Reliability Assessment of Passive Safety Systems for Nuclear Energy Applications: State-of-the-Art and Open Issues

Passive systems are fundamental for the safe development of Nuclear Power Plant (NPP) technology. The accurate assessment of their reliability is crucial for their use in the nuclear industry. In this paper, we present a review of the approaches and procedures for the reliability assessment of passive systems. We complete the work by discussing the pending open issues, in particular with respect to the need of novel sensitivity analysis methods, the role of empirical modelling and the integration of passive safety systems assessment in the (static/dynamic) Probabilistic Safety Assessment (PSA) framework.

[1]  J. Devooght,et al.  Probabilistic Reactor Dynamics —I: The Theory of Continuous Event Trees , 1992 .

[2]  B. Sudret,et al.  Metamodel-based importance sampling for structural reliability analysis , 2011, 1105.0562.

[3]  George E. Apostolakis,et al.  The Impact of Uncertainties on the Performance of Passive Systems , 2005 .

[4]  Ali Mosleh,et al.  Methodology for the use of experimental data to enhance model output uncertainty assessment in thermal hydraulics codes , 2010, Reliab. Eng. Syst. Saf..

[5]  D. M. Hutton,et al.  The Cross‐Entropy Method: A Unified Approach to Combinatorial Optimisation, Monte‐Carlo Simulation and Machine Learning , 2005 .

[6]  Zhenzhou Lu,et al.  Reliability sensitivity method by line sampling , 2008 .

[7]  Enrico Zio,et al.  Monte Carlo simulation-based sensitivity analysis of the model of a thermal-hydraulic passive system , 2012, Reliab. Eng. Syst. Saf..

[8]  B. Iooss,et al.  Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site , 2008 .

[9]  C. Bassi,et al.  Reliability Assessment of 2400 MWth Gas-Cooled Fast Reactor Natural Circulation Decay Heat Removal in Pressurized Situations , 2008 .

[10]  Siu-Kui Au,et al.  Uncertainty Quantification in Estimating Critical Spacecraft Component Temperatures , 2007 .

[11]  Tunc Aldemir,et al.  A methodology for generating dynamic accident progression event trees for level-2 PRA. , 2006 .

[12]  Enrico Zio,et al.  Building confidence in the reliability assessment of thermal-hydraulic passive systems , 2009, Reliab. Eng. Syst. Saf..

[13]  Enrico Zio,et al.  Dynamic Accident Scenario Generation, Modeling and Post-Processing for the Integrated Deterministic and Probabilistic Safety Analysis of Nuclear Power Plants , 2018 .

[14]  Tomasz Kozlowski,et al.  Kriging-based inverse uncertainty quantification of nuclear fuel performance code BISON fission gas release model using time series measurement data , 2018, Reliab. Eng. Syst. Saf..

[15]  Dirk P. Kroese,et al.  An Efficient Algorithm for Rare-event Probability Estimation, Combinatorial Optimization, and Counting , 2008 .

[16]  Jinzhao Zhang,et al.  SAPIUM: A Generic Framework for a Practical and Transparent Quantification of Thermal-Hydraulic Code Model Input Uncertainty , 2020 .

[17]  Francesco Saverio D'Auria,et al.  Thermohydraulics of Emergency Core Cooling in Light Water Reactors - A State-of-the-Art Report. CSNI Report , 1989 .

[18]  Jon C. Helton,et al.  Extension of Latin hypercube samples with correlated variables , 2008, Reliab. Eng. Syst. Saf..

[19]  Enrico Zio,et al.  Monte Carlo approach to PSA for dynamic process systems , 1996 .

[20]  Jian Deng,et al.  Structural reliability analysis for implicit performance function using radial basis function network , 2006 .

[21]  A. John Arul,et al.  Efficient reliability estimate of passive thermal hydraulic safety system with automatic differentiation , 2010 .

[22]  Francesc Reventos,et al.  Uncertainty and sensitivity analysis of a LBLOCA in a PWR Nuclear Power Plant: Results of the Phase V of the BEMUSE programme , 2011 .

