


Politecnico di Torino  
Academic Year 2016/17  
02OKEND Monte Carlo methods, safety and risk analysis 

Master of sciencelevel of the Bologna process in Energy And Nuclear Engineering  Torino 





Subject fundamentals
The course is divided in two parts. In the first part, 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, 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). Lectures are complemented with exercise sessions where specific problems are analysed and worked out as applications of the theoretical presentations. 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. 
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 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. 
Prerequisites / Assumed knowledge
Basic concepts of mathematics, chemistry and physics as obtained in the bachelor's degree program, concepts on process plants, thermalhydraulics and fluid dynamics.

Contents
FIRST PART  MONTE CARLO METHODS
a. Concept of probability and its properties b. Probability density functions, expected value and variance c. Simulation of random event  sample average d. Techebycheff inequality and Central Limit Theorem e. Statistical laws of interest for applications in the energy engineering field f. Properties of correlated statistical quantities a. Origin ad motivations b. discrete and continuous random walk c. Applications of the Monte Carlo method to engineering problems (e.g. radiative heat transfer, evaluation of performance of energy plants) SECOND PART  SAFETY AND RISK ANALYSIS a. Hazard identification b. Methodologies for the reliability assessment of complex systems, c. Methodologies for the study of accidental sequences, d. Risk Assessment, 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. 
Delivery modes
FIRST PART – 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. SECOND PART  SAFETY AND RISK ANALYSIS Students have to apply the content of the lectures to perform a safety assessment of a part of a real industrial plant. They have to prepare a report describing the analysis performed, that will be discussed during the final examination. 
Texts, readings, handouts and other learning resources
FIRST PART – MONTE CARLO METHODS
 G. Vicario and R. Levi, Statistica e probabilità 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 SECOND PART  SAFETY AND RISK ANALYSIS The professor provides a booklet and the set of slides used in class during lectures 
Assessment and grading criteria
FIRST PART – 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. 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. SECOND PART  SAFETY AND RISK ANALYSIS The final exam is organised as a written text that is mandatory. In the written text students have to develop some exercises in order to demonstrate their ability in applying theory and solve practical problems related to safety and risk assessment. The maximum grade that can be obtained in the written test is 27/30. Student can ask, at the beginning of the course, to enroll for the Project Work, a practical application of Risk Analysis to a portion of a real plant. The Project Work must be made in team working with other 2 or 3 students. Project work will be discussed by an oral exam, planned when the written test has been already passed. The oral discussion of the Project Work can add maximum 3/30 marks. 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 and Safety and Risk Analysis, rounded to the upper integer. 
