Date:

Monday, June 18, 2018, 12:00am - Wednesday, June 20, 2018, 12:00am **Mini-Curso | 18-20 de Junho 2018**

Nowadays computational predictive models are standard tools for analysis of complex systems and phenomena. However, any computational model may be uncertain with respect to the system/phenomenon of interest, due to variabilities on its parameters and, mainly, because of assumptions made on its conception that may not be in agreement with the reality. The first source of uncertainty is inherent to measurements limitations, imperfections in manufacturing process, material and geometric variabilities, etc. Meanwhile, the second type is essentially due to lack of knowledge about the underlying governing laws. Uncertainty Quantification (UQ) can be thought of as a multi-disciplinary area that deals with quantitative characterization and reduction of uncertainties in applications, which is extremely necessary to give robustness to computational forecasts. The lectures will cover the basic vocabulary of UQ, the possible approaches to modelling uncertainties, the main techniques for uncertainty propagation. Basic topics of probability and statistics will be reviewed. Computer activities will be developed in parallel to theoretical expositions, as a way to give a hands-on tone to the course.

**Day 1:**

Lecture 1: A Prime on Uncertainty Quantification

Tutorial 1: Verification and Validation

Lecture 2: Elements of Probability Theory

Tutorial 2: Probabilistic Warm-up

Lecture 3: Elements of Statistics

Tutorial 3: Statistical Analysis of Data

**Day 2:**

Lecture 4: Sampling and Monte Carlo Method

Tutorial 4: Monte Carlo in Action

Lecture 5: Probabilistic Modeling of Uncertainties

Tutorial 5: A Random Oscillator

Lecture 6: Stochastic Model Updating (probabilistic and non-probabilistic methods)

**Day 3:**

Lecture 7: Notions of Polynomial Chaos

Lecture 8: Bayesian Approach: a flavour

Lecture 9: Research Topics in UQ

Discussion

Monday (18/06) - Wendesday (20/06)

Start: 9h00 | 17h00

** Prof. Américo Cunha**

Assistant Professor of Applied Mathematics

Universidade do Estado do Rio de Janeiro (UERJ), Instituto de Matemática e Estatística.

** Prof. Tiago Silva**

Assistant Professor of Structural Mechanics

DEMI FCT NOVA, UNIDEMI

** Prof. Alda Carvalho**

Professor of Statistics

ISEL IPL

** Location:** Lab. Mecânica Estrutural (DEMI - Ed.VIII)

** Bring your own Laptop with MatLab (or similar) for the hands-on exercises.**

** This is a free course. **If you are interested send email to** tan.silva @ fct.unl.pt **