[23]  Enrico Zio,et al.  How to effectively compute the reliability of a thermal–hydraulic nuclear passive system , 2011 .

[24]  G. Apostolakis.  The concept of probability in safety assessments of technological systems. , 1990, Science.

[25]  Enrico Zio,et al.  Quantitative functional failure analysis of a thermal-hydraulic passive system by means of bootstrapped Artificial Neural Networks , 2010 .

[26]  A. John Arul,et al.  Adjoint operator approach to functional reliability analysis of passive fluid dynamical systems , 2009, Reliab. Eng. Syst. Saf..

[27]  A. Olsson,et al.  On Latin hypercube sampling for structural reliability analysis , 2003 .

[28]  G. I. Schueller,et al.  Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis - recent advances , 2009 .

[29]  P. Diaconis,et al.  Updating Subjective Probability , 1982 .

[30]  Enrico Zio,et al.  Ensemble-based sensitivity analysis of a Best Estimate Thermal Hydraulics model: Application to a Passive Containment Cooling System of an AP1000 Nuclear Power Plant , 2014 .

[31]  Enrico Zio,et al.  Comparison of bootstrapped artificial neural networks and quadratic response surfaces for the estimation of the functional failure probability of a thermal-hydraulic passive system , 2010, Reliab. Eng. Syst. Saf..

[32]  James L. Beck,et al.  SUBSET SIMULATION AND ITS APPLICATION TO SEISMIC RISK BASED ON DYNAMIC ANALYSIS , 2003 .

[33]  Jin Jiang,et al.  Efficient estimation of the functional reliability of a passive system by means of an improved Line Sampling method , 2013 .

[34]  Tomasz Kozlowski,et al.  Inverse uncertainty quantification of trace physical model parameters using BFBT benchmark data , 2016 .

[35]  Joe Wiart,et al.  A new surrogate modeling technique combining Kriging and polynomial chaos expansions - Application to uncertainty analysis in computational dosimetry , 2015, J. Comput. Phys..

[36]  Jon C. Helton,et al.  Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models , 2009, Reliab. Eng. Syst. Saf..

[37]  Francesco Saverio D'Auria,et al.  Development of a Code with the Capability of Internal Assessment of Uncertainty , 2000 .

[38]  Edzer J. Pebesma,et al.  Latin Hypercube Sampling of Gaussian Random Fields , 1999, Technometrics.

[39]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[40]  Max D. Morris,et al.  Three Technomefrics Experimental Design Classics , 2000, Technometrics.

[41]  Lénárd Pál,et al.  Best estimate method and safety analysis II , 2006, Reliab. Eng. Syst. Saf..

[42]  Enrico Zio,et al.  Determination of prime implicants by differential evolution for the dynamic reliability analysis of non-coherent nuclear systems , 2017 .

[43]  E. Zio,et al.  A study of the bootstrap method for estimating the accuracy of artificial neural networks in predicting nuclear transient processes , 2006, IEEE Transactions on Nuclear Science.

[44]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[45]  Jose Reyes,et al.  Natural Circulation in Water Cooled Nuclear Power Plants Phenomena, models, and methodology for system reliability assessments , 2005 .

[46]  Enrico Zio,et al.  Improved metamodel-based importance sampling for the performance assessment of radioactive waste repositories , 2015, Reliab. Eng. Syst. Saf..

[47]  Gerardo Rubino,et al.  Rare Event Simulation using Monte Carlo Methods , 2009 .

[48]  Jon C. Helton,et al.  Alternative representations of epistemic uncertainty , 2004, Reliab. Eng. Syst. Saf..

[49]  Neil E. Todreas,et al.  Reliability analysis of a passive cooling system using a response surface with an application to the Flexible Conversion Ratio Reactor , 2009 .

[50]  Kevin Coyne and Ali Mosleh.  Nuclear Plant Control Room Operator Modeling Within the ADS-IDAC, Version 2, Dynamic PRA Environment: Part 1 - General Description and Cognitive Foundations , 2014 .

