Robust Optimization with Reliability Constraints considering Approximate Models

Resumo

Reliability-Based Robust Design Optimization (RBRDO), where random variables are statistically
treated, have been gaining space in practical engineering since it allows to compute the structural probability of
failure associated with a design criteria. The mathematical formulation for robust optimization can falls into a
multiobjective optimization (MO) problem involving as objectives the mean and the standard deviation of a given
function. The most appropriate approach to solve these problems is through a class of strategies based on the Pareto
concept. The uncertainties in the optimization process to obtain robust and reliable projects will be considered
both in the objective function and in the constraints. Robustness measures required by objective functions are
computed by Monte Carlo simulation (MC). For reliability constraints two approaches will be used: RIA
(Reliability index approach) and PMA (Performance Measure Approach). The process of reliability analysis and
optimization requires multiple function evaluations. When applied to real engineering problems it involves
numerical simulations, resulting in a high computational cost procedure. Alternatives to overcome that here is
through two distinct strategies for metamodels: the use of data fitting approximation and a reduced order model.
For the application of the above process, a reinforced concrete frame with three floors will be used.