Abrate, N.

Dulla, S.

Massone, M.

Nallo, G. F.

Ravetto, P.

Valerio, D.

English

KITopen

KIT – The Research University in the Helmholtz Association www.kit.eduGenetic Algorithm-Based Optimisation of the Few-GroupStructure for Lead Fast Reactors AnalysisM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioPHYSOR Conference, 2022, May 17thM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 20222Motivation• 2-group calculation, common for LWRs, is often inaccurate for fast reactorsNeed for accurate computational models for design safety assessment and operation• Especially transient, coupled analyses• Only few-groups analyses are actually viableFull-core analyses are based on deterministic multi-group calculations• Lack of a general algorithm and problem stiffness• Somewhat of an art.The definition of a few-groups energy structure for a fast system is still an open problemM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisThe problem is often addressed by expert judgementCriteria are vague and arbitraryAim an automated and reproducible resultsApproach the problem with Artificial IntelligenceOptimization algorithmAccess to non-obvious solutionsThe problem is sensitive to schemesEach group influence the others, especially neighboring onesGenetic algorithm is an excellent option for its ability to preserve schemesJuly 19, 20223MotivationM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 20224The genetic algorithm (GA)Generate populationBreed new populationElitismMutationFitness evaluation for II≤N?I=1I++NYEnd?YNRepairStart from a random possible solution set (population)For each of these solutions (individuals), the value to optimize (fitness) is calculatedIndividuals are selected based on their fitness and they breed the next generation by crossing-overBest individuals from the old population can survive and pass to the next one (elitism)New individuals can change due to mutation.Repeat until a termination condition occursM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 20225Methodology summaryGeneration of the fine-group librariesSerpent 2HDF format to improve data readability, memorymanagement, consistency, flexibilityImport these libraries into SIMMER Development for SIMMER to read HDF librariesCross-section processing in SIMMER skippedSet the fitness function Import Serpent flux and keffObjective values for optimizationRun the genetic algorithm Results compared with the Serpent objective valuesMany few-groups calculationsM. MASSONE, N. ABRATE, G. F. NALLO, D. VALERIO, S. DULLA, P. RAVETTO, „Code-to-code SIMMER/FRENETIC comparison for the neutronic simulation of lead-cooled fast reactors”, Ann. Nucl. En. 174 (2022)**M. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisStart from continuous-energy ENDF-B/VIII.0 librariesSerpent 2 model to generate:Fine-group cross section libraryCalculation of neutron flux and multiplication factorALFRED core model (LEADER project)Uniform temperature: 673 KBoC conditionsClose-to-critical system ( 1.00002 4 )We will not be able to subdivide fine-groupsLarge number at the beginning: 120 groups114 equally spaced (in lethargy) groups in the central spectrum zoneCompromise at the energy space extremes to limit statistical noiseJuly 19, 20226Fine-group cross section generationG. F. NALLO, N. ABRATE, S. DULLA, P. RAVETTO, D. VALERIO, „Neutronic benchmark of the FRENETIC code for the Multiphysics analysis of lead fast reactors.”, European Physical Journal Plus 135 (2020)M. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 20227Fine-group cross section libraryM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisSIMMER is a mechanistic, multi-velocity-field, multiphase, multicomponent, Eulerian fluid-dynamics code coupled with a space-dependent neutron kinetics model and a structure model.Developed for safety studies of liquid-metal-cooled fast reactorsFurther developed and improved, it has been applied successfully to LWRs and general multiphase problemsExtended to read fine libraries from Serpent and with a cross-section condensation toolJuly 19, 20228Introduction to SIMMERM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisThe fitness function is the driving force of the algorithmIts choice reflects the aim given to the GA by its designerOur objective: Energy discretization that best allows SIMMER to match the Monte Carlo resultsJuly 19, 20229The fitness function, ,⋅1min∈max∈min∈⋅ 9⋅EqualweightingM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisThe way genetic information is expressedJuly 19, 202210Individual representationM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisThe way genetic information is expressedInteger representationEasy crossing-overLimited allele poolChromosomes are combinations of allelesJuly 19, 202211Individual representation3 4 5 92 5 8 10New gen.3 4 5 102 5 8 92 34597 6 810M. MASSONE, F. GABRIELLI, A. RINEISKI, “A genetic algorithm for multigroup energy structure search”, Annals of Nuclear Energy 105, p. 369-387 (2017)M. