Portale della Didattica

Monte Carlo methods, safety and risk analysis

02OKEND

A.A. 2023/24

Course Language

Inglese

Degree programme(s)

Course structure

Teaching	Hours
Lezioni	32
Esercitazioni in aula	18

Lecturers

Teacher	Status	SSD	h.Les	h.Ex	h.Lab	h.Tut	Years teaching

Co-lectures

Espandi

Teacher	Status	SSD	h.Les	h.Ex
Abrate Nicolo'	Ricercatore L240/10	IIND-07/C	0	6
Abrate Nicolo'	Ricercatore L240/10	IIND-07/C	0	4,5
Carpignano Andrea	Professore Associato	IIND-07/D	3	0
Froio Antonio	Professore Associato	IIND-07/D	0	12

Context

SSD	CFU	Activities	Area context

Date d'appello

Orario delle lezioni

Statistiche superamento esami

Anno accademico di inizio validit�

2023/24

Presentazione
Course description

The course is divided in two parts. In the first part (A), concerning statistical methods and Monte Carlo techniques, the fundamentals of probability and statistics are given, the Monte Carlo method is introduced and its possible applications to various technical fields are illustrated. The objective of this part of the course is to give the students the required knowledge to solve a technical problem with a statistical approach. In the second part of the course (B), focused on risk analysis, the methodologies adopted for the improvement workers' safety and prevent/mitigate the risks associated to major accidents are presented in relations to different technological applications. Deterministic and statistical techniques adopted for risk analysis are presented and some specific information and procedures for the evaluation and management of major hazards in process plants are given (Seveso Directive). For both parts, lectures are complemented with exercise sessions where specific problems are analysed and worked out as applications of the theoretical presentations. For part (B), the students are required to carry out independent activities on the subjects of the course and to present a written report on the work done.

The course Monte Carlo methods, safety and risk analysis is composed of two, complementary modules aiming at providing competences relevant for the analysis of complex systems, with a direct application to the field of nuclear and energy engineering, as well as other technical fields characterized by various complex, interconnected phenomena and possibly subject to major accidents. In the first part of the course (module A - Monte Carlo methods), the students are provided with the necessary competences in order to approach the study of energy system behavior adopting a statistical approach. The fundamentals of probability and statistics are given to allow the students to appreciate the potentialities of the Monte Carlo techniques for the solution of very different engineering problems. The approach to a proper analysis of uncertainties in engineering applications is described, and the possible applications of the Monte Carlo method to various technical fields is illustrated, in particular in the topics of interest for nuclear and energy engineering. In the second part of the course (module B � Safety and risk analysis), focused on risk analysis, the methodologies adopted for the improvement workers' safety and prevent/mitigate the risks associated to major accidents are presented in relations to different technological applications. Deterministic and statistical techniques adopted for risk analysis are presented; also, some specific information and procedures for the evaluation and management of major hazards in energy (e.g., nuclear) and, in general, industrial plants are given.

Risultati attesi
Expected Learning Outcomes

At the end of the course the student should: - know the fundaments of probability and statistiscs and of the Monte Carlo method; - be able to apply the Monte Carlo method for the solution of problems, by correctly identifying the statistical phenomena involved, carry our the random sampling and perform the corresponding statistical analysis to evaluate averages and uncertainties - apply the Monte Carlo approach to problems involving statistical phenomena in different fields of application, including risk analysis - be able to provide the structure of the risk analysis in the industrial field, identifiying relevant hazards, defining the expected accidental sequences, estimating their probability, and assessing, by simplified tools, the related consequences. - be able to suggest prevention and mitigation measures to reach an acceptable risk level.

PART A � MONTE CARLO METHODS At the end of the course the student should know: ELO 1 - the fundaments of probability and statistics; ELO 2 - the theory and main concepts at the basis of the Monte Carlo method; ELO 3 - the correct approach to the generation of averages ans statistical error when dealing with sampling and experimental measurements; ELO 4 - the correct approach to the interpretation of measurements and computational results affected by statistical uncertainty; At the end of the course the students should be able to: ELO 5 - apply the Monte Carlo method for the solution of problems, by i) correctly identifying the statistical phenomena involved, ii) carry our the random sampling and iii) perform the corresponding statistical analysis to evaluate averages and uncertainties ELO 6 - apply the Monte Carlo approach to problems involving statistical phenomena in different fields of application of interest for the enegy and nuclear engineering field (e.g. risk analysis, safety assessments, neutral particle transport) ELO 7 - critically evaluate the results obtained by the application of the Monte Carlo method, understanding the role of the statistical uncertainity and its impact on the reliability of the results obtained

Prerequisiti
Pre-requirements

Basic concepts of mathematics, chemistry and physics as obtained in the bachelor's degree program, concepts on process plants, thermal-hydraulics and fluid dynamics.

Fundamentals of mathematics, applied thermodynamics and physics; concepts on process plants, thermal-hydraulics and fluid dynamics, basics of radiation and particle transport. Basic knowledge of MATLAB.

Programma
Course topics

PART A - MONTE CARLO METHODS -1- Probability and statistics a. Concept of probability and its properties b. Probability density functions, expected value and variance c. Simulation of random event - sample average d. Tchebycheff inequality and Central Limit Theorem e. Statistical laws of interest for applications in the energy engineering field f. Properties of correlated statistical quantities -2- The Monte Carlo method a. Origin ad motivations b. sampling methodologies c. simulation of discrete and continuous random walks c. Applications of the Monte Carlo method to engineering problems: radiative heat transfer, evaluation of energy plants performance, evaluation of integrals, ... PART B - SAFETY AND RISK ANALYSIS -1- The Risk concept: definition, assessment and tolerability -2- Methodologies for the safety assessment: a. Hazard identification b. Methodologies for the reliability assessment of complex systems, c. Methodologies for the study of accidental sequences, d. Risk Assessment, -3- Major hazards: a. EU and Italian legislation, b. Description of accidental phenomena by simple methods (loss of containment, fires, explosions, gas dispersion), c. Vulnerability analysis, d. Emergency planning.

