Robust design considering optimization tools and reduced-basis approximations

This paper performs Robust Design Optimization (RDO) to obtain optimum solutions since some degree of uncertainty in characterizing any real engineering system is inevitable. The robustness measures considered here are the expected value and standard deviation of the function involved in the optimization problem. To calculate such quantities, we employ two nonintrusive uncertainty propagation analysis techniques that exploit deterministic computer models: Monte Carlo (MC) method and Probabilistic Collocation Method (PCM). The uncertainty propagation essentially involves computing the statistical moments of the output. When using these robustness measures combined, the search for optimal design appears as a robust multiobjetive optimization (RMO) problem. Several strategies are implemented to obtain the Pareto front (multiobjective solutions). To overcome the time consuming problem inherent in a RMO problem reduced basis (RB) approximation methodology is added to the optimization system, in the whole optimization process. The integration of all the methodologies described allows the computation of robust design, using a finite element model of 3.900 degrees of freedom, in a practical time (less than a minute).