Seminar - Multi-Level Monte Carlo Methods for stochastic analysis and robust optimum design in aeronautics, by Gabriel Bugeda
Thursday, October 13th, 2016. Time: 12 p.m.
Place: O.C. Zienkiewicz Conference Room, C1 Building, UPC Campus Nord, Barcelona.
Most of the numerical analysis of real life problems in any engineering discipline present a big number of uncertainties in their data definition. For instance, in aeronautical problems there are uncertainties in the geometry (manufacturing tolerances) and in the flight conditions (Mach number, angle of attack, etc). In structural problems there are also uncertainties in the values of the mechanical properties of any material. This justifies the integration of these uncertainties in the analysis of this type of problems.
Typically, values with uncertainties are characterized by a probabilistic density function (PDF). One of the usual ways of performing numerical analysis with data uncertainties is the use of the classical Monte Carlo (MC) method. Basically, it consists of sampling all the data values with uncertainties in terms of their PDF and performing a deterministic analysis for each sample. Nevertheless, due to the necessary big number of sampling points for obtaining a good statistical representation of the problem MC methods are computationally very expensive.
An cheaper alternative are the so-called Multi-Level Monte Carlo Methods (MLMC). This lecture demonstrates the capabilities of MLMC for the stochastic analysis of CFD aeronautical problems with uncertainties. These capabilities are compared with the classical MC Methods in terms of accuracy and computational cost through a set of benchmark test cases. The real possibilities of solving CFD aeronautical analysis with uncertainties by using MLMC methods with a reasonable computational cost are demonstrated.
On the other side, the superior performance of MLMC methods compared with classical MC ones will allow to solve robust optimum design problems with a much lower computational cost. Using the Takuchi approach, these problems will be solved as traditional multiobjective ones in which not only the mean of each stochastic analysis but also the variance will be minimised.
Gabriel Bugeda. Bs.C. Civil Engineer and Ph.D. in Civil Engineering (UPC). Full Research Professor at CIMNE.