Uncertainty quantification aims at studying the impact of aleatory and epistemic uncertainty onto computational models used in science and engineering. The course introduces the basic concepts of uncertainty quantification: probabilistic modelling of data (copula theory), uncertainty propagation techniques (Monte Carlo simulation, polynomial chaos expansions), and sensitivity analysis.
Learning objective
After this course students will be able to properly pose an uncertainty quantification problem, select the appropriate computational methods and interpret the results in meaningful statements for field scientists, engineers and decision makers. The course is suitable for any master/Ph.D. student in engineering or natural sciences, physics, mathematics, computer science with a basic knowledge in probability theory.
Content
The course introduces uncertainty quantification through a set of practical case studies that come from civil, mechanical, nuclear and electrical engineering, from which a general framework is introduced. The course in then divided into three blocks: probabilistic modelling (introduction to copula theory), uncertainty propagation (Monte Carlo simulation and polynomial chaos expansions) and sensitivity analysis (correlation measures, Sobol' indices). Each block contains lectures and tutorials using Matlab and the in-house software UQLab (www.uqlab.com).
Lecture notes
Detailed slides are provided for each lecture. A printed script gathering all the lecture slides may be bought at the beginning of the semester.
Prerequisites / Notice
A basic background in probability theory and statistics (bachelor level) is required. A summary of useful notions will be handed out at the beginning of the course.
A good knowledge of Matlab is required to participate in the tutorials and for the mini-project.
Performance assessment
Performance assessment information (valid until the course unit is held again)
Repetition only possible after re-enrolling for the course unit.
Additional information on mode of examination
Final grade: 80% on final exam, 20% on mini-project
Conditions for the exam: -2 hour written exam -all lecture notes (printed / manuscript) allowed -a standard simple calculator is needed (see DBAUG list provided before the exam) -Computers, laptops, phones, tablets, advanced programmable calculators NOT allowed.
Performance assessment as a semester course