Chaire Science des Systèmes et Défi Énergétique

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1 Chaire Science des Systèmes et Défi Énergétique Fondation Européenne pour les Énergies de Demain - Électricité de France (EDF)

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3 Chaire Science des Systèmes et Défi Energétique (SSDE) Chair on Systems Science and the Energy Challenge (SSEC) La Chaire Science des Systèmes et Défi Énergétique (SSDE, est partagée entre l'école Centrale Paris (ECP, et Supélec ( avec le soutien de la Fondation Européenne pour les Énergies de Demain (FEED) d Électricité de France (EDF, Les activités de la chaire ont commencé en mars 2010 avec l'arrivée d'enrico Zio, professeur et ancien directeur de l'école doctorale au Politecnico di Milano, Italie. Les activités de la chaire ont été orientées sur le développement, la mise en œuvre et l'utilisation de modèles computationnels et de méthodes et algorithmes numériques pour analyser le comportement lors de défaillances des systèmes énergétiques complexes et des incertitudes associées. Les thèmes de recherche de la chaire sont l ingénierie de la fiabilité, de la disponibilité et de la maintenance, de l étude de risques, de l'évaluation de la sécurité et de la sûreté, et l analyse de la vulnérabilité. Plus précisément, le cadre de recherche sur les systèmes énergétiques et les composants s intéresse aux méthodes de (Figure 1) : Simulation Prévision Optimisation Modélisation de modes de défaillance et de dégradation Analyse du risque, de la vulnérabilité, de la résilience The Chair on Systems Science and the Energy Challenge (SSEC, is shared between Ecole Centrale Paris (ECP, and Supelec ( and is supported by the European Foundation for New Energy of Electricite De France (EDF, The Chair activities, started in Mars 2010 with the arrival of Enrico Zio, professor and former Director of the PhD School at the Politecnico di Milano, Italy. The Chair activities have focused on the development, implementation and use of computational models, methods and algorithms for the analysis of the failure behavior of complex energy systems and the related uncertainties. Then, the research topics of interest for the Chair cover aspects related to reliability, availability and maintainability (RAM) engineering, risk assessment, safety and security evaluation, vulnerability and resilience analysis. More specifically, the research on energy systems and components involves methods for (Figure 1): Simulation Prediction Optimization Degradation and Failure Modeling RAM, Risk, Vulnerability, Resilience Analysis 3

4 Modélisation de modes de défaillance et de dégradation Modélisation du risque, de la vulnérabilité, de la résilience Systèmes énergétiques et composants Simulation Prédiction Optimisation Figure 1: cadre de recherche Degradation/Failure Modeling RAM/Risk/Vulnerability/Resilience Modeling Energy Systems and components Simulation Prediction Optimization Figure 1: Research framework Deux axes de recherche principaux peuvent être distingués (Figure 2) : Axe 1 : Caractérisation du vieillissement et de la défaillance des composants des usines de production Axe 2 : Analyse des systèmes énergétiques Ces deux axes se subdivisent en un certain nombre de recherches (Figure 2) faites par : les deux professeurs adjoints : le Dr Yanfu Li de l'université Nationale de Singapour (génie industriel) et le Dr Nicola Pedroni de Politecnico di Milano (génie nucléaire) Une post-doc : le Dr Ionela Prodan de Supélec (automatique) Two main research axes can be distinguished (Figure 2): Axis 1: Characterization of the aging and failure behavior of production plant components Axis 2: Energy systems analysis These two axes develop into a number of individual researches (Figure2) carried out by: 2 assistant professors: Dr. Yanfu Li from National University of Singapore (industrial engineering) and Dr. Nicola Pedroni from Politecnico di Milano (nuclear engineering) 1 post-doc: Dr. Ionela Prodan from Su- pelec (control engineering) 4

