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Development and Application of Uncertainty Analysis Approaches for MELCOR Simulations of Severe Accidents
KTH, Skolan för teknikvetenskap (SCI), Fysik, Kärnkraftssäkerhet.ORCID-id: 0000-0001-5778-6778
2024 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

The contemporary needs in advancing safety analysis methods and the increasing stringency in light water reactor (LWR) safety in the post-Fukushima era require more advanced and systematical approaches for severe accident analyses. The best estimate plus uncertainty (BEPU) methods are among such approaches and have been widely used for deterministic safety analysis (DSA) of design basis accidents (DBAs). However, the BEPU analyses of severe accidents (SAs) are not straightforward due to the complexity of SA phenomena and the specialties of SA simulation tools. It is therefore necessary to develop BEPU approaches for severe accidents.  

This thesis work starts from an application of the conventional BEPU approach using various uncertainty quantification (UQ) methods of 95/95 tolerance limits to MELCOR simulations of severe accidents, with the aim to identify their capabilities in MELCOR simulations of severe accidents. Both parametric and nonparametric UQ methods, including goodness-of-fit test, Wilks’ methods, Baren and Hall’s linear interpolation and Hutson fractional statistics, are applied to postulated severe accident scenarios in a Nordic boiling water reactor (BWR). It is found that (i) a small sample size or a low order in these UQ methods tends to cause conservative estimates, and (ii) a large sample size has many unsuccessful MELCOR calculation cases and fixing of the cases incurs an explosive computational cost. To solve this problem, two alternative approaches are supposed to be developed in the next step.

The first alternative approach is to develop a bootstrapped artificial neural network (ANN) model to be employed in UQ; and the second alternative approach is to couple deterministic sampling (DS) methods with a fixed/dynamic coverage factor. The first alternative approach overcomes the problem in the conventional BEPU approach, i.e. the explosive computation cost due to fixing many crashed MELCOR cases otherwise it ruins randomness of samples. The idea behind this approach is to use surrogate models (SMs) developed from successful MELCOR calculations to predict the relation between major uncertain inputs and outputs. As a result, an UQ with numerically equivalent estimate of 95/95 tolerance limits can be done. The approach is applied to a severe accident scenario due to station blackout (SBO) in a Nordic BWR and results are compared with those of the conventional approach. The second approach is proposed for realistic estimates with reduced computational costs. Its theoretical basis is that DS methods can use far fewer samples to produce approximately convergent estimates of the statistical moments of outputs (figures of merits). By introducing a fixed or dynamic coverage factor, the information on the first two statistical moments can be extended to 95th percentiles or so-called numerically equivalent estimates of 95/95 tolerance limits. The second approach is applied to a severe accident scenario of SBO in a Swedish PWR and compared with the conventional approach.

The comparative results show that the two alternative approaches work well in uncertainty quantification of MELCOR simulations of the postulated severe accident scenarios chosen. For instance, given the mass of H2 production and the timing of vessel failure as the figures of merit (FOMs), the first alternative approach predicts the 95/95 estimates similar to those of the conventional approach. Besides, a high order nonparametric method can be used in the bootstrapped ANN model for stable and realistic estimates, which is almost impossible for the conventional approach due to the requirement of numerous MELCOR calculations. For the second approach, a fixed coverage factor 1.65 should be used when the outputs (figures of merits) are symmetrically distributed like normal distribution. Otherwise, a dynamic coverage factor from a fitted beta distribution should be used to avoid unrealistic estimates when the outputs are strongly skewed. It is thus concluded that the two proposed alternative approaches have potentials to replace the conventional approach of uncertainty quantification for MELCOR simulations of severe accidents, in case of too high computational cost due to a large sample size or many unsuccessful MELCOR calculations incurred in the conventional approach.

