Uncertainty Quantification in Engineering Science

The goals of this course are the understanding and management of uncertainties in engineering simulations and the understanding and use of the analytical and computational techniques used to quantify and propagate uncertainties in engineering simulations.

Probabilistic analysis for quantifying and propagating uncertainties as well as estimating reliability (analysis of small failure probabilities) of engineering systems. Measures of uncertainty and reliability formulation (limit state functions and probability of failure integrals). Αnalytical approximate techniques (perturbation, Laplace asymptotics, polynomial chaos, sparse grid methods). Advanced stochastic simulation algorithms (Monte Carlo, importance sampling, subset simulation, line sampling). Bayesian analysis for updating and propagating uncertainties using observations/measurements from system or its components. Bayesian updating and model selection. Οptimal experimental design. Analytical approximate techniques (Laplace asymptotics) and stochastic simulation algorithms (variants of Markov Chain Monte CarloMCMC, Transitional MCMC). Advanced computational tools for handling computation burden: adjoint techniques, surrogate techniques (kriging methods). High performance computing (Parallel processing).

Elementary knowledge in probability and statistics, elementary knowledge in dynamics and vibrations, programming (Matlab or equivalent software)

D.S. Sivia and J. Skilling, Data Analysis: A Bayesian Tutorial, Oxford Science Publications, 2006

C.M. Bishop, Pattern Recognition and Machine Learning, Springer, New York, 2006

K.V. Yuen, Bayesian Methods for Structural Dynamics and Civil Engineering, John Wiley & Sons, 2010

Karl-Rudolf Koch, Introduction to Bayesian Statistics, Springer-Verlag Berlin Heidelberg 2007

W.M. Bolstad, Introduction to Bayesian Statistics, John Wiley & Sons, Inc., Hoboken, New Jersey, 2007

R.Y. Rubinstein, Simulation and the Monte Carlo Method, John Wiley & Sons, Inc., 1981