[51]  Graham B. Wallis,et al.  Evaluation of nuclear safety from the outputs of computer codes in the presence of uncertainties , 2004, Reliab. Eng. Syst. Saf..

[52]  Luciano Burgazzi.  Addressing the uncertainties related to passive system reliability , 2007 .

[53]  Maurice Lemaire,et al.  Assessing small failure probabilities by combined subset simulation and Support Vector Machines , 2011 .

[54]  Francesco Saverio D'Auria,et al.  Passive Safety Systems and Natural Circulation in Water Cooled Nuclear Power Plants , 2009 .

[55]  Edoardo Patelli,et al.  A multivariate interval approach for inverse uncertainty quantification with limited experimental data , 2019, Mechanical Systems and Signal Processing.

[56]  Francesco Saverio D'Auria,et al.  Assessment of an Isolation Condenser of an Integral Reactor in View of Uncertainties in Engineering Parameters , 2011 .

[57]  Jérôme Morio,et al.  Extreme quantile estimation with nonparametric adaptive importance sampling , 2012, Simul. Model. Pract. Theory.

[58]  Enrico Zio,et al.  Finite mixture models for sensitivity analysis of thermal hydraulic codes for passive safety systems analysis , 2015 .

[59]  Enrico Zio,et al.  Bootstrapped-ensemble-based Sensitivity Analysis of a trace thermal-hydraulic model based on a limited number of PWR large break loca simulations , 2016, Reliab. Eng. Syst. Saf..

[60]  Enrico Zio,et al.  Passive systems failure probability estimation by the meta-AK-IS 2 algorithm , 2014 .

[61]  Pedro G. Coelho,et al.  Structural reliability analysis using Monte Carlo simulation and neural networks , 2008, Adv. Eng. Softw..

[62]  Enrico Zio,et al.  Functional failure analysis of a thermal-hydraulic passive system by means of Line Sampling , 2009, Reliab. Eng. Syst. Saf..

[63]  Francesco Saverio D'Auria,et al.  Reliability evaluation of a natural circulation system , 2003 .

[64]  Enrico Zio,et al.  Safety margins confidence estimation for a passive residual heat removal system , 2010, Reliab. Eng. Syst. Saf..

[65]  Ling Li,et al.  Sequential design of computer experiments for the estimation of a probability of failure , 2010, Statistics and Computing.

[66]  G. Schuëller,et al.  Chair of Engineering Mechanics Ifm-publication 2-374 a Critical Appraisal of Reliability Estimation Procedures for High Dimensions , 2022 .

[67]  Enrico Zio,et al.  Safety margin sensitivity analysis for model selection in nuclear power plant probabilistic safety assessment , 2017, Reliab. Eng. Syst. Saf..

[68]  B. E. Boyack,et al.  Quantifying reactor safety margins Part 5: Evaluation of scale-up capabilities of best estimate codes☆ , 1990 .

[69]  Hee-Dong Kim,et al.  A Formal Procedure for Probabilistic Quantification of Modeling Uncertainties Employed in Phenomenological Transient Models , 2000 .

[70]  Olivier Roustant,et al.  Calculations of Sobol indices for the Gaussian process metamodel , 2008, Reliab. Eng. Syst. Saf..

[71]  Luciano Burgazzi.  Failure Mode and Effect Analysis Application for the Safety and Reliability Analysis of a Thermal-Hydraulic Passive System , 2006 .

[72]  T. L. Schulz,et al.  Westinghouse AP1000 advanced passive plant , 2006 .

[73]  A. John Arul,et al.  Functional reliability analysis of Safety Grade Decay Heat Removal System of Indian 500 MWe PFBR , 2008 .

[74]  Enrico Zio,et al.  An optimized Line Sampling method for the estimation of the failure probability of nuclear passive systems , 2010, Reliab. Eng. Syst. Saf..

[75]  Enrico Zio,et al.  Reliability methods for passive system (RMPS) study – strategy and results , 2002 .

[76]  Pavel Kudinov,et al.  A PSA Level-1 method with repairable components : An application to ASTRID Decay Heat Removal systems , 2015 .

