Uncertainty quantification aims at studying the impact of aleatory - (e.g. natural variability) or epistemic uncertainty onto computational models used in science and engineering. The course introduces the basic concepts of uncertainty quantification: probabilistic modelling of data, uncertainty propagation techniques (polynomial chaos expansions), and sensitivity analysis.
After this course students will be able to properly define an uncertainty quantification problem, select the appropriate computational methods and interpret the results in meaningful statements for field scientists, engineers and decision makers. Although the course is primarily intended to civil, mechanical and electrical engineers, it is suitable to any master student with a basic knowledge in probability theory.
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.
Detailed slides are provided for each lecture.
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 work out assignments.