5 les 10 doctorants : Ronay Ak (Turquie, 3 ème année), Yiping Fang (Chine, 2 éme année), Elisa Ferrario (Italie, 2 ème année), Elizaveta Kuznetsova (Russie, 3 ème année), Yanhui Lin (Chine, 1 ère année), Chung-Kung Lo (Taiwan, 2 ème année), Jie Liu (Chine, 2 ème année), Liu Xing (Chine, 1 ère année), Rodrigo Mena (Chili, 2 ème année), Tairan Wang (Chine, 2 ème année) les deux étudiants en Master : Roberto Rocchetta (Italie) et Sébastien Valla (France) ainsi que diverses collaborations internationales 10 PhD students (see at the end, the list of thesis subjects): Ronay Ak (Turkey, 3rd year), Yiping Fang (China, 2nd year), Elisa Ferrario (Italy, 2nd year), Elizaveta Kuznetsova (Russia, 3nd year), Yanhui Lin (China, 1st year), Chung-Kung Lo (Taiwan, 2nd year), Jie Liu (China, 2nd year), Xing Liu (China, 1st year), Rodrigo Mena (Chile, 2nd year), Tairan Wang (China, 2nd year), 2 Master students: Roberto Rochetta (Italy) and Sébastien Valla (France) and several international collabrations Figure 2 : Axes de recherche Figure 2: Research axes 5

6 Voici des exemples de thèmes de recherche abordés : Estimation des intervalles de prédiction d indicateurs d'énergie, par exemple, l'énergie éolienne, la charge, la capacité de transfert, etc. Méthodes «kernel-based» du traitement du signal pour le diagnostic et le pronostic de défaillance des composants du système électrique Modélisation multi-états fondée sur la physique des processus de dégradation des composants et des structures Agent de la modélisation, simulation et l'analyse des systèmes de micro-réseaux Modèle prédictif de contrôle pour la gestion de l'énergie en micro-réseau Algorithmes évolutionnistes pour une optimisation multi-objectifs robuste en cas d incertitude Analyse d incertitude dans l évaluation des risques sismiques Système de systèmes d analyse des risques liés à des événements extérieurs ; Analyse complexe des systèmes de vulnérabilité : échec en cascade et modélisation de la résilience Prise de décision selon plusieurs critères pour l analyse de la vulnérabilité des systèmes énergétiques complexes Intégration de la théorie du contrôle et de la théorie de fiabilité pour l analyse des systèmes complexes Méthodes de simulation avancées de type Monte Carlo pour l analyse de la fiabilité des systèmes énergétiques complexes Techniques avancées pour les systèmes évolutifs d optimisation de l énergie Les premiers résultats de la recherche ont donné lieu à : des publications dans des revues scientifiques à l international avec évaluation par Examples of topics addressed in the research are: Prediction intervals estimation of energy quantities, e.g. wind power, load, available transfer capacity, etc. Kernel-based pattern recognition methods for fault diagnosis and prognosis of electrical system components Multi-state physics-based modeling of degradation processes in components and structures Agent-based modeling, simulation and analysis of micro-grid systems Model Predictive Control for micro-grid energy management Evolutionary algorithms for robust multi-objective optimization under uncertainty Uncertainty analysis in seismic risk assessment System-of-systems analysis of risk from external events Complex systems vulnerability analysis: failure cascade and resilience modeling Multi-criteria decision making for the vulnerability analysis of complex energy systems Integration of control theory and reliability theory for the analysis of complex systems Advanced Monte Carlo simulation methods for the reliability analysis of complex energy systems Advanced evolutionary techniques for energy systems optimization Outcomes of the research are in the form of: Publications on international, peer-reviewed scientific journals 6

