Safety is a mandatory and strategic requirement for nuclear engineering applications. For this, technical and organizational measures are put in place during all phases of the lifecycle of a nuclear energy production facility to prevent accidents of different nature and/or mitigate their effects. In the current era of strong technological evolution and transition (e.g., energetic and digital), partly motivated by the concerns of climate change, new designs of nuclear plants are being put forward. Their licensing for deployment requires verification of the design objectives for operation and safety. Within this framework, the course will provide PhD students with an overview and understanding of the most relevant issues, methods and state-of-the-art solutions for the Deterministic (D) and Probabilistic (P) Safety (S) Analyses (A) of nuclear systems, and their Integration (IDPSA). This requires innovative, pioneering approaches such as Artificial Intelligence (AI), Machine Learning (ML) and advanced (stochastic) simulation methods to face the relevant challenges arising in the present era of energy transition and digitalization: i) systems complexity and high-dimensionality (they involve a large number of interconnected components and functional, time- and space-dependent variables and data); ii) computationally-demanding, black-box system models and detailed, best-estimate simulation codes (they require a long time to run a simulation compared to the available computational resources); iii) strong “dynamic” features, given by time-dependent interactions of the stochastic processes of hardware component failures, the deterministic responses of the system process, the effects of the control and operator actions, software and firmware; iv) severe uncertainties (often due to the scarcity of quantitative data available for new energy and nuclear technologies). These issues and the corresponding solutions will be mainly presented with reference to practical cases of nuclear (fission and fusion) systems. However, the methodological, multidisciplinary and transversal nature of the course makes it suitable also for PhD students with a non-nuclear background, and interested in any safety-critical, possibly high-consequence system and application (including critical infrastructures, electrical grids, automotive, aerospace and chemical industries).

Fundamentals of statistics. Basic concepts on energy (and nuclear) systems would be a plus, but - given the transversal nature of the course - not strictly necessary.

Introduction to Deterministic and Probabilistic Safety Analyses (DSA and PSA) for nuclear systems and plants: concepts, methods, tools, strengths, weaknesses. Need for an Integrated Deterministic and Probabilistic Safety Analysis (IDPSA) for dynamic systems in the presence of uncertainties. Issue 1 – The problem of uncertainty in nuclear systems behavior, modeling and simulation: * Sources and types: aleatory, epistemic (model and parameter). * The curse of dimensionality. Need for dimensionality reduction for improving model explainability and predictivity. Feature extraction methods for reducing the dimensionality of functional (time- and space-dependent) data and variables (PCA, POD, AutoEncoders). Screening of (large) model inputs by advanced sensitivity analysis (local and global measures, elementary effects methods). * Comprehensive Bayesian framework for Inverse Uncertainty Quantification and Best-Estimate model (codes) calibration (using data and expert knowledge). Issue 2 – Dynamic accident scenarios generation: * Multi-Valued Logic for modeling accident scenarios. * Advanced stochastic methods for sampling accident scenarios: Subset Simulation, Line Sampling, Markov Chain Monte Carlo, Non-parametric Adaptive Importance Sampling. Issue 3 - Dynamic accident scenarios simulation: * Efficient uncertainty analysis of Best-Estimate nuclear codes for accurate, precise and robust risk-informed safety margins estimation and failure probability quantification (Order Statistics, Finite Mixture Models, Kernel Density Functions). * AI/ML methods (e.g., bootstrapped Artificial Neural Networks) for reduced order modeling, metamodeling and computationally efficient accident scenarios simulation. Issue 4 - Dynamic accident scenarios post-processing: * AI/ML techniques (e.g., Artificial Neural Networks, ensembles) and adaptive hybrid methods (Kriging metamodels combined with Design of Experiments) for system failure domain identification. * AI/ML methods (e.g., supervised and unsupervised clustering algorithms) for: scenario grouping, analysis and information retrieval (optimal selection of prevention and mitigation measures); identification of accident precursors/root causes.

In presenza

Presentazione report scritto

P.D.2-2 - Settembre

TENTATIVE schedule (some lectures might be moved from the morning to the afternoon, and some days could be changed depending on the availability of teachers, rooms, etc.): * 11/09/2025: 10-13 * 16/09/2025: 10-13 * 18/09/2025: 10-13 * 22/09/2025: 14.30-17.30 * 25/09/2025: 10-13 * 30/09/2025: 10-13 * 02/10/2025: 10-13 * 06/10/2025: 14.30-17.30 * 09/10/2025: 10-13 * 14/10/2025: 10-13