Syllabus

In the modern product development process, the prevailing uncertainty is increasingly coming into focus. In many cases, it is not possible to specify single number values for model parameters, such as friction and damping parameters, but only intervals or distributions. To increase the predictive accuracy of models, it is therefore important to quantify and reduce uncertainty. The resulting improvement in the predictive ability of models contributes to the development of products whose load capacity is better adapted to the load and can thus be designed in a more resource-efficient way. In this course, students are taught the basic methods to describe, quantify, and evaluate uncertainty in real engineering systems.

Learning Outcomes

On successful completion of this module, students should be able to:

• Recognize the different types of uncertainty in real technical systems and independently develop an approach to quantify and evaluate them
• Perform a sensitivity analysis to identify the most important parameters of a model using methods such as Sobol Indices, Morris Screening
• Quantify the uncertainty of models using Markov chain Monte Carlo methods and interpret the results (see figures)
• Consider the quantified uncertainty through a model (Monte-Carlo-Simulation and Stochastic Spectral Methods)
• Build fast surrogate models of complex computationally intensive models to make them also amenable to uncertainty quantification using Gaussian Process Regression (GPR), Support?Vector-Machine (SVM), Polynomial Chaos Expansion (PCE)
• Evaluate the failure probabilities of a system based on the quantified uncertainty using subset simulation

The lecture is complemented by a guest lecture from industry and a demo workshop by Mathworks. An essential part of the exercises consists of solving programming tasks with MATLAB Grader directly in the Moodle course. Coding sessions and a consultation hour are offered in addition.