7 un comité de lecture ; des présentations à des conférences internationalement reconnues ; un logiciel pour la démonstration des concepts et méthodes (la mise en œuvre pratique et / ou la commercialisation des outils développés ne fait pas partie de l objectif de la recherche). La Chaire est également impliquée dans les activités d enseignement avec, en particulier, des contributions à la formation Master International de l énergie nucléaire. Les efforts de la chaire visent à contribuer à résoudre certains des défis des systèmes énergétiques de demain, qui sont multiples et systémiques et qui impliquent une pluridisciplinarité des compétences et de l expertise. Pour le scénario selon lequel les systèmes énergétiques sont vivants, des questions se posent sur la vulnérabilité et les risques associés à leur développement et exploitation futurs, c est à dire à la possibilité que les capacités et les marges de sécurité soient conçues, gérées et maintenues pour répondre à une demande de plus en plus grande dans des conditions d intégration croissante avec d autres infrastructures critiques (systèmes de systèmes) et de la déréglementation du marché, sans pour autant diminuer la sureté, la sécurité et la fiabilité des opérations et de service. Le degré élevé d inter- et intra-connectivités peut rendre ces systèmes de systèmes vulnérables à une perturbation mondiale, lorsqu ils sont exposés à des risques variés, que ce soit des défaillances aléatoires, mécaniques ou physiques, des défaillances de matériel suite à des événements naturels ou à des attaques malveillantes intentionnelles, ou suite à des erreurs humaines. Ce large éventail de dangers et de menaces requiert une approche tout risque pour comprendre la dynamique de défaillance Presentations at internationally recognized conferences Software for proof of concepts and methods (the practical implementation and/or commercialization of the tools developed is not with in the objective of the research). The Chair is also involved in teaching activities including, in particular, contributions to the International Master of Nuclear Energy and the Master of Industrial Engineering. In the end, the Chair efforts are aimed at contributing to address some of the challenges of the energy systems for the future, which are multiple and systemic and involve a multidisciplinarity of competences and expertise. In the scenario of re/ evolution that energy systems are living, concerns are arising with regards to the vulnerabilities and risks associated to their future development and operation, i.e., to the possibility that capacities and safety margins be designed, managed and maintained to support the anticipated growing demand under conditions of greater integration with other critical infrastructures (systems-of-systems) and of market deregulation, without diminishing safety, security and reliability of operation and service. The high degree of inter- and intra-connectedness, can make these systems-of-systems vulnerable to global disruption, when exposed to hazards of various nature, from random mechanical/physical/material failures to natural events, intentional malevolent attacks, human errors. This broader spectrum of hazards and threats, calls for an all-hazards approach for the understanding of the failure behavior of such systems, in view of their consequent protection. New approaches are needed to look into these complex systems (of systems),and their 7

8 de tels systèmes, en vue de leur protection. De nouvelles approches sont nécessaires pour étudier ces systèmes (de systèmes) complexes, et leurs défis, d un point de vue holistique, pour fournir des prévisions fiables sur leur comportement pour permettre leur fonctionnement sûr. En outre, de grandes incertitudes existent dans la caractérisation du comportement des composants du système, de leurs interconnexions et de leurs interactions. En fin de compte, l analyse de ces systèmes ne peut pas être effectuée uniquement par des méthodes classiques de décomposition du système et d analyse logique. Il est nécessaire d intégrer un certain nombre de méthodes permettant d envisager le problème sous des angles différents (topologique et fonctionnelle, statique et dynamique...), compte tenu des incertitudes existantes. Plus d informations sur les activités de la Chaire peuvent être trouvées sur challenges,from a holistic viewpoint to provide reliable predictions of their behavior for their safe control. Furthermore, large uncertainties exist in the characterization of the behavior of the system components, of their interconnections and interactions. In the end, the analysis of these systems cannot be carried out only with classical methods of system decomposition and logic analysis; a framework is needed to integrate a number of methods capable of viewing the problem from different perspectives (topological and functional, static and dynamic,...), under the existing uncertainties. More information on the activities of the Chair can be found on the web site Enrico Zio Chair Director 8

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11 AGING AND FAILURE PROCESSES IN COMPONENTS OF ENERGY PRODUCTION PLANTS 11

