Fully decoupled reliability-based design optimization of structural systems subject to uncertain loads

Reliability-based optimization (RBO) offers the possibility of finding the best design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. Although the importance and usefulness of RBO is undisputed, it is rarely applied to practical problems, as the associated numerical efforts are usually extremely large due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure. To alleviate this issue, this contribution proposes an approach for solving a particular class of problems in RBO: the minimization of the failure probability of a linear system subjected to an uncertain load. The main characteristic of this approach is that it is fully decoupled. That is, the solution of the RBO problem is reduced to the solution of a single deterministic optimization problem followed by a single reliability analysis. Such an approach implies a complete change of paradigm with respect to the more classical double-loop and sequential methods for RBO. The theoretical basis for the proposed approach lies in the application of the operator norm theorem. The application and capabilities of the proposed approach are illustrated by means of three examples.