Abstract [sv]

Rådande behov av att utveckla säkerhetsanalysmetoder och den ökande stringensen i lättvattenreaktorsäkerhet (LWR) efter Fukushima kräver mer avancerade och systematiska tillvägagångssätt för att analysera svåra haverier. Metoderna för bästa skattning plus osäkerhet (BEPU) är ett sådant tillvägagångssätt och har använts brett för deterministiska säkerhetsanalyser (DSA) av konstruktionsstyrande haverier (DBA). Däremot är BEPU-analys av svåra haverier (SA) mer komplicerat på grund av SA-fenomens komplexitet och SA-simuleringsverktygens specialiteter. BEPU-metoder för svåra haverier behöver därför utvecklas.

Denna doktorsavhandling utgår från den konventionella BEPU-metoden där olika metoder för att bestämma osäkerheter (UQ) med 95/95 toleransgränser används i MELCOR-simuleringar av svåra haverier i syfte att fastställa deras tillämplighet. Både parametriska och icke-parametriska UQ-metoder, inklusive goodness-of-fit-test, Wilks-metoder, Baren och Halls linjära interpolering och metoder utvecklade av Hutson, tillämpas på postulerade scenarier med svåra haverier i en nordisk kokvattenreaktor (BWR). Det har visat sig att (i) en liten urvalsstorlek eller en låg ordning i dessa UQ-metoder tenderar att ge konservativa uppskattningar, och (ii) en stor urvalsstorlek medför många misslyckade beräkningsfall med MELCOR och att åtgärda fallen medför en explosionsartad beräkningskostnad. För att lösa detta problem föreslås två alternativa ansatser som kan utvecklas vidare i ett senare steg.

Den första alternativa ansatsen är att utveckla en modell med artificiellt neuronnät (ANN) baserad på ”bootstrapping” som ska användas i UQ; och den andra alternativa ansatsen är att koppla deterministiska urvalsmetoder (DS) med en fast/dynamisk täckningsfaktor. Det första alternativa tillvägagångssättet löser problemet med den konventionella BEPU-metoden, d.v.s. den explosionsartade beräkningskostnaden till följd av att åtgärda många kraschade MELCOR-fall som annars förstör det slumpmässiga urvalet. Tanken bakom ansatsen är att använda surrogatmodeller (SM) baserade på framgångsrika MELCOR-beräkningar för att förutspå sambandet mellan osäkra in- och utdata. Som ett resultat kan en UQ med numeriskt ekvivalent uppskattning med 95/95-toleransgräns göras. Ansatsen tillämpas för ett scenario med svårt haveri på grund av totalt elbortfall (SBO) i en nordisk BWR och resultaten jämförs med resultat som baserats på konventionella metoder. Den andra metoden föreslås användas för realistiska uppskattningar till lägre beräkningskostnader. Dess teoretiska grund är att DS-metoder behöver färre stickprov för att ge ungefärliga konvergenta uppskattningar av de statistiska momenten för utdata. Genom att införa en fast eller dynamisk täckningsfaktor kan informationen om de två första statistiska momenten utökas till 95:e percentil, eller så kallade numeriskt ekvivalenta uppskattningar av 95/95-toleransgränser. Det andra tillvägagångssättet tillämpas för ett svårt haveri av SBO i en svensk PWR och jämförs med resultat som baserats på konventionella metoder.