12 Line 1 Prediction and prognostics Multi-Objective Genetic Algorithm approach for the Estimation of Neural Network (NN) based Prediction Intervals (PIs) Ronay AK A multi-objective genetic algorithm approach (the non-dominated sorting genetic algorithm II (NSGA-II)) is applied to determine the weights of a neural network trained to provide prediction intervals (PIs) in output. We test our model in real case studies: short-term wind speed prediction, and wind power forecasting with interval-input data, by considering both the variability in the input and the uncertainty in the model structure. Unlike the existing papers on wind speed and power prediction, we provide prediction intervals (PIs), optimal both in terms of accuracy (coverage probability) and efficacy (width). References R. Ak, V. Vitelli, and E. Zio, 2013, An interval-valued Neural Network approach for prediction uncertainty quantification, IEEE Transactions on Neural Networks and Learning Systems. (Submitted). R. Ak, Y. F. Li, V. Vitelli, E. Zio, E. López Droguett, and C. Magno Couto Jacinto, 2013, NSGA-IItrained neural network approach to the estimation of prediction intervals of scale deposition rate in oil & gas equipment, Expert Systems with Applications, 40 (4), pp A. Khosravi, S. Nahavandi, D. Creighton, and A. F. Atiya, 2011, Lower upper bound estimation method for construction of neural network-based prediction intervals, IEEE Transactions on Neural Networks, 22 (3), pp K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, 2002, A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6 (2), pp R.E. Moore, R.B. Kearfott, and M.J. Cloud, 2009, Introduction to Interval Analysis, 1st ed. Society for Industrial and Applied Mathematics. 12

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14 Kernel-based Pattern Recognition Methods for Prognostics of Nuclear Components' ETTF (Expected Time To Failure) Jie LIU An approach for the prediction of the condition of Nuclear Power Plant (NPP) components is proposed, for the purposes of condition monitoring. In particular, we aim at short-term forecasting the drifting leak flow in a Reactor Coolant Pump (RCP). The method builds on a modified version of the Probabilistic Support Vector Regression (PSVR) method, in which specific techniques are introduced for the tuning of the PSVR hyerparameters, the model identification and the uncertainty analysis. References Gao, J.B., Gunn, S.R., Harriset, C.J., Brown, M., A probabilistic framework for SVM regression and error bar estimation. Mach. Learn. 46 (1 3): Liu, J., Seraoui, R., Vitelli, V., Zio, E Nuclear Power Plant Components Condition Monitoring by Probabilistic Support Vector Machine. Ann. Nucl. Energy 55: Martin, M., On-line support vector machine regression. Preceeding ECML 02 proceeding of the 13th European Conference on Machine Learning Zio, E. & Di Maio, F A data-driven fuzzy approach for predicting the remaining useful life in dynamic failure scenarios of a nuclear system. Reliab. Eng. Syst. Saf. 95:

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16 Line 2 Component degradation, maintenance modeling and simulation Degradation and Maintenance Modeling for Multi-component Systems Yan-Hui LIN We propose to integrate component degradation physics, influencing factors and information into a single modeling framework for the purpose of component degradation modeling and maintenance planning. The preliminary framework was developed upon the multi-state physics model and different solution methods, such as stochastic Petri net-based Monte Carlo simulation, were investigated. Influencing factors, e.g. random shocks, are now under research. The methods of handling the dependences among multiple degradation paths and the uncertainties in various modeling parameters will be studied in future. References Y.-H. Lin, Y.-F. Li and E. Zio. Multi-State Physics Model for the Reliability Assessment of a Component under Degradation Processes and Random Shocks. ESREL2013, Amsterdam, Netherlands. Y.-F. Li, E. Zio, and Y.-H. Lin, «A Multistate Physics Model of Component Degradation Based on Stochastic Petri Nets and Simulation,» Reliability, IEEE Transactions on, vol. 61, pp , Stephen D. Unwin, Peter P. Lowry, Robert F. Layton, Jr., Patrick G. Heasler, and Mychailo B. Toloczko MULTI-STATE PHYSICS MODELS OF AGING PASSIVE COMPONENTS IN PRO- BABILISTIC RISK ASSESSMENT. ANS PSA 2011 International Topical Meeting on Probabilistic Safety Assessment and Analysis Wilmington, NC, March 13-17,

