pro
ance on evidence - based simulations providing inputs for safety analysis and assessment, and even for a decision making process implying an existence of the following components:  Q ualified computational tools including numerical codes dealing with different disciplines, interface services, well elaborated input decks etc.;  M ethods and integrated tools intended to uncertainties evaluation and propagation; and H igh - fidelity experim ental data devoted to reduce epistemic uncertainties against observations. ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 BEPU requires full justification of all of these components without exception. It means inter alia that it might not be reduced only to a mere uncertainty propagation tool. All sources of uncertainties - whatever aleatory or epistemic ones - should be well understood and comprehensively assessed. In the domain of nuclear safety, BEPU - being a logical process which stands on and relies upon understanding of phenomena - can be implemented to establish realistic and quantified limits of such an understanding. Metrics for consideration and characterisation of BEPU includes feedback experience from other fields of human activities including engineering, risk perception as well as nuclear safety evaluation and regulation practice providing clear vision on a readiness of BEPU technology entirely and by its components (as the following)  Best estimate modelli ng, e.g. robust models that comply the all phenomena of interest (multi - physics usually) and basis of High - fidelity evidences to validate Best estimate tools;  Methodology of validation of tools and relevant experimental data treatment and transposition on an application domain; and  Competent framework on BEPU application. Each component should be characterized in terms of their readiness and adequacy. The components taken all together should be characterized in terms of readiness too It would be worth investigating how expensive could be a novel R&D program to spread BEPU to other fields and disciplines . It should be noted, of course, that new experts‟ competences will be needed to explore the credibility and consistence of V& UQ processes. Unfortunately , a large majority of applications requires the use of multi - physics tools combining best estimate modules and conservative ones ( to bridge the lac

13 ks of knowledge) , validated on an exh
ks of knowledge) , validated on an exhaustive and stringent experimental - base [9] , [13] , [18] . The selection of such representative sets of experiments is high priority , since the biggest part of design and operati ng experience outcomes might be unavailable for independent assess ment . On one hand , because it provides the users with inputs for risk informed decision , the BEPU complies with the well - known IAEA safety assess ment standards [2] . On other hand, d espite a successful feedback experience in the US regulation practice [20] , until now, the BEPU has not been comprehensively adopted for assessment outside a few domain s , and has not yet become an internationally recognized technology so far. Nevertheless, in the near future, the implementation of the BEPU can become an element of experts‟ toolbox applicable together with experts ‟ judgement stimul at ing the development and the deployment of high - fidelity codes and models . 7. ACKNOWLEDGEMENTS P art of the research leading to the conclusions presented in the paper has been founded by the Euratom research and training programme 2014 - 2018 under grant agreement No 754501. The statements of the article are partially based on lectures provided to and supported by the organizers of Frédéric Joliot/Otto Hahn Summer School the Uncertainties in Nuclear Reactor Systems Analysis: Improving Understanding, Confidence and Quantification August 23 – September 1, 2017, Karlsruhe, Germany ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 REFERENCES [1] G. Wilson, Historical insights in the develo pment of Best Estimate Plus Uncertainty safety analysis, In Annals of Nuclear Energy, Volume 52, 2013 [2] Safety Assessment for Facilities and Activities, General Safety Requirements, IAEA Safety Standards Series No. GSR Part 4 [3] T. Ivanova, V. Rouyer, Y. Rozh ikhin, A. Tsiboulia, Towards validation of criticality calculations for systems with MOX powders, Annals of Nuclear Energy, v 36, 3, 2009 [4] International Handbook of Evaluated Criticality Safety Benchmark Experiments, NEA/NSC/DOC (95)03, OECD Nuclear Energy Agency, (2014). [5] International Handbook of Evaluated Reactor Physics Benchmark Experiments, OECD Nuclear Energy Agency, NEA/NSC/DOC(2006)1, (2011 Edition). [6] E . Nouy, A. de Crécy, Quantification of the uncertainty of physical models in

14 tegrated into system thermo - hydrauli
tegrated into system thermo - hydraulic codes, In Nuclear Engineering and Design, v 321, 2017 [7] J. Hou et al., „Benchmark for Uncertainty Analysis in Modelling (UAM) for Design, Operation and Safety Analysis of LWR, Phase II‟, NEA/NSC/DOC(2014), April 2017 [8] T. Ivanova et al, OECD/ NEA EGUACSA, (2012) International Conference on the Physics of Reactors 2012, PHYSOR 2012, 4, pp. 2762 - 2780 [9] G. Palmiotti, M. Salvatores « The Role of Experiments and of Sensitivity Analysis in Simulation Validation Strategies with Emphasis on Reactor Physi cs”, Ann. Nucl. Energy, 52 (2013), pp. 10 – 21 [10] J. Baccou, et al, Towards a systematic approach to input uncertainty quantification methodology, NURETH - 17, Qujiang Int‟l Conference Center, Xi‟an, China ， (2017), [11] J. Joucla, P. Probst, “DIPE: determination of i nput parameters uncertainties methodology applied to CATHARE v2.5_1 thermal - hydraulics code”, 15th ICONE, Nagoya, Japan, April 22 - 26, 2007 [12] The need for Integral Critical Experiments with Low - moderated MOX Fuels, OECD - NEA/NSC Workshop proceedings, Paris, F rance, 2004 [13] T. Ivanova, E. Ivanov and I. Hill, “Methodology and issues of integral experiments selection for nuclear data validation”, EPJ Web Conf ., 146 (2017), Article ID 06002 [14] Y. Chegrani et al, “SIMMER code validation for coupled physical processes mod elling in material testing reactors”, ICONE18, 2010 [15] R. Smith, «Radiological consequences of BORAX/SPERT/SNAPTRAN experiments», Nuclear Technology, 53, p. 147 - 154 (1981) [16] T. Ivanova, E. Ivanov, “Step towards integral validation of energetic re - criticality prediction for sodium cooled fast reactor”, Proc PHYSOR2014, Kioto, (2014). Japan [17] K. Mikityuk et al “ESFR - SMART: new Horizon - 2020 project on SFR safety”, (2017) [18] F. D'Auria, “ 14 - Best - Estimate Plus Uncertainty (BEPU) approach for accident analysis ” , Ther mal - Hydraulics of Water Cooled Nuclear Reactors, Woodhead Publishing, 2017, Pages 905 - 950 [19] R. Wiser, “Loss Reserving,” Foundations of Casualty Actuarial Science, Foundations of Casualty Actuarial Science, Casualty Actuarial Society, 1990 ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018) BEPU2018 - 309 Real Collegio, Lucca, Italy , May 13 - 19, 2018 [20] Standard Review Pla n for the Review of Safety Analysis Reports for Nuclear Power Plants NUREG 0800, Washington, DC (20