PART A - MONTE CARLO METHODS -1- Probability and statistics a. Concept of probability and its properties b. Probability density functions, expected value and variance c. Simulation of random event - sample average d. Tchebycheff inequality and Central Limit Theorem e. Statistical laws of interest for applications in the energy and nuclear engineering field f. Properties of correlated statistical quantities -2- The Monte Carlo method a. Origin ad motivations b. Sampling methodologies c. Simulation of discrete and continuous random walks d. Applications of the Monte Carlo method to engineering problems: neutron propagation, radiative heat transfer, evaluation of energy plants performance, evaluation of integrals, uncertainty quantification ... e. Introduction to the Monte Carlo neutron transport code Serpent

Sustainable development goals

Assicurare a tutti l�accesso a sistemi di energia economici, affidabili, sostenibili e moderni

Fornire un�educazione di qualit�, equa ed inclusiva, e opportunit� di apprendimento per tutti

Costruire un'infrastruttura resiliente e promuovere l'innovazione ed una industrializzazione equa, responsabile e sostenibile

Note
Additional information

Organizzazione dell'insegnamento
Course structure

PART A � MONTE CARLO METHODS All the concepts explained during lectures are applied directly by the professor during the exercise session in class. The students are given suggestions for further individual exercises to be carried out at home.

PART A � MONTE CARLO METHODS All the concepts explained during lectures are applied directly by the professor during the lectures. Dedicated exercise sessions in class complement the understanding and allow the students to be confronted with more exercises. The students are also given suggestions for further individual exercises to be carried out at home. Exercise sessions at the computer are also envisaged, with the use of the programming language MATLAB. An introduction to the use of the Serpent code for the simulation of neutron transport for applications if interest in nuclear engineering is provided.

Bibliografia
Reading materials

PART A � MONTE CARLO METHODS - G. Vicario and R. Levi, Statistica e probabilit� per ingegneri, Progetto Leonardo, Bologna, 2001 - S. M. Ross, Introduction to probability and statistics for engineers and scientists, Wiley, New York, 1987 - Lux and L. Koblinger, Monte Carlo particle transport methods : neutron and photon calculations, CRC, Boca Raton, 1991. - Lecture notes provided by the professor

PART A � MONTE CARLO METHODS - G. Vicario and R. Levi, Statistica e probabilit� per ingegneri, Progetto Leonardo, Bologna, 2001 - S. M. Ross, Introduction to probability and statistics for engineers and scientists, Wiley, New York, 1987 - L. Lux and L. Koblinger, Monte Carlo particle transport methods : neutron and photon calculations, CRC, Boca Raton, 1991. - J. Spanier and E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems, Dover, 2008 - Lecture notes provided by the professor

Materiale di supporto allo studio
Study materials

Slides; Esercizi; Esercizi risolti; Video lezioni tratte da anni precedenti;

Lecture slides; Exercises; Exercise with solutions ; Video lectures (previous years);

Criteri, regole e procedure per l'esame
Assessment and grading criteria

Modalit� di esame: Test informatizzato in laboratorio; Prova scritta (in aula);

Exam: Computer lab-based test; Written test;

... PART A � MONTE CARLO METHODS The exam is at the computer (in PoliTO LAIB). The students are requested to solve some exercises, ranging from basic statistics to applications of the Monte Carlo method to simplified problems (duration: 2 hours). The grade obtained by the exercise part can be modified (max +4 points, min -2 points, not compulsory) by answering to two theoretical questions provided at the end of the exercise part (duration: 30 minutes). Students are not allowed to bring any material (books, notes, ...) to the final exam. FINAL MARK The final mark of the exam is evaluated as the average of the marks obtained in the two parts of the exam, i.e. Monte Carlo Methods (part A) and Safety and Risk Analysis (part B), rounded to the upper integer.

Gli studenti e le studentesse con disabilit� o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unit� Special Needs, al fine di permettere al/la docente la declinazione pi� idonea in riferimento alla specifica tipologia di esame.

Exam: Computer lab-based test; Written test;

For Part A + B: The exam is carried out separately for the two parts of the course (A+B) and a grade >=18 is to be obtained on both parts. PART A � MONTE CARLO METHODS The exam aims at verifying the competence of the students on both basics statistics and on the application of the Monte Carlo Method. Therefore, the students are requested to solve some exercises, ranging from basic statistics to applications of the Monte Carlo method to simplified problems by developing small MATLAB programs (exam carried out at the PoliTO LAIB). The correct solution of all exercises proposed allows to obtain a maximum grade of 30/30 cum laude. The grade obtained by the exercise part can be modified (max +3 points, min -2 points, not compulsory) by answering to a theoretical question provided together with the exercises. The final grade saturates at 30/30 cum laude. The total duration of the test is 2.5 hours. Students are not allowed to use any material (books, notes, ...) during the final exam. FINAL GRADE The final grade of the exam is evaluated as the average of the grades obtained in the two parts of the exam, i.e. Monte Carlo Methods (part A) and Safety and Risk Analysis (part B), rounded to the upper integer.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.