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20 Line 1 Dynamic system modeling A Control Theoretic Approach for the Analysis of Energy Systems Exposed to Vulnerabilities and Risks Ionela PRODAN The underlying goal of this research is to develop a control theory framework for the analysis of energy complex systems of generation, distribution and transition, under different scenarios, including anomalous and accidental ones. Elements from control theory, reliability, risk analysis, optimization and information technology are merged together in order to provide solutions to problems of optimal energy system design, control and management. The work is currently focused on microgrid energy dynamical systems. In the control framework for these systems it is necessary to take into account not only exogenous factors (e.g. change in consumer load, wind speed, price profile, etc.) but also the internal (state) dynamics and the structural properties of the individual components (as wind or solar energy equipment, on-site storage etc.) which may change (stochastically) due to degradation, failure, aging and so on. References J. Rawlings and D.Q. Mayne, Model Predictive Control: Theory and Design, Madison, WI: Nob Hill Publishing, LCC, S.V. Rakovi c, B. Kouvaritakis, M. Cannon, C. Panos, and R. Findeisen, Fully parameterized tube MPC, in Proceedings of the 18th IFAC World Congress, Milano, Italy, pp ,

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22 Agent-based Modelling and Simulation of Microgrids Elizaveta KUZNETSOVA We consider a microgrid that is connected to an external grid via a transformer. The microgrid includes the following players: a middle-size train station with integrated photovoltaic power production system, a small energy production plant composed of urban wind turbines and a surrounding district including residences and small businesses. Each player is modeled as an individual agent aiming at a particular goal, (i) decreasing its expenses for power purchase or (ii) increasing its revenues from power selling. The context in which the agents operate is uncertain due to the stochasticity of operational and environmental parameters. A generalized energy management framework for the optimization of individual objectives is proposed. The framework gives the capability to intelligent agents to learn from the stochastic environment and to make use of their experience to select optimal energy management actions. Artificial Intelligence techniques for prediction under uncertainty are integrated directly in the decision-making and actiontaking behaviors of each individual agent. 22

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24 Line 2 Complex energy systems modeling and analysis Advanced Simulation Methods for Complex Energy Systems Modeling and Analysis Nicola PEDRONI Power transmission networks are complex systems for which modeling uncertainties are usually quite large. Due to these uncertainties, a failure of the system has always a nonzero probability to happen. Such a failure may trigger other failures with increasing levels of gravity. Therefore, it is of utmost importance to be able to assess the probability of undesirable events that can occur in a system. The operation of a system and the chain of events leading to a failure are generally simulated using computer models of the critical parts of the system. Then, the probability of a failure event can be estimated by repeated Monte Carlo (MC) sampling of the operating conditions of the system. However, this method often requires high computational efforts for two reasons. First, when the probability of failure is small, a large number of simulations of the complex system must be carried out to observe a few failure events. Second, long calculations (several hours) are typically necessary for each run of the detailed computer model. Thus, alternative methods must be sought to tackle the computational burden associated to the analysis. The above mentioned computational challenge is here tackled in two different ways: from one side, efficient Monte Carlo Simulation techniques are employed to perform robust estimations with a limited number of random samples drawn and associated low computational time; from the other side, fast-running, surrogate regression models (also called response surfaces or meta-models) are used to replace the long-running computer model code in the system failure analysis. References Blanchet, J., Lam, H., State-dependent importance sampling for rare-event simulation: An overview and recent advances. Surveys in Operations Research and Management Science, 17, pp Botev, Z.I., L Ecuyer, P., Rubino, G., Simard R.,Tuffin, B., Static Network Reliability Estimation via Generalized Splitting. INFORMS Journal on Computing Winter, 25(1), pp Cancela, H., El Khadiri, M., Rubino, G., Rare Event Analysis by Monte Carlo Techniques in Static Models. In: Rubino, G., Tuffin, B. (Eds.), Rare Event Simulation Using Monte Carlo Methods, John Wiley and Sons, pp Echard, B., Gayton, N., Lemaire, M., Kriging-based monte carlo simulation to compute the probability of failure efficiently: AK-MCS method. In: 6èmes Journées Nationales de Fiabilité, mars, Toulouse, France Hui, K.P., Bean, N., Kraetzl, M., Kroese, D.P., The Cross-Entropy Method for Network Reliability Estimation. Annals of Operations Research, 134(1), pp Marrel, A., Iooss, B., Laurent, B., Roustant, O., Calculations of Sobol indices for the Gaussian process metamodel. Reliability Engineering and System Safety, vol., 94, pp Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R.T., Kim, N.H., Adaptive designs of experiments for accurate approximation of target regions. Journal of Mechanical Design, 132(7), (9 pages) Zio, E., The Monte Carlo Simulation Method for System Reliability and Risk Analysis. Springer Series in Reliability Engineering, Springer Ed., London, UK Zio, E., Pedroni, N., How to effectively compute the reliability of a thermal-hydraulic passive system. Nuclear Engineering and Design, 241(1), pp