[77]  M. Morris.  Three Technometrics experimental design classics , 2000 .

[78]  Siu-Kui Au,et al.  Engineering Risk Assessment with Subset Simulation , 2014 .

[79]  Enrico Zio,et al.  Invariant methods for an ensemble-based sensitivity analysis of a passive containment cooling system of an AP1000 nuclear power plant , 2016, Reliab. Eng. Syst. Saf..

[80]  Nicolas Gayton,et al.  A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models , 2013, Reliab. Eng. Syst. Saf..

[81]  J. Beck,et al.  A new adaptive importance sampling scheme for reliability calculations , 1999 .

[82]  Luciano Burgazzi,et al.  Thermal-hydraulic passive system reliability-based design approach , 2007, Reliab. Eng. Syst. Saf..

[83]  George E. Apostolakis,et al.  Incorporating reliability analysis into the design of passive cooling systems with an application to a gas-cooled reactor , 2008 .

[84]  P. Mohanakrishnan,et al.  Passive system reliability analysis using Response Conditioning Method with an application to failure frequency estimation of Decay Heat Removal of PFBR , 2011 .

[85]  D. Cacuci,et al.  A Comparative Review of Sensitivity and Uncertainty Analysis of Large-Scale Systems—II: Statistical Methods , 2004 .

[86]  Hari Prasad,et al.  Reliability assessment of passive isolation condenser system of AHWR using APSRA methodology , 2009, Reliab. Eng. Syst. Saf..

[87]  Luciano Burgazzi,et al.  EVALUATION OF UNCERTAINTIES RELATED TO PASSIVE SYSTEMS PERFORMANCE , 2004 .

[88]  Bolado Lavin Ricardo,et al.  Natural Circulation Phenomena and Modelling for Advanced Water Cooled Reactors , 2012 .

[89]  Henri P. Gavin,et al.  High-order limit state functions in the response surface method for structural reliability analysis , 2008 .

[90]  F. D'Auria,et al.  Methodology for the reliability evaluation of a passive system and its integration into a Probabilistic Safety Assessment , 2005 .

[91]  Luciano Burgazzi.  About time-variant reliability analysis with reference to passive systems assessment , 2008, Reliab. Eng. Syst. Saf..

[92]  Jon C. Helton,et al.  Survey of sampling-based methods for uncertainty and sensitivity analysis , 2006, Reliab. Eng. Syst. Saf..

[93]  Alison L Gibbs,et al.  On Choosing and Bounding Probability Metrics , 2002, math/0209021.

[94]  Fabio Nobile,et al.  A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data , 2010, SIAM Rev..

[95]  Luciano Burgazzi,et al.  Passive System Reliability Analysis: A Study on the Isolation Condenser , 2002 .

[96]  V. Gopika,et al.  Development of the APSRA+ Methodology for Passive System Reliability Analysis and Its Application to the Passive Isolation Condenser System of an Advanced Reactor , 2016 .

[97]  Jorge E. Hurtado,et al.  Filtered importance sampling with support vector margin: A powerful method for structural reliability analysis , 2007 .

[98]  Helmut J. Pradlwarter,et al.  Realistic and efficient reliability estimation for aerospace structures , 2005 .

[99]  Enrico Zio,et al.  An Adaptive Simulation Framework for the Exploration of Extreme and Unexpected Events in Dynamic Engineered Systems , 2017, Risk analysis : an official publication of the Society for Risk Analysis.

[100]  M. Kloos,et al.  MCDET: A Probabilistic Dynamics Method Combining Monte Carlo Simulation with the Discrete Dynamic Event Tree Approach , 2006 .

[101]  Enrico Zio,et al.  Quantifying uncertainties in the estimation of safety parameters by using bootstrapped artificial neural networks , 2008 .

[102]  Enrico Zio,et al.  The future of risk assessment , 2018, Reliab. Eng. Syst. Saf..

[103]  Gabriel Lorenzo,et al.  Integration of the functional reliability of two passive safety systems to mitigate a SBLOCA+BO in a CAREM-like reactor PSA , 2014 .

