Uncertainty Quantification of numerical simulations has had increased interest in recent years and, as a consequence, so has an interest in a procedure of Optimization under Uncertainty. One of the main challenges in this field is the efficiency of propagating uncertainties from the sources to the quantities of interest, especially when there are many sources of uncertainty. Other important challenges are the coupling of the optimization procedure with the uncertainty quantification routines, usually approached as two independent problems, and the necessity to efficiently perform a massive ensemble of numerical simulations. The primary goal of this work is to develop algorithms for efficient Uncertainty Quantification and Optimization under Uncertainty.
Two industrial applications will be presented: the optimization of wind turbine blade shapes and the optimization of a Formula 1 tire brake duct. Both problems are multi-objective and the presence of uncertainties significantly impacts the estimation of their responses making them well suited to assess the theoretical framework and the algorithms that will be presented in this book.