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26 Vulnerability and Risk Analysis of Networked Engineering Systems Yi-Ping FANG The complexity of large-scale network systems made of a large number of nonlinearly interconnected components is a restrictive facet for their modeling and analysis. We propose a framework of hierarchical modeling of a complex network system, based on a recursive unsupervised spectral clustering method. The hierarchical model serves the purpose of facilitating the management of complexity in the analysis of real-world critical infrastructures. References Final Report on the August 14, 2003 Blackout in the United States and Canada, US- Canada Power System Outrage Task Force, Tech. Rep., Zio, E. From complexity science to reliability efficiency: a new way of looking at complex network, systems and crical infrastructures. Internaonal journal of crical infrastructures 3, no. 3 (2007): Clauset A., Moore C., and Newman M. E. J. Hierarchical structure and the predicon of missing links in networks, Nature, 453: , Fang Y.- P., Zio E. Unsupervised spectral clustering for hierarchical modelling and cricality analysis of complex networks, Reliability Engineering & System Safety, Volume 116, 2013, Pages Fang Y.-P., Pedroni N., Zio E. Opmal Producon Facility Allocaon for Failure Resilient Crical Infrastructures, submied to ESREL2013, Amsterdam, Netherlands. 26

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28 Multi-criteria Decision Making for the Vulnerability Analysis of Complex Energy Systems Tairan WANG Embracing an all-hazard view to deal with random failures, natural disasters, accidents and malevolent intentional acts, a framework for the vulnerability analysis of safety-critical systems and infrastructures is set up. A hierarchical structure is used to organize the information on the hazards, which is then manipulated through a decision-making process for vulnerability evaluation. We present the framework and its hierarchical model by way of assessing the susceptibility of a safety-critical system to intentional hazards, considering criteria of diverse nature, such as physical characteristics, social criticality characteristics, exposition to cascading failures, resilience. We use a ranking method to first have a pair-wise comparison of the systems of different characteristics. Then an absolute judgment by assigning the alternatives into preference-ordered categories is considered. In introducing the function of the cost of possible improvement measures and its effects corresponding to the criteria for the alternatives, we may select the choice of amelioration reactions regarding to the given limits of problems. The uncertainty of the solving model is also considered in a study of robustness of the decision of reactions. The systematic process of analysis is presented with reference to nuclear power plants. References Wang,T., V. Mousseau, E. Zio (2013). A Hierarchical Decision Making Framework for Vulnerability Analysis, European Safety and RELiability Conference (ESREL 2013) Kröger, W & E. Zio (2011). Vulnerable Systems. UK: Springer. Bous, G., P. Fortemps, F. Glineur, & M. Pirlot (2010). ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements. European Journal of Operational Research 206(2), Sonnevend, G. (1985). An analytical centre for polyhedrons and new classes of global algorithms for linear (smooth, convex) program- ming. Lecture Notes in Control and Information Sciences,

