Duration
16h Th, 16h Pr, 28h Proj.
Number of credits
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Engineering structures and systems are rarely perfectly known, may present defects, and are often subjected to loadings that can be random or difficult to predict, thus making their design, fabrication, operation, reliability, maintenance, and simulation uncertain. This course aims at familiarizing the students with probabilistic methods that can be used to account for uncertainties in engineering analyses and to ascertain the accuracy of simulation predictions.
After a brief review of the basic concepts from the probability theory and from statistics, the course will be divided into two parts. The first part is dedicated to stochastic modeling in science and engineering. Some emphasis will be placed on the role that stochastic modeling can play in so-called inverse problems, in which model parameters must be estimated from data. Among other illustrations, we will consider applications in the biomedical sciences and engineering, including stochastic modeling of infectious disease spread and epidemiology.
The second part is dedicated to probabilistic methods for the quantification of uncertainties in engineering analysis. After presenting the most widespread and most used probabilistic methods (ISO98 Guide), attention will be turned towards more leading-edge probabilistic methods that are still the subject of ongoing scientific research (Monte Carlo methods, surrogate modeling, polynomial chaos methods, sensitivity analysis).
Learning outcomes of the learning unit
- Understanding of the uncertainties that may affect the behavior, evolution, and simulation of structures and systems in mechanics and physics.
- Ability to apply probabilistic methods for the quantification of uncertainties.
- Ability to find and read papers from the scientific literature.
- Ability to communicate effectively in written reports and oral presentations.
Prerequisite knowledge and skills
Students ideally have a background in probability theory (MATH0062 "Elements of probability calculus" or an equivalent course), statistics (MATH0487 "Elements of statistics" or an equivalent course), and stochastic processes (MATH0488 "Elements of stochastic processes" or an equivalent course). The required background material will be recalled in class as needed.
Planned learning activities and teaching methods
The course involves a series of lectures. In addition, students work on two projects. The first one revolves around probabilistic inverse methods. The second one is related to uncertainty quantification.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Additional information:
In person learning.
Recommended or required readings
Each lecture is supported by slides prepared by the instructor. Papers from the historic and current international scientific literature complement the slides.
Students are required to prepare two reports for their projects. The final grade is a weighted average of the grades obtained for the reports, which takes into account their content, clarity, and neatness.
Work placement(s)
Organisational remarks and main changes to the course
The course will be offered in the Fall semester.
Contacts
Maarten ARNST : maarten.arnst@uliege.be