Resultatjämförelsen visar att de två alternativa tillvägagångssätten lämpar sig väl för att bestämma osäkerheter i MELCOR-simuleringar av de valda scenarierna med svåra haverier.  Exempelvis förutspår den första alternativa metoden, vid beräkning av H2-massa och tidpunkten för tankgenombrott, 95/95-uppskattningar som liknar de som är genomförda med konventionella metoder. Dessutom kan en icke-parametrisk metod av hög ordning användas i ANN-modellen för stabila och realistiska uppskattningar, vilket är nästan omöjligt för den konventionella metoden på grund av kravet på många MELCOR-beräkningar. För det andra tillvägagångssättet bör en fast täckningsfaktor på 1,65 användas när utdata är symmetriskt normalfördelade. I annat fall bör en dynamisk täckningsfaktor från en anpassad betadistribution användas för att undvika orealistiska uppskattningar när utdatafördelningen är kraftigt skev. Således dras slutsatsen att de två föreslagna alternativa tillvägagångssätten har potential att ersätta den konventionella metoden för bestämning av osäkerheter för MELCOR-simuleringar av svåra haverier vid höga beräkningskostnader på grund av en stor urvalsstorlek eller vid många misslyckade MELCOR-beräkningar genomförda med konventionella metoder.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2024. , s. 70
Serie
TRITA-SCI-FOU ; 2024:18
Nyckelord [en]
Severe accident, MELCOR, uncertainty analysis, Wilks’ method, Bootstrapped artificial neural network, deterministic sampling method, 95/95 tolerance limit.
Nyckelord [sv]
Svåra haverier, MELCOR, osäkerhetsanalys, Wilks’ metod, artificiella neuronnät, deterministiska urvalsmetoder, 95/95-toleransgränser.
Nationell ämneskategori
Energiteknik
Identifikatorer
URN: urn:nbn:se:kth:diva-344664ISBN: 978-91-8040-881-3 (tryckt)OAI: oai:DiVA.org:kth-344664DiVA, id: diva2:1846845
Disputation
2024-04-24, FA32, Albanova University Center, Roslagstullsbacken 21, Stockholm, 09:30 (Engelska)
Opponent
Handledare
Anmärkning

QC 2024-03-25

Tillgänglig från: 2024-03-25 Skapad: 2024-03-25 Senast uppdaterad: 2024-03-26Bibliografiskt granskad
Delarbeten
1. Bootstrapped artificial neural network model for uncertainty analysis in MELCOR simulation of severe accident
Öppna denna publikation i ny flik eller fönster >>Bootstrapped artificial neural network model for uncertainty analysis in MELCOR simulation of severe accident
2023 (Engelska)Ingår i: Progress in nuclear energy (New series), ISSN 0149-1970, E-ISSN 1878-4224, Vol. 157, artikel-id 104556Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

This study is concerned with uncertainty analysis of MELCOR simulation of a hypothetical severe accident initiated by station blackout (SBO) in a Nordic boiling water reactor (BWR). The hydrogen mass from cladding oxidation and the vessel failure timing in the accident are selected as the figures of merit (FOMs) in this study. As a conventional approach of uncertainty analysis, 456 cases with random sampling of 31 MELCOR input pa-rameters are executed by the code to produce the empirical cumulative distribution functions (CDFs) and the empirical 95th percentiles of the FOMs. Given the sufficient sample cases, uncertainty analyses through two nonparametric methods at various orders, i.e., the Wilks' method and the Wald & Guba's method, can then be performed to obtain the distributions of 95/95 estimates (95th percentiles estimated at a 95% confidence level) of single FOM and two FOMs. However, the conventional approach turns out to be time consuming and computationally expensive since many sample cases require iterative tuning of MELCOR input to restart and finish calculations. To overcome this issue encountered in the conventional approach of uncertainty analysis, an alternative approach is developed in the present study, in which 150 and 170 MELCOR calculation cases are used to develop bootstrapped artificial neural network (ANN) models which predict single FOM and two FOMs, respectively. The bootstrapped ANN models are then employed in uncertainty analyses through the two nonparametric methods of 95/95 estimates mentioned above. The comparative results show that the alternative approach can reproduce the distributions of 95/95 estimates for both single FOM and two FOMs with less computational costs. Moreover, while the Wilks' method or the Wald & Guba's method at a very high order (e.g., 100th order) can be used in the alternative approach to produce 95/95 estimates closer to the empirical 95th percentile, it is practically impossible to do so in the conventional approach due to unaffordable computational cost of excessive MELCOR runs. Hence, it can be concluded that the alternative approach of uncertainty analysis is not only effective (much less MELCOR cases with least fixing of unsuccessful runs), but also enabling high -order nonparametric methods for 95/95 estimates.

Ort, förlag, år, upplaga, sidor
Elsevier BV, 2023
Nyckelord
Severe accident, MELCOR, Best estimate plus uncertainty analysis, Nonparametric method, Bootstrapped ANN model
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:kth:diva-324531 (URN)10.1016/j.pnucene.2022.104556 (DOI)000926196700001 ()2-s2.0-85145771421 (Scopus ID)
Anmärkning

QC 20230307

Tillgänglig från: 2023-03-07 Skapad: 2023-03-07 Senast uppdaterad: 2024-03-26Bibliografiskt granskad
2. Application of uncertainty analysis methods to MELCOR simulation of postulated severe accidents in a Nordic BWR
Öppna denna publikation i ny flik eller fönster >>Application of uncertainty analysis methods to MELCOR simulation of postulated severe accidents in a Nordic BWR
2022 (Engelska)Ingår i: Nuclear Engineering and Design, ISSN 0029-5493, E-ISSN 1872-759X, Vol. 392, artikel-id 111764Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

Different uncertainty analysis methods are applied to MELCOR simulation of two postulated severe accidents in a Nordic boiling water reactor (BWR): (i) station blackout (SBO) accident, and (ii) large break loss-of-coolant accident (LBLOCA) combined with SBO, with the objective to compare their performances in the estimates of 95/95 tolerance limits of two figures of merit (FOMs) - the hydrogen mass produced from core degradation and the timing of vessel failure. Given 17 uncertain input parameters of MELCOR with probability density functions (PDFs), the 95/95 estimates of the two FOMs are obtained through the uncertainty analysis. From the uncertainty analysis results, it is found that for the quantification of single FOM a larger sample size leads to a much more accurate and stable 95/95 estimate at a higher computational cost, and the three nonparametric methods (Wilks' method, Beran and Hall's linear interpolation method as well as Hutson fractional statistics method) behave similarly in both accidents, while the goodness-of-fit test method performs differently and tends to provide a more realistic 95/95 estimate in both accidents. For the quantification of multiple FOMs the bracketing method tends to provide a smaller 95/95 estimate than the Wald and Guba method does, in consistent with their mathematical definitions. The Wald and Guba method is more stringent than the bracketing method when all percentiles (coverage) are set as the same. The sensitivity analysis results show that the several most significant input parameters are ranked almost identically by Spearman rank correlation coefficient (SRCC) and Pearson correlation coefficient (PCC), but these coefficients are dependent on accident scenarios and output parameters. Among the 17 parameters chosen, molten cladding drainage rate is the most influential to the output parameters (timing of initial melt relocation, timing of vessel failure, residual heat, etc.) considered in the present study, probably due to its impacts on molten Zr exposure to steam and resulting oxidation.

Ort, förlag, år, upplaga, sidor
Elsevier BV, 2022
Nyckelord
BEPU, Severe accidents, Uncertainty and sensitivity analysis, Parametric and nonparametric methods, MELCOR
Nationell ämneskategori
Sannolikhetsteori och statistik Subatomär fysik
Identifikatorer
urn:nbn:se:kth:diva-314823 (URN)10.1016/j.nucengdes.2022.111764 (DOI)000807473000004 ()2-s2.0-85128344606 (Scopus ID)
Anmärkning

QC 20220627

Tillgänglig från: 2022-06-27 Skapad: 2022-06-27 Senast uppdaterad: 2024-03-26Bibliografiskt granskad
3. Application of deterministic sampling methods to uncertainty quantification in MELCOR severe accident simulation
Öppna denna publikation i ny flik eller fönster >>Application of deterministic sampling methods to uncertainty quantification in MELCOR severe accident simulation
2023 (Engelska)Ingår i: Nuclear Engineering and Design, ISSN 0029-5493, E-ISSN 1872-759X, Vol. 403, artikel-id 112121Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