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30 System of Systems Vulnerability and Risk Modeling and Analysis Xing LIU The dynamic behavior of a system of systems in response to disturbances and failures can propagate into catastrophic effects. This research addresses the problem of modeling and analyzing interconnected dynamical systems with respect to prevention of unexpected events by diagnosability, robustness to disturbances and capability to recover by controllability. References R. Filippini, A. Silva, Resilience Analysis of Networked systems-of-systems based on Structural and Dynamic interdependencies, conference PSAM11 & ESREL 2012, Helsinki June F. Blanchini and S. Miani, Set-Theoretic Methods in Control, Springer,

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32 Line 3 External event risk assessment (Seismic) Safety and resilience Assessment of Multistate Systems of Systems Elisa FERRARIO We consider a safety-critical plant, e.g., a nuclear power plant, exposed to an external hazard, e.g., an earthquake. We propose an original framework of analysis, which extends the boundaries of the study to the interdependent infrastructures which support the plant. We resort to a hierarchical model representation by Dynamic Master Logic Diagram (DMLD) and we evaluate by Monte Carlo simulation the probability that the critical plant enters in an unsafe state and the time needed to recover its safety. References Brissaud, F. Barros, A. Bérenguer, C. Charpentier, D Reliability analysis for new technology-based transmitters. Reliability Engineering and System Safety 96: Cimellaro, GP. Reinhorn, AM. Bruneau, M Framework for analytical quantification of disaster resilience. Engineering Structures 32: EPRI Seismic Probabilistic Risk Assessment Implementation Guide. Palo Alto, CA. TR Hu, YS. Modarres, M Evaluating system behavior through Dynamic Master Logic Diagram (DMLD) modeling. Reliability Engineering and System Safety 64: Zio, E. Ferrario, E A framework for the system-of-systems analysis of the risk for a safety- critical plant exposed to external events. Reliability Engineering and System Safety 114:

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34 Methods for Accounting of Uncertainties in System Analysis and Decision Making Chung-Kung LO In nuclear power plants (NPP), the risk indicators computed with Probabilistic Risk Assessment (PRA) play important roles for decision making. In this context, the calculation of these indicators has to be robust, in particular uncertainties must be taken into account seriously. In the traditional PRA practice the epistemic uncertainty of basic events is treated by using a presumed probability distribution, e.g. lognormal, Gamma, or Beta distribution. Many recent studies concluded that it is more appropriate to use a family of probability distributions for representing the imprecise and incomplete information rather than a unique presumed probability distribution. We used belief functions of Dempster- Shafer Theory (DST) to represent the probability bounds of basic events and simulated the uncertainty propagation for core damage frequency (CDF) calculation. For easier decision, we also introduced Bayes update process to narrow down the uncertainty bound when new information such as plant specific data is available. References Baudrit C, Couso I, Dubois D, Joint propagation of probability and possibility in risk analysis: Toward s a formal framework. International Journal of Approximate Reasoning, 45: Baudrit C, Dubois D, Practical Representations of Incomplete Probabilistic Knowledge. Computational Statistics & Data Analysis, 51(1): Dubois D, Guyonnet, D, Risk-Informed Decision Making in the Presence of Epistemic Uncertainty. Int. J. General Systems, 40(2): Lapointe S, Bobeè B, Revision of possibility distributions: A Bayesian inference pattern. Fuzzy Sets and Systems, 116: Le Duy TD, Dieulle L, Vasseur D, Berenguer C, Couplet M, An alternative framework using belief functions for parameter and model uncertainty analysis in nuclear probabilistic risk assessment applications. Proceedings of the Institution of Mechanical Engineers, Journal of Risk and Reliability, doi: / X