[104]  Tomasz Kozlowski,et al.  Inverse uncertainty quantification of input model parameters for thermal-hydraulics simulations using expectation–maximization under Bayesian framework , 2015 .

[105]  Nicolas Gayton,et al.  AK-SYS: An adaptation of the AK-MCS method for system reliability , 2014, Reliab. Eng. Syst. Saf..

[106]  Anil K. Jain,et al.  Simultaneous feature selection and clustering using mixture models , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[107]  Bruno Sudret,et al.  Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: Application to urban drainage simulation , 2017, Reliability Engineering & System Safety.

[108]  Nicola Pedroni,et al.  An Adaptive Metamodel-Based Subset Importance Sampling approach for the assessment of the functional failure probability of a thermal-hydraulic passive system , 2017 .

[109]  Enrico Zio,et al.  Estimation of the Functional Failure Probability of a Thermal Hydraulic Passive System by Subset Simulation , 2009 .

[110]  Attila Guba,et al.  Statistical aspects of best estimate method - I , 2003, Reliab. Eng. Syst. Saf..

[111]  D. M. Hutton,et al.  Smart Environments: Technology, Protocols and Applications , 2005 .

[112]  Luciano Burgazzi.  State of the art in reliability of thermal-hydraulic passive systems , 2007, Reliab. Eng. Syst. Saf..

[113]  S. S. Wilks.  Statistical Prediction with Special Reference to the Problem of Tolerance Limits , 1942 .

[114]  Shie Mannor,et al.  A Tutorial on the Cross-Entropy Method , 2005, Ann. Oper. Res..

[115]  Nicolas Gayton,et al.  AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation , 2011 .

[116]  Enrico Zio,et al.  Postprocessing of Accidental Scenarios by Semi-Supervised Self-Organizing Maps , 2017 .

[117]  M. Valdebenito,et al.  The role of the design point for calculating failure probabilities in view of dimensionality and structural nonlinearities , 2010 .

[118]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[119]  Bruno Tuffin,et al.  Markov chain importance sampling with applications to rare event probability estimation , 2011, Stat. Comput..

[120]  Jack W. Baker,et al.  Incorporating modeling uncertainties in the assessment of seismic collapse risk of buildings , 2009 .

[121]  J. C. Helton,et al.  Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty , 1997 .

[122]  Enrico Zio,et al.  A Bayesian framework of inverse uncertainty quantification with principal component analysis and Kriging for the reliability analysis of passive safety systems , 2021 .

[123]  David Grabaskas,et al.  Advanced Reactor Passive System Reliability Demonstration Analysis for an External Event , 2017 .

[124]  Enrico Zio,et al.  Risk-Based Clustering for Near Misses Identification in Integrated Deterministic and Probabilistic Safety Analysis , 2015 .

[125]  H. Meidani,et al.  Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process, Part 1: Theory , 2018, Nuclear Engineering and Design.

[126]  L. Burgazzi.  Reliability Evaluation of Passive Systems Through Functional Reliability Assessment , 2003 .

[127]  Juozas Augutis,et al.  Dynamic reliability and risk assessment of the accident localization system of the Ignalina NPP RBMK-1500 reactor , 2005, Reliab. Eng. Syst. Saf..

[128]  Murat Emre Kartal,et al.  Probabilistic nonlinear analysis of CFR dams by MCS using Response Surface Method , 2011 .

[129]  Peter W. Glynn,et al.  Stochastic Simulation: Algorithms and Analysis , 2007 .

[130]  Jon C. Helton,et al.  A comparison of uncertainty and sensitivity analysis results obtained with random and Latin hypercube sampling , 2005, Reliab. Eng. Syst. Saf..

[131]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[132]  Thomas Most,et al.  A comparison of approximate response functions in structural reliability analysis , 2008 .

[133]  G. I. Schuëller,et al.  Benchmark Study on Reliability Estimation in Higher Dimensions of Structural Systems – An Overview , 2007 .