This study is concerned with uncertainty analysis of MELCOR simulation of a hypothetical severe accident initiated by station blackout (SBO) in a Swedish pressurized water reactor (PWR). 9 input parameters are chosen, and 12 safety-related output parameters are selected as the figures of merit (FOMs). In random sampling (RS) method, 800 MELCOR cases are run to produce empirical cumulative distribution functions (CDFs) and empirical 95th percentiles of FOMs. Given this sufficient sample size, uncertainty analyses through statistical analysis, can be performed to obtain the first two statistical moments and 95/95 estimates from the first order Wilks' method. However, RS method including Wilks' method turns out to be time consuming and computationally expensive since many MELCOR cases require iterative tuning of MELCOR input to restart and finish calculations. To overcome this issue encountered in RS method, in the present study three deterministic sampling (DS) methods are applied to uncertainty analyses, and a coupled approach by combining DS methods with a coverage factor 1.65 is proposed. Comparable results show that DS methods can generally capture the first two statistical mo-ments quickly, and acceptably accurate 95th percentiles can be calculated by the coupled approach when the output parameters can be described as normal distributions. Besides, estimated 95th percentiles from the coupled approach are covered by estimates (boxplots) from the first order Wilks' method. Hence, it can be concluded that the coupled approach has its potential to work as an alternative in engineering to RS method including Wilks' method for numerically equivalent estimates of 95/95 tolerance limit with an acceptable accuracy and a significantly less computational cost in MELCOR severe accident simulation.

Ort, förlag, år, upplaga, sidor
Elsevier BV, 2023
Nyckelord
Deterministic sampling method, Random sampling method, Severe accident, Uncertainty analysis
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:kth:diva-323752 (URN)10.1016/j.nucengdes.2022.112121 (DOI)000915829700001 ()2-s2.0-85145021186 (Scopus ID)
Anmärkning

QC 20230214

Tillgänglig från: 2023-02-14 Skapad: 2023-02-14 Senast uppdaterad: 2024-03-26Bibliografiskt granskad
4. Deterministic sampling methods coupled with dynamic coverage factors for uncertainty analyses in MELCOR simulation
Öppna denna publikation i ny flik eller fönster >>Deterministic sampling methods coupled with dynamic coverage factors for uncertainty analyses in MELCOR simulation
2023 (Engelska)Ingår i: Nuclear Engineering and Design, ISSN 0029-5493, E-ISSN 1872-759X, Vol. 413, artikel-id 112511Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

This study proposed a modified uncertainty quantification (UQ) approach which couples deterministic sampling (DS) methods with dynamic coverage factors, to overcome the disadvantage of the previous UQ approach (Wang and Ma, 2023b) in obtaining numerically equivalent estimates of 95/95 tolerance limits for MELCOR simulations of postulated severe accidents in a Swedish pressurized water reactor (PWR). In the modified UQ approach two deterministic sampling (DS) methods were used to obtain the first two statistical moments, and dynamic coverage factors calculated from fitted beta distributions are employed to extend the moment information to the 95th percentile. The modified UQ approach was compared with the previous UQ approach (coupling DS methods with a fixed coverage factor) and conventional UQ approach of the first order Wilks' method. The comparative results showed that the modified UQ approach not only enabled eliminating unrealistic estimates in the previous UQ approach, but also offered estimates that are covered by boxplots from the first order Wilks' method with a significant reduction of computational cost. In the modified UQ approach 10-18 samples were sufficient, while at least 59 samples were required for the first order Wilks' method. In the scope of the present study, DS-Standard method was recommended in the modified UQ approach in view of conservatism, while DS-Simplex method was preferred in view of accuracy and computational cost. Since the behavior of a DS method is dependent of time and outputs, in practice different DS methods should be integrated to the modified UQ approach for numerically equivalent estimates of 95/95 tolerance limits in MELCOR severe accident simulations.

Ort, förlag, år, upplaga, sidor
Elsevier BV, 2023
Nyckelord
Severe accident, MELCOR simulation, Uncertainty quantification, Deterministic sampling method, Wilks' method
Nationell ämneskategori
Energiteknik Tillförlitlighets- och kvalitetsteknik
Identifikatorer
urn:nbn:se:kth:diva-335134 (URN)10.1016/j.nucengdes.2023.112511 (DOI)001047587000001 ()2-s2.0-85165964132 (Scopus ID)
Anmärkning

QC 20230901

Tillgänglig från: 2023-09-01 Skapad: 2023-09-01 Senast uppdaterad: 2024-03-26Bibliografiskt granskad

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