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR Analysis5 identical runsExclude genetic driftFitness improvement is concentrated in the first 30 generationsLater adjustments (exploitation)Spiky patternAccommodated in few generationsUsual exploration of new zonesDefinition of the fitness function: the fitness is rescaled at every improvementJuly 19, 202212ConvergenceM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR Analysis5 identical runsExclude genetic driftFitness improvement is concentrated in the first 30 generationsLater adjustments (exploitation)Spiky patternAccommodated in few generationsUsual exploration of new zonesDefinition of the fitness function: the fitness is rescaled at every improvementJuly 19, 202213ConvergenceM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 202214Fitness distributionDots are darker for older generationsM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 202215Fitness distributionDots are darker for older generationsM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 202216Be careful what you wish for…A cluster of candidate solutions with good and badThe GA found a vulnerability in the definitionGood score, but fail to represent the physicsNot necessarily bad: slower convergence, butpreserve variaty in the gene poolUniformity harms the exploration capability of the GARecall our objective: Energy discretizationthat best allows SIMMER to match the Monte Carlo resultsThat’s what we get!M. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisPositive traits tend to survive, negative ones do not last.July 19, 202217Traits success and extinctionM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisPositive traits tend to survive, negative ones do not last.All simulations agree in a first energy boundary at 1.4-1.6 MeVTail of the fission spectrumLarge empty regionEnergy groups are a scarce resourceThey are better invested in other zones of the spectrumJuly 19, 202218Successful allelesLast 5 generationsM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 202219Structures comparisonM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 202220RationalizationGroup 1:Fission productionGroup 2Pb resonancesGroup 3, 4, (5)U and Pu resonancesHigh frequenciesobserved around200 eV: the limitfor the major Pu resonancesGroup 6Low energyA low energygroup must existalso for fast coresRarely more thanoneM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisIn the framework of FR development (especially for accidental transients) theenergy structure problem plays an important role.We have employed a genetic algorithm for the condensation of fine-groups libraries generated with Serpent 2.The SIMMER code has been used for the few-groups calculations.The fitness function has been chosen such that the SIMMER transport solvermatches the Monte Carlo results.The GA finds satisfactory solutions for the given objectives.Accurate results in terms of both multiplication factor and flux distribution.The results can be reasonably interpreted in light of the underlying physics.July 19, 202221Conclusion and perspectivesM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 202222Conclusion and perspectivesStudy the impact of the initial number of fine-groupsDifferent fitness functionsAdjoint flux weightingFeedback effectsConsider transient case Multiple temperatures and conditionsLeave the GA free to choose the number of groupsModel the trade-off accuracy/computational time/convergence trendIncrease the procedure flexibility Standalone GA framework for nuclear applicationsM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 202223Thank you for your attention!Questions?M. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisJuly 19, 202224Energy structuresOriginalGA optimizedM. Massone, N. Abrate, G. F. Nallo, S. Dulla, P. Ravetto, D. ValerioGA-Based Optimisation of the Few-Group Structure for LFR AnalysisPopulation size: 80Tournament selection30 tournamentsProbability parameter: 0.15Mutation rate: 15%Elitist selection: 5%Termination conditionsMaximum number of generations: 15030 generations without improvementsTime limit: 105 sJuly 19, 202225Hyperparameters

Genetic algorithm-based optimisation of the few-group structure for lead fast reactors analysis

https://publikationen.bibliothek.kit.edu/1000148864/149044865

Genetic algorithm-based optimisation of the few-group structure for lead fast reactors analysis

Abstract

Similar works

Full